Finite Group Databasebeta

← AGL(1,ℤ/8)×H(5,𝔽2) #72267602

Subgroups — AGL(1,ℤ/8)×H(5,𝔽2) #72267602

Order 1024.

Only the 32031 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 1026 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×D4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#10583066C2112yesmaximal, complemented
4#10583065C2112yesmaximal, complemented
5#10583024C2118yesmaximal, complemented
6#10583022C2118yesmaximal, complemented
7SD16×H(5,𝔽2)C212yesmaximal, complemented
8D8×H(5,𝔽2)C212yesmaximal, complemented
9#10579229C216yesmaximal, complemented
10#10578900C216yesmaximal, complemented
11#10578892C216yesmaximal, complemented
12#10577652C219yesmaximal, complemented
13#10577308C219yesmaximal, complemented
14#10577301C219yesmaximal, complemented
15#41×AGL(1,ℤ/8)C216yesmaximal, complemented
16C2×D4×AGL(1,ℤ/8)C219yesmaximal, complemented
17M16×H(5,𝔽2)C211yesmaximal, characteristic, complemented
18C23×AGL(1,ℤ/8)C2216yescomplemented
19#62986C2216yescomplemented
20#62985C2216yescomplemented
21#62984C2219yescomplemented
22#62983C2219yescomplemented
23Q8×H(5,𝔽2)C2211yescharacteristic, complemented
24D4×H(5,𝔽2)C2212yes—
25D4×H(5,𝔽2)C22118yescomplemented
26D4×H(5,𝔽2)C22112yescomplemented
27D4×H(5,𝔽2)C2211yescharacteristic, complemented
28#62800C2216yescomplemented
29C2×#3498C2216yescomplemented
30#62773C2219yescomplemented
31C2×#3496C2219yescomplemented
32#412C2216yescomplemented
33C2×D4×#41C2219yescomplemented
34C2×D4×#41C2216yescomplemented
35C22×D42C2219yescomplemented
36C2×C4×H(5,𝔽2)C2211yescharacteristic
37#62453C22124yescomplemented
38#62447C22172yescomplemented
39#62423C22136yescomplemented
40#62421C22136yescomplemented
41#62415C22112yescomplemented
42#62413C22112yescomplemented
43#62299C22172yescomplemented
44#62295C22172yescomplemented
45#62259C22136yescomplemented
46#62253C22172yescomplemented
47#62245C22118yescomplemented
48#62243C22118yescomplemented
49#62003C22124yescomplemented
50#62001C22112yescomplemented
51#61999C22112yescomplemented
52#61989C22172yescomplemented
53#61983C22136yescomplemented
54#61979C22136yescomplemented
55#61963C22136yescomplemented
56#61962C22136yescomplemented
57#61961C22136yescomplemented
58#61959C22136yescomplemented
59#61951C22112yescomplemented
60#61948C22112yescomplemented
61#61947C22112yescomplemented
62#61947C22112yescomplemented
63#61600C22172yescomplemented
64#61598C22172yescomplemented
65#61598C22172yescomplemented
66#61591C22172yescomplemented
67#61587C22118yescomplemented
68#61585C22118yescomplemented
69#61582C22136yescomplemented
70#61572C22136yescomplemented
71#61571C22172yescomplemented
72#61569C22136yescomplemented
73#61562C22118yescomplemented
74#61560C22118yescomplemented
75#61559C22118yescomplemented
76#61559C22118yescomplemented
77#61466C22112yescomplemented
78#61465C22112yescomplemented
79#61452C22136yescomplemented
80#61451C22136yescomplemented
81#61439C22136yescomplemented
82#61437C22136yescomplemented
83SD16×#41C22112yescomplemented
84D8×#41C22112yescomplemented
85#61402C2216yescomplemented
86#61402C22112yescomplemented
87Q8×AGL(1,ℤ/8)C2212yescomplemented
88#61321C2216yescomplemented
89#61317C2216yescomplemented
90#61252C22118yescomplemented
91#61161C22118yescomplemented
92#61161C22136yescomplemented
93#61155C22118yescomplemented
94#61155C22136yescomplemented
95D4×AGL(1,ℤ/8)C22118yescomplemented
96D4×AGL(1,ℤ/8)C22172yescomplemented
97D4×AGL(1,ℤ/8)C22172yescomplemented
98D4×AGL(1,ℤ/8)C22136yescomplemented
99D4×AGL(1,ℤ/8)C22136yescomplemented
100D4×AGL(1,ℤ/8)C22136yescomplemented
101D4×AGL(1,ℤ/8)C22136yescomplemented
102C2×D4×SD16C22118yescomplemented
103C2×D4×D8C22118yescomplemented
104C2×#3274C22118yescomplemented
105C2×#3272C22118yescomplemented
106C2×#3265C22136yescomplemented
107C2×#3264C22136yescomplemented
108#60916C22118yescomplemented
109#60803C22118yescomplemented
110#60798C22118yescomplemented
111#60750C22136yescomplemented
112#60700C22118yescomplemented
113C2×#3151C2219yescomplemented
114#60561C22118yescomplemented
115#60558C22118yescomplemented
116C2×#3055C22118yescomplemented
117C2×#3038C2219yescomplemented
118C2×#3036C2219yescomplemented
119C2×#3006C22118yescomplemented
120C2×#3003C22118yescomplemented
121#60325C22112yescomplemented
122#60309C22118yescomplemented
123C8×H(5,𝔽2)C2212yescomplemented
124#60263C2216yescomplemented
125#60230C2219yescomplemented
126M16×#41C2216yescomplemented
127C2×C4×AGL(1,ℤ/8)C2219yescomplemented
128C2×D4×M16C2219yescomplemented
129C22×H(5,𝔽2)D411yescharacteristic
130C23×#41C2316yescomplemented
131C24×D4C2316yescomplemented
132C22×AGL(1,ℤ/8)C2319yes—
133C22×AGL(1,ℤ/8)C23118yescomplemented
134C22×AGL(1,ℤ/8)C23118yescomplemented
135C22×AGL(1,ℤ/8)C23118yescomplemented
136C22×AGL(1,ℤ/8)C23118yescomplemented
137C22×AGL(1,ℤ/8)C23136yescomplemented
138C22×AGL(1,ℤ/8)C23136yescomplemented
139C23×SD16C23112yescomplemented
140C23×D8C23112yescomplemented
141C23×M16C2316yescomplemented
142#3520C23136yescomplemented
143#3519C23136yescomplemented
144#3517C23112yescomplemented
145#3514C23136yescomplemented
146#3511C23118yescomplemented
147#3508C23118yescomplemented
148#3506C23118yescomplemented
149#3505C23136yescomplemented
150#3503C2316yescomplemented
151#3501C2319yescomplemented
152#3498C23112yes—
153#3498C23136yescomplemented
154#3498C23136yescomplemented
155#3498C23112yescomplemented
156#3498C2316yescomplemented
157#3496C23118yes—
158#3496C23136yescomplemented
159#3496C23118yescomplemented
160#3496C23172yescomplemented
161#3496C2319yescomplemented
162#3483C2316yescomplemented
163#3482C23118yescomplemented
164#3482C2316yescomplemented
165#3481C23118yescomplemented
166#3480C2316yescomplemented
167#3480C23118yescomplemented
168Q8×#41C2312yescomplemented
169Q8×#41C2316yescomplemented
170#3475C23118yescomplemented
171#3475C23118yescomplemented
172D4×#41C23112yes—
173D4×#41C23136yescomplemented
174D4×#41C23136yescomplemented
175D4×#41C23112yescomplemented
176D4×#41C23136yescomplemented
177D4×#41C23118yescomplemented
178D4×#41C23136yescomplemented
179D4×#41C23136yescomplemented
180D4×#41C2316yescomplemented
181C2×#550C2316yescomplemented
182C2×#550C2319yescomplemented
183C2×D4×Q8C2312yescomplemented
184C2×D4×Q8C2319yescomplemented
185C2×#548C23118yescomplemented
186C2×#547C23118yescomplemented
187C2×#547C2319yescomplemented
188C2×#546C23118yescomplemented
189C2×D42C23118yes—
190C2×D42C23136yescomplemented
191C2×D42C23118yescomplemented
192C2×D42C23172yescomplemented
193C2×D42C23136yescomplemented
194C2×D42C23118yescomplemented
195C2×D42C2319yescomplemented
196#3444C23118yescomplemented
197C2×#532C23118yescomplemented
198C2×#532C2319yescomplemented
199C22×#127C2319yescomplemented
200C2×#525C23118yescomplemented
201C22×#121C23118yescomplemented
202C4×H(5,𝔽2)D419yes—
203C4×H(5,𝔽2)D416yes—
204C4×H(5,𝔽2)D411yescharacteristic
205C4×H(5,𝔽2)C2311yescharacteristic
206C4×H(5,𝔽2)C2319yes—
207C4×H(5,𝔽2)C2316yes—
208C2×#520D416yes—
209C2×#518D419yes—
210C2×C4×#41C2316yes—
211C2×C4×#41C2319yescomplemented
212C22×C4×D4C2319yes—
213C22×C4×D4C2319yescomplemented
214#3399C23172yescomplemented
215#3399C23136yescomplemented
216#3397C23172yescomplemented
217#3397C23136yescomplemented
218#3392C23112yescomplemented
219#3392C23124yescomplemented
220#3391C23112yescomplemented
221#3391C23124yescomplemented
222#3386C23112yescomplemented
223#3384C23112yescomplemented
224Q8×SD16C2314yescomplemented
225Q8×D8C2314yescomplemented
226#3373C23136yescomplemented
227#3368C23136yescomplemented
228#3367C23136yescomplemented
229#3366C23136yescomplemented
230#3362C23112yescomplemented
231#3359C23112yescomplemented
232#3358C23112yescomplemented
233#3358C23112yescomplemented
234#3354C23136yescomplemented
235#3353C23136yescomplemented
236#3345C23172yescomplemented
237#3343C23172yescomplemented
238#3335C23136yescomplemented
239#3334C23136yescomplemented
240#3332C23172yescomplemented
241#3332C23136yescomplemented
242#3330C23172yescomplemented
243#3330C23136yescomplemented
244#3325C23136yescomplemented
245#3325C23172yescomplemented
246#3324C23136yescomplemented
247#3324C23172yescomplemented
248#3318C23172yescomplemented
249#3318C231144yescomplemented
250#3310C23172yescomplemented
251#3310C231144yescomplemented
252#3308C231144yescomplemented
253#3308C23172yescomplemented
254#3306C231144yescomplemented
255#3306C23172yescomplemented
256#3298C23136yescomplemented
257#3298C23172yescomplemented
258#3295C23136yescomplemented
259#3295C23172yescomplemented
260#3294C23136yescomplemented
261#3294C23172yescomplemented
262#3294C23136yescomplemented
263#3294C23172yescomplemented
264D4×SD16C23136yescomplemented
265D4×SD16C23172yescomplemented
266D4×SD16C23172yescomplemented
267D4×SD16C23172yescomplemented
268D4×SD16C23172yescomplemented
269D4×D8C23136yescomplemented
270D4×D8C23172yescomplemented
271D4×D8C23172yescomplemented
272D4×D8C23172yescomplemented
273D4×D8C23172yescomplemented
274#3274C23172yescomplemented
275#3274C23136yescomplemented
276#3274C23172yescomplemented
277#3274C23172yescomplemented
278#3274C23172yescomplemented
279#3272C23172yescomplemented
280#3272C23136yescomplemented
281#3272C23172yescomplemented
282#3272C23172yescomplemented
283#3272C23172yescomplemented
284#3265C231144yescomplemented
285#3265C23172yescomplemented
286#3265C231144yescomplemented
287#3265C231144yescomplemented
288#3265C231144yescomplemented
289#3264C231144yescomplemented
290#3264C23172yescomplemented
291#3264C231144yescomplemented
292#3264C231144yescomplemented
293#3264C231144yescomplemented
294#3254C23136yescomplemented
295#3253C23136yescomplemented
296#3251C23172yescomplemented
297#3247C23172yescomplemented
298#3246C23136yescomplemented
299#3245C23136yescomplemented
300#3217C23172yescomplemented
301#3217C23172yescomplemented
302#3214C23172yescomplemented
303#3213C23172yescomplemented
304#3208C23136yescomplemented
305#3208C23136yescomplemented
306#3207C23172yescomplemented
307#3206C23136yescomplemented
308#3205C23136yescomplemented
309#3205C23136yescomplemented
310#3205C23136yescomplemented
311#3194C231144yescomplemented
312#3193C23172yescomplemented
313#3192C23172yescomplemented
314#3188C231144yescomplemented
315#3187C23172yescomplemented
316#3186C23172yescomplemented
317#3184C23136yescomplemented
318#3182C23136yescomplemented
319#3180C23172yescomplemented
320#3171C23172yescomplemented
321#3169C23136yescomplemented
322#3167C23136yescomplemented
323#3165C2316yescomplemented
324#3151C23118yescomplemented
325#3151C23136yescomplemented
326#3151C23172yescomplemented
327C2×#496C23136yescomplemented
328C2×#493C23118yescomplemented
329C2×#492C23118yescomplemented
330#3141C23118yescomplemented
331#3138C23118yescomplemented
332#3115C23136yescomplemented
333#3115C23136yescomplemented
334#3114C23172yescomplemented
335#3112C23136yescomplemented
336#3110C23136yescomplemented
337#3109C23136yescomplemented
338#3109C23136yescomplemented
339#3106C23136yescomplemented
340#3106C23136yescomplemented
341#3105C23172yescomplemented
342#3103C23136yescomplemented
343#3101C23136yescomplemented
344#3100C23136yescomplemented
345#3100C23136yescomplemented
346#3094C23136yescomplemented
347#3092C23136yescomplemented
348#3079C23118yescomplemented
349#3079C2316yescomplemented
350#3077C2316yescomplemented
351#3077C23118yescomplemented
352#3055C23136yescomplemented
353#3055C23172yescomplemented
354#3055C23136yescomplemented
355#3055C231144yescomplemented
356C2×#469C23136yescomplemented
357C2×#468C23136yescomplemented
358C2×#466C23136yescomplemented
359C2×#465C23136yescomplemented
360#3038C23118yescomplemented
361#3038C23136yescomplemented
362#3038C23118yescomplemented
363#3038C23136yescomplemented
364#3038C23136yescomplemented
365#3036C23118yescomplemented
366#3036C23118yescomplemented
367#3036C23136yescomplemented
368#3036C23172yescomplemented
369C2×#460C23118yescomplemented
370C2×#460C23118yescomplemented
371C2×#463C23136yescomplemented
372C2×#461C23118yescomplemented
373C2×#459C23118yescomplemented
374C2×#459C23118yescomplemented
375C2×#459C23118yescomplemented
376#3006C23172yescomplemented
377#3006C23136yescomplemented
378#3006C23172yescomplemented
379#3006C23172yescomplemented
380#3003C23136yescomplemented
381#3003C23172yescomplemented
382#3003C231144yescomplemented
383C2×#449C23136yescomplemented
384C2×#449C23136yescomplemented
385C2×#448C23136yescomplemented
386C2×#450C23136yescomplemented
387C2×#450C23136yescomplemented
388C2×#447C23136yescomplemented
389C2×#447C23136yescomplemented
390C2×#447C23136yescomplemented
391#2991C23112yescomplemented
392#2990C23136yescomplemented
393#2989C23136yescomplemented
394#2988C23112yescomplemented
395#2975C23118yescomplemented
396#2974C23172yescomplemented
397#2973C23136yescomplemented
398#2972C23118yescomplemented
399#2971C23112yescomplemented
400#2970C23136yescomplemented
401#2965C23136yescomplemented
402C8×#41C23112yescomplemented
403Q8×M16C2312yescomplemented
404Q8×M16C2316yescomplemented
405C4×AGL(1,ℤ/8)C2316yes—
406C4×AGL(1,ℤ/8)C23118yescomplemented
407C4×AGL(1,ℤ/8)C23118yescomplemented
408C4×AGL(1,ℤ/8)C23136yescomplemented
409C4×AGL(1,ℤ/8)C23118yescomplemented
410C4×AGL(1,ℤ/8)C23136yescomplemented
411C4×AGL(1,ℤ/8)C23136yescomplemented
412C2×#442C23118yescomplemented
413C2×#440C23118yescomplemented
414C2×C4×SD16C23118yescomplemented
415C2×C4×D8C23118yescomplemented
416D4×M16C23118yescomplemented
417D4×M16C23118yescomplemented
418D4×M16C23136yescomplemented
419D4×M16C23172yescomplemented
420C2×#436C23118yescomplemented
421C2×#435C23136yescomplemented
422C2×C8×D4C23118yescomplemented
423#2920C23118yescomplemented
424C2×#428C2319yescomplemented
425C2×#423C2319yescomplemented
426C2×#417C23118yescomplemented
427C2×#417C2319yescomplemented
428C2×#418C2319yescomplemented
429C2×#418C23118yescomplemented
430C2×#407C23118yescomplemented
431C2×C4×M16C2319yescomplemented
432C2×H(5,𝔽2)C2×D419yes—
433C2×H(5,𝔽2)C2×D416yes—
434C2×H(5,𝔽2)C2×D411yescharacteristic
435C22×#41C2×D416yes—
436C22×#41C2419yes—
437C22×#41C24118yes—
438C22×#41C24118yescomplemented
439C22×#41C24118yescomplemented
440C23×Q8C2416yescomplemented
441C23×D4C2×D419yes—
442C23×D4C2419yes—
443C23×D4C24118yes—
444C23×D4C24112yes—
445C23×D4C24136yes—
446C23×D4C2416yescomplemented
447C24×C4C2416yes—
448C2×AGL(1,ℤ/8)C2411yescharacteristic
449C2×AGL(1,ℤ/8)C2419yes—
450C2×AGL(1,ℤ/8)C24136yes—
451C2×AGL(1,ℤ/8)C24136yes—
452C2×AGL(1,ℤ/8)C2419yes—
453C2×AGL(1,ℤ/8)C2419yes—
454C2×AGL(1,ℤ/8)C24118yes—
455C2×AGL(1,ℤ/8)C24118yes—
456C2×AGL(1,ℤ/8)C24172yes—
457C2×AGL(1,ℤ/8)C24172yescomplemented
458C2×AGL(1,ℤ/8)C24172yescomplemented
459C2×AGL(1,ℤ/8)C24136yescomplemented
460C2×AGL(1,ℤ/8)C24136yescomplemented
461C22×SD16C24118yes—
462C22×SD16C24136yes—
463C22×SD16C24136yescomplemented
464C22×SD16C24136yescomplemented
465C22×SD16C24136yescomplemented
466C22×D8C24118yes—
467C22×D8C24136yes—
468C22×D8C24136yescomplemented
469C22×D8C24136yescomplemented
470C22×D8C24136yescomplemented
471C22×M16C2419yes—
472C22×M16C2419yes—
473C22×M16C24118yes—
474C22×M16C24136yescomplemented
475C23×C8C24112yescomplemented
476#559C24118yescomplemented
477Q82C2412yescomplemented
478#557C2416yescomplemented
479#557C2416yescomplemented
480#556C24118yescomplemented
481#556C24118yescomplemented
482#555C24118yescomplemented
483#554C24118yescomplemented
484#554C2416yescomplemented
485#553C24136yescomplemented
486#552C24136yescomplemented
487#550C24112yes—
488#550C24136yes—
489#550C2416yescomplemented
490#550C24118yescomplemented
491#550C24136yescomplemented
492D4×Q8C2414yes—
493D4×Q8C24112yes—
494D4×Q8C2412yescomplemented
495D4×Q8C24118yescomplemented
496D4×Q8C24136yescomplemented
497#548C24136yescomplemented
498#548C24172yescomplemented
499#547C24136yes—
500#547C24136yes—
501#547C24172yes—
502#547C24118yescomplemented
503#547C24118yescomplemented
504#547C24136yescomplemented
505#546C24136yescomplemented
506#546C24172yescomplemented
507D42C24136yes—
508D42C24172yes—
509D42C24172yes—
510D42C24136yes—
511D42C241144yes—
512D42C24172yes—
513D42C24118yescomplemented
514D42C24136yescomplemented
515#533C2416yes—
516#533C24118yescomplemented
517#533C24118yescomplemented
518#532C24136yes—
519#532C24136yes—
520#532C24136yes—
521#532C24136yes—
522#532C24118yes—
523#532C24118yescomplemented
524#532C24118yescomplemented
525#532C24136yescomplemented
526C2×C4⋊Q8C2416yes—
527C2×C4⋊Q8C2419yescomplemented
528C2×#127C24118yes—
529C2×#127C24118yes—
530C2×#127C24118yes—
531C2×#127C24136yes—
532C2×#127C2419yescomplemented
533#529C24136yescomplemented
534#529C24136yescomplemented
535C2×#124C24118yescomplemented
536#525C24136yes—
537#525C24172yescomplemented
538C2×C22⋊Q8C24118yescomplemented
539C2×C22⋊Q8C24118yescomplemented
540C2×#121C24136yes—
541C2×#121C24136yes—
542C2×#121C24172yes—
543C2×#121C24136yes—
544C2×#121C24118yescomplemented
545C2×#121C24118yescomplemented
546#520C2×D4118yes—
547#520C2×D4136yes—
548#520C2×D4118yes—
549#520C2×D4112yes—
550#520C2×D416yes—
551#520C2×D416yes—
552#518C2×D419yes—
553#518C2×D419yes—
554#518C2×D4136yes—
555#518C2×D4136yes—
556#518C2×D4136yes—
557#518C2×D4118yes—
558C4×#41C2×D4118yes—
559C4×#41C2×D416yes—
560C4×#41C2×D4118yes—
561C4×#41C2×D416yes—
562C4×#41C2416yes—
563C4×#41C24118yes—
564C4×#41C24118yes—
565C4×#41C2416yes—
566C4×#41C2416yes—
567C4×#41C24118yes—
568C4×#41C24118yescomplemented
569C4×#41C24118yescomplemented
570C2×C4×Q8C2×D416yes—
571C2×C4×Q8C2412yes—
572C2×C4×Q8C2419yescomplemented
573C2×C4×Q8C2419yescomplemented
574C2×C4×D4C2×D4136yes—
575C2×C4×D4C2×D419yes—
576C2×C4×D4C2×D419yes—
577C2×C4×D4C2×D4118yes—
578C2×C4×D4C2×D4136yes—
579C2×C4×D4C2×D4118yes—
580C2×C4×D4C24118yes—
581C2×C4×D4C2419yes—
582C2×C4×D4C24118yes—
583C2×C4×D4C2419yes—
584C2×C4×D4C24136yes—
585C2×C4×D4C2416yes—
586C2×C4×D4C24118yes—
587C2×C4×D4C24118yes—
588C2×C4×D4C24136yes—
589C2×C4×D4C24118yes—
590C2×C4×D4C2419yescomplemented
591C2×C4×D4C2419yescomplemented
592C2×#117C2×D4118yes—
593C2×#117C2419yes—
594C22×C4⋊C4C2×D419yes—
595C22×C4⋊C4C2419yes—
596C22×C22⋊C4C2×D4118yes—
597C22×C42C2419yes—
598#501C24124yescomplemented
599#500C24112yescomplemented
600#498C24112yescomplemented
601#496C24172yescomplemented
602#496C241144yescomplemented
603#493C24136yescomplemented
604#493C24172yescomplemented
605#492C24136yescomplemented
606#492C24172yescomplemented
607#490C24172yescomplemented
608#489C24172yescomplemented
609#487C24136yescomplemented
610#486C24136yescomplemented
611#486C24136yescomplemented
612#486C24136yescomplemented
613#484C24172yescomplemented
614#483C24172yescomplemented
615#482C24172yescomplemented
616#482C24172yescomplemented
617#481C24172yescomplemented
618#481C24172yescomplemented
619#480C24172yescomplemented
620#480C24172yescomplemented
621#478C24124yes—
622#478C24172yescomplemented
623#477C24136yescomplemented
624#477C24112yescomplemented
625#476C24112yes—
626#476C24136yescomplemented
627#476C24136yescomplemented
628#476C24112yescomplemented
629#475C24112yescomplemented
630#475C24136yescomplemented
631#474C24112yes—
632#474C24112yescomplemented
633#474C24136yescomplemented
634#474C24136yescomplemented
635#469C24172yescomplemented
636#469C241144yescomplemented
637#469C24172yescomplemented
638#468C24172yescomplemented
639#468C241144yescomplemented
640#468C24172yescomplemented
641#466C24172yescomplemented
642#466C24172yescomplemented
643#466C241144yescomplemented
644#465C24172yescomplemented
645#465C24172yescomplemented
646#465C241144yescomplemented
647#463C24172yes—
648#463C24172yescomplemented
649#463C241144yescomplemented
650#461C24136yes—
651#461C24136yescomplemented
652#461C24172yescomplemented
653#460C24136yescomplemented
654#460C24136yescomplemented
655#460C24136yescomplemented
656#460C24136yescomplemented
657#460C24172yescomplemented
658#460C24172yescomplemented
659#459C24136yes—
660#459C24136yescomplemented
661#459C24172yescomplemented
662#459C24136yescomplemented
663#459C24136yescomplemented
664#459C24136yescomplemented
665#459C24136yescomplemented
666#459C24172yescomplemented
667#459C24172yescomplemented
668#450C24172yes—
669#450C24172yes—
670#450C241144yescomplemented
671#450C241144yescomplemented
672#449C24172yescomplemented
673#449C241144yescomplemented
674#449C24172yescomplemented
675#449C241144yescomplemented
676#448C24172yescomplemented
677#448C241144yescomplemented
678#447C24172yes—
679#447C24172yes—
680#447C24172yescomplemented
681#447C241144yescomplemented
682#447C241144yescomplemented
683#447C241144yescomplemented
684#446C24136yescomplemented
685#446C24112yescomplemented
686C8×Q8C24112yescomplemented
687C8×Q8C2414yescomplemented
688#442C24136yes—
689#442C24112yes—
690#442C24136yescomplemented
691#442C24136yescomplemented
692#442C24172yescomplemented
693#440C24136yes—
694#440C24112yes—
695#440C24136yescomplemented
696#440C24172yescomplemented
697#440C24136yescomplemented
698C4×SD16C24136yes—
699C4×SD16C24112yes—
700C4×SD16C24172yescomplemented
701C4×SD16C24136yescomplemented
702C4×SD16C24136yescomplemented
703C4×D8C24136yes—
704C4×D8C24112yes—
705C4×D8C24136yescomplemented
706C4×D8C24172yescomplemented
707C4×D8C24136yescomplemented
708#436C24172yescomplemented
709#436C24136yescomplemented
710#436C24136yescomplemented
711#435C24172yescomplemented
712#435C241144yescomplemented
713#435C24172yescomplemented
714C8×D4C24136yescomplemented
715C8×D4C24172yescomplemented
716C8×D4C24136yescomplemented
717#432C24136yescomplemented
718#432C24136yescomplemented
719#431C24136yescomplemented
720#431C24136yescomplemented
721#428C24118yes—
722#428C24112yes—
723#428C2416yes—
724#428C24136yescomplemented
725C2×#107C24118yescomplemented
726C2×#106C24118yescomplemented
727#423C24118yes—
728#423C2416yes—
729#423C24136yescomplemented
730C2×C4⋊C8C24118yescomplemented
731C2×C4⋊C8C24118yescomplemented
732#418C2416yes—
733#418C24136yes—
734#418C24118yes—
735#418C24136yes—
736#418C24172yescomplemented
737#417C2416yes—
738#417C24136yes—
739#417C24118yes—
740#417C24118yescomplemented
741#417C24172yescomplemented
742#417C24118yescomplemented
743C2×#103C24118yescomplemented
744C2×#103C24136yescomplemented
745C2×#102C24118yes—
746C2×#102C24118yes—
747C2×#102C24136yescomplemented
748C2×#102C24136yescomplemented
749C2×#102C24118yescomplemented
750C2×#102C24136yescomplemented
751#407C24136yes—
752#407C24172yescomplemented
753C2×C22⋊C8C24136yescomplemented
754C2×C22⋊C8C24136yescomplemented
755C4×M16C2416yes—
756C4×M16C24118yes—
757C4×M16C24136yescomplemented
758C2×#97C24118yescomplemented
759C2×C4×C8C24118yescomplemented
760C25C22×D416yes—
761H(5,𝔽2)AGL(1,ℤ/8)116yesdirect product factor
762C2×#41C22×D4118yes—
763C2×#41C22×D4118yes—
764C2×#41C22×D416yes—
765C2×#41C22×D416yes—
766C2×#41C2519yes—
767C2×#41C2519yes—
768C2×#41C2519yes—
769C2×#41C25136yes—
770C2×#41C2511yescharacteristic
771C22×Q8C22×D412yes—
772C22×Q8C2519yes—
773C22×Q8C25118yes—
774C22×D4C22×D419yes—
775C22×D4C22×D4118yes—
776C22×D4C22×D419yes—
777C22×D4C22×D4136yes—
778C22×D4C22×D4118yes—
779C22×D4C2511yescharacteristic
780C22×D4C2519yes—
781C22×D4C25118yes—
782C22×D4C25118yes—
783C22×D4C2519yes—
784C22×D4C25136yes—
785C22×D4C25136yes—
786C22×D4C25118yes—
787C23×C4C22×D419yes—
788C23×C4C22×D4118yes—
789C23×C4C22×D419yes—
790C23×C4C22×D4118yes—
791C23×C4C22×D416yes—
792C23×C4C2519yes—
793C23×C4C2516yes—
794C23×C4C25118yes—
795AGL(1,ℤ/8)H(5,𝔽2)18yesdirect product factor
796C2×SD16C2512yes—
797C2×SD16C25118yes—
798C2×SD16C25118yes—
799C2×SD16C25118yes—
800C2×SD16C25172yes—
801C2×SD16C25172yes—
802C2×D8C2512yes—
803C2×D8C25118yes—
804C2×D8C25118yes—
805C2×D8C25118yes—
806C2×D8C25172yes—
807C2×D8C25172yes—
808C2×M16C2511yescharacteristic
809C2×M16C2519yes—
810C2×M16C2516yes—
811C2×M16C25118yes—
812C2×M16C25136yes—
813C2×M16C25118yes—
814C22×C8C25118yes—
815C22×C8C25136yes—
816C22×C8C25118yes—
817C4⋊Q8C25112yes—
818C4⋊Q8C25112yes—
819C4⋊Q8C2516yes—
820C4⋊Q8C2516yes—
821C4⋊Q8C25118yes—
822#127C25136yes—
823#127C25136yes—
824#127C25118yes—
825#125C25112yes—
826#124C25136yes—
827C22⋊Q8C25136yes—
828C22⋊Q8C25136yes—
829#121C25172yes—
830#121C25172yes—
831#121C25136yes—
832#121C25136yes—
833C4×Q8C22×D4118yes—
834C4×Q8C22×D4118yes—
835C4×Q8C22×D416yes—
836C4×Q8C22×D416yes—
837C4×Q8C22×D416yes—
838C4×Q8C22×D412yes—
839C4×Q8C2512yes—
840C4×Q8C2516yes—
841C4×Q8C2516yes—
842C4×Q8C2516yes—
843C4×Q8C25118yes—
844C4×Q8C25118yes—
845C4×D4C22×D4118yes—
846C4×D4C22×D4118yes—
847C4×D4C22×D4136yes—
848C4×D4C22×D4136yes—
849C4×D4C22×D4136yes—
850C4×D4C22×D4172yes—
851C4×D4C22×D4136yes—
852C4×D4C22×D4136yes—
853C4×D4C22×D4172yes—
854C4×D4C22×D4118yes—
855C4×D4C22×D4118yes—
856C4×D4C22×D4118yes—
857C4×D4C22×D4136yes—
858C4×D4C22×D4136yes—
859C4×D4C22×D4118yes—
860C4×D4C25118yes—
861C4×D4C25136yes—
862C4×D4C25118yes—
863C4×D4C25112yes—
864C4×D4C25112yes—
865C4×D4C25136yes—
866C4×D4C25136yes—
867C4×D4C2516yes—
868C4×D4C2516yes—
869C4×D4C25118yes—
870C4×D4C25118yes—
871#117C22×D4118yes—
872#117C22×D4118yes—
873#117C22×D4136yes—
874#117C22×D4118yes—
875#117C22×D4136yes—
876#117C22×D4118yes—
877#117C2516yes—
878#117C25118yes—
879C2×C4⋊C4C22×D4118yes—
880C2×C4⋊C4C22×D419yes—
881C2×C4⋊C4C22×D419yes—
882C2×C4⋊C4C22×D4118yes—
883C2×C4⋊C4C22×D4136yes—
884C2×C4⋊C4C22×D416yes—
885C2×C4⋊C4C2516yes—
886C2×C4⋊C4C25118yes—
887C2×C4⋊C4C25118yes—
888C2×C4⋊C4C2519yes—
889C2×C4⋊C4C2519yes—
890C2×C22⋊C4C22×D4136yes—
891C2×C22⋊C4C22×D4118yes—
892C2×C22⋊C4C22×D4118yes—
893C2×C22⋊C4C22×D4172yes—
894C2×C22⋊C4C22×D4118yes—
895C2×C22⋊C4C22×D4118yes—
896C2×C42C22×D4118yes—
897C2×C42C22×D419yes—
898C2×C42C22×D4118yes—
899C2×C42C22×D419yes—
900C2×C42C2516yes—
901C2×C42C2519yes—
902C2×C42C2519yes—
903C2×C42C25118yes—
904#107C25112yes—
905#107C25136yes—
906#107C25124yes—
907#106C25112yes—
908#106C25136yes—
909#106C25124yes—
910C4⋊C8C25136yes—
911C4⋊C8C25136yes—
912C4⋊C8C25112yes—
913C4⋊C8C25112yes—
914#103C25112yes—
915#103C25172yes—
916#103C25136yes—
917#102C25112yes—
918#102C25112yes—
919#102C25136yes—
920#102C25136yes—
921#102C25112yes—
922#102C25172yes—
923#102C25172yes—
924#102C25172yes—
925#102C25136yes—
926C22⋊C8C25172yes—
927C22⋊C8C25172yes—
928#97C25112yes—
929#97C25136yes—
930C4×C8C25112yes—
931C4×C8C25136yes—
932C24C23×D4118yes—
933C24C23×D419yes—
934C24C23×D416yes—
935#41C2×AGL(1,ℤ/8)148yescomplemented
936#41C2×H(5,𝔽2)14yescomplemented
937C2×Q8C23×D416yes—
938C2×Q8C23×D412yes—
939C2×Q8C2619yes—
940C2×Q8C2611yescharacteristic
941C2×D4C2×AGL(1,ℤ/8)172yescomplemented
942C2×D4C23×D4118yes—
943C2×D4C23×D4118yes—
944C2×D4C23×D4136yes—
945C2×D4C2×H(5,𝔽2)14yescomplemented
946C2×D4C2619yes—
947C2×D4C26118yes—
948C2×D4C2612yes—
949C2×D4C2611yescharacteristic
950C22×C4C23×D419yes—
951C22×C4C23×D416yes—
952C22×C4C23×D416yes—
953C22×C4C23×D419yes—
954C22×C4C23×D419yes—
955C22×C4C23×D419yes—
956C22×C4C23×D419yes—
957C22×C4C23×D419yes—
958C22×C4C23×D4118yes—
959C22×C4C23×D4118yes—
960C22×C4C23×D419yes—
961C22×C4C23×D4118yes—
962C22×C4C23×D4118yes—
963C22×C4C23×D4136yes—
964C22×C4C2611yescharacteristic
965C22×C4C2619yes—
966C22×C4C2619yes—
967SD16C2×H(5,𝔽2)18yescomplemented
968D8C2×H(5,𝔽2)18yescomplemented
969M16C2×H(5,𝔽2)14yescomplemented
970C2×C8C2612yes—
971C2×C8C26112yes—
972C2×C8C26118yes—
973C4⋊C4C23×D4118yes—
974C4⋊C4C23×D4118yes—
975C4⋊C4C23×D4136yes—
976C4⋊C4C23×D416yes—
977C4⋊C4C23×D416yes—
978C4⋊C4C23×D4112yes—
979C4⋊C4C2616yes—
980C4⋊C4C2616yes—
981C4⋊C4C26112yes—
982C22⋊C4C23×D4136yes—
983C22⋊C4C23×D4136yes—
984C22⋊C4C23×D4136yes—
985C22⋊C4C23×D4136yes—
986C42C23×D416yes—
987C42C23×D416yes—
988C42C23×D4118yes—
989C42C23×D4118yes—
990C42C23×D4118yes—
991C42C23×D4118yes—
992C42C2616yes—
993C42C2616yes—
994C23C22×AGL(1,ℤ/8)124yescomplemented
995C23C24×D411yescharacteristic
996C23C24×D419yes—
997C23C24×D419yes—
998Q8C22×AGL(1,ℤ/8)18yescomplemented
999Q8C22×H(5,𝔽2)12yescomplemented
1000D4C22×AGL(1,ℤ/8)172yescomplemented
1001D4C22×H(5,𝔽2)14yes—
1002D4C22×H(5,𝔽2)12yescomplemented
1003C2×C4C22×AGL(1,ℤ/8)136yescomplemented
1004C2×C4C24×D411yescharacteristic
1005C2×C4C24×D416yes—
1006C2×C4C24×D416yes—
1007C2×C4C24×D416yes—
1008C2×C4C24×D416yes—
1009C2×C4C24×D419yes—
1010C2×C4C24×D419yes—
1011C2×C4C22×H(5,𝔽2)12yes—
1012C2×C4H(7,𝔽2)12yes—
1013C2×C4C2711yescharacteristic
1014C8C22×H(5,𝔽2)14yescomplemented
1015C22D4×H(5,𝔽2)12yes—
1016C22C23×AGL(1,ℤ/8)118yes—
1017C22C25×D411yescharacteristic
1018C4D4×H(5,𝔽2)12yes—
1019C4C23×AGL(1,ℤ/8)112yes—
1020C4C23×H(5,𝔽2)11yescharacteristic
1021C4C2×H(7,𝔽2)11yescharacteristic
1022C2C2×D4×H(5,𝔽2)11yescharacteristic
1023C2C24×AGL(1,ℤ/8)11yescharacteristic
1024C2#1058699911yescharacteristic
subgroupG/H
center, socleC22C25×D4
commutator, Frattini, cosocleC2×C4C27
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×H(5,𝔽2) ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #41×H(5,𝔽2)C2semidirect
2. C2×D4×H(5,𝔽2)C2semidirect
3. #10583066C2semidirect
4. #10583065C2semidirect
5. #10583024C2semidirect
6. #10583022C2semidirect
7. SD16×H(5,𝔽2)C2semidirect
8. D8×H(5,𝔽2)C2semidirect
9. #10579229C2semidirect
10. #10578900C2semidirect
11. #10578892C2semidirect
12. #10577652C2semidirect
13. #10577308C2semidirect
14. #10577301C2semidirect
15. #41×AGL(1,ℤ/8)C2semidirect
16. C2×D4×AGL(1,ℤ/8)C2semidirect
17. M16×H(5,𝔽2)C2semidirect
18. C23×AGL(1,ℤ/8)C22semidirect
19. #62986C22semidirect
20. #62985C22semidirect
21. #62984C22semidirect
22. #62983C22semidirect
23. Q8×H(5,𝔽2)C22semidirect
25. D4×H(5,𝔽2)C22semidirect
26. D4×H(5,𝔽2)C22semidirect
27. D4×H(5,𝔽2)C22semidirect
28. #62800C22semidirect
29. C2×#3498C22semidirect
30. #62773C22semidirect
31. C2×#3496C22semidirect
32. #412C22semidirect
33. C2×D4×#41C22semidirect
34. C2×D4×#41C22semidirect
35. C22×D42C22semidirect
37. #62453C22semidirect
38. #62447C22semidirect
39. #62423C22semidirect
40. #62421C22semidirect
41. #62415C22semidirect
42. #62413C22semidirect
43. #62299C22semidirect
44. #62295C22semidirect
45. #62259C22semidirect
46. #62253C22semidirect
47. #62245C22semidirect
48. #62243C22semidirect
49. #62003C22semidirect
50. #62001C22semidirect
51. #61999C22semidirect
52. #61989C22semidirect
53. #61983C22semidirect
54. #61979C22semidirect
55. #61963C22semidirect
56. #61962C22semidirect
57. #61961C22semidirect
58. #61959C22semidirect
59. #61951C22semidirect
60. #61948C22semidirect
61. #61947C22semidirect
62. #61947C22semidirect
63. #61600C22semidirect
64. #61598C22semidirect
65. #61598C22semidirect
66. #61591C22semidirect
67. #61587C22semidirect
68. #61585C22semidirect
69. #61582C22semidirect
70. #61572C22semidirect
71. #61571C22semidirect
72. #61569C22semidirect
73. #61562C22semidirect
74. #61560C22semidirect
75. #61559C22semidirect
76. #61559C22semidirect
77. #61466C22semidirect
78. #61465C22semidirect
79. #61452C22semidirect
80. #61451C22semidirect
81. #61439C22semidirect
82. #61437C22semidirect
83. SD16×#41C22semidirect
84. D8×#41C22semidirect
85. #61402C22semidirect
86. #61402C22semidirect
87. Q8×AGL(1,ℤ/8)C22semidirect
88. #61321C22semidirect
89. #61317C22semidirect
90. #61252C22semidirect
91. #61161C22semidirect
92. #61161C22semidirect
93. #61155C22semidirect
94. #61155C22semidirect
95. D4×AGL(1,ℤ/8)C22semidirect
96. D4×AGL(1,ℤ/8)C22semidirect
97. D4×AGL(1,ℤ/8)C22semidirect
98. D4×AGL(1,ℤ/8)C22semidirect
99. D4×AGL(1,ℤ/8)C22semidirect
100. D4×AGL(1,ℤ/8)C22semidirect
101. D4×AGL(1,ℤ/8)C22semidirect
102. C2×D4×SD16C22semidirect
103. C2×D4×D8C22semidirect
104. C2×#3274C22semidirect
105. C2×#3272C22semidirect
106. C2×#3265C22semidirect
107. C2×#3264C22semidirect
108. #60916C22semidirect
109. #60803C22semidirect
110. #60798C22semidirect
111. #60750C22semidirect
112. #60700C22semidirect
113. C2×#3151C22semidirect
114. #60561C22semidirect
115. #60558C22semidirect
116. C2×#3055C22semidirect
117. C2×#3038C22semidirect
118. C2×#3036C22semidirect
119. C2×#3006C22semidirect
120. C2×#3003C22semidirect
121. #60325C22semidirect
122. #60309C22semidirect
123. C8×H(5,𝔽2)C22semidirect
124. #60263C22semidirect
125. #60230C22semidirect
126. M16×#41C22semidirect
127. C2×C4×AGL(1,ℤ/8)C22semidirect
128. C2×D4×M16C22semidirect
130. C23×#41C23semidirect
131. C24×D4C23semidirect
133. C22×AGL(1,ℤ/8)C23semidirect
134. C22×AGL(1,ℤ/8)C23semidirect
135. C22×AGL(1,ℤ/8)C23semidirect
136. C22×AGL(1,ℤ/8)C23semidirect
137. C22×AGL(1,ℤ/8)C23semidirect
138. C22×AGL(1,ℤ/8)C23semidirect
139. C23×SD16C23semidirect
140. C23×D8C23semidirect
141. C23×M16C23semidirect
142. #3520C23semidirect
143. #3519C23semidirect
144. #3517C23semidirect
145. #3514C23semidirect
146. #3511C23semidirect
147. #3508C23semidirect
148. #3506C23semidirect
149. #3505C23semidirect
150. #3503C23semidirect
151. #3501C23semidirect
153. #3498C23semidirect
154. #3498C23semidirect
155. #3498C23semidirect
156. #3498C23semidirect
158. #3496C23semidirect
159. #3496C23semidirect
160. #3496C23semidirect
161. #3496C23semidirect
162. #3483C23semidirect
163. #3482C23semidirect
164. #3482C23semidirect
165. #3481C23semidirect
166. #3480C23semidirect
167. #3480C23semidirect
168. Q8×#41C23semidirect
169. Q8×#41C23semidirect
170. #3475C23semidirect
171. #3475C23semidirect
173. D4×#41C23semidirect
174. D4×#41C23semidirect
175. D4×#41C23semidirect
176. D4×#41C23semidirect
177. D4×#41C23semidirect
178. D4×#41C23semidirect
179. D4×#41C23semidirect
180. D4×#41C23semidirect
181. C2×#550C23semidirect
182. C2×#550C23semidirect
183. C2×D4×Q8C23semidirect
184. C2×D4×Q8C23semidirect
185. C2×#548C23semidirect
186. C2×#547C23semidirect
187. C2×#547C23semidirect
188. C2×#546C23semidirect
190. C2×D42C23semidirect
191. C2×D42C23semidirect
192. C2×D42C23semidirect
193. C2×D42C23semidirect
194. C2×D42C23semidirect
195. C2×D42C23semidirect
196. #3444C23semidirect
197. C2×#532C23semidirect
198. C2×#532C23semidirect
199. C22×#127C23semidirect
200. C2×#525C23semidirect
201. C22×#121C23semidirect
211. C2×C4×#41C23semidirect
213. C22×C4×D4C23semidirect
214. #3399C23semidirect
215. #3399C23semidirect
216. #3397C23semidirect
217. #3397C23semidirect
218. #3392C23semidirect
219. #3392C23semidirect
220. #3391C23semidirect
221. #3391C23semidirect
222. #3386C23semidirect
223. #3384C23semidirect
224. Q8×SD16C23semidirect
225. Q8×D8C23semidirect
226. #3373C23semidirect
227. #3368C23semidirect
228. #3367C23semidirect
229. #3366C23semidirect
230. #3362C23semidirect
231. #3359C23semidirect
232. #3358C23semidirect
233. #3358C23semidirect
234. #3354C23semidirect
235. #3353C23semidirect
236. #3345C23semidirect
237. #3343C23semidirect
238. #3335C23semidirect
239. #3334C23semidirect
240. #3332C23semidirect
241. #3332C23semidirect
242. #3330C23semidirect
243. #3330C23semidirect
244. #3325C23semidirect
245. #3325C23semidirect
246. #3324C23semidirect
247. #3324C23semidirect
248. #3318C23semidirect
249. #3318C23semidirect
250. #3310C23semidirect
251. #3310C23semidirect
252. #3308C23semidirect
253. #3308C23semidirect
254. #3306C23semidirect
255. #3306C23semidirect
256. #3298C23semidirect
257. #3298C23semidirect
258. #3295C23semidirect
259. #3295C23semidirect
260. #3294C23semidirect
261. #3294C23semidirect
262. #3294C23semidirect
263. #3294C23semidirect
264. D4×SD16C23semidirect
265. D4×SD16C23semidirect
266. D4×SD16C23semidirect
267. D4×SD16C23semidirect
268. D4×SD16C23semidirect
269. D4×D8C23semidirect
270. D4×D8C23semidirect
271. D4×D8C23semidirect
272. D4×D8C23semidirect
273. D4×D8C23semidirect
274. #3274C23semidirect
275. #3274C23semidirect
276. #3274C23semidirect
277. #3274C23semidirect
278. #3274C23semidirect
279. #3272C23semidirect
280. #3272C23semidirect
281. #3272C23semidirect
282. #3272C23semidirect
283. #3272C23semidirect
284. #3265C23semidirect
285. #3265C23semidirect
286. #3265C23semidirect
287. #3265C23semidirect
288. #3265C23semidirect
289. #3264C23semidirect
290. #3264C23semidirect
291. #3264C23semidirect
292. #3264C23semidirect
293. #3264C23semidirect
294. #3254C23semidirect
295. #3253C23semidirect
296. #3251C23semidirect
297. #3247C23semidirect
298. #3246C23semidirect
299. #3245C23semidirect
300. #3217C23semidirect
301. #3217C23semidirect
302. #3214C23semidirect
303. #3213C23semidirect
304. #3208C23semidirect
305. #3208C23semidirect
306. #3207C23semidirect
307. #3206C23semidirect
308. #3205C23semidirect
309. #3205C23semidirect
310. #3205C23semidirect
311. #3194C23semidirect
312. #3193C23semidirect
313. #3192C23semidirect
314. #3188C23semidirect
315. #3187C23semidirect
316. #3186C23semidirect
317. #3184C23semidirect
318. #3182C23semidirect
319. #3180C23semidirect
320. #3171C23semidirect
321. #3169C23semidirect
322. #3167C23semidirect
323. #3165C23semidirect
324. #3151C23semidirect
325. #3151C23semidirect
326. #3151C23semidirect
327. C2×#496C23semidirect
328. C2×#493C23semidirect
329. C2×#492C23semidirect
330. #3141C23semidirect
331. #3138C23semidirect
332. #3115C23semidirect
333. #3115C23semidirect
334. #3114C23semidirect
335. #3112C23semidirect
336. #3110C23semidirect
337. #3109C23semidirect
338. #3109C23semidirect
339. #3106C23semidirect
340. #3106C23semidirect
341. #3105C23semidirect
342. #3103C23semidirect
343. #3101C23semidirect
344. #3100C23semidirect
345. #3100C23semidirect
346. #3094C23semidirect
347. #3092C23semidirect
348. #3079C23semidirect
349. #3079C23semidirect
350. #3077C23semidirect
351. #3077C23semidirect
352. #3055C23semidirect
353. #3055C23semidirect
354. #3055C23semidirect
355. #3055C23semidirect
356. C2×#469C23semidirect
357. C2×#468C23semidirect
358. C2×#466C23semidirect
359. C2×#465C23semidirect
360. #3038C23semidirect
361. #3038C23semidirect
362. #3038C23semidirect
363. #3038C23semidirect
364. #3038C23semidirect
365. #3036C23semidirect
366. #3036C23semidirect
367. #3036C23semidirect
368. #3036C23semidirect
369. C2×#460C23semidirect
370. C2×#460C23semidirect
371. C2×#463C23semidirect
372. C2×#461C23semidirect
373. C2×#459C23semidirect
374. C2×#459C23semidirect
375. C2×#459C23semidirect
376. #3006C23semidirect
377. #3006C23semidirect
378. #3006C23semidirect
379. #3006C23semidirect
380. #3003C23semidirect
381. #3003C23semidirect
382. #3003C23semidirect
383. C2×#449C23semidirect
384. C2×#449C23semidirect
385. C2×#448C23semidirect
386. C2×#450C23semidirect
387. C2×#450C23semidirect
388. C2×#447C23semidirect
389. C2×#447C23semidirect
390. C2×#447C23semidirect
391. #2991C23semidirect
392. #2990C23semidirect
393. #2989C23semidirect
394. #2988C23semidirect
395. #2975C23semidirect
396. #2974C23semidirect
397. #2973C23semidirect
398. #2972C23semidirect
399. #2971C23semidirect
400. #2970C23semidirect
401. #2965C23semidirect
402. C8×#41C23semidirect
403. Q8×M16C23semidirect
404. Q8×M16C23semidirect
406. C4×AGL(1,ℤ/8)C23semidirect
407. C4×AGL(1,ℤ/8)C23semidirect
408. C4×AGL(1,ℤ/8)C23semidirect
409. C4×AGL(1,ℤ/8)C23semidirect
410. C4×AGL(1,ℤ/8)C23semidirect
411. C4×AGL(1,ℤ/8)C23semidirect
412. C2×#442C23semidirect
413. C2×#440C23semidirect
414. C2×C4×SD16C23semidirect
415. C2×C4×D8C23semidirect
416. D4×M16C23semidirect
417. D4×M16C23semidirect
418. D4×M16C23semidirect
419. D4×M16C23semidirect
420. C2×#436C23semidirect
421. C2×#435C23semidirect
422. C2×C8×D4C23semidirect
423. #2920C23semidirect
424. C2×#428C23semidirect
425. C2×#423C23semidirect
426. C2×#417C23semidirect
427. C2×#417C23semidirect
428. C2×#418C23semidirect
429. C2×#418C23semidirect
430. C2×#407C23semidirect
431. C2×C4×M16C23semidirect
438. C22×#41C24semidirect
439. C22×#41C24semidirect
440. C23×Q8C24semidirect
446. C23×D4C24semidirect
457. C2×AGL(1,ℤ/8)C24semidirect
458. C2×AGL(1,ℤ/8)C24semidirect
459. C2×AGL(1,ℤ/8)C24semidirect
460. C2×AGL(1,ℤ/8)C24semidirect
463. C22×SD16C24semidirect
464. C22×SD16C24semidirect
465. C22×SD16C24semidirect
468. C22×D8C24semidirect
469. C22×D8C24semidirect
470. C22×D8C24semidirect
474. C22×M16C24semidirect
475. C23×C8C24semidirect
476. #559C24semidirect
477. Q82C24semidirect
478. #557C24semidirect
479. #557C24semidirect
480. #556C24semidirect
481. #556C24semidirect
482. #555C24semidirect
483. #554C24semidirect
484. #554C24semidirect
485. #553C24semidirect
486. #552C24semidirect
489. #550C24semidirect
490. #550C24semidirect
491. #550C24semidirect
494. D4×Q8C24semidirect
495. D4×Q8C24semidirect
496. D4×Q8C24semidirect
497. #548C24semidirect
498. #548C24semidirect
502. #547C24semidirect
503. #547C24semidirect
504. #547C24semidirect
505. #546C24semidirect
506. #546C24semidirect
513. D42C24semidirect
514. D42C24semidirect
516. #533C24semidirect
517. #533C24semidirect
523. #532C24semidirect
524. #532C24semidirect
525. #532C24semidirect
527. C2×C4⋊Q8C24semidirect
532. C2×#127C24semidirect
533. #529C24semidirect
534. #529C24semidirect
535. C2×#124C24semidirect
537. #525C24semidirect
538. C2×C22⋊Q8C24semidirect
539. C2×C22⋊Q8C24semidirect
544. C2×#121C24semidirect
545. C2×#121C24semidirect
568. C4×#41C24semidirect
569. C4×#41C24semidirect
572. C2×C4×Q8C24semidirect
573. C2×C4×Q8C24semidirect
590. C2×C4×D4C24semidirect
591. C2×C4×D4C24semidirect
598. #501C24semidirect
599. #500C24semidirect
600. #498C24semidirect
601. #496C24semidirect
602. #496C24semidirect
603. #493C24semidirect
604. #493C24semidirect
605. #492C24semidirect
606. #492C24semidirect
607. #490C24semidirect
608. #489C24semidirect
609. #487C24semidirect
610. #486C24semidirect
611. #486C24semidirect
612. #486C24semidirect
613. #484C24semidirect
614. #483C24semidirect
615. #482C24semidirect
616. #482C24semidirect
617. #481C24semidirect
618. #481C24semidirect
619. #480C24semidirect
620. #480C24semidirect
622. #478C24semidirect
623. #477C24semidirect
624. #477C24semidirect
626. #476C24semidirect
627. #476C24semidirect
628. #476C24semidirect
629. #475C24semidirect
630. #475C24semidirect
632. #474C24semidirect
633. #474C24semidirect
634. #474C24semidirect
635. #469C24semidirect
636. #469C24semidirect
637. #469C24semidirect
638. #468C24semidirect
639. #468C24semidirect
640. #468C24semidirect
641. #466C24semidirect
642. #466C24semidirect
643. #466C24semidirect
644. #465C24semidirect
645. #465C24semidirect
646. #465C24semidirect
648. #463C24semidirect
649. #463C24semidirect
651. #461C24semidirect
652. #461C24semidirect
653. #460C24semidirect
654. #460C24semidirect
655. #460C24semidirect
656. #460C24semidirect
657. #460C24semidirect
658. #460C24semidirect
660. #459C24semidirect
661. #459C24semidirect
662. #459C24semidirect
663. #459C24semidirect
664. #459C24semidirect
665. #459C24semidirect
666. #459C24semidirect
667. #459C24semidirect
670. #450C24semidirect
671. #450C24semidirect
672. #449C24semidirect
673. #449C24semidirect
674. #449C24semidirect
675. #449C24semidirect
676. #448C24semidirect
677. #448C24semidirect
680. #447C24semidirect
681. #447C24semidirect
682. #447C24semidirect
683. #447C24semidirect
684. #446C24semidirect
685. #446C24semidirect
686. C8×Q8C24semidirect
687. C8×Q8C24semidirect
690. #442C24semidirect
691. #442C24semidirect
692. #442C24semidirect
695. #440C24semidirect
696. #440C24semidirect
697. #440C24semidirect
700. C4×SD16C24semidirect
701. C4×SD16C24semidirect
702. C4×SD16C24semidirect
705. C4×D8C24semidirect
706. C4×D8C24semidirect
707. C4×D8C24semidirect
708. #436C24semidirect
709. #436C24semidirect
710. #436C24semidirect
711. #435C24semidirect
712. #435C24semidirect
713. #435C24semidirect
714. C8×D4C24semidirect
715. C8×D4C24semidirect
716. C8×D4C24semidirect
717. #432C24semidirect
718. #432C24semidirect
719. #431C24semidirect
720. #431C24semidirect
724. #428C24semidirect
725. C2×#107C24semidirect
726. C2×#106C24semidirect
729. #423C24semidirect
730. C2×C4⋊C8C24semidirect
731. C2×C4⋊C8C24semidirect
736. #418C24semidirect
740. #417C24semidirect
741. #417C24semidirect
742. #417C24semidirect
743. C2×#103C24semidirect
744. C2×#103C24semidirect
747. C2×#102C24semidirect
748. C2×#102C24semidirect
749. C2×#102C24semidirect
750. C2×#102C24semidirect
752. #407C24semidirect
753. C2×C22⋊C8C24semidirect
754. C2×C22⋊C8C24semidirect
757. C4×M16C24semidirect
758. C2×#97C24semidirect
759. C2×C4×C8C24semidirect
761. H(5,𝔽2)AGL(1,ℤ/8)direct (N × H)
795. AGL(1,ℤ/8)H(5,𝔽2)direct (N × H)
935. #41C2×AGL(1,ℤ/8)semidirect
936. #41C2×H(5,𝔽2)semidirect
941. C2×D4C2×AGL(1,ℤ/8)semidirect
945. C2×D4C2×H(5,𝔽2)semidirect
967. SD16C2×H(5,𝔽2)semidirect
968. D8C2×H(5,𝔽2)semidirect
969. M16C2×H(5,𝔽2)semidirect
994. C23C22×AGL(1,ℤ/8)semidirect
998. Q8C22×AGL(1,ℤ/8)semidirect
999. Q8C22×H(5,𝔽2)semidirect
1000. D4C22×AGL(1,ℤ/8)semidirect
1002. D4C22×H(5,𝔽2)semidirect
1003. C2×C4C22×AGL(1,ℤ/8)semidirect
1014. C8C22×H(5,𝔽2)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×H(5,𝔽2)2
C2×D4×H(5,𝔽2)2
#105830662
#105830652
#105830242
#105830222
SD16×H(5,𝔽2)2
D8×H(5,𝔽2)2
#105792292
#105789002
#105788922
#105776522
#105773082
#105773012
#41×AGL(1,ℤ/8)2
C2×D4×AGL(1,ℤ/8)2
M16×H(5,𝔽2)2