Finite Group Databasebeta

← #7625910

Subgroups — #7625910

Order 512.

7438 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic
2#34336C212yesmaximal, complemented
3#34329C216yesmaximal, complemented
4#34307C216yesmaximal, complemented
5#34305C216yesmaximal, complemented
6#34295C212yesmaximal, complemented
7#34294C212yesmaximal, complemented
8#34237C213yesmaximal, complemented
9#34236C213yesmaximal, complemented
10#34230C213yesmaximal, complemented
11#34227C213yesmaximal, complemented
12#34222C213yesmaximal, complemented
13#34220C213yesmaximal, complemented
14#34197C211yesmaximal, characteristic, complemented
15#34193C211yesmaximal, characteristic, complemented
16#34192C211yesmaximal, characteristic, complemented
17C4×#553C216yesmaximal, complemented
18C4×#548C212yesmaximal, complemented
19#34127C213yesmaximal, complemented
20#34123C213yesmaximal, complemented
21C4×#520C211yesmaximal, characteristic, complemented
22#33999C211yesmaximal, characteristic, complemented
23C2×#2276C211yesmaximal, characteristic, complemented
24#3480C4132yescomplemented
25C2×#559C2213yes—
26C2×#557C2211yescharacteristic
27C2×#556C2213yes—
28C2×#553C2213yes—
29C2×#553C2213yes—
30C2×#550C2211yescharacteristic
31C2×#548C2211yescharacteristic
32C2×#548C2211yescharacteristic
33C2×#532C2213yes—
34C2×#529C2213yes—
35C2×#529C2213yes—
36C2×#520C2212yes—
37C2×C4×#41C2212yes—
38C2×C4×#41C2213yes—
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2212yes—
42C22×C4×Q8C2211yescharacteristic
43#2374C22112yes—
44#2373C22112yes—
45#2373C22112yes—
46#2372C22112yes—
47#2370C2216yes—
48#2370C2216yes—
49#2369C2216yes—
50#2367C2216yes—
51#2367C2216yes—
52#2366C2216yes—
53#2364C22112yes—
54#2363C2216yes—
55#2362C2216yes—
56#2361C2216yes—
57#2361C2216yes—
58#2361C2216yes—
59#2360C2216yes—
60#2359C22112yes—
61#2357C2216yes—
62#2357C2216yes—
63#2356C2216yes—
64#2356C2216yes—
65#2355C2216yes—
66#2354C2216yes—
67#2353C2216yes—
68#2353C2216yes—
69#2353C2216yes—
70#2353C2216yes—
71#2352C2216yes—
72#2352C2216yes—
73#2351C2212yes—
74#2351C2212yes—
75Q8×C4⋊C4C2212yes—
76#2349C2216yes—
77#2349C2216yes—
78D4×C4⋊C4C2216yes—
79#2347C2216yes—
80#2347C2216yes—
81#2346C2216yes—
82#2346C2213yes—
83#2346C2213yes—
84#2345C2216yes—
85#2343C2211yescharacteristic
86#2343C2213yes—
87#2343C2213yes—
88#2343C2213yes—
89#2343C2216yes—
90#2341C2212yes—
91#2341C2212yes—
92Q8×C22⋊C4C2212yes—
93#2339C2213yes—
94#2339C2213yes—
95#2339C2216yes—
96#2337C22112yes—
97#2335C22112yes—
98#2334C22112yes—
99#2331C2216yes—
100#2330C2216yes—
101#2328C2216yes—
102#2326C2216yes—
103#2324C2216yes—
104#2323C2216yes—
105#2320C2213yes—
106#2320C2213yes—
107#2319C2213yes—
108#2319C2213yes—
109#2319C2213yes—
110#2319C2213yes—
111C4×#125C2216yes—
112C4×#126C22112yes—
113C4×#124C2216yes—
114C4×C22⋊Q8C2216yes—
115C4×#123C22112yes—
116C4×#121C2216yes—
117C4×#121C22112yes—
118C4×#121C2216yes—
119C4×#121C2216yes—
120#2295C2216yes—
121#2295C2216yes—
122#2290C2216yes—
123#2290C2216yes—
124#2290C2216yes—
125#2290C2216yes—
126#2285C2213yes—
127#2283C2213yes—
128#2283C2213yes—
129#2283C2213yes—
130#2283C2213yes—
131#2283C2213yes—
132#2276C2216yes—
133#2276C2212yes—
134#2276C2212yes—
135#2276C2211yescharacteristic
136#2276C2211yescharacteristic
137#2276C2211yescharacteristic
138#2276C2213yes—
139#2276C2213yes—
140#2276C2211yescharacteristic
141#2275C2216yes—
142#2275C2213yes—
143#2275C2213yes—
144#2275C2213yes—
145#2275C2213yes—
146#2274C2216yes—
147C42×Q8C2212yes—
148C42×D4C2216yes—
149C42×D4C2216yes—
150C42×D4C2216yes—
151C4×#117C2216yes—
152C4×#117C2213yes—
153C4×#117C2213yes—
154C2×C4×C4⋊C4C2216yes—
155C2×C4×C4⋊C4C2213yes—
156C2×C4×C4⋊C4C2213yes—
157C2×#376C2213yes—
158C2×#376C2213yes—
159C22×#41C2311yescharacteristic
160C22×#41C2311yescharacteristic
161C22×#41C2313yes—
162C23×Q8C2311yescharacteristic
163#559C2×C4148yescomplemented
164#557C2×C4116yescomplemented
165#556C2×C4148yescomplemented
166#553C2×C4148yescomplemented
167#553C2×C4148yescomplemented
168#550C2×C4116yescomplemented
169#548C2×C4116yescomplemented
170#548C2×C4116yescomplemented
171#532C2×C4148yescomplemented
172C2×C4⋊Q8C2313yes—
173C2×#127C2313yes—
174#529C2×C4148yescomplemented
175#529C2×C4148yescomplemented
176C2×#126C2316yes—
177C2×#126C2316yes—
178C2×#125C2313yes—
179C2×#125C2313yes—
180C2×#124C2313yes—
181C2×#124C2316yes—
182C2×#124C2313yes—
183C2×#123C2316yes—
184C2×#123C2316yes—
185C2×C22⋊Q8C2313yes—
186C2×C22⋊Q8C2313yes—
187C2×#121C2313yes—
188C2×#121C2313yes—
189C2×#121C2313yes—
190C2×#121C2313yes—
191C2×#121C2316yes—
192#520—216no—
193C4×#41—216no—
194C4×#41C2×C4148yescomplemented
195C4×#41C2×C4116yescomplemented
196C4×#41C2×C4116yescomplemented
197C2×C4×Q8—216no—
198C2×C4×Q8C2×C4116yescomplemented
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2313yes—
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2313yes—
210C2×C4×Q8C2313yes—
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2312yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C23112yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C23112yes—
221C2×C4×D4C2313yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2313yes—
224C2×C4×D4C2313yes—
225C2×C4×D4C2316yes—
226C2×C4×D4C2313yes—
227C2×C4×D4C2313yes—
228C2×C4×D4C2313yes—
229C2×C4×D4C2313yes—
230C2×C4×D4C2313yes—
231C2×C4×D4C2313yes—
232C2×#117C2316yes—
233C2×#117C2316yes—
234C2×#117C2316yes—
235C2×#117C2311yescharacteristic
236C2×#117C2313yes—
237C2×#117C2313yes—
238C2×#117C2313yes—
239C2×#117C2313yes—
240C22×C4⋊C4C2316yes—
241C22×C4⋊C4C2316yes—
242C22×C4⋊C4C2313yes—
243C22×C42C2316yes—
244C22×C42C2316yes—
245C22×C42C2316yes—
246C22×C42C2316yes—
247C22×C42C2313yes—
248C22×C42C2313yes—
249C22×C42C2313yes—
250#391C2316yes—
251#391C2316yes—
252#391C2316yes—
253#391C23112yes—
254#391C2316yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2316yes—
259#390C23112yes—
260#389C2316yes—
261#389C2316yes—
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C23112yes—
267#389C2316yes—
268#389C23112yes—
269#389C2316yes—
270#388C2316yes—
271#388C23112yes—
272#388C23112yes—
273#388C23112yes—
274#388C23112yes—
275#388C23112yes—
276#388C23112yes—
277#388C23112yes—
278#388C2316yes—
279#388C23112yes—
280#388C2316yes—
281#388C23112yes—
282#388C2316yes—
283#388C23112yes—
284#387C23112yes—
285#387C23112yes—
286#387C23112yes—
287#387C2316yes—
288#387C23112yes—
289#387C23112yes—
290#387C2316yes—
291#387C23112yes—
292#387C2316yes—
293#387C2316yes—
294#387C2312yes—
295#387C2316yes—
296#387C2316yes—
297#387C2312yes—
298#386C23112yes—
299#386C2316yes—
300#386C23112yes—
301#386C23112yes—
302#386C2316yes—
303#386C23112yes—
304#386C2316yes—
305#386C2316yes—
306#385C2316yes—
307#385C23112yes—
308#385C23112yes—
309#385C2316yes—
310#385C23112yes—
311#385C2316yes—
312#385C2312yes—
313#384C2316yes—
314#383C2316yes—
315#383C2316yes—
316#383C2316yes—
317#383C2311yescharacteristic
318#383C2313yes—
319#382C2316yes—
320#382C2313yes—
321#382C2313yes—
322#382C2316yes—
323#382C2316yes—
324#382C2313yes—
325#382C2311yescharacteristic
326#381C2313yes—
327#381C2316yes—
328#381C2313yes—
329#381C2311yescharacteristic
330#381C2313yes—
331#381C2316yes—
332#380C2313yes—
333#380C2313yes—
334#380C2316yes—
335#380C2316yes—
336#380C2316yes—
337#380C2316yes—
338#380C2316yes—
339#380C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C23112yes—
342C4×C4⋊C4C23112yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C23112yes—
346C4×C4⋊C4C2313yes—
347C4×C4⋊C4C2313yes—
348C4×C4⋊C4C2313yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2311yescharacteristic
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⋊C4C2316yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C23112yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2316yes—
373C4×C22⋊C4C23112yes—
374C4×C22⋊C4C23112yes—
375C4×C22⋊C4C23112yes—
376C4×C22⋊C4C23112yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2313yes—
379C4×C22⋊C4C2313yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C2316yes—
382C4×C22⋊C4C2316yes—
383C4×C22⋊C4C2316yes—
384C4×C22⋊C4C2316yes—
385C4×C22⋊C4C2312yes—
386C4×C22⋊C4C2316yes—
387C4×C22⋊C4C2316yes—
388C4×C22⋊C4C2316yes—
389C4×C22⋊C4C2316yes—
390C4×C22⋊C4C23112yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C23112yes—
393C4×C22⋊C4C23112yes—
394#376C2313yes—
395#376C2313yes—
396#376C2313yes—
397#376C2316yes—
398#376C2316yes—
399#376C2313yes—
400#376C2311yescharacteristic
401#376C2313yes—
402#376C2313yes—
403#376C2316yes—
404#376C2316yes—
405#376C2316yes—
406#376C2316yes—
407#376C2313yes—
408C2×#95C2311yescharacteristic
409C2×#95C2313yes—
410C2×#95C2313yes—
411C2×#95C2316yes—
412C2×#95C2313yes—
413C2×#95C2316yes—
414C2×#95C2316yes—
415C43C2316yes—
416C43C2316yes—
417C2×#41—28no—
418C2×#41—28no—
419C2×#41—412no—
420C2×#41C22×C418yes—
421C2×#41C22×C418yes—
422C2×#41C22×C4124yes—
423C22×Q8—28no—
424C22×Q8C22×C418yes—
425C22×Q8C2413yes—
426C22×Q8C2413yes—
427C22×Q8C2411yescharacteristic
428C22×D4C2413yes—
429C22×D4C2413yes—
430C22×D4C2413yes—
431C22×D4C2413yes—
432C22×D4C2416yes—
433C22×D4C2413yes—
434C23×C4C2416yes—
435C23×C4C2412yes—
436C23×C4C2413yes—
437C23×C4C2413yes—
438C23×C4C2413yes—
439C23×C4C2411yescharacteristic
440C23×C4C24112yes—
441C23×C4C2416yes—
442C23×C4C2416yes—
443C23×C4C2413yes—
444C23×C4C2413yes—
445C23×C4C2413yes—
446C23×C4C2413yes—
447C23×C4C2413yes—
448C4⋊Q8C22×C4124yes—
449#127C22×C4124yes—
450#126C22×C4148yes—
451#126C22×C4148yes—
452#125C22×C4124yes—
453#125C22×C4124yes—
454#124C22×C4124yes—
455#124C22×C4124yes—
456#124C22×C4148yes—
457#123C22×C4148yes—
458#123C22×C4148yes—
459C22⋊Q8C22×C4124yes—
460C22⋊Q8C22×C4124yes—
461#121C22×C4124yes—
462#121C22×C4124yes—
463#121C22×C4124yes—
464#121C22×C4124yes—
465#121C22×C4148yes—
466C4×Q8—28no—
467C4×Q8—28no—
468C4×Q8—28no—
469C4×Q8—224no—
470C4×Q8—224no—
471C4×Q8C22×C418yes—
472C4×Q8C22×C4124yes—
473C4×Q8C22×C418yes—
474C4×Q8C22×C4124yes—
475C4×Q8C22×C418yes—
476C4×Q8C22×C418yes—
477C4×Q8C22×C4124yes—
478C4×Q8C22×C4124yes—
479C4×Q8#41116yescomplemented
480C4×D4—224no—
481C4×D4—224no—
482C4×D4—224no—
483C4×D4—224no—
484C4×D4—424no—
485C4×D4—412no—
486C4×D4—412no—
487C4×D4—812no—
488C4×D4C22×C4124yes—
489C4×D4C22×C4124yes—
490C4×D4C22×C4124yes—
491C4×D4C22×C4124yes—
492C4×D4C22×C4124yes—
493C4×D4C22×C4124yes—
494C4×D4C22×C4124yes—
495C4×D4C22×C4124yes—
496C4×D4C22×C4124yes—
497C4×D4C22×C4124yes—
498C4×D4C22×C4148yes—
499#117—224no—
500#117—224no—
501#117—86no—
502#117C22×C418yes—
503#117C22×C4124yes—
504#117C22×C4124yes—
505#117C22×C4124yes—
506#117C22×C4124yes—
507C2×C4⋊C4—224no—
508C2×C4⋊C4—224no—
509C2×C4⋊C4C22×C4124yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C24112yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C24112yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2413yes—
524C2×C4⋊C4C2413yes—
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2413yes—
529C2×C4⋊C4C2413yes—
530C2×C4⋊C4C2413yes—
531C2×C4⋊C4C2413yes—
532C2×C4⋊C4C2413yes—
533C2×C4⋊C4C2413yes—
534C2×C4⋊C4C2416yes—
535C2×C4⋊C4C2416yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C24112yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C24112yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C24112yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2411yescharacteristic
548C2×C22⋊C4C2411yescharacteristic
549C2×C22⋊C4C2413yes—
550C2×C22⋊C4C2413yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2416yes—
553C2×C22⋊C4C2413yes—
554C2×C22⋊C4C2413yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C42—224no—
558C2×C42—224no—
559C2×C42—86no—
560C2×C42—86no—
561C2×C42C22×C4124yes—
562C2×C42C22×C4124yes—
563C2×C42C22×C4124yes—
564C2×C42C2416yes—
565C2×C42C2416yes—
566C2×C42C2416yes—
567C2×C42C2416yes—
568C2×C42C2416yes—
569C2×C42C2416yes—
570C2×C42C2412yes—
571C2×C42C2416yes—
572C2×C42C2416yes—
573C2×C42C2416yes—
574C2×C42C24112yes—
575C2×C42C2416yes—
576C2×C42C24112yes—
577C2×C42C2412yes—
578C2×C42C2416yes—
579C2×C42C2416yes—
580C2×C42C2416yes—
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2413yes—
584C2×C42C2413yes—
585C2×C42C2413yes—
586C2×C42C2413yes—
587C2×C42C2413yes—
588C2×C42C2413yes—
589C2×C42C2413yes—
590C2×C42C2413yes—
591C2×C42C2416yes—
592#95C2411yescharacteristic
593#95C2413yes—
594#95C2411yescharacteristic
595#95C2412yes—
596#95C2416yes—
597#95C2413yes—
598#95C2411yescharacteristic
599#95C2412yes—
600#95C2413yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2413yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C24112yes—
611#95C2411yescharacteristic
612#95C2416yes—
613#95C2416yes—
614#95C2416yes—
615#95C24112yes—
616#95C24112yes—
617#95C2416yes—
618#95C2412yes—
619#95C2416yes—
620#95C2412yes—
621#95C2412yes—
622#95C2416yes—
623#95C2416yes—
624#95C24112yes—
625#95C2416yes—
626#95C2412yes—
627#95C2416yes—
628C24C2513yes—
629C24C2513yes—
630C24C2511yescharacteristic
631#41—232no—
632#41—232no—
633#41—448no—
634C2×Q8—232no—
635C2×Q8—212no—
636C2×Q8—46no—
637C2×Q8C23×C4112yes—
638C2×Q8C23×C4112yes—
639C2×Q8C23×C414yes—
640C2×Q8C2×#4118yes—
641C2×D4—212no—
642C2×D4—212no—
643C2×D4—212no—
644C2×D4—212no—
645C2×D4—46no—
646C2×D4—46no—
647C2×D4—46no—
648C2×D4C23×C4112yes—
649C2×D4C23×C4112yes—
650C2×D4C23×C4112yes—
651C2×D4C23×C4112yes—
652C2×D4C23×C4112yes—
653C2×D4C23×C4124yes—
654C22×C4—24no—
655C22×C4—212no—
656C22×C4—212no—
657C22×C4—212no—
658C22×C4—212no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—212no—
662C22×C4—212no—
663C22×C4—212no—
664C22×C4—224no—
665C22×C4—43no—
666C22×C4—43no—
667C22×C4—46no—
668C22×C4—43no—
669C22×C4—43no—
670C22×C4—43no—
671C22×C4—43no—
672C22×C4—42no—
673C22×C4—46no—
674C22×C4—46no—
675C22×C4—412no—
676C22×C4—46no—
677C22×C4—412no—
678C22×C4—46no—
679C22×C4—46no—
680C22×C4—46no—
681C22×C4C23×C414yes—
682C22×C4C23×C4112yes—
683C22×C4C23×C4112yes—
684C22×C4C23×C4112yes—
685C22×C4C23×C4112yes—
686C22×C4C23×C4112yes—
687C22×C4C23×C4112yes—
688C22×C4C23×C4112yes—
689C22×C4C23×C4112yes—
690C22×C4C2512yes—
691C22×C4C2516yes—
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2516yes—
695C22×C4C2516yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2511yescharacteristic
699C22×C4C2513yes—
700C22×C4C2511yescharacteristic
701C22×C4C2513yes—
702C22×C4C2513yes—
703C22×C4C2513yes—
704C22×C4C2513yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2512yes—
708C22×C4C2516yes—
709C22×C4C2513yes—
710C4⋊C4—212no—
711C4⋊C4—212no—
712C4⋊C4—224no—
713C4⋊C4—212no—
714C4⋊C4—24no—
715C4⋊C4—212no—
716C4⋊C4—42no—
717C4⋊C4—46no—
718C4⋊C4—46no—
719C4⋊C4—46no—
720C4⋊C4—412no—
721C4⋊C4—46no—
722C4⋊C4—46no—
723C4⋊C4C23×C4112yes—
724C4⋊C4C23×C4112yes—
725C4⋊C4C23×C4124yes—
726C4⋊C4C23×C414yes—
727C4⋊C4C23×C414yes—
728C4⋊C4C23×C4112yes—
729C4⋊C4C23×C4112yes—
730C4⋊C4C23×C4112yes—
731C4⋊C4C23×C4112yes—
732C4⋊C4C23×C4112yes—
733C4⋊C4C23×C4112yes—
734C4⋊C4C23×C4124yes—
735C4⋊C4C2×#41124yes—
736C22⋊C4—24no—
737C22⋊C4—212no—
738C22⋊C4—212no—
739C22⋊C4—224no—
740C22⋊C4—212no—
741C22⋊C4—46no—
742C22⋊C4—412no—
743C22⋊C4—46no—
744C22⋊C4—412no—
745C22⋊C4—46no—
746C22⋊C4—46no—
747C22⋊C4C23×C414yes—
748C22⋊C4C23×C414yes—
749C22⋊C4C23×C4112yes—
750C22⋊C4C23×C4112yes—
751C22⋊C4C23×C4124yes—
752C22⋊C4C23×C4124yes—
753C22⋊C4C23×C4112yes—
754C22⋊C4C23×C4112yes—
755C22⋊C4C23×C4124yes—
756C22⋊C4C23×C4124yes—
757C42—24no—
758C42—212no—
759C42—212no—
760C42—212no—
761C42—212no—
762C42—212no—
763C42—212no—
764C42—46no—
765C42—46no—
766C42—46no—
767C42—46no—
768C42—412no—
769C42—42no—
770C42—46no—
771C42—46no—
772C42—412no—
773C42—46no—
774C42C23×C414yes—
775C42C23×C414yes—
776C42C23×C4112yes—
777C42C23×C4112yes—
778C42C23×C4112yes—
779C42C23×C4112yes—
780C42C23×C4112yes—
781C42C23×C4112yes—
782C42C23×C4112yes—
783C42C23×C4112yes—
784C42C2×#41124yes—
785C23—22no—
786C23—21no—
787C23—21no—
788C23—26no—
789C23—26no—
790C23—26no—
791C23—26no—
792C23—23no—
793C23—23no—
794C23—23no—
795C23—23no—
796C23C24×C416yes—
797C23C24×C416yes—
798C23C24×C412yes—
799C23#58514yes—
800C23C2611yescharacteristic
801Q8—224no—
802Q8—412no—
803Q8C4×#41116yes—
804D4—224no—
805D4—224no—
806D4—224no—
807D4—224no—
808D4—424no—
809D4—412no—
810C2×C4—22no—
811C2×C4—26no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—26no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—23no—
821C2×C4—26no—
822C2×C4—23no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—23no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—23no—
829C2×C4—28no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—224no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—26no—
837C2×C4—26no—
838C2×C4—26no—
839C2×C4—22no—
840C2×C4—26no—
841C2×C4—26no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—26no—
845C2×C4—26no—
846C2×C4—26no—
847C2×C4—22no—
848C2×C4—26no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—412no—
852C2×C4—412no—
853C2×C4—412no—
854C2×C4—412no—
855C2×C4—412no—
856C2×C4—48no—
857C2×C4—424no—
858C2×C4—812no—
859C2×C4—824no—
860C2×C4—812no—
861C2×C4C24×C412yes—
862C2×C4C24×C412yes—
863C2×C4C24×C412yes—
864C2×C4C24×C412yes—
865C2×C4C24×C412yes—
866C2×C4C24×C412yes—
867C2×C4C24×C416yes—
868C2×C4C24×C416yes—
869C2×C4C24×C416yes—
870C2×C4C24×C416yes—
871C2×C4C24×C416yes—
872C2×C4C24×C416yes—
873C2×C4C22×#4114yes—
874C2×C4C22×#41112yes—
875C2×C4C22×#41112yes—
876C22—24no—
877C22—24no—
878C22—22no—
879C22—22no—
880C22—26no—
881C22—26no—
882C22—26no—
883C22—26no—
884C22—26no—
885C22—26no—
886C22—46no—
887C22—46no—
888C22—46no—
889C22—46no—
890C22#342814yes—
891C22C25×C411yescharacteristic
892C22C23×#4112yes—
893C22C2×#58512yes—
894C22H(7,𝔽2)11yescharacteristic
895C222−1+611yescharacteristic
896C4—24no—
897C4—212no—
898C4—22no—
899C4—22no—
900C4—26no—
901C4—22no—
902C4—22no—
903C4—26no—
904C4—26no—
905C4—22no—
906C4—26no—
907C4—22no—
908C4—26no—
909C4—42no—
910C4—42no—
911C4—46no—
912C4—46no—
913C4—46no—
914C4—42no—
915C4C2×C4×#41112yes—
916C2—24no—
917C2—46no—
918C2—46no—
919C2C22×C4×#4111yescharacteristic
920C2C2×#342811yescharacteristic
921C2#6265411yescharacteristic
922C2#6300512yes—
923C2#6300812yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34336C2semidirect
3. #34329C2semidirect
4. #34307C2semidirect
5. #34305C2semidirect
6. #34295C2semidirect
7. #34294C2semidirect
8. #34237C2semidirect
9. #34236C2semidirect
10. #34230C2semidirect
11. #34227C2semidirect
12. #34222C2semidirect
13. #34220C2semidirect
14. #34197C2semidirect
15. #34193C2semidirect
16. #34192C2semidirect
17. C4×#553C2semidirect
18. C4×#548C2semidirect
19. #34127C2semidirect
20. #34123C2semidirect
21. C4×#520C2semidirect
22. #33999C2semidirect
23. C2×#2276C2semidirect
24. #3480C4semidirect
163. #559C2×C4semidirect
164. #557C2×C4semidirect
165. #556C2×C4semidirect
166. #553C2×C4semidirect
167. #553C2×C4semidirect
168. #550C2×C4semidirect
169. #548C2×C4semidirect
170. #548C2×C4semidirect
171. #532C2×C4semidirect
174. #529C2×C4semidirect
175. #529C2×C4semidirect
194. C4×#41C2×C4semidirect
195. C4×#41C2×C4semidirect
196. C4×#41C2×C4semidirect
198. C2×C4×Q8C2×C4semidirect
479. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
#343362
#343292
#343072
#343052
#342952
#342942
#342372
#342362
#342302
#342272
#342222
#342202
#341972
#341932
#341922
C4×#5532
C4×#5482
#341272
#341232
C4×#5202
#339992
C2×#22762