Finite Group Databasebeta

← #7627340

Subgroups — #7627340

Order 512.

6976 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic
2#34485C213yesmaximal, complemented
3#34481C213yesmaximal, complemented
4#34463C216yesmaximal, complemented
5#34429C216yesmaximal, complemented
6#34419C216yesmaximal, complemented
7#34383C213yesmaximal, complemented
8#34335C211yesmaximal, characteristic, complemented
9#34324C216yesmaximal, complemented
10#34322C213yesmaximal, complemented
11#34321C213yesmaximal, complemented
12#34311C211yesmaximal, characteristic, complemented
13#34293C212yesmaximal, complemented
14#34262C212yesmaximal, complemented
15#34249C212yesmaximal, complemented
16#34225C213yesmaximal, complemented
17#34213C213yesmaximal, complemented
18C4×Q82C211yesmaximal, characteristic, complemented
19C4×D4×Q8C211yesmaximal, characteristic, complemented
20C4×#548C212yesmaximal, complemented
21#34153C213yesmaximal, complemented
22#34129C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24#3518C4132yescomplemented
25C2×Q82C2211yescharacteristic
26C2×#556C2213yes—
27C2×#556C2216yes—
28C2×#555C2213yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#548C2212yes—
31C2×#542C2216yes—
32C2×#533C2213yes—
33C2×#529C2213yes—
34C2×#519C2212yes—
35C2×#519C2212yes—
36C2×C4×#41C2212yes—
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2212yes—
39#2383C22112yes—
40#2379C22112yes—
41#2376C22112yes—
42#2373C22112yes—
43#2373C2216yes—
44#2373C2216yes—
45#2370C2216yes—
46#2370C2213yes—
47#2370C2213yes—
48#2369C2213yes—
49#2369C2213yes—
50#2369C2216yes—
51#2367C22112yes—
52#2367C2216yes—
53#2367C2213yes—
54#2367C2211yescharacteristic
55#2367C2216yes—
56#2365C2213yes—
57#2365C2213yes—
58#2365C2216yes—
59#2363C2216yes—
60#2362C2216yes—
61#2362C2216yes—
62#2362C2216yes—
63#2361C2213yes—
64#2361C2213yes—
65#2361C2216yes—
66#2360C2213yes—
67#2360C2213yes—
68#2360C2216yes—
69#2359C2216yes—
70#2359C2216yes—
71#2356C2216yes—
72#2355C2213yes—
73#2355C22112yes—
74#2355C2216yes—
75#2354C2213yes—
76#2354C2216yes—
77#2354C2213yes—
78#2354C2213yes—
79#2352C2216yes—
80#2351C2216yes—
81#2351C2212yes—
82#2351C2212yes—
83#2351C2216yes—
84Q8×C4⋊C4C2211yescharacteristic
85Q8×C4⋊C4C2216yes—
86Q8×C4⋊C4C2211yescharacteristic
87Q8×C4⋊C4C2213yes—
88Q8×C4⋊C4C2211yescharacteristic
89Q8×C4⋊C4C2211yescharacteristic
90Q8×C4⋊C4C2212yes—
91Q8×C4⋊C4C2216yes—
92#2349C2216yes—
93D4×C4⋊C4C2213yes—
94D4×C4⋊C4C2213yes—
95D4×C4⋊C4C2213yes—
96#2347C2216yes—
97#2347C2216yes—
98#2346C2216yes—
99#2346C2213yes—
100#2346C2216yes—
101#2346C2213yes—
102#2341C2211yescharacteristic
103#2341C2211yescharacteristic
104Q8×C22⋊C4C2212yes—
105Q8×C22⋊C4C2212yes—
106#2337C22112yes—
107#2334C22112yes—
108#2334C22112yes—
109#2334C22112yes—
110#2331C2216yes—
111#2329C22112yes—
112#2326C22112yes—
113#2326C2216yes—
114#2324C2216yes—
115#2324C2216yes—
116#2323C2216yes—
117#2323C2216yes—
118#2323C2216yes—
119#2323C2216yes—
120#2320C2216yes—
121#2320C2216yes—
122#2317C2216yes—
123#2317C2216yes—
124#2317C2216yes—
125#2314C2216yes—
126C4×C4⋊Q8C2213yes—
127C4×C4⋊Q8C2213yes—
128C4×C4⋊Q8C2216yes—
129C4×C4⋊Q8C2213yes—
130C4×C4⋊Q8C2213yes—
131C4×#124C2216yes—
132C4×C22⋊Q8C2216yes—
133C4×C22⋊Q8C2216yes—
134C4×C22⋊Q8C2216yes—
135C4×#121C2216yes—
136#2298C2216yes—
137#2296C2216yes—
138#2296C2216yes—
139#2296C2216yes—
140#2295C2216yes—
141#2295C2213yes—
142#2293C2213yes—
143#2293C2213yes—
144#2293C2213yes—
145#2290C2216yes—
146#2285C2213yes—
147#2285C2213yes—
148#2276C2216yes—
149#2276C2212yes—
150#2274C2216yes—
151C42×Q8C2211yescharacteristic
152C42×Q8C2213yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2212yes—
155C42×D4C2213yes—
156C42×D4C2216yes—
157C4×#117C2213yes—
158C2×C4×C4⋊C4C2213yes—
159C22×#41C2311yescharacteristic
160C23×Q8C2312yes—
161Q82C2×C4116yescomplemented
162#556C2×C4196yescomplemented
163#556C2×C4148yescomplemented
164#555C2×C4148yescomplemented
165D4×Q8C2×C4116yescomplemented
166#548C2×C4132yescomplemented
167#542C2×C4196yescomplemented
168#533C2×C4148yescomplemented
169C2×C4⋊Q8C2313yes—
170C2×C4⋊Q8C2313yes—
171C2×C4⋊Q8C2316yes—
172#529C2×C4148yescomplemented
173C2×#126C2316yes—
174C2×#126C23112yes—
175C2×#125C2313yes—
176C2×#124C23112yes—
177C2×#124C2316yes—
178C2×#124C2311yescharacteristic
179C2×#123C2316yes—
180C2×C22⋊Q8C2316yes—
181C2×C22⋊Q8C2313yes—
182C2×C22⋊Q8C2316yes—
183C2×C22⋊Q8C2316yes—
184C2×#121C2313yes—
185C2×#121C2316yes—
186#519—48no—
187#519C2×C4132yescomplemented
188C4×#41—48no—
189C4×#41C2×C4116yescomplemented
190C2×C4×Q8—48no—
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2316yes—
202C2×C4×Q8C2313yes—
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2316yes—
205C2×C4×Q8C2316yes—
206C2×C4×Q8C2316yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2316yes—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2313yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2313yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2313yes—
221C2×C4×D4C2316yes—
222C2×#117C2316yes—
223C2×#117C2316yes—
224C2×#117C2316yes—
225C2×#117C2313yes—
226C2×#117C2313yes—
227C2×#117C2316yes—
228C2×#117C2316yes—
229C2×#117C2316yes—
230C2×#117C2316yes—
231C2×#117C2313yes—
232C22×C4⋊C4C2313yes—
233C22×C4⋊C4C2313yes—
234C22×C4⋊C4C2316yes—
235C22×C42C2316yes—
236C22×C42C2316yes—
237C22×C42C2313yes—
238#391C2316yes—
239#391C2316yes—
240#391C2316yes—
241#391C23112yes—
242#391C2316yes—
243#391C2316yes—
244#391C2313yes—
245#391C23112yes—
246#391C2316yes—
247#391C2311yescharacteristic
248#390C23112yes—
249#390C2313yes—
250#390C2313yes—
251#390C2313yes—
252#390C2313yes—
253#390C2313yes—
254#390C2311yescharacteristic
255#389C2313yes—
256#389C2313yes—
257#389C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C2316yes—
262#389C23112yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2313yes—
267#389C2313yes—
268#389C2313yes—
269#389C2316yes—
270#389C23112yes—
271#389C23112yes—
272#389C2316yes—
273#389C2313yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2313yes—
280#389C2313yes—
281#389C2316yes—
282#388C2316yes—
283#388C23112yes—
284#388C2316yes—
285#388C23112yes—
286#388C23112yes—
287#388C23112yes—
288#388C23112yes—
289#388C23112yes—
290#388C23112yes—
291#388C23112yes—
292#388C2316yes—
293#388C2316yes—
294#388C2316yes—
295#388C2316yes—
296#388C2316yes—
297#388C2316yes—
298#388C2316yes—
299#388C2316yes—
300#388C2312yes—
301#388C2312yes—
302#387C23112yes—
303#387C23112yes—
304#387C2316yes—
305#387C2316yes—
306#387C23112yes—
307#387C2316yes—
308#387C23112yes—
309#387C2316yes—
310#387C23112yes—
311#387C2316yes—
312#387C23112yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#386C2316yes—
317#386C23112yes—
318#386C2316yes—
319#385C23112yes—
320#385C2316yes—
321#385C2316yes—
322#385C23112yes—
323#385C23112yes—
324#385C2316yes—
325#385C23112yes—
326#385C23112yes—
327#385C2316yes—
328#385C23112yes—
329#385C2312yes—
330#385C2316yes—
331#384C2313yes—
332#384C2313yes—
333#384C2316yes—
334#384C2313yes—
335#384C23112yes—
336#384C2313yes—
337#383C23112yes—
338#382C2316yes—
339#382C23112yes—
340#382C23112yes—
341#382C2316yes—
342#382C2316yes—
343#380C2316yes—
344#380C2316yes—
345#380C2316yes—
346#380C2316yes—
347#380C2316yes—
348#380C2313yes—
349#380C2313yes—
350C4×C4⋊C4C2313yes—
351C4×C4⋊C4C2313yes—
352C4×C4⋊C4C2316yes—
353C4×C4⋊C4C2313yes—
354C4×C4⋊C4C2316yes—
355C4×C4⋊C4C2316yes—
356C4×C4⋊C4C2316yes—
357C4×C4⋊C4C2316yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2316yes—
360C4×C4⋊C4C2316yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2316yes—
363C4×C4⋊C4C2313yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2313yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C23112yes—
368C4×C4⋊C4C23112yes—
369C4×C4⋊C4C23112yes—
370C4×C4⋊C4C23112yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2316yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2316yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2311yescharacteristic
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2311yescharacteristic
390C4×C4⋊C4C2313yes—
391C4×C22⋊C4C23112yes—
392C4×C22⋊C4C23112yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2313yes—
402C4×C22⋊C4C2316yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2312yes—
405#376C2313yes—
406#376C2316yes—
407#376C23112yes—
408#376C2313yes—
409C2×#95C2316yes—
410C43C2313yes—
411C43C2313yes—
412C43C2316yes—
413C2×#41—24no—
414C2×#41—24no—
415C2×#41C22×C418yes—
416C22×Q8—28no—
417C22×Q8—28no—
418C22×Q8C22×C4116yes—
419C22×Q8C2411yescharacteristic
420C22×Q8C2416yes—
421C22×Q8C2416yes—
422C22×Q8C2411yescharacteristic
423C22×D4C2411yescharacteristic
424C22×D4C2413yes—
425C22×D4C2416yes—
426C23×C4C2412yes—
427C23×C4C2413yes—
428C23×C4C2416yes—
429C23×C4C2413yes—
430C23×C4C2416yes—
431C23×C4C2416yes—
432C23×C4C2416yes—
433C23×C4C2413yes—
434C4⋊Q8C22×C4124yes—
435C4⋊Q8C22×C4124yes—
436C4⋊Q8C22×C4148yes—
437#126C22×C4148yes—
438#126C22×C4196yes—
439#125C22×C4124yes—
440#124C22×C418yes—
441#124C22×C4148yes—
442#124C22×C4196yes—
443#123C22×C4148yes—
444C22⋊Q8C22×C4124yes—
445C22⋊Q8C22×C4148yes—
446C22⋊Q8C22×C4148yes—
447C22⋊Q8C22×C4148yes—
448#121C22×C4124yes—
449#121C22×C4148yes—
450C4×Q8—24no—
451C4×Q8—28no—
452C4×Q8—28no—
453C4×Q8—24no—
454C4×Q8—24no—
455C4×Q8—24no—
456C4×Q8—24no—
457C4×Q8—412no—
458C4×Q8—412no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8—46no—
462C4×Q8—412no—
463C4×Q8—412no—
464C4×Q8C22×C418yes—
465C4×Q8C22×C418yes—
466C4×Q8C22×C4148yes—
467C4×Q8C22×C4116yes—
468C4×Q8C22×C4148yes—
469C4×Q8C22×C4124yes—
470C4×Q8C22×C4148yes—
471C4×D4—24no—
472C4×D4—412no—
473C4×D4—46no—
474C4×D4—412no—
475C4×D4—412no—
476C4×D4—412no—
477C4×D4C22×C4124yes—
478C4×D4C22×C4124yes—
479C4×D4C22×C4148yes—
480C4×D4C22×C4124yes—
481#117—412no—
482#117—412no—
483#117—46no—
484#117—46no—
485#117—412no—
486#117—412no—
487#117C22×C4124yes—
488#117C22×C4148yes—
489#117C22×C4148yes—
490#117C22×C4148yes—
491C2×C4⋊C4—212no—
492C2×C4⋊C4—46no—
493C2×C4⋊C4—412no—
494C2×C4⋊C4C2411yescharacteristic
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2413yes—
498C2×C4⋊C4C2413yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2411yescharacteristic
501C2×C4⋊C4C2411yescharacteristic
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2413yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2413yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C24112yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2413yes—
513C2×C4⋊C4C2413yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C24112yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2413yes—
523C2×C4⋊C4C2413yes—
524C2×C4⋊C4C2413yes—
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C2416yes—
527C2×C4⋊C4C2416yes—
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2416yes—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C22⋊C4C2413yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C24112yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2413yes—
542C2×C22⋊C4C2413yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C24112yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2416yes—
552C2×C42—412no—
553C2×C42—412no—
554C2×C42C22×C4124yes—
555C2×C42C2413yes—
556C2×C42C2413yes—
557C2×C42C2413yes—
558C2×C42C2416yes—
559C2×C42C2413yes—
560C2×C42C2413yes—
561C2×C42C2416yes—
562C2×C42C2416yes—
563C2×C42C2411yescharacteristic
564C2×C42C2413yes—
565C2×C42C2412yes—
566C2×C42C2411yescharacteristic
567C2×C42C2413yes—
568C2×C42C2413yes—
569C2×C42C2416yes—
570C2×C42C24112yes—
571C2×C42C2413yes—
572C2×C42C2413yes—
573C2×C42C2416yes—
574C2×C42C2416yes—
575C2×C42C2416yes—
576C2×C42C2416yes—
577C2×C42C24112yes—
578C2×C42C2412yes—
579C2×C42C2413yes—
580C2×C42C24112yes—
581C2×C42C2413yes—
582C2×C42C2416yes—
583C2×C42C2413yes—
584C2×C42C2411yescharacteristic
585#95C2412yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2413yes—
590#95C2411yescharacteristic
591#95C2411yescharacteristic
592#95C2412yes—
593#95C2416yes—
594#95C2413yes—
595#95C2413yes—
596#95C2413yes—
597#95C2413yes—
598#95C2413yes—
599#95C24112yes—
600#95C24112yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2412yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C24112yes—
611#95C24112yes—
612#95C2416yes—
613#95C2416yes—
614#95C2416yes—
615#95C24112yes—
616C24C2512yes—
617C24C2513yes—
618#41—232no—
619C2×Q8—264no—
620C2×Q8—212no—
621C2×Q8—22no—
622C2×Q8—212no—
623C2×Q8—22no—
624C2×Q8—46no—
625C2×Q8—46no—
626C2×Q8C23×C414yes—
627C2×Q8C23×C4124yes—
628C2×Q8C23×C4124yes—
629C2×Q8C23×C414yes—
630C2×Q8H(5,𝔽2)14yes—
631C2×Q82−1+414yes—
632C2×D4—26no—
633C2×D4—22no—
634C2×D4—26no—
635C2×D4—22no—
636C2×D4—46no—
637C2×D4—46no—
638C2×D4C23×C414yes—
639C2×D4C23×C4112yes—
640C2×D4C23×C4124yes—
641C22×C4—26no—
642C22×C4—212no—
643C22×C4—26no—
644C22×C4—212no—
645C22×C4—26no—
646C22×C4—26no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—212no—
650C22×C4—42no—
651C22×C4—43no—
652C22×C4—43no—
653C22×C4—46no—
654C22×C4—46no—
655C22×C4—46no—
656C22×C4—46no—
657C22×C4—46no—
658C22×C4—46no—
659C22×C4—46no—
660C22×C4—46no—
661C22×C4C23×C4112yes—
662C22×C4C23×C4112yes—
663C22×C4C23×C4124yes—
664C22×C4C23×C4112yes—
665C22×C4C2511yescharacteristic
666C22×C4C2513yes—
667C22×C4C2513yes—
668C22×C4C2516yes—
669C22×C4C2512yes—
670C22×C4C2511yescharacteristic
671C22×C4C2516yes—
672C22×C4C2513yes—
673C22×C4C2513yes—
674C22×C4C2511yescharacteristic
675C22×C4C2512yes—
676C22×C4C2516yes—
677C22×C4C2513yes—
678C22×C4C2516yes—
679C22×C4C2513yes—
680C22×C4C2511yescharacteristic
681C22×C4C2512yes—
682C22×C4C2511yescharacteristic
683C22×C4C2511yescharacteristic
684C22×C4C2513yes—
685C22×C4C2511yescharacteristic
686C4⋊C4—26no—
687C4⋊C4—212no—
688C4⋊C4—212no—
689C4⋊C4—26no—
690C4⋊C4—212no—
691C4⋊C4—26no—
692C4⋊C4—24no—
693C4⋊C4—26no—
694C4⋊C4—26no—
695C4⋊C4—22no—
696C4⋊C4—26no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—212no—
700C4⋊C4—46no—
701C4⋊C4—412no—
702C4⋊C4—43no—
703C4⋊C4—43no—
704C4⋊C4—46no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—46no—
710C4⋊C4—46no—
711C4⋊C4—412no—
712C4⋊C4—46no—
713C4⋊C4C23×C4112yes—
714C4⋊C4C23×C4112yes—
715C4⋊C4C23×C4112yes—
716C4⋊C4C23×C4112yes—
717C4⋊C4C23×C4124yes—
718C4⋊C4C23×C4124yes—
719C4⋊C4C23×C4124yes—
720C4⋊C4C23×C4124yes—
721C4⋊C4C23×C4124yes—
722C4⋊C4C23×C4124yes—
723C4⋊C42−1+414yes—
724C22⋊C4—24no—
725C22⋊C4—26no—
726C22⋊C4—26no—
727C22⋊C4—24no—
728C22⋊C4—43no—
729C22⋊C4—46no—
730C22⋊C4—46no—
731C22⋊C4—43no—
732C22⋊C4—42no—
733C22⋊C4—46no—
734C22⋊C4—412no—
735C22⋊C4—46no—
736C22⋊C4—46no—
737C22⋊C4C23×C4124yes—
738C22⋊C4C23×C418yes—
739C22⋊C4C23×C4124yes—
740C22⋊C4C23×C4148yes—
741C22⋊C4C23×C418yes—
742C22⋊C4C23×C4124yes—
743C22⋊C4C23×C4124yes—
744C42—212no—
745C42—26no—
746C42—212no—
747C42—26no—
748C42—22no—
749C42—24no—
750C42—26no—
751C42—22no—
752C42—26no—
753C42—26no—
754C42—26no—
755C42—26no—
756C42—26no—
757C42—212no—
758C42—42no—
759C42—46no—
760C42—46no—
761C42—46no—
762C42—43no—
763C42—43no—
764C42—412no—
765C42—46no—
766C42—412no—
767C42—46no—
768C42C23×C414yes—
769C42C23×C4112yes—
770C42C23×C4112yes—
771C42C23×C4112yes—
772C42C23×C4148yes—
773C42C23×C4124yes—
774C23—22no—
775C23—23no—
776C23—22no—
777C23—22no—
778C23—23no—
779C23—23no—
780C23—23no—
781C23—23no—
782C23—22no—
783C23—23no—
784C23—22no—
785C23—22no—
786C23C24×C414yes—
787C23C24×C416yes—
788C23C2611yescharacteristic
789Q8—248no—
790Q8—28no—
791Q8—424no—
792Q8#520116yes—
793D4—224no—
794D4—28no—
795D4—424no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—26no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—23no—
805C2×C4—21no—
806C2×C4—26no—
807C2×C4—23no—
808C2×C4—23no—
809C2×C4—26no—
810C2×C4—26no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—23no—
816C2×C4—248no—
817C2×C4—224no—
818C2×C4—224no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—23no—
822C2×C4—26no—
823C2×C4—26no—
824C2×C4—23no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—23no—
829C2×C4—23no—
830C2×C4—26no—
831C2×C4—23no—
832C2×C4—23no—
833C2×C4—23no—
834C2×C4—23no—
835C2×C4—23no—
836C2×C4—23no—
837C2×C4—26no—
838C2×C4—23no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—26no—
842C2×C4—23no—
843C2×C4—26no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—412no—
847C2×C4—48no—
848C2×C4—812no—
849C2×C4—812no—
850C2×C4—812no—
851C2×C4C24×C416yes—
852C2×C4C24×C412yes—
853C2×C4C24×C412yes—
854C2×C4C24×C414yes—
855C2×C4C24×C4112yes—
856C2×C4C24×C4112yes—
857C2×C4C24×C416yes—
858C2×C4C24×C416yes—
859C2×C4C24×C412yes—
860C2×C4C2×H(5,𝔽2)16yes—
861C2×C4C2×2−1+414yes—
862C2×C4C2×2−1+416yes—
863C2×C4C2×2−1+412yes—
864C2×C4#58512yes—
865C2×C4#58512yes—
866C2×C4#58512yes—
867C22—24no—
868C22—26no—
869C22—26no—
870C22—24no—
871C22—26no—
872C22—24no—
873C22—42no—
874C22—43no—
875C22—42no—
876C22—43no—
877C22—42no—
878C22—43no—
879C22—42no—
880C22—43no—
881C22C25×C411yescharacteristic
882C22C22×H(5,𝔽2)11yescharacteristic
883C22C22×2−1+411yescharacteristic
884C22C22×2−1+411yescharacteristic
885C22C2×#58511yescharacteristic
886C22C2×#58511yescharacteristic
887C22C2×#58511yescharacteristic
888C4—22no—
889C4—24no—
890C4—22no—
891C4—22no—
892C4—212no—
893C4—26no—
894C4—24no—
895C4—22no—
896C4—26no—
897C4—212no—
898C4—41no—
899C4—46no—
900C4—43no—
901C4—46no—
902C4—43no—
903C4—42no—
904C4—43no—
905C4—43no—
906C4—41no—
907C4C2×#520112yes—
908C4C4×2−1+414yes—
909C2—44no—
910C2—46no—
911C2C22×#52011yescharacteristic
912C2C2×C4×2−1+411yescharacteristic
913C2C4×#58511yescharacteristic
914C2#6301511yescharacteristic
915C2#6302211yescharacteristic
916C2#6303411yescharacteristic
917C2#6303811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3518C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34485C2semidirect
3. #34481C2semidirect
4. #34463C2semidirect
5. #34429C2semidirect
6. #34419C2semidirect
7. #34383C2semidirect
8. #34335C2semidirect
9. #34324C2semidirect
10. #34322C2semidirect
11. #34321C2semidirect
12. #34311C2semidirect
13. #34293C2semidirect
14. #34262C2semidirect
15. #34249C2semidirect
16. #34225C2semidirect
17. #34213C2semidirect
18. C4×Q82C2semidirect
19. C4×D4×Q8C2semidirect
20. C4×#548C2semidirect
21. #34153C2semidirect
22. #34129C2semidirect
23. C4⋊C4×#41C2semidirect
24. #3518C4semidirect
161. Q82C2×C4semidirect
162. #556C2×C4semidirect
163. #556C2×C4semidirect
164. #555C2×C4semidirect
165. D4×Q8C2×C4semidirect
166. #548C2×C4semidirect
167. #542C2×C4semidirect
168. #533C2×C4semidirect
172. #529C2×C4semidirect
187. #519C2×C4semidirect
189. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
#344852
#344812
#344632
#344292
#344192
#343832
#343352
#343242
#343222
#343212
#343112
#342932
#342622
#342492
#342252
#342132
C4×Q822
C4×D4×Q82
C4×#5482
#341532
#341292
C4⋊C4×#412