Finite Group Databasebeta

← #7642499

Subgroups — #7642499

Order 512.

6920 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic
3#38363C2116yesmaximal, complemented
4#38040C218yesmaximal, complemented
5#38027C218yesmaximal, complemented
6#36970C212yesmaximal, complemented
7#36966C212yesmaximal, complemented
8#36962C212yesmaximal, complemented
9#36959C212yesmaximal, complemented
10C2×#2855C212yesmaximal, complemented
11#35455C212yesmaximal, complemented
12#35448C212yesmaximal, complemented
13#35391C212yesmaximal, complemented
14#35351C212yesmaximal
15#35325C212yesmaximal, complemented
16#35311C212yesmaximal, complemented
17#35248C212yesmaximal, complemented
18#35084C212yesmaximal, complemented
19#35010C212yesmaximal, complemented
20#34185C211yesmaximal, characteristic, complemented
21#3501—216no—
22C2×#554C2214yescomplemented
23C2×#554C2218yescomplemented
24C2×D4×Q8C2214yescomplemented
25C2×#544C2212yes—
26C2×#543C2212yes—
27C2×#543C2212yes—
28C2×#533C2212yes—
29C2×#529—216no—
30C2×#529C2218yes—
31C2×#529C2218yes—
32C22×#126C2211yescharacteristic
33C22×#126C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C22×#123C2211yescharacteristic
37C22×#123C2211yescharacteristic
38C22×C22⋊Q8C2212yes—
39C22×C22⋊Q8C2212yes—
40C22×C22⋊Q8C2211yescharacteristic
41C22×#121C2211yescharacteristic
42C2×#518C2212yes—
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×C4×D4C2211yescharacteristic
46C22×C4×D4C2211yescharacteristic
47C22×#117C2211yescharacteristic
48C22×#117C2211yescharacteristic
49C23×C42C2211yescharacteristic
50#2855C2214yes—
51#2855C2214yes—
52#2855C2214yes—
53#2855C2214yes—
54#2855C2214yes—
55#2855C2218yescomplemented
56#2855C2218yescomplemented
57#2848C2214yes—
58#2721C22116yescomplemented
59#2719C22116yescomplemented
60#2716C22116yescomplemented
61#2713C22116yescomplemented
62#2700C22116yescomplemented
63#2698C22116yescomplemented
64#2689C22116yescomplemented
65#2674C22116yescomplemented
66#2638C2218yescomplemented
67#2634C2218yescomplemented
68#2628C2214yescomplemented
69#2627C2214yes—
70#2626C2214yes—
71#2625C2218yescomplemented
72#2621C2214yescomplemented
73#2611C2218yescomplemented
74#2599C2218yescomplemented
75#2583C2214yes—
76#2583C2214yes—
77#2581C2218yescomplemented
78#2579C2218yescomplemented
79#2568C2214yescomplemented
80#2564C2218yescomplemented
81#2561C2214yes—
82#2561C2214yes—
83#2549C22116yescomplemented
84#2546C2214yescomplemented
85#2503C2214yes—
86#2503C2214yes—
87#2502C2214yes—
88#2499C2218yescomplemented
89#2488C22116yescomplemented
90#2488C22116yescomplemented
91#2487C2214yescomplemented
92#2486C2214yescomplemented
93#2484C2214yes—
94#2484C2214yes—
95#2484C2214yes—
96#2484C2218yescomplemented
97#2483C2214yes—
98#2483C2214yes—
99#2483C2214yes—
100#2482C2214yes—
101#2444C22116yes—
102#2443C22116yes—
103#2440C22116yescomplemented
104#2434C2214yes—
105#2419C22116yescomplemented
106#2419C22116yescomplemented
107#2417C2218yescomplemented
108#2415C2218yescomplemented
109#2409C2214yescomplemented
110#2409C2214yescomplemented
111#2405C2214yes—
112#2353C2218yescomplemented
113#2352C2218yescomplemented
114#2327C2218yescomplemented
115#2323C2218yescomplemented
116#2322C2218yescomplemented
117#2317C2214yescomplemented
118#2315C2214yes—
119#2313C2212yes—
120#2312C2212yes—
121#2310C2214yescomplemented
122#2308C2212yes—
123#2308C2214yes—
124C2×#391C2214yescomplemented
125C2×#389C2214yescomplemented
126C2×#387C2218yescomplemented
127C2×#385C2214yes—
128#2283C2212yes—
129#2280C2212yes—
130C2×#381C2214yes—
131C2×#380C2212yes—
132#2273C2212yes—
133C23×Q8C2312yes—
134C23×Q8C2311yescharacteristic
135C23×Q8C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144#554—264no—
145#554—232no—
146D4×Q8—232no—
147#544—216no—
148#543—216no—
149#543—216no—
150#533—216no—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2318yes—
154C2×C4⋊Q8C2318yes—
155#529—264no—
156#529—264no—
157C2×#126—28no—
158C2×#126—28no—
159C2×#126C2318yes—
160C2×#126C2318yes—
161C2×#125—28no—
162C2×#125C2314yes—
163C2×#125C2318yes—
164C2×#125C2318yes—
165C2×#124—28no—
166C2×#124C2318yes—
167C2×#123—28no—
168C2×#123—28no—
169C2×#123C2318yes—
170C2×#123C2318yes—
171C2×#123C2318yes—
172C2×C22⋊Q8—216no—
173C2×C22⋊Q8—216no—
174C2×C22⋊Q8—28no—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×#121—28no—
190C2×#121C2318yes—
191#518—216no—
192C2×C4×Q8—28no—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×D4—28no—
198C2×C4×D4—28no—
199C2×C4×D4D4116yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×#117—28no—
209C2×#117—28no—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2318yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2314yes—
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2314yes—
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2311yescharacteristic
245C22×C42—28no—
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2314yes—
252C22×C42C2314yes—
253C22×C42C2311yescharacteristic
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C23116yes—
258#400C2318yes—
259#400C23116yes—
260#399C2318yes—
261#399C2318yes—
262#398C23116yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C23116yes—
267#398C2318yes—
268#398C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C23116yes—
273#397C23116yes—
274#397C23116yes—
275#396C23116yes—
276#395C2318yes—
277#395C23116yes—
278#395C2318yes—
279#395C2318yes—
280#394C23116yes—
281#393C2318yes—
282#393C2318yes—
283#393C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2318yes—
287#391C2318yes—
288#391C2318yes—
289#391C2318yes—
290#391C2318yes—
291#391C2318yes—
292#391C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C23116yes—
296#389C23116yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#388C23116yes—
301#388C23116yes—
302#388C23116yes—
303#388C23116yes—
304#387C23116yes—
305#387C23116yes—
306#387C23116yes—
307#387C23116yes—
308#387C23116yes—
309#387C23116yes—
310#387C23116yes—
311#387C23116yes—
312#387C23116yes—
313#386C23116yes—
314#386C2318yes—
315#386C2318yes—
316#386C23116yes—
317#386C2318yes—
318#385C23116yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2318yes—
326#385C2318yes—
327#385C2318yes—
328#385C23116yes—
329#384C2318yes—
330#383C2314yes—
331#382C2318yes—
332#382C2318yes—
333#382C2314yes—
334#381C2318yes—
335#381C2318yes—
336#381C2314yes—
337#381C2318yes—
338#381C2318yes—
339#381C2318yes—
340#381C2318yes—
341#381C23116yes—
342#381C2314yes—
343#380C23116yes—
344#380C2314yes—
345#380C2318yes—
346#380C2314yes—
347#380C2314yes—
348#380C2314yes—
349#380C2314yes—
350#379C2318yes—
351#379C2314yes—
352C4×C4⋊C4C2314yes—
353C4×C22⋊C4C2314yes—
354C4×C22⋊C4C2314yes—
355C4×C22⋊C4C2314yes—
356C4×C22⋊C4C23116yes—
357#376C2314yes—
358C2×#95C2314yes—
359C2×#95C2318yes—
360C2×#95C2318yes—
361C2×#95C2318yes—
362C25C2411yescharacteristic
363C25C2411yescharacteristic
364C25C2411yescharacteristic
365C22×Q8—24no—
366C22×Q8—28no—
367C22×Q8—28no—
368C22×Q8—44no—
369C22×Q8—48no—
370C22×Q8—48no—
371C22×Q8C2414yes—
372C22×Q8C2414yes—
373C22×Q8C2414yes—
374C22×Q8C2414yes—
375C22×Q8C2414yes—
376C22×D4—28no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—28no—
380C22×D4—44no—
381C22×D4C2×D418yes—
382C22×D4C2414yes—
383C22×D4C2414yes—
384C22×D4C2414yes—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—28no—
388C23×C4—24no—
389C23×C4—44no—
390C23×C4—44no—
391C23×C4—44no—
392C23×C4—44no—
393C23×C4C2×D418yes—
394C23×C4C2×D418yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2412yes—
400C23×C4C2414yes—
401C23×C4C2414yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2414yes—
410C23×C4C2414yes—
411C23×C4C2418yes—
412C23×C4C2414yes—
413C23×C4C2414yes—
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2412yes—
420C4⋊Q8—232no—
421C4⋊Q8—28no—
422C4⋊Q8—28no—
423C4⋊Q8—416no—
424#126—232no—
425#126—232no—
426#125—232no—
427#125—232no—
428#125—216no—
429#124—232no—
430#123—232no—
431#123—232no—
432#123—416no—
433C22⋊Q8—216no—
434C22⋊Q8—216no—
435C22⋊Q8—216no—
436C22⋊Q8—216no—
437C22⋊Q8—216no—
438C22⋊Q8—216no—
439C22⋊Q8—216no—
440C22⋊Q8—216no—
441C22⋊Q8—232no—
442C22⋊Q8—232no—
443C22⋊Q8—232no—
444C22⋊Q8—232no—
445C22⋊Q8—232no—
446C22⋊Q8—416no—
447#121—232no—
448C4×Q8—216no—
449C4×Q8—216no—
450C4×Q8—216no—
451C4×Q8—216no—
452C4×D4—232no—
453C4×D4—232no—
454C4×D4—216no—
455C4×D4—216no—
456C4×D4—216no—
457C4×D4—216no—
458C4×D4C2×D4132yes—
459C4×D4C2×D4132yes—
460#117—216no—
461#117—216no—
462#117—216no—
463#117—216no—
464#117—216no—
465#117—48no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—216no—
476C2×C4⋊C4—216no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—48no—
480C2×C4⋊C4—416no—
481C2×C4⋊C4C2×D418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C24116yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C24116yes—
505C2×C4⋊C4C24116yes—
506C2×C4⋊C4C24116yes—
507C2×C4⋊C4C2414yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—216no—
513C2×C22⋊C4—216no—
514C2×C22⋊C4—216no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4C2×D418yes—
520C2×C22⋊C4C2×D418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2414yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C24116yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C24116yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C42—24no—
541C2×C42—24no—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—24no—
545C2×C42—216no—
546C2×C42—216no—
547C2×C42C2×D418yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2418yes—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2414yes—
556C2×C42C2414yes—
557C2×C42C2418yes—
558C2×C42C2418yes—
559C2×C42C2412yes—
560C2×C42C2412yes—
561#95C2418yes—
562#95C2418yes—
563#95C24116yes—
564#95C24116yes—
565#95C24116yes—
566#95C24116yes—
567#95C24116yes—
568#95C24116yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C24116yes—
574#95C24116yes—
575#95C24116yes—
576#95C24116yes—
577C24—24no—
578C24—22no—
579C24—24no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24C22×D414yes—
587C24C22×D414yes—
588C242−1+418yes—
589C24C2512yes—
590C24C2512yes—
591C24C2511yescharacteristic
592C24C2512yes—
593C2×Q8—28no—
594C2×Q8—28no—
595C2×Q8—28no—
596C2×Q8—28no—
597C2×Q8—28no—
598C2×Q8—216no—
599C2×Q8—28no—
600C2×Q8—44no—
601C2×Q8—48no—
602C2×Q8—48no—
603C2×Q8—48no—
604C2×Q8—416no—
605C2×Q8—816no—
606C2×Q8—816no—
607C2×D4—232no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—416no—
617C2×D4—416no—
618C2×D4C22×D4116yes—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—24no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—216no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—416no—
648C22×C4—416no—
649C22×C4—42no—
650C22×C4—44no—
651C22×C4—42no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—48no—
664C22×C4—48no—
665C22×C4—416no—
666C22×C4—416no—
667C22×C4—416no—
668C22×C4C22×D414yes—
669C22×C4C22×D418yes—
670C22×C4C22×D414yes—
671C22×C4C22×D418yes—
672C22×C4C22×D414yes—
673C22×C4C22×D418yes—
674C22×C4C22×D414yes—
675C22×C4C22×D414yes—
676C22×C4C22×D418yes—
677C22×C4C2512yes—
678C22×C4C2512yes—
679C22×C4C25116yes—
680C22×C4C2512yes—
681C22×C4C2518yes—
682C22×C4C2512yes—
683C22×C4C2512yes—
684C22×C4C2518yes—
685C22×C4C2512yes—
686C22×C4C2511yescharacteristic
687C22×C4C2512yes—
688C22×C4C2512yes—
689C22×C4C2512yes—
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2511yescharacteristic
693C4⋊C4—216no—
694C4⋊C4—28no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—216no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—232no—
714C4⋊C4—48no—
715C4⋊C4—416no—
716C4⋊C4—416no—
717C4⋊C4—416no—
718C4⋊C4C22×D4116yes—
719C22⋊C4—216no—
720C22⋊C4—28no—
721C22⋊C4—28no—
722C22⋊C4—216no—
723C22⋊C4—216no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—216no—
727C22⋊C4—216no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—48no—
733C22⋊C4—416no—
734C22⋊C4—48no—
735C22⋊C4—416no—
736C22⋊C4C22×D4116yes—
737C22⋊C4C22×D4116yes—
738C42—24no—
739C42—24no—
740C42—24no—
741C42—24no—
742C42—28no—
743C42—28no—
744C42—24no—
745C42—24no—
746C42—216no—
747C42—48no—
748C42—48no—
749C42C22×D418yes—
750C42C22×D418yes—
751C23—24no—
752C23—24no—
753C23—22no—
754C23—22no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—28no—
759C23—22no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—44no—
764C23—44no—
765C23—416no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—88no—
772C23—88no—
773C23#536116yes—
774C23C23×D414yes—
775C23C23×D412yes—
776C23C23×D414yes—
777C23C2×2−1+414yes—
778C23C2×2−1+414yes—
779C23C2×2−1+414yes—
780C23C2611yescharacteristic
781Q8—416no—
782Q8—416no—
783Q8—88no—
784Q8—88no—
785Q8—88no—
786D4—232no—
787D4—416no—
788D4—416no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—216no—
800C2×C4—216no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—22no—
809C2×C4—216no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—216no—
814C2×C4—216no—
815C2×C4—216no—
816C2×C4—216no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—416no—
826C2×C4—48no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—416no—
833C2×C4—44no—
834C2×C4—48no—
835C2×C4—88no—
836C2×C4—88no—
837C2×C4—816no—
838C2×C4—88no—
839C2×C4—88no—
840C2×C4C23×D412yes—
841C2×C4C23×D414yes—
842C2×C4C23×D414yes—
843C2×C4C23×D414yes—
844C2×C4C23×D414yes—
845C2×C4C23×D412yes—
846C2×C4#58514yes—
847C2×C4#58514yes—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—24no—
852C22—28no—
853C22—28no—
854C22—28no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—416no—
859C22—48no—
860C22—42no—
861C22—42no—
862C22—48no—
863C22—42no—
864C22—88no—
865C22—88no—
866C22C2×#53614yes—
867C22C2×#53618yes—
868C22C24×D411yescharacteristic
869C22C22×2−1+412yes—
870C22C2×#58512yes—
871C22C2×#58512yes—
872C4—22no—
873C4—24no—
874C4—24no—
875C4—24no—
876C4—24no—
877C4—24no—
878C4—42no—
879C4—48no—
880C4—42no—
881C4—42no—
882C4—48no—
883C4—416no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4#348514yes—
888C2—24no—
889C2—28no—
890C2—44no—
891C2—82no—
892C2C22×#53611yescharacteristic
893C2C2×#348511yescharacteristic
894C2#6281111yescharacteristic
895C2#6282314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
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×#3501C2semidirect
3. #38363C2semidirect
4. #38040C2semidirect
5. #38027C2semidirect
6. #36970C2semidirect
7. #36966C2semidirect
8. #36962C2semidirect
9. #36959C2semidirect
10. C2×#2855C2semidirect
11. #35455C2semidirect
12. #35448C2semidirect
13. #35391C2semidirect
15. #35325C2semidirect
16. #35311C2semidirect
17. #35248C2semidirect
18. #35084C2semidirect
19. #35010C2semidirect
20. #34185C2semidirect
22. C2×#554C22semidirect
23. C2×#554C22semidirect
24. C2×D4×Q8C22semidirect
55. #2855C22semidirect
56. #2855C22semidirect
58. #2721C22semidirect
59. #2719C22semidirect
60. #2716C22semidirect
61. #2713C22semidirect
62. #2700C22semidirect
63. #2698C22semidirect
64. #2689C22semidirect
65. #2674C22semidirect
66. #2638C22semidirect
67. #2634C22semidirect
68. #2628C22semidirect
71. #2625C22semidirect
72. #2621C22semidirect
73. #2611C22semidirect
74. #2599C22semidirect
77. #2581C22semidirect
78. #2579C22semidirect
79. #2568C22semidirect
80. #2564C22semidirect
83. #2549C22semidirect
84. #2546C22semidirect
88. #2499C22semidirect
89. #2488C22semidirect
90. #2488C22semidirect
91. #2487C22semidirect
92. #2486C22semidirect
96. #2484C22semidirect
103. #2440C22semidirect
105. #2419C22semidirect
106. #2419C22semidirect
107. #2417C22semidirect
108. #2415C22semidirect
109. #2409C22semidirect
110. #2409C22semidirect
112. #2353C22semidirect
113. #2352C22semidirect
114. #2327C22semidirect
115. #2323C22semidirect
116. #2322C22semidirect
117. #2317C22semidirect
121. #2310C22semidirect
124. C2×#391C22semidirect
125. C2×#389C22semidirect
126. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
C22×#5292
#383632
#380402
#380272
#369702
#369662
#369622
#369592
C2×#28552
#354552
#354482
#353912
#353512
#353252
#353112
#352482
#350842
#350102
#341852