Finite Group Databasebeta

← #7626924

Subgroups — #7626924

Order 512.

6900 conjugacy classes of subgroups.

The subgroup lattice has 913 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#34481C216yesmaximal, complemented
5#34463C216yesmaximal, complemented
6#34428C216yesmaximal, complemented
7#34422C216yesmaximal, complemented
8#34394C213yesmaximal, complemented
9#34384C213yesmaximal, complemented
10#34335C211yesmaximal, characteristic, complemented
11#34322C213yesmaximal, complemented
12#34321C213yesmaximal, complemented
13#34312C212yesmaximal, complemented
14#34311C211yesmaximal, characteristic, complemented
15#34294C212yesmaximal, complemented
16#34262C212yesmaximal, complemented
17#34249C212yesmaximal, complemented
18#34214C213yesmaximal, complemented
19#34183C211yesmaximal, characteristic, complemented
20C4×Q82C211yesmaximal, characteristic, complemented
21C4×D4×Q8C211yesmaximal, characteristic, complemented
22#34125C211yesmaximal, characteristic, complemented
23#34084C213yesmaximal, complemented
24#3518C4132yescomplemented
25C2×Q82C2211yescharacteristic
26C2×#556C2213yes—
27C2×#556C2216yes—
28C2×#555C2213yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#548C2212yes—
31C2×#542C2216yes—
32C2×#533C2213yes—
33C2×#529C2213yes—
34C2×#520C2212yes—
35C2×#519C2212yes—
36C2×#519C2212yes—
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2212yes—
39#2383C22112yes—
40#2383C22112yes—
41#2379C22112yes—
42#2378C22112yes—
43#2373C22112yes—
44#2369C2213yes—
45#2369C2213yes—
46#2369C2216yes—
47#2367C2216yes—
48#2367C22112yes—
49#2367C2216yes—
50#2365C2213yes—
51#2365C2216yes—
52#2365C2213yes—
53#2363C2216yes—
54#2362C2216yes—
55#2361C2216yes—
56#2361C2216yes—
57#2360C2216yes—
58#2360C2216yes—
59#2360C2216yes—
60#2360C2216yes—
61#2360C2216yes—
62#2360C2216yes—
63#2357C2213yes—
64#2357C2213yes—
65#2356C2216yes—
66#2355C2213yes—
67#2355C2216yes—
68#2355C2216yes—
69#2354C2213yes—
70#2352C2216yes—
71#2351C2212yes—
72#2351C2216yes—
73#2351C2211yescharacteristic
74#2351C2211yescharacteristic
75#2351C2216yes—
76Q8×C4⋊C4C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic
78Q8×C4⋊C4C2213yes—
79Q8×C4⋊C4C2216yes—
80Q8×C4⋊C4C2212yes—
81Q8×C4⋊C4C2212yes—
82Q8×C4⋊C4C2216yes—
83Q8×C4⋊C4C2216yes—
84D4×C4⋊C4C2213yes—
85D4×C4⋊C4C2213yes—
86D4×C4⋊C4C2213yes—
87D4×C4⋊C4C2216yes—
88D4×C4⋊C4C2216yes—
89#2347C2216yes—
90#2347C2216yes—
91#2347C2213yes—
92#2347C2213yes—
93#2346C2216yes—
94#2346C2216yes—
95#2341C2211yescharacteristic
96#2341C2211yescharacteristic
97Q8×C22⋊C4C2212yes—
98Q8×C22⋊C4C2212yes—
99#2337C22112yes—
100#2335C2216yes—
101#2335C2216yes—
102#2334C22112yes—
103#2334C2216yes—
104#2334C2216yes—
105#2334C22112yes—
106#2331C2216yes—
107#2330C2213yes—
108#2330C2213yes—
109#2330C2216yes—
110#2326C2211yescharacteristic
111#2326C2213yes—
112#2326C22112yes—
113#2326C2216yes—
114#2324C2216yes—
115#2324C2213yes—
116#2324C2213yes—
117#2323C2216yes—
118#2323C2216yes—
119#2323C2213yes—
120#2323C2213yes—
121#2323C2216yes—
122#2322C22112yes—
123#2320C22112yes—
124#2320C2216yes—
125#2317C2216yes—
126#2317C2216yes—
127#2317C2216yes—
128#2317C2216yes—
129#2314C2216yes—
130C4×C4⋊Q8C2213yes—
131C4×C4⋊Q8C2213yes—
132C4×C4⋊Q8C2213yes—
133C4×C4⋊Q8C2213yes—
134C4×C4⋊Q8C2216yes—
135C4×#124C2216yes—
136C4×C22⋊Q8C2216yes—
137C4×#121C2216yes—
138#2298C2216yes—
139#2296C2216yes—
140#2296C2216yes—
141#2295C2216yes—
142#2295C2213yes—
143#2293C2213yes—
144#2293C2216yes—
145#2293C2213yes—
146#2293C2213yes—
147#2290C2216yes—
148#2285C2213yes—
149C2×#384C2213yes—
150#2283C2213yes—
151#2276C2212yes—
152#2274C2216yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2212yes—
155C42×Q8C2213yes—
156C42×Q8C2211yescharacteristic
157C42×D4C2213yes—
158C4×#117C2213yes—
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×#126C23112yes—
174C2×#126C2316yes—
175C2×#125C2313yes—
176C2×#124C2311yescharacteristic
177C2×#124C23112yes—
178C2×#124C2316yes—
179C2×#123C2316yes—
180C2×C22⋊Q8C2313yes—
181C2×C22⋊Q8C2316yes—
182C2×C22⋊Q8C2316yes—
183C2×C22⋊Q8C2316yes—
184C2×#121C2313yes—
185C2×#121C2316yes—
186#520—48no—
187#519—48no—
188#519C2×C4132yescomplemented
189C4×#41C2×C4116yescomplemented
190C2×C4×Q8—48no—
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2311yescharacteristic
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2313yes—
201C2×C4×Q8C2316yes—
202C2×C4×Q8C2316yes—
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×D4C23112yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2313yes—
221C2×#117C2313yes—
222C2×#117C2313yes—
223C2×#117C2316yes—
224C2×#117C2316yes—
225C2×#117C2316yes—
226C2×#117C2316yes—
227C2×#117C2313yes—
228C2×#117C2316yes—
229C2×#117C2316yes—
230C22×C4⋊C4C2316yes—
231C22×C4⋊C4C2316yes—
232C22×C4⋊C4C2316yes—
233C22×C4⋊C4C2316yes—
234C22×C42C2316yes—
235C22×C42C2313yes—
236#391C2316yes—
237#391C23112yes—
238#391C2316yes—
239#391C2316yes—
240#391C2316yes—
241#391C2316yes—
242#391C23112yes—
243#391C2311yescharacteristic
244#391C2316yes—
245#391C2313yes—
246#390C2316yes—
247#390C2311yescharacteristic
248#390C2313yes—
249#390C2313yes—
250#390C2316yes—
251#390C2313yes—
252#390C2313yes—
253#390C2313yes—
254#389C2313yes—
255#389C2313yes—
256#389C2316yes—
257#389C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C23112yes—
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2313yes—
267#389C2316yes—
268#389C23112yes—
269#389C2316yes—
270#389C23112yes—
271#389C2316yes—
272#389C2313yes—
273#389C23112yes—
274#389C2313yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2313yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C2313yes—
283#389C2313yes—
284#388C2316yes—
285#388C23112yes—
286#388C23112yes—
287#388C2316yes—
288#388C23112yes—
289#388C2316yes—
290#388C23112yes—
291#388C23112yes—
292#388C2316yes—
293#388C23112yes—
294#388C2316yes—
295#388C2316yes—
296#388C2316yes—
297#388C2316yes—
298#388C2316yes—
299#388C2312yes—
300#388C2316yes—
301#388C2312yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#387C23112yes—
307#387C23112yes—
308#387C2316yes—
309#387C2316yes—
310#387C23112yes—
311#387C23112yes—
312#387C23112yes—
313#387C23112yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C2316yes—
320#386C23112yes—
321#386C2316yes—
322#386C2316yes—
323#385C2316yes—
324#385C2316yes—
325#385C23112yes—
326#385C23112yes—
327#385C23112yes—
328#385C23112yes—
329#385C23112yes—
330#385C23112yes—
331#385C23112yes—
332#385C2316yes—
333#385C2312yes—
334#385C2316yes—
335#385C2312yes—
336#384C2313yes—
337#384C2313yes—
338#384C2316yes—
339#384C2316yes—
340#384C23112yes—
341#384C2316yes—
342#384C2313yes—
343#384C2311yescharacteristic
344#383C23112yes—
345#383C2316yes—
346#382C2313yes—
347#382C2316yes—
348#382C2313yes—
349#382C23112yes—
350#382C23112yes—
351#382C2316yes—
352#381C2316yes—
353#380C2316yes—
354#380C2316yes—
355#380C2313yes—
356#380C2313yes—
357#380C2313yes—
358#380C2313yes—
359#380C2316yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2313yes—
362C4×C4⋊C4C2316yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2313yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C2316yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C23112yes—
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2316yes—
382C4×C4⋊C4C23112yes—
383C4×C4⋊C4C23112yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2316yes—
386C4×C4⋊C4C2313yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2313yes—
393C4×C4⋊C4C2313yes—
394C4×C22⋊C4C23112yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C23112yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C23112yes—
401C4×C22⋊C4C2316yes—
402C4×C22⋊C4C2316yes—
403C4×C22⋊C4C2313yes—
404C4×C22⋊C4C2313yes—
405C4×C22⋊C4C2316yes—
406#376C2316yes—
407#376C23112yes—
408#376C2311yescharacteristic
409#376C2313yes—
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×C4C2413yes—
427C23×C4C2413yes—
428C23×C4C2416yes—
429C23×C4C2412yes—
430C23×C4C24112yes—
431C23×C4C2416yes—
432C23×C4C2413yes—
433C4⋊Q8C22×C4124yes—
434C4⋊Q8C22×C4124yes—
435C4⋊Q8C22×C4148yes—
436#126C22×C4148yes—
437#126C22×C4196yes—
438#125C22×C4124yes—
439#124C22×C418yes—
440#124C22×C4148yes—
441#124C22×C4196yes—
442#123C22×C4148yes—
443C22⋊Q8C22×C4124yes—
444C22⋊Q8C22×C4148yes—
445C22⋊Q8C22×C4148yes—
446C22⋊Q8C22×C4148yes—
447#121C22×C4124yes—
448#121C22×C4148yes—
449C4×Q8—24no—
450C4×Q8—28no—
451C4×Q8—24no—
452C4×Q8—28no—
453C4×Q8—24no—
454C4×Q8—24no—
455C4×Q8—24no—
456C4×Q8—412no—
457C4×Q8—412no—
458C4×Q8—46no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8—86no—
462C4×Q8—86no—
463C4×Q8C22×C418yes—
464C4×Q8C22×C418yes—
465C4×Q8C22×C4148yes—
466C4×Q8C22×C4116yes—
467C4×Q8C22×C4148yes—
468C4×Q8C22×C4124yes—
469C4×Q8C22×C4148yes—
470C4×D4—24no—
471C4×D4—46no—
472C4×D4—412no—
473C4×D4—412no—
474C4×D4—812no—
475C4×D4C22×C4124yes—
476C4×D4C22×C4124yes—
477C4×D4C22×C4148yes—
478C4×D4C22×C4124yes—
479#117—212no—
480#117—46no—
481#117—412no—
482#117—412no—
483#117—412no—
484#117C22×C4124yes—
485#117C22×C4148yes—
486#117C22×C4148yes—
487#117C22×C4148yes—
488C2×C4⋊C4—412no—
489C2×C4⋊C4—412no—
490C2×C4⋊C4—412no—
491C2×C4⋊C4—86no—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2413yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2413yes—
498C2×C4⋊C4C2413yes—
499C2×C4⋊C4C2413yes—
500C2×C4⋊C4C2411yescharacteristic
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2413yes—
503C2×C4⋊C4C2411yescharacteristic
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C24112yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C24112yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2413yes—
515C2×C4⋊C4C2413yes—
516C2×C4⋊C4C24112yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2416yes—
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×C22⋊C4C2413yes—
532C2×C22⋊C4C2413yes—
533C2×C22⋊C4C2412yes—
534C2×C22⋊C4C2416yes—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2413yes—
539C2×C22⋊C4C2413yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2412yes—
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×C42C22×C4124yes—
554C2×C42C2411yescharacteristic
555C2×C42C2416yes—
556C2×C42C2413yes—
557C2×C42C2416yes—
558C2×C42C2413yes—
559C2×C42C2413yes—
560C2×C42C2413yes—
561C2×C42C2413yes—
562C2×C42C2412yes—
563C2×C42C2413yes—
564C2×C42C24112yes—
565C2×C42C24112yes—
566C2×C42C2413yes—
567C2×C42C2416yes—
568C2×C42C2413yes—
569C2×C42C2416yes—
570C2×C42C2416yes—
571C2×C42C2416yes—
572C2×C42C2416yes—
573C2×C42C2413yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C24112yes—
577C2×C42C2413yes—
578C2×C42C2416yes—
579C2×C42C2413yes—
580C2×C42C2411yescharacteristic
581C2×C42C2411yescharacteristic
582#95C2412yes—
583#95C2416yes—
584#95C2416yes—
585#95C2416yes—
586#95C2411yescharacteristic
587#95C2411yescharacteristic
588#95C2411yescharacteristic
589#95C2411yescharacteristic
590#95C2413yes—
591#95C2413yes—
592#95C24112yes—
593#95C2413yes—
594#95C2413yes—
595#95C2416yes—
596#95C2416yes—
597#95C2416yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C2416yes—
602#95C2416yes—
603#95C24112yes—
604#95C2416yes—
605#95C2416yes—
606#95C24112yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C2416yes—
611#95C2416yes—
612#95C24112yes—
613#95C2412yes—
614C24C2512yes—
615C24C2513yes—
616#41—232no—
617C2×Q8—264no—
618C2×Q8—212no—
619C2×Q8—22no—
620C2×Q8—212no—
621C2×Q8—22no—
622C2×Q8—46no—
623C2×Q8—46no—
624C2×Q8C23×C414yes—
625C2×Q8C23×C4124yes—
626C2×Q8C23×C4124yes—
627C2×Q8C23×C414yes—
628C2×Q8H(5,𝔽2)14yes—
629C2×Q82−1+414yes—
630C2×D4—26no—
631C2×D4—22no—
632C2×D4—26no—
633C2×D4—22no—
634C2×D4—46no—
635C2×D4—46no—
636C2×D4C23×C414yes—
637C2×D4C23×C4112yes—
638C2×D4C23×C4124yes—
639C22×C4—212no—
640C22×C4—26no—
641C22×C4—26no—
642C22×C4—212no—
643C22×C4—26no—
644C22×C4—26no—
645C22×C4—24no—
646C22×C4—42no—
647C22×C4—43no—
648C22×C4—42no—
649C22×C4—43no—
650C22×C4—46no—
651C22×C4—46no—
652C22×C4—46no—
653C22×C4—412no—
654C22×C4—412no—
655C22×C4—412no—
656C22×C4C23×C4112yes—
657C22×C4C23×C4112yes—
658C22×C4C23×C4124yes—
659C22×C4C23×C4112yes—
660C22×C4C2511yescharacteristic
661C22×C4C2513yes—
662C22×C4C2513yes—
663C22×C4C2512yes—
664C22×C4C2512yes—
665C22×C4C2513yes—
666C22×C4C2516yes—
667C22×C4C2516yes—
668C22×C4C2513yes—
669C22×C4C2511yescharacteristic
670C22×C4C2512yes—
671C22×C4C2516yes—
672C22×C4C2513yes—
673C22×C4C2516yes—
674C22×C4C2513yes—
675C22×C4C2511yescharacteristic
676C22×C4C2511yescharacteristic
677C22×C4C2511yescharacteristic
678C22×C4C2511yescharacteristic
679C22×C4C2513yes—
680C22×C4C2511yescharacteristic
681C4⋊C4—212no—
682C4⋊C4—26no—
683C4⋊C4—212no—
684C4⋊C4—26no—
685C4⋊C4—26no—
686C4⋊C4—26no—
687C4⋊C4—22no—
688C4⋊C4—24no—
689C4⋊C4—26no—
690C4⋊C4—26no—
691C4⋊C4—22no—
692C4⋊C4—26no—
693C4⋊C4—26no—
694C4⋊C4—46no—
695C4⋊C4—412no—
696C4⋊C4—412no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—46no—
700C4⋊C4—46no—
701C4⋊C4—42no—
702C4⋊C4—43no—
703C4⋊C4—43no—
704C4⋊C4—42no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—412no—
708C4⋊C4—46no—
709C4⋊C4—46no—
710C4⋊C4C23×C4112yes—
711C4⋊C4C23×C4112yes—
712C4⋊C4C23×C4112yes—
713C4⋊C4C23×C4112yes—
714C4⋊C4C23×C4124yes—
715C4⋊C4C23×C4124yes—
716C4⋊C4C23×C4124yes—
717C4⋊C4C23×C4124yes—
718C4⋊C4C23×C4124yes—
719C4⋊C4C23×C4124yes—
720C22⋊C4—26no—
721C22⋊C4—26no—
722C22⋊C4—24no—
723C22⋊C4—42no—
724C22⋊C4—46no—
725C22⋊C4—43no—
726C22⋊C4—43no—
727C22⋊C4—42no—
728C22⋊C4—46no—
729C22⋊C4—46no—
730C22⋊C4—46no—
731C22⋊C4—46no—
732C22⋊C4—46no—
733C22⋊C4—46no—
734C22⋊C4C23×C4124yes—
735C22⋊C4C23×C418yes—
736C22⋊C4C23×C4124yes—
737C22⋊C4C23×C4148yes—
738C22⋊C4C23×C418yes—
739C22⋊C4C23×C4124yes—
740C22⋊C4C23×C4124yes—
741C42—26no—
742C42—212no—
743C42—212no—
744C42—26no—
745C42—26no—
746C42—26no—
747C42—24no—
748C42—26no—
749C42—22no—
750C42—26no—
751C42—46no—
752C42—46no—
753C42—43no—
754C42—43no—
755C42—46no—
756C42—412no—
757C42—412no—
758C42—46no—
759C42—46no—
760C42—43no—
761C42—43no—
762C42C23×C414yes—
763C42C23×C4112yes—
764C42C23×C4112yes—
765C42C23×C4112yes—
766C42C23×C4148yes—
767C42C23×C4124yes—
768C422−1+414yes—
769C23—22no—
770C23—23no—
771C23—23no—
772C23—22no—
773C23—22no—
774C23—23no—
775C23—22no—
776C23—23no—
777C23—22no—
778C23—23no—
779C23—23no—
780C23—22no—
781C23C24×C414yes—
782C23C24×C416yes—
783C23C2611yescharacteristic
784Q8—248no—
785Q8—28no—
786Q8—424no—
787Q8#520116yes—
788D4—224no—
789D4—28no—
790D4—424no—
791C2×C4—21no—
792C2×C4—26no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—23no—
797C2×C4—21no—
798C2×C4—26no—
799C2×C4—22no—
800C2×C4—23no—
801C2×C4—21no—
802C2×C4—26no—
803C2×C4—23no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—23no—
807C2×C4—26no—
808C2×C4—21no—
809C2×C4—248no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—23no—
816C2×C4—26no—
817C2×C4—23no—
818C2×C4—26no—
819C2×C4—21no—
820C2×C4—23no—
821C2×C4—23no—
822C2×C4—22no—
823C2×C4—23no—
824C2×C4—23no—
825C2×C4—22no—
826C2×C4—23no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—23no—
830C2×C4—26no—
831C2×C4—26no—
832C2×C4—23no—
833C2×C4—21no—
834C2×C4—26no—
835C2×C4—23no—
836C2×C4—26no—
837C2×C4—21no—
838C2×C4—23no—
839C2×C4—22no—
840C2×C4—23no—
841C2×C4—22no—
842C2×C4—412no—
843C2×C4—48no—
844C2×C4—812no—
845C2×C4—1612no—
846C2×C4C24×C416yes—
847C2×C4C24×C412yes—
848C2×C4C24×C412yes—
849C2×C4C24×C414yes—
850C2×C4C24×C4112yes—
851C2×C4C24×C4112yes—
852C2×C4C24×C416yes—
853C2×C4C24×C416yes—
854C2×C4C24×C412yes—
855C2×C4C2×H(5,𝔽2)16yes—
856C2×C4C2×2−1+412yes—
857C2×C4C2×2−1+412yes—
858C2×C4C2×2−1+416yes—
859C2×C4C2×2−1+412yes—
860C2×C4#58512yes—
861C22—24no—
862C22—26no—
863C22—26no—
864C22—24no—
865C22—26no—
866C22—24no—
867C22—42no—
868C22—43no—
869C22—42no—
870C22—43no—
871C22—43no—
872C22—42no—
873C22—42no—
874C22—43no—
875C22C25×C411yescharacteristic
876C22C22×H(5,𝔽2)11yescharacteristic
877C22C22×2−1+411yescharacteristic
878C22C22×2−1+411yescharacteristic
879C22C2×#58511yescharacteristic
880C22H(7,𝔽2)11yescharacteristic
881C222−1+611yescharacteristic
882C4—22no—
883C4—212no—
884C4—26no—
885C4—24no—
886C4—22no—
887C4—26no—
888C4—212no—
889C4—22no—
890C4—22no—
891C4—42no—
892C4—43no—
893C4—42no—
894C4—41no—
895C4—43no—
896C4—46no—
897C4—46no—
898C4—43no—
899C4—41no—
900C4—43no—
901C4C2×#520112yes—
902C4C4×2−1+414yes—
903C2—44no—
904C2—46no—
905C2C22×#52011yescharacteristic
906C2C2×C4×2−1+411yescharacteristic
907C2#6265411yescharacteristic
908C2#6291311yescharacteristic
909C2#6292311yescharacteristic
910C2#6294311yescharacteristic
911C2#6295311yescharacteristic
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. #34481C2semidirect
5. #34463C2semidirect
6. #34428C2semidirect
7. #34422C2semidirect
8. #34394C2semidirect
9. #34384C2semidirect
10. #34335C2semidirect
11. #34322C2semidirect
12. #34321C2semidirect
13. #34312C2semidirect
14. #34311C2semidirect
15. #34294C2semidirect
16. #34262C2semidirect
17. #34249C2semidirect
18. #34214C2semidirect
19. #34183C2semidirect
20. C4×Q82C2semidirect
21. C4×D4×Q8C2semidirect
22. #34125C2semidirect
23. #34084C2semidirect
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
188. #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
#344282
#344222
#343942
#343842
#343352
#343222
#343212
#343122
#343112
#342942
#342622
#342492
#342142
#341832
C4×Q822
C4×D4×Q82
#341252
#340842