Finite Group Databasebeta

← #7645743

Subgroups — #7645743

Order 512.

6542 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#3458C211yesmaximal, characteristic, complemented
3#42150C218yesmaximal, complemented
4#41939C218yesmaximal, complemented
5#38371C2116yesmaximal, complemented
6#37548C212yesmaximal, complemented
7#37540C212yesmaximal, complemented
8#36962C212yesmaximal, complemented
9#36959C212yesmaximal, complemented
10#36959C212yesmaximal, complemented
11#36708C212yesmaximal, complemented
12#35455C212yesmaximal
13#35391C212yesmaximal, complemented
14#35325C212yesmaximal, complemented
15#35248C212yesmaximal, complemented
16#35097C212yesmaximal
17#35090C212yesmaximal, complemented
18#34985C212yesmaximal
19C2×#2484C212yesmaximal, complemented
20#34177C211yesmaximal, characteristic, complemented
21C2×#552—216no—
22C2×#552C2218yes—
23C2×#552C2218yes—
24#3458—216no—
25C2×#544C2212yes—
26C2×#544C2212yes—
27C2×#544C2214yescomplemented
28C2×#544C2214yescomplemented
29C2×#543C2212yes—
30C2×#543C2212yes—
31C2×#533C2212yes—
32C2×#533C2212yes—
33C2×#533C2218yescomplemented
34C22×#126C2211yescharacteristic
35C22×#126C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×#125C2211yescharacteristic
39C22×#123C2211yescharacteristic
40C22×#123C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic
42C22×C22⋊Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×#117C2211yescharacteristic
46C22×#117C2212yes—
47C22×#117C2211yescharacteristic
48C22×#117C2211yescharacteristic
49C23×C4⋊C4C2211yescharacteristic
50#2855C2214yes—
51#2855C2214yes—
52#2855C2214yes—
53#2853C2218yes—
54#2848C2214yes—
55#2822C2218yescomplemented
56#2821C2214yescomplemented
57#2821C2214yescomplemented
58#2721C22116yescomplemented
59#2719C22116yescomplemented
60#2719C22116yescomplemented
61#2716C22116yescomplemented
62#2713C22116yescomplemented
63#2713C22116yescomplemented
64#2690C22116yescomplemented
65#2677C22116yescomplemented
66#2664C2218yescomplemented
67#2660C2214yescomplemented
68#2642C2214yescomplemented
69#2637C2218yescomplemented
70#2634C2218yescomplemented
71#2634C2218yescomplemented
72#2628C2214yescomplemented
73#2627C2214yes—
74#2627C2214yes—
75#2627C2214yes—
76#2626C2214yes—
77#2623C2214yes—
78#2623C2214yes—
79#2621C2214yescomplemented
80#2611C2218yescomplemented
81#2604C2218yescomplemented
82#2599C2218yescomplemented
83#2583C2214yes—
84#2583C2214yes—
85#2581C2218yescomplemented
86#2568C2214yescomplemented
87#2565C2218yescomplemented
88#2561C2214yes—
89#2561C2214yes—
90#2549C22116yescomplemented
91#2546C2214yescomplemented
92#2503C2214yes—
93#2503C2214yes—
94#2502C2214yes—
95#2498C2218yes—
96#2498C2218yes—
97#2488C22116yes—
98#2488C22116yes—
99#2484C2214yes—
100#2484C2214yes—
101#2484C2214yes—
102#2484C2214yes—
103#2484C2214yes—
104#2484C2214yes—
105#2484C2218yescomplemented
106#2484C2218yescomplemented
107#2482C2214yes—
108#2482C2214yes—
109#2450C22116yes—
110#2449C22116yes—
111#2440C22116yescomplemented
112#2438C22116yescomplemented
113#2438C22116yescomplemented
114#2434C2214yes—
115C2×#400C2214yescomplemented
116C2×#398C2214yescomplemented
117#2343C2218yescomplemented
118#2343C2218yescomplemented
119#2327C2218yescomplemented
120#2323C2218yescomplemented
121#2315C2214yes—
122#2315C2212yes—
123#2313C2212yes—
124#2313C2212yes—
125#2308C2214yes—
126C2×#387C2218yescomplemented
127C2×#385C2214yes—
128#2283C2212yes—
129#2283C2212yes—
130C2×#381C2214yes—
131C2×#381C2212yes—
132#2273C2212yes—
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139#552—264no—
140#552—264no—
141#544—232no—
142#544—232no—
143#544—216no—
144#544—216no—
145#543—216no—
146#543—216no—
147#533—264no—
148#533—216no—
149#533—216no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2318yes—
155C2×C4⋊Q8C2318yes—
156C2×C4⋊Q8C2318yes—
157C2×#126—28no—
158C2×#126—28no—
159C2×#126C2314yes—
160C2×#126C2314yes—
161C2×#126C2318yes—
162C2×#125—28no—
163C2×#125—28no—
164C2×#125—28no—
165C2×#125C2314yes—
166C2×#125C2314yes—
167C2×#125C2314yes—
168C2×#125C2314yes—
169C2×#125C2318yes—
170C2×#125C2318yes—
171C2×#125C2318yes—
172C2×#125C2318yes—
173C2×#123—28no—
174C2×#123—28no—
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×#123C2318yes—
178C2×C22⋊Q8—28no—
179C2×C22⋊Q8—28no—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C4×Q8—28no—
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×D4—28no—
199C2×C4×D4C2318yes—
200C2×#117—216no—
201C2×#117—28no—
202C2×#117—28no—
203C2×#117D4116yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2314yes—
207C2×#117C2314yes—
208C2×#117C2314yes—
209C2×#117C2314yes—
210C2×#117C2318yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C22×C4⋊C4—28no—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2318yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2311yescharacteristic
245C22×C42C2314yes—
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C23116yes—
255#400C2318yes—
256#400C23116yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#399C2318yes—
263#399C2318yes—
264#399C2318yes—
265#398C23116yes—
266#398C23116yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C23116yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C23116yes—
275#398C2318yes—
276#398C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#396C23116yes—
282#395C2318yes—
283#395C2318yes—
284#395C23116yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#391C2318yes—
292#391C2318yes—
293#391C2318yes—
294#391C2318yes—
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#389C23116yes—
299#389C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C23116yes—
303#388C23116yes—
304#388C23116yes—
305#388C23116yes—
306#388C23116yes—
307#387C23116yes—
308#387C23116yes—
309#387C23116yes—
310#387C23116yes—
311#387C23116yes—
312#387C23116yes—
313#387C23116yes—
314#387C23116yes—
315#387C23116yes—
316#387C23116yes—
317#387C23116yes—
318#386C2318yes—
319#386C2318yes—
320#386C23116yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#385C23116yes—
325#385C2318yes—
326#385C2318yes—
327#385C2318yes—
328#385C23116yes—
329#385C23116yes—
330#384C2318yes—
331#383C2314yes—
332#383C2314yes—
333#382C2318yes—
334#382C2314yes—
335#382C2318yes—
336#382C2314yes—
337#381C2318yes—
338#381C2318yes—
339#381C2318yes—
340#381C2314yes—
341#381C2314yes—
342#381C2314yes—
343#381C23116yes—
344#381C2314yes—
345#380C2314yes—
346#380C2314yes—
347#380C23116yes—
348#380C2318yes—
349#379C2318yes—
350C4×C4⋊C4C2314yes—
351C4×C4⋊C4C2314yes—
352C4×C22⋊C4C2314yes—
353C4×C22⋊C4C2314yes—
354C4×C22⋊C4C23116yes—
355#376C2314yes—
356#376C2314yes—
357C2×#95C2314yes—
358C2×#95C2314yes—
359C2×#95C2318yes—
360C2×#95C2318yes—
361C2×#95C2318yes—
362C25C2411yescharacteristic
363C25C2411yescharacteristic
364C22×Q8—24no—
365C22×Q8—44no—
366C22×Q8C2414yes—
367C22×Q8C2414yes—
368C22×Q8C2414yes—
369C22×Q8C2414yes—
370C22×Q8C2414yes—
371C22×D4—24no—
372C22×D4—28no—
373C22×D4C2414yes—
374C23×C4—28no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—28no—
378C23×C4—24no—
379C23×C4—44no—
380C23×C4—44no—
381C23×C4C2×D418yes—
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2414yes—
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2414yes—
397C23×C4C2414yes—
398C23×C4C2418yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C4⋊Q8—232no—
404C4⋊Q8—232no—
405C4⋊Q8—28no—
406C4⋊Q8—28no—
407C4⋊Q8—28no—
408C4⋊Q8—28no—
409C4⋊Q8—416no—
410#126—232no—
411#126—216no—
412#126—216no—
413#125—232no—
414#125—232no—
415#125—232no—
416#125—232no—
417#125—216no—
418#125—216no—
419#125—216no—
420#125—216no—
421#123—216no—
422#123—216no—
423#123—232no—
424C22⋊Q8—216no—
425C22⋊Q8—216no—
426C22⋊Q8—216no—
427C22⋊Q8—216no—
428C22⋊Q8—232no—
429C22⋊Q8—232no—
430C22⋊Q8—232no—
431C22⋊Q8—232no—
432C22⋊Q8—232no—
433C22⋊Q8—232no—
434C22⋊Q8—416no—
435C4×Q8—216no—
436C4×Q8—216no—
437C4×Q8—216no—
438C4×Q8—216no—
439C4×Q8—216no—
440C4×Q8—216no—
441C4×D4—232no—
442#117—216no—
443#117—216no—
444#117—216no—
445#117—216no—
446#117—232no—
447#117—216no—
448#117—216no—
449#117C2×D4132yes—
450#117C2×D4132yes—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—216no—
456C2×C4⋊C4—216no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—28no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—416no—
470C2×C4⋊C4C2×D418yes—
471C2×C4⋊C4C2×D418yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2412yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C24116yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C24116yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C24116yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C24116yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—216no—
511C2×C22⋊C4—216no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4C2×D418yes—
518C2×C22⋊C4C2×D418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2412yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2412yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C24116yes—
531C2×C22⋊C4C24116yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2414yes—
534C2×C42—24no—
535C2×C42—24no—
536C2×C42—216no—
537C2×C42—24no—
538C2×C42C2×D418yes—
539C2×C42C2×D418yes—
540C2×C42C2414yes—
541C2×C42C2418yes—
542C2×C42C2414yes—
543C2×C42C2418yes—
544C2×C42C2414yes—
545C2×C42C2418yes—
546C2×C42C2418yes—
547C2×C42C2412yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551#95C2418yes—
552#95C2418yes—
553#95C24116yes—
554#95C24116yes—
555#95C24116yes—
556#95C2418yes—
557#95C2418yes—
558#95C24116yes—
559#95C24116yes—
560#95C24116yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C24116yes—
566#95C24116yes—
567#95C24116yes—
568#95C24116yes—
569C24—22no—
570C24—24no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24C22×D414yes—
576C242−1+418yes—
577C24C2512yes—
578C24C2511yescharacteristic
579C24C2512yes—
580C2×Q8—28no—
581C2×Q8—28no—
582C2×Q8—28no—
583C2×Q8—28no—
584C2×Q8—28no—
585C2×Q8—28no—
586C2×Q8—44no—
587C2×Q8—48no—
588C2×Q8—48no—
589C2×Q8—48no—
590C2×Q8—48no—
591C2×Q8—416no—
592C2×D4—28no—
593C2×D4—216no—
594C2×D4—416no—
595C22×C4—232no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—216no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—216no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—42no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—416no—
634C22×C4—416no—
635C22×C4—416no—
636C22×C4C22×D418yes—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D418yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C22×D414yes—
643C22×C4C22×D414yes—
644C22×C4C25116yes—
645C22×C4C2512yes—
646C22×C4C2512yes—
647C22×C4C2512yes—
648C22×C4C2518yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2518yes—
652C22×C4C2512yes—
653C22×C4C2511yescharacteristic
654C22×C4C2512yes—
655C22×C4C2511yescharacteristic
656C22×C4C2512yes—
657C22×C4C2512yes—
658C22×C4C2512yes—
659C22×C4C2512yes—
660C22×C4C2512yes—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—216no—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—216no—
686C4⋊C4—28no—
687C4⋊C4—216no—
688C4⋊C4—28no—
689C4⋊C4—216no—
690C4⋊C4—232no—
691C4⋊C4—416no—
692C4⋊C4—48no—
693C4⋊C4—416no—
694C4⋊C4—48no—
695C4⋊C4—416no—
696C4⋊C4C22×D4116yes—
697C4⋊C4C22×D4116yes—
698C22⋊C4—216no—
699C22⋊C4—216no—
700C22⋊C4—28no—
701C22⋊C4—216no—
702C22⋊C4—216no—
703C22⋊C4—28no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—416no—
710C22⋊C4—416no—
711C22⋊C4C22×D4116yes—
712C22⋊C4C22×D4116yes—
713C42—28no—
714C42—216no—
715C42—28no—
716C42—216no—
717C42—28no—
718C42—48no—
719C42—48no—
720C42C22×D418yes—
721C42C22×D418yes—
722C42C22×D418yes—
723C42C22×D418yes—
724C23—24no—
725C23—22no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—44no—
733C23—44no—
734C23—416no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—88no—
739C23#536116yes—
740C23C23×D412yes—
741C23C23×D414yes—
742C23C2×2−1+414yes—
743C23C2×2−1+418yes—
744C23C2611yescharacteristic
745Q8—416no—
746Q8—88no—
747Q8—88no—
748Q8—88no—
749Q8—88no—
750D4—416no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—216no—
764C2×C4—216no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—216no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—216no—
778C2×C4—216no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—216no—
782C2×C4—216no—
783C2×C4—24no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—416no—
789C2×C4—416no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—416no—
796C2×C4—44no—
797C2×C4—88no—
798C2×C4—88no—
799C2×C4—816no—
800C2×C4C23×D412yes—
801C2×C4C23×D414yes—
802C2×C4C23×D414yes—
803C2×C4C23×D414yes—
804C2×C4C23×D412yes—
805C2×C4C23×D414yes—
806C2×C4C23×D414yes—
807C2×C4#58514yes—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—24no—
812C22—216no—
813C22—28no—
814C22—416no—
815C22—42no—
816C22—42no—
817C22—48no—
818C22—42no—
819C22—88no—
820C22C2×#53614yes—
821C22C2×#53618yes—
822C22C24×D411yescharacteristic
823C22C22×2−1+412yes—
824C22C2×#58512yes—
825C222−1+612yes—
826C4—24no—
827C4—24no—
828C4—24no—
829C4—24no—
830C4—24no—
831C4—22no—
832C4—24no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—48no—
837C4—42no—
838C4—48no—
839C4—416no—
840C4—42no—
841C4—42no—
842C4—42no—
843C2—24no—
844C2—28no—
845C2—82no—
846C2C22×#53611yescharacteristic
847C2#6281111yescharacteristic
848C2#6285911yescharacteristic
849C2#6290414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3458C2semidirect
3. #42150C2semidirect
4. #41939C2semidirect
5. #38371C2semidirect
6. #37548C2semidirect
7. #37540C2semidirect
8. #36962C2semidirect
9. #36959C2semidirect
10. #36959C2semidirect
11. #36708C2semidirect
13. #35391C2semidirect
14. #35325C2semidirect
15. #35248C2semidirect
17. #35090C2semidirect
19. C2×#2484C2semidirect
20. #34177C2semidirect
27. C2×#544C22semidirect
28. C2×#544C22semidirect
33. C2×#533C22semidirect
55. #2822C22semidirect
56. #2821C22semidirect
57. #2821C22semidirect
58. #2721C22semidirect
59. #2719C22semidirect
60. #2719C22semidirect
61. #2716C22semidirect
62. #2713C22semidirect
63. #2713C22semidirect
64. #2690C22semidirect
65. #2677C22semidirect
66. #2664C22semidirect
67. #2660C22semidirect
68. #2642C22semidirect
69. #2637C22semidirect
70. #2634C22semidirect
71. #2634C22semidirect
72. #2628C22semidirect
79. #2621C22semidirect
80. #2611C22semidirect
81. #2604C22semidirect
82. #2599C22semidirect
85. #2581C22semidirect
86. #2568C22semidirect
87. #2565C22semidirect
90. #2549C22semidirect
91. #2546C22semidirect
105. #2484C22semidirect
106. #2484C22semidirect
111. #2440C22semidirect
112. #2438C22semidirect
113. #2438C22semidirect
115. C2×#400C22semidirect
116. C2×#398C22semidirect
117. #2343C22semidirect
118. #2343C22semidirect
119. #2327C22semidirect
120. #2323C22semidirect
126. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#34582
#421502
#419392
#383712
#375482
#375402
#369622
#369592
#367082
#354552
#353912
#353252
#352482
#350972
#350902
#349852
C2×#24842
#341772