Finite Group Databasebeta

← #7632264

Subgroups — #7632264

Order 512.

7622 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3492C211yesmaximal, characteristic, complemented
2C22×#554C211yesmaximal, characteristic, complemented
3#36561C218yesmaximal, complemented
4#36518C218yesmaximal, complemented
5#35773C218yesmaximal, complemented
6#35697C218yesmaximal, complemented
7#35644C211yesmaximal, characteristic, complemented
8#35634C211yesmaximal, characteristic, complemented
9#35592C211yesmaximal, characteristic, complemented
10#35576C211yesmaximal, characteristic, complemented
11#35468C214yesmaximal, complemented
12#35397C214yesmaximal, complemented
13#35306C212yesmaximal, complemented
14#35085C214yesmaximal, complemented
15#34957C214yesmaximal, complemented
16#34737C212yesmaximal, complemented
17#34266C212yesmaximal, complemented
18#34200C212yesmaximal, complemented
19C2×#2274C211yesmaximal, characteristic, complemented
20#3492—216no—
21C2×#554—216no—
22C2×#554C2218yes—
23C2×#554C2218yes—
24C2×#554C2214yescomplemented
25C2×#553C2214yescomplemented
26C2×#552C2214yescomplemented
27C2×#547C2214yescomplemented
28C2×#544C2211yescharacteristic
29C2×#539C2214yes—
30C2×#537C2211yescharacteristic
31C2×#536C2212yes—
32C22×C4⋊Q8C2211yescharacteristic
33C22×#125C2212yes—
34C2×#525C2214yes—
35C2×#525C2212yes—
36C2×#525C2212yes—
37C22×C22⋊Q8C2212yes—
38C22×C22⋊Q8C2211yescharacteristic
39C22×C22⋊Q8C2212yes—
40C22×C22⋊Q8C2211yescharacteristic
41C2×#520C2212yes—
42C22×C4×Q8C2211yescharacteristic
43C22×C4×D4C2212yes—
44C22×C4×D4C2211yescharacteristic
45C22×#117C2212yes—
46C23×C4⋊C4C2211yescharacteristic
47C23×C4⋊C4C2211yescharacteristic
48#2857C2218yescomplemented
49#2857C2214yescomplemented
50#2850C2218yescomplemented
51#2850C2214yescomplemented
52#2663C22116yescomplemented
53#2621C2214yescomplemented
54#2620C2214yescomplemented
55#2602C22116yes—
56#2591C2214yes—
57#2583C2214yes—
58#2564C2218yes—
59#2564C22116yescomplemented
60#2561C2214yes—
61#2560C22116yescomplemented
62#2558C22116yescomplemented
63#2556C22116yescomplemented
64#2556C22116yescomplemented
65#2551C2218yescomplemented
66#2550C2218yescomplemented
67#2543C2218yes—
68#2542C2218yescomplemented
69#2540C2218yescomplemented
70#2539C2214yes—
71#2519C22116yescomplemented
72#2506C22116yescomplemented
73#2503C2214yes—
74#2501C2214yes—
75#2499C2218yescomplemented
76#2492C2218yescomplemented
77#2492C2218yescomplemented
78#2491C2218yescomplemented
79#2489C2218yescomplemented
80#2461C22116yescomplemented
81#2452C22116yescomplemented
82#2436C2214yes—
83#2434C2214yes—
84#2432C2218yescomplemented
85#2417C2214yes—
86#2417C2218yescomplemented
87#2416C2214yes—
88#2415C2214yes—
89#2415C2218yescomplemented
90#2414C2214yes—
91#2413C2218yes—
92#2413C2214yes—
93#2412C2214yes—
94#2412C2218yes—
95#2411C2214yes—
96#2410C2214yes—
97#2395C2218yes—
98#2392C2218yes—
99#2388C2218yes—
100#2367C2218yescomplemented
101#2365C2218yescomplemented
102#2362C2218yescomplemented
103#2361C2218yescomplemented
104#2360C2218yescomplemented
105#2360C2218yescomplemented
106#2352C2218yescomplemented
107D4×C4⋊C4C2218yescomplemented
108#2322C2218yes—
109#2322C2218yes—
110#2317C2212yes—
111#2311C2212yes—
112#2310C2212yes—
113C4×#123C2218yes—
114C4×#121C22116yes—
115C4×#121C2218yes—
116C4×#120C2218yes—
117#2297C2212yes—
118#2296C2212yes—
119#2280C2212yes—
120#2274C2211yescharacteristic
121#2274C2211yescharacteristic
122#2274C2214yes—
123#2274C2212yes—
124#2274C2218yescomplemented
125C2×C4×C4⋊C4C2218yescomplemented
126C2×C4×C22⋊C4C2214yes—
127C22×#41C2312yes—
128C22×#41C2314yes—
129C23×Q8C2311yescharacteristic
130C23×Q8C2312yes—
131C23×D4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136#554—264no—
137#554—264no—
138#554—232no—
139#553—232no—
140#552—232no—
141#547—232no—
142#544—28no—
143#539—232no—
144#537—28no—
145#536—216no—
146C2×C4⋊Q8—28no—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2318yes—
149C2×C4⋊Q8C2314yes—
150C2×C4⋊Q8C2318yes—
151C2×#126C2318yes—
152C2×#125—216no—
153C2×#125C23116yes—
154C2×#125C2318yes—
155C2×#125C2314yes—
156C2×#124C2314yes—
157C2×#124C2318yes—
158#525—216no—
159#525—232no—
160#525—216no—
161C2×#123C2314yes—
162C2×#123C2318yes—
163C2×#123C2318yes—
164C2×#123C2314yes—
165C2×#123C2318yes—
166C2×C22⋊Q8—216no—
167C2×C22⋊Q8—28no—
168C2×C22⋊Q8—216no—
169C2×C22⋊Q8—28no—
170C2×C22⋊Q8C23116yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2318yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2312yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×#121C2314yes—
185C2×#121C2312yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2312yes—
189C2×#121C2318yes—
190C2×#121C2314yes—
191C2×#120C2314yes—
192C2×#120C2314yes—
193#520—216no—
194C2×C4×Q8—28no—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2318yes—
197C2×C4×D4—216no—
198C2×C4×D4—28no—
199C2×C4×D4C2318yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C23116yes—
210C2×#117—216no—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C2×#117C2314yes—
217C2×#117C2314yes—
218C2×#117C2312yes—
219C22×C4⋊C4—28no—
220C22×C4⋊C4D4116yescomplemented
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2318yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2314yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2311yescharacteristic
241C22×C42C2314yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2318yes—
245#400C2318yes—
246#400C23116yes—
247#399C2318yes—
248#399C23116yes—
249#398C23116yes—
250#398C2318yes—
251#398C2318yes—
252#397C2318yes—
253#397C23116yes—
254#397C2318yes—
255#396C23116yes—
256#396C2318yes—
257#396C2318yes—
258#395C2318yes—
259#395C23116yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C23116yes—
264#394C2318yes—
265#393C23116yes—
266#393C2318yes—
267#392C2318yes—
268#392C2318yes—
269#391C2318yes—
270#391C2314yes—
271#391C2314yes—
272#391C2318yes—
273#391C2314yes—
274#391C2318yes—
275#391C2318yes—
276#391C2314yes—
277#390C23116yes—
278#390C2314yes—
279#390C2318yes—
280#390C2314yes—
281#390C2318yes—
282#389C2318yes—
283#389C23116yes—
284#389C23116yes—
285#389C23116yes—
286#389C23116yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#388C2318yes—
291#388C23116yes—
292#388C23116yes—
293#388C23116yes—
294#388C23116yes—
295#388C23116yes—
296#388C23116yes—
297#388C2318yes—
298#387C23116yes—
299#387C23116yes—
300#387C23116yes—
301#386C23116yes—
302#386C2318yes—
303#386C2318yes—
304#386C23116yes—
305#386C2318yes—
306#386C2314yes—
307#386C2314yes—
308#385C23116yes—
309#385C23116yes—
310#385C23116yes—
311#385C2318yes—
312#385C2314yes—
313#385C2314yes—
314#384C2314yes—
315#384C2318yes—
316#382C2314yes—
317#382C2318yes—
318#381C2318yes—
319#381C2314yes—
320#380C23116yes—
321#380C2318yes—
322#380C2318yes—
323#380C2314yes—
324#380C2314yes—
325#379C2314yes—
326C4×C4⋊C4C23116yes—
327C4×C4⋊C4C2318yes—
328C4×C4⋊C4C2318yes—
329C4×C4⋊C4C23116yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C23116yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2318yes—
334C4×C22⋊C4C23116yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C2318yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C4×C22⋊C4C23116yes—
342C4×C22⋊C4C2318yes—
343C2×#95C2318yes—
344C25C2411yescharacteristic
345C25C2411yescharacteristic
346C2×#41—28no—
347C2×#41—216no—
348C2×#41—28no—
349C2×#41—28no—
350C2×#41—88no—
351C22×Q8—24no—
352C22×Q8—28no—
353C22×Q8—28no—
354C22×Q8—84no—
355C22×Q8C2414yes—
356C22×Q8C2412yes—
357C22×Q8C2418yes—
358C22×Q8C2414yes—
359C22×D4—24no—
360C22×D4—28no—
361C22×D4C2412yes—
362C22×D4C2414yes—
363C22×D4C2414yes—
364C22×D4C2412yes—
365C22×D4C2418yes—
366C22×D4C2412yes—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C23×C4—28no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—84no—
374C23×C4—84no—
375C23×C4C2×D418yes—
376C23×C4C2×D4116yes—
377C23×C4C2412yes—
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2414yes—
381C23×C4C2414yes—
382C23×C4C2418yes—
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2418yes—
389C23×C4C2418yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2414yes—
393C23×C4C2414yes—
394C23×C4C2411yescharacteristic
395C4⋊Q8—232no—
396C4⋊Q8—216no—
397C4⋊Q8—216no—
398C4⋊Q8—88no—
399#126—232no—
400#125—264no—
401#125—232no—
402#125—216no—
403#124—216no—
404#124—88no—
405#123—216no—
406#123—232no—
407#123—232no—
408#123—216no—
409#123—232no—
410C22⋊Q8—232no—
411C22⋊Q8—232no—
412C22⋊Q8—216no—
413C22⋊Q8—216no—
414C22⋊Q8—216no—
415C22⋊Q8—28no—
416C22⋊Q8—28no—
417C22⋊Q8—216no—
418C22⋊Q8—264no—
419C22⋊Q8—232no—
420C22⋊Q8—216no—
421C22⋊Q8—232no—
422C22⋊Q8—216no—
423C22⋊Q8—232no—
424#121—232no—
425#121—216no—
426#121—28no—
427#121—216no—
428#121—28no—
429#121—216no—
430#121—216no—
431#120—216no—
432#120—216no—
433C4×Q8—232no—
434C4×Q8—216no—
435C4×D4—232no—
436C4×D4—232no—
437C4×D4—216no—
438C4×D4—216no—
439C4×D4—232no—
440C4×D4—216no—
441C4×D4—232no—
442C4×D4—216no—
443C4×D4—216no—
444C4×D4—232no—
445C4×D4—816no—
446#117—28no—
447#117—216no—
448#117—28no—
449#117—216no—
450#117—216no—
451#117—216no—
452#117—216no—
453#117#41116yescomplemented
454C2×C4⋊C4—28no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—28no—
458C2×C4⋊C4—28no—
459C2×C4⋊C4—28no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—232no—
462C2×C4⋊C4—216no—
463C2×C4⋊C4—216no—
464C2×C4⋊C4C2×D418yes—
465C2×C4⋊C4C2×D4116yes—
466C2×C4⋊C4C2×D418yes—
467C2×C4⋊C4C2×D4132yes—
468C2×C4⋊C4C2×D4132yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C24116yes—
489C2×C4⋊C4C24116yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2414yes—
495C2×C22⋊C4—28no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—28no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—216no—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2412yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2412yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2414yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C24116yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C24116yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2414yes—
524C2×C42—28no—
525C2×C42—24no—
526C2×C42—216no—
527C2×C42—88no—
528C2×C42C2418yes—
529C2×C42C2414yes—
530C2×C42C2418yes—
531C2×C42C2414yes—
532C2×C42C2418yes—
533C2×C42C2414yes—
534C2×C42C24116yes—
535C2×C42C2418yes—
536C2×C42C2418yes—
537C2×C42C2414yes—
538#95C24116yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C24116yes—
545#95C2418yes—
546#95C24116yes—
547#95C2418yes—
548#95C24116yes—
549#95C24116yes—
550#95C2418yes—
551C24—22no—
552C24—24no—
553C24—24no—
554C24—24no—
555C24—24no—
556C24—42no—
557C24—42no—
558C24C22×D414yes—
559C24C2514yes—
560C24C2511yescharacteristic
561C24C2512yes—
562C24C2511yescharacteristic
563C24C2511yescharacteristic
564#41—432no—
565#41—832no—
566C2×Q8—28no—
567C2×Q8—24no—
568C2×Q8—216no—
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—24no—
572C2×Q8—28no—
573C2×Q8—24no—
574C2×Q8—48no—
575C2×Q8—48no—
576C2×Q8—48no—
577C2×Q8—416no—
578C2×Q8—816no—
579C2×D4—232no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—216no—
590C2×D4—216no—
591C2×D4—24no—
592C2×D4—28no—
593C2×D4—216no—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—48no—
600C2×D42−1+418yes—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—232no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—216no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—216no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—216no—
624C22×C4—216no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—48no—
631C22×C4—42no—
632C22×C4—416no—
633C22×C4—416no—
634C22×C4—416no—
635C22×C4—816no—
636C22×C4—816no—
637C22×C4C22×D414yes—
638C22×C4C22×D418yes—
639C22×C4C22×D418yes—
640C22×C4C22×D418yes—
641C22×C4C22×D418yes—
642C22×C4C22×D4116yes—
643C22×C4C22×D4116yes—
644C22×C4C22×D414yes—
645C22×C4C2×#4118yes—
646C22×C4C2518yes—
647C22×C4C2514yes—
648C22×C4C2514yes—
649C22×C4C2512yes—
650C22×C4C2514yes—
651C22×C4C2514yes—
652C22×C4C2512yes—
653C22×C4C2514yes—
654C22×C4C2514yes—
655C22×C4C2514yes—
656C22×C4C2512yes—
657C22×C4C2518yes—
658C22×C4C2512yes—
659C22×C4C2512yes—
660C4⋊C4—216no—
661C4⋊C4—28no—
662C4⋊C4—24no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—216no—
666C4⋊C4—216no—
667C4⋊C4—216no—
668C4⋊C4—216no—
669C4⋊C4—24no—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—216no—
674C4⋊C4—28no—
675C4⋊C4—216no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—232no—
679C4⋊C4—216no—
680C4⋊C4—416no—
681C4⋊C4—48no—
682C4⋊C4C22×D4116yes—
683C4⋊C4C22×D4116yes—
684C4⋊C4C22×D4132yes—
685C4⋊C4C2×#41116yes—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—28no—
694C22⋊C4—216no—
695C22⋊C4—216no—
696C22⋊C4—28no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—216no—
702C22⋊C4—216no—
703C22⋊C4—216no—
704C22⋊C4—232no—
705C22⋊C4—216no—
706C22⋊C4—48no—
707C22⋊C4—416no—
708C22⋊C4—48no—
709C22⋊C4C2×#41116yes—
710C42—216no—
711C42—28no—
712C42—216no—
713C42—28no—
714C42—216no—
715C42—28no—
716C42—416no—
717C42—48no—
718C42—48no—
719C42C2×#41116yes—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—28no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—22no—
732C23—28no—
733C23—28no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—28no—
738C23—28no—
739C23—44no—
740C23—416no—
741C23—416no—
742C23—44no—
743C23—44no—
744C23C23×D412yes—
745C23C23×D412yes—
746C23C23×D412yes—
747C23C22×#4114yes—
748C23C2×2−1+414yes—
749C23C2×2−1+414yes—
750C23C2611yescharacteristic
751Q8—416no—
752Q8—48no—
753Q8—816no—
754Q8—88no—
755D4—216no—
756D4—216no—
757D4—432no—
758D4—416no—
759D4—416no—
760D4—416no—
761D4—48no—
762D4—88no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—216no—
774C2×C4—216no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—416no—
796C2×C4—48no—
797C2×C4—416no—
798C2×C4—432no—
799C2×C4—48no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—416no—
804C2×C4—416no—
805C2×C4—816no—
806C2×C4—816no—
807C2×C4#532116yes—
808C2×C4C23×D418yes—
809C2×C4C23×D414yes—
810C2×C4C23×D418yes—
811C2×C4C23×D414yes—
812C2×C4C22×#41116yes—
813C2×C4C22×#4114yes—
814C2×C4C22×#4114yes—
815C2×C4C2×2−1+414yes—
816C22—28no—
817C22—28no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—28no—
823C22—22no—
824C22—24no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—416no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—48no—
834C22—48no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22C2×#53214yes—
839C22#348614yes—
840C22C24×D411yescharacteristic
841C22C23×#4112yes—
842C22C22×2−1+412yes—
843C22H(7,𝔽2)12yes—
844C4—216no—
845C4—24no—
846C4—28no—
847C4—28no—
848C4—24no—
849C4—48no—
850C4—44no—
851C4—44no—
852C4—42no—
853C4—44no—
854C4—42no—
855C4—44no—
856C4—44no—
857C4C2×#53218yes—
858C2—24no—
859C2—24no—
860C2—44no—
861C2—42no—
862C2—84no—
863C2C22×#53211yescharacteristic
864C2C2×#348611yescharacteristic
865C2#6284211yescharacteristic
866C2#6300014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3492C2semidirect
2. C22×#554C2semidirect
3. #36561C2semidirect
4. #36518C2semidirect
5. #35773C2semidirect
6. #35697C2semidirect
7. #35644C2semidirect
8. #35634C2semidirect
9. #35592C2semidirect
10. #35576C2semidirect
11. #35468C2semidirect
12. #35397C2semidirect
13. #35306C2semidirect
14. #35085C2semidirect
15. #34957C2semidirect
16. #34737C2semidirect
17. #34266C2semidirect
18. #34200C2semidirect
19. C2×#2274C2semidirect
24. C2×#554C22semidirect
25. C2×#553C22semidirect
26. C2×#552C22semidirect
27. C2×#547C22semidirect
48. #2857C22semidirect
49. #2857C22semidirect
50. #2850C22semidirect
51. #2850C22semidirect
52. #2663C22semidirect
53. #2621C22semidirect
54. #2620C22semidirect
59. #2564C22semidirect
61. #2560C22semidirect
62. #2558C22semidirect
63. #2556C22semidirect
64. #2556C22semidirect
65. #2551C22semidirect
66. #2550C22semidirect
68. #2542C22semidirect
69. #2540C22semidirect
71. #2519C22semidirect
72. #2506C22semidirect
75. #2499C22semidirect
76. #2492C22semidirect
77. #2492C22semidirect
78. #2491C22semidirect
79. #2489C22semidirect
80. #2461C22semidirect
81. #2452C22semidirect
84. #2432C22semidirect
86. #2417C22semidirect
89. #2415C22semidirect
100. #2367C22semidirect
101. #2365C22semidirect
102. #2362C22semidirect
103. #2361C22semidirect
104. #2360C22semidirect
105. #2360C22semidirect
106. #2352C22semidirect
107. D4×C4⋊C4C22semidirect
124. #2274C22semidirect
125. C2×C4×C4⋊C4C22semidirect
220. C22×C4⋊C4D4semidirect
453. #117#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34922
C22×#5542
#365612
#365182
#357732
#356972
#356442
#356342
#355922
#355762
#354682
#353972
#353062
#350852
#349572
#347372
#342662
#342002
C2×#22742