Finite Group Databasebeta

← #7631719

Subgroups — #7631719

Order 512.

8588 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#36361C218yesmaximal, complemented
4#36157C218yesmaximal, complemented
5#36032C218yesmaximal, complemented
6#35840C218yesmaximal, complemented
7#35454C214yesmaximal, complemented
8#35354C214yesmaximal, complemented
9#35351C212yesmaximal, complemented
10#35347C212yesmaximal, complemented
11#35138C212yesmaximal, complemented
12#35076C212yesmaximal, complemented
13#35000C212yesmaximal, complemented
14#34963C212yesmaximal, complemented
15#34809C212yesmaximal, complemented
16C2×#2487C212yesmaximal, complemented
17#34264C214yesmaximal, complemented
18#34185C211yesmaximal, characteristic, complemented
19C22×H(5,𝔽2)C2211yescharacteristic
20C2×#553—216no—
21C2×#553C2218yescomplemented
22C2×#553C2218yescomplemented
23C2×#534C2214yes—
24C22×#126C2212yescomplemented
25C22×#125C2211yescharacteristic, complemented
26C22×#123C2212yescomplemented
27C22×#121C2212yes—
28C22×#121C2211yescharacteristic, complemented
29C22×#121C2211yescharacteristic, complemented
30C4×H(5,𝔽2)—216no—
31C2×#520C2212yes—
32C2×#520C2214yescomplemented
33C2×#518C2211yescharacteristic
34C2×#518C2212yes—
35C2×#518C2212yes—
36C2×#518C2214yescomplemented
37C2×C4×#41C2212yes—
38C2×C4×#41C2214yescomplemented
39C22×C4×D4C2212yes—
40C22×C4×D4C2212yes—
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2214yescomplemented
43C22×C4×D4C2211yescharacteristic, complemented
44C22×C4×D4C2212yescomplemented
45C22×#117C2211yescharacteristic, complemented
46C23×C4⋊C4C2211yescharacteristic, complemented
47#2854C2214yescomplemented
48#2854C2214yescomplemented
49#2851C2218yescomplemented
50#2847C2214yescomplemented
51#2847C2214yescomplemented
52#2635C2218yescomplemented
53#2634C2214yescomplemented
54#2633C2214yescomplemented
55#2618C2214yescomplemented
56#2617C2214yescomplemented
57#2611C2218yescomplemented
58#2598C2218yescomplemented
59#2591C2214yescomplemented
60#2584C2214yescomplemented
61#2580C2214yescomplemented
62#2562C2214yescomplemented
63#2543C2218yescomplemented
64#2539C2214yescomplemented
65#2535C2214yescomplemented
66#2534C2218yescomplemented
67#2487C2218yescomplemented
68#2487C2214yescomplemented
69#2487C2218yescomplemented
70#2487C2218yescomplemented
71#2487C2214yescomplemented
72#2486C2214yescomplemented
73#2485C2218yescomplemented
74#2484C2214yescomplemented
75#2484C2214yescomplemented
76#2483C2214yescomplemented
77#2482C2214yescomplemented
78#2482C2214yescomplemented
79#2481C22116yescomplemented
80#2479C22116yescomplemented
81#2470C22116yescomplemented
82#2469C22116yescomplemented
83#2467C22116yescomplemented
84#2457C22116yescomplemented
85#2455C22116yescomplemented
86#2444C22116yescomplemented
87#2443C22116yescomplemented
88#2430C22116yescomplemented
89#2418C22116yescomplemented
90#2416C2218yescomplemented
91#2414C2218yescomplemented
92#2410C22116yescomplemented
93#2408C2214yescomplemented
94#2406C2214yes—
95#2405C2214yes—
96#2405C2214yescomplemented
97#2404C2214yes—
98#2403C2214yes—
99#2398C2214yescomplemented
100#2397C2214yescomplemented
101#2395C2218yescomplemented
102C2×#400C2214yescomplemented
103C2×#399C2214yescomplemented
104#2364C22116yescomplemented
105#2361C22116yescomplemented
106#2359C22116yescomplemented
107#2358C22116yescomplemented
108#2353C2218yescomplemented
109#2352C2218yescomplemented
110#2322C2218yescomplemented
111#2321C2218yescomplemented
112#2313C2212yescomplemented
113#2312C2212yescomplemented
114#2308C2212yes—
115#2308C2214yescomplemented
116C4×#123C2218yescomplemented
117C4×#121C2218yescomplemented
118C4×#120C2218yescomplemented
119#2296C2214yescomplemented
120C2×#389C2214yescomplemented
121C2×#386C2214yes—
122C2×#385C2214yescomplemented
123#2283C2212yescomplemented
124#2280C2212yescomplemented
125#2280C2214yescomplemented
126C2×#380C2214yescomplemented
127C2×#380C2212yescomplemented
128#2273C2212yescomplemented
129C2×H(5,𝔽2)—28no—
130C2×H(5,𝔽2)—216no—
131C22×#41C2312yes—
132C22×#41C2314yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2314yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2312yes—
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146#553—264no—
147#553—264no—
148#534—232no—
149C2×#126—216no—
150C2×#126C23116yes—
151C2×#125—28no—
152C2×#125C2314yes—
153C2×#125C2314yes—
154C2×#123—216no—
155C2×#123C2318yes—
156C2×#123C2318yes—
157C2×#123C23116yes—
158C2×#123C2318yes—
159C2×#121—216no—
160C2×#121—28no—
161C2×#121—28no—
162C2×#121C2314yes—
163C2×#121C2314yes—
164C2×#121C2314yes—
165C2×#121C23116yes—
166C2×#121C2314yes—
167C2×#121C23116yes—
168C2×#121C2318yes—
169C2×#120C2318yes—
170C2×#120C2318yes—
171C2×#120C2318yes—
172#520—232no—
173#520—216no—
174#518—28no—
175#518—232no—
176#518—216no—
177#518—216no—
178C4×#41—232no—
179C4×#41—216no—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2314yes—
183C2×C4×D4—216no—
184C2×C4×D4—216no—
185C2×C4×D4—232no—
186C2×C4×D4—216no—
187C2×C4×D4—28no—
188C2×C4×D4D4116yescomplemented
189C2×C4×D4C2312yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C23116yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C23116yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×#117—28no—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C22×C4⋊C4—28no—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2314yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2318yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4C2314yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2318yes—
248C22×C22⋊C4C2311yescharacteristic
249C22×C22⋊C4C2311yescharacteristic
250C22×C42C2314yes—
251C22×C42C2312yes—
252C22×C42C2312yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C23116yes—
259#399C2318yes—
260#399C2318yes—
261#399C2318yes—
262#399C23116yes—
263#398C2318yes—
264#398C2318yes—
265#397C2318yes—
266#397C23116yes—
267#397C2318yes—
268#396C23116yes—
269#395C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C23116yes—
273#394C23116yes—
274#394C23116yes—
275#393C2318yes—
276#392C2318yes—
277#392C23116yes—
278#392C2318yes—
279#390C23116yes—
280#390C2318yes—
281#389C23116yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C23116yes—
286#388C23116yes—
287#388C23116yes—
288#388C23116yes—
289#388C23116yes—
290#388C23116yes—
291#388C23116yes—
292#388C23116yes—
293#387C23116yes—
294#387C23116yes—
295#387C23116yes—
296#387C23116yes—
297#386C23116yes—
298#386C2318yes—
299#386C2318yes—
300#386C23116yes—
301#386C2318yes—
302#386C23116yes—
303#386C2318yes—
304#386C2318yes—
305#386C23116yes—
306#386C23116yes—
307#386C23116yes—
308#386C23116yes—
309#386C2318yes—
310#385C2318yes—
311#385C23116yes—
312#385C23116yes—
313#385C23116yes—
314#385C23116yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#383C2314yes—
319#382C2314yes—
320#381C2314yes—
321#381C2318yes—
322#381C2314yes—
323#381C2318yes—
324#380C2318yes—
325#380C2318yes—
326#380C2314yes—
327#380C2314yes—
328#380C2314yes—
329#380C2314yes—
330#380C2314yes—
331#380C23116yes—
332#380C2318yes—
333#379C2314yes—
334#379C2318yes—
335#379C2318yes—
336C4×C4⋊C4C2314yes—
337C4×C4⋊C4C23116yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C23116yes—
342C4×C22⋊C4C23116yes—
343C4×C22⋊C4C23116yes—
344#376C2314yes—
345C2×#95C2314yes—
346C2×#95C2318yes—
347C2×#95C2318yes—
348C25C2412yes—
349C25C2412yes—
350C25C2411yescharacteristic
351C25C2412yes—
352C25C2411yescharacteristic
353H(5,𝔽2)—2128no—
354C2×#41—216no—
355C2×#41—216no—
356C2×#41—216no—
357C2×#41—28no—
358C2×#41—216no—
359C22×Q8C2412yes—
360C22×D4—28no—
361C22×D4—28no—
362C22×D4—216no—
363C22×D4—28no—
364C22×D4—28no—
365C22×D4—216no—
366C22×D4—216no—
367C22×D4—216no—
368C22×D4—28no—
369C22×D4—216no—
370C22×D4—28no—
371C22×D4—24no—
372C22×D4—44no—
373C22×D4—84no—
374C22×D4C2×D418yes—
375C22×D4#41116yes—
376C22×D4C2412yes—
377C22×D4C2414yes—
378C22×D4C2418yes—
379C22×D4C2412yes—
380C22×D4C2414yes—
381C22×D4C2414yes—
382C22×D4C2414yes—
383C22×D4C2412yes—
384C22×D4C24116yes—
385C22×D4C2418yes—
386C23×C4—28no—
387C23×C4—28no—
388C23×C4—28no—
389C23×C4—28no—
390C23×C4—44no—
391C23×C4—44no—
392C23×C4—48no—
393C23×C4—48no—
394C23×C4—84no—
395C23×C4—84no—
396C23×C4C2×D418yes—
397C23×C4C2×D418yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2414yes—
401C23×C4C2414yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2418yes—
409C23×C4C2412yes—
410C23×C4C2414yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2418yes—
414C23×C4C2412yes—
415C23×C4C2414yes—
416C23×C4C2414yes—
417C23×C4C2412yes—
418C23×C4C2418yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424#126—264no—
425#125—216no—
426#125—216no—
427#123—232no—
428#123—232no—
429#123—264no—
430#123—88no—
431#121—264no—
432#121—264no—
433#121—216no—
434#121—216no—
435#121—216no—
436#121—216no—
437#121—416no—
438#120—232no—
439#120—232no—
440#120—88no—
441C4×Q8—216no—
442C4×Q8—28no—
443C4×Q8—28no—
444C4×D4—216no—
445C4×D4—216no—
446C4×D4—216no—
447C4×D4—216no—
448C4×D4—216no—
449C4×D4—216no—
450C4×D4—216no—
451C4×D4—216no—
452C4×D4—216no—
453C4×D4—216no—
454C4×D4—216no—
455C4×D4—216no—
456C4×D4—216no—
457C4×D4—264no—
458C4×D4—216no—
459C4×D4—216no—
460C4×D4—28no—
461C4×D4—216no—
462C4×D4—216no—
463C4×D4—28no—
464C4×D4—816no—
465C4×D4C2×D4132yes—
466C4×D4C2×D4132yes—
467#117—216no—
468#117—216no—
469#117—28no—
470#117—216no—
471#117—216no—
472#117—216no—
473#117—216no—
474#117—48no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—216no—
479C2×C4⋊C4—216no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—28no—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—28no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—216no—
486C2×C4⋊C4—48no—
487C2×C4⋊C4—88no—
488C2×C4⋊C4C2×D418yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C24116yes—
506C2×C4⋊C4C24116yes—
507C2×C4⋊C4C24116yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C22⋊C4—28no—
511C2×C22⋊C4—28no—
512C2×C22⋊C4—28no—
513C2×C22⋊C4—216no—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—28no—
516C2×C22⋊C4—28no—
517C2×C22⋊C4—28no—
518C2×C22⋊C4—28no—
519C2×C22⋊C4—216no—
520C2×C22⋊C4—216no—
521C2×C22⋊C4—88no—
522C2×C22⋊C4C2×D418yes—
523C2×C22⋊C4C2×D418yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C24116yes—
538C2×C22⋊C4C24116yes—
539C2×C22⋊C4C24116yes—
540C2×C22⋊C4C24116yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C24116yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C24116yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C42—28no—
548C2×C42—28no—
549C2×C42—28no—
550C2×C42—216no—
551C2×C42C2×D418yes—
552C2×C42C2414yes—
553C2×C42C2414yes—
554C2×C42C2414yes—
555C2×C42C2414yes—
556C2×C42C2418yes—
557C2×C42C2414yes—
558C2×C42C2418yes—
559C2×C42C2418yes—
560C2×C42C2412yes—
561C2×C42C2412yes—
562#95C2418yes—
563#95C24116yes—
564#95C24116yes—
565#95C24116yes—
566#95C2418yes—
567#95C24116yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C24116yes—
572#95C2418yes—
573#95C24116yes—
574C24—24no—
575C24—24no—
576C24—28no—
577C24—24no—
578C24—24no—
579C24—24no—
580C24—28no—
581C24—42no—
582C24—42no—
583C24—44no—
584C24—44no—
585C24—42no—
586C24—44no—
587C24—44no—
588C24—42no—
589C24—44no—
590C24—44no—
591C24C22×D414yes—
592C24C22×D414yes—
593C24C2×#4118yes—
594C24C2×#4118yes—
595C24C2514yes—
596C24C2512yes—
597C24C2514yes—
598C24C2511yescharacteristic
599C24C2512yes—
600#41—264no—
601#41—2128no—
602C2×Q8—24no—
603C2×Q8—28no—
604C2×D4—2128no—
605C2×D4—264no—
606C2×D4—232no—
607C2×D4—264no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—216no—
618C2×D4—216no—
619C2×D4—216no—
620C2×D4—216no—
621C2×D4—232no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—44no—
628C2×D4—416no—
629C2×D4—416no—
630C2×D4—48no—
631C2×D4—416no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—816no—
635C2×D4C22×D4116yes—
636C2×D4C2×#41116yes—
637C2×D4C2×#41116yes—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—28no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—28no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—216no—
658C22×C4—216no—
659C22×C4—28no—
660C22×C4—216no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—216no—
665C22×C4—416no—
666C22×C4—416no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—42no—
670C22×C4—44no—
671C22×C4—42no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—44no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4—416no—
681C22×C4—44no—
682C22×C4—48no—
683C22×C4—48no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—816no—
687C22×C4—816no—
688C22×C4—816no—
689C22×C4—816no—
690C22×C4C22×D418yes—
691C22×C4C22×D418yes—
692C22×C4C22×D414yes—
693C22×C4C22×D414yes—
694C22×C4C22×D414yes—
695C22×C4C22×D414yes—
696C22×C4C22×D414yes—
697C22×C4C22×D418yes—
698C22×C4C22×D418yes—
699C22×C4C2×#4118yes—
700C22×C4C25116yes—
701C22×C4C2514yes—
702C22×C4C2514yes—
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2512yes—
707C22×C4C2511yescharacteristic
708C22×C4C2512yes—
709C22×C4C2512yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2511yescharacteristic
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—216no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—28no—
727C4⋊C4—24no—
728C4⋊C4—232no—
729C4⋊C4—216no—
730C4⋊C4—48no—
731C4⋊C4—416no—
732C4⋊C4—416no—
733C4⋊C4C22×D4116yes—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—216no—
738C22⋊C4—216no—
739C22⋊C4—216no—
740C22⋊C4—232no—
741C22⋊C4—28no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—216no—
746C22⋊C4—216no—
747C22⋊C4—216no—
748C22⋊C4—232no—
749C22⋊C4—416no—
750C22⋊C4—416no—
751C22⋊C4—48no—
752C22⋊C4—416no—
753C22⋊C4—48no—
754C22⋊C4—416no—
755C22⋊C4C22×D4116yes—
756C22⋊C4C22×D4116yes—
757C42—28no—
758C42—28no—
759C42—28no—
760C42—28no—
761C42—28no—
762C42—216no—
763C42—48no—
764C42—48no—
765C42C22×D418yes—
766C42C22×D418yes—
767C23—24no—
768C23—22no—
769C23—24no—
770C23—22no—
771C23—216no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—28no—
777C23—28no—
778C23—24no—
779C23—28no—
780C23—216no—
781C23—24no—
782C23—28no—
783C23—28no—
784C23—28no—
785C23—44no—
786C23—44no—
787C23—416no—
788C23—44no—
789C23—44no—
790C23—416no—
791C23—48no—
792C23—48no—
793C23—48no—
794C23—84no—
795C23—84no—
796C23—88no—
797C23—88no—
798C23—816no—
799C23—84no—
800C23—816no—
801C23—84no—
802C23#525116yes—
803C23C23×D414yes—
804C23C23×D412yes—
805C23C23×D414yes—
806C23C22×#4118yes—
807C23C22×#4114yes—
808C23C22×#4114yes—
809C23C22×#4114yes—
810C23C2611yescharacteristic
811Q8—216no—
812D4—216no—
813D4—232no—
814D4—232no—
815D4—232no—
816D4—232no—
817D4—48no—
818D4—432no—
819D4—48no—
820D4—832no—
821D4—816no—
822C2×C4—232no—
823C2×C4—216no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—216no—
833C2×C4—28no—
834C2×C4—216no—
835C2×C4—216no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—216no—
842C2×C4—28no—
843C2×C4—216no—
844C2×C4—28no—
845C2×C4—216no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—48no—
856C2×C4—48no—
857C2×C4—48no—
858C2×C4—416no—
859C2×C4—88no—
860C2×C4—88no—
861C2×C4—88no—
862C2×C4—816no—
863C2×C4—816no—
864C2×C4—84no—
865C2×C4—84no—
866C2×C4—84no—
867C2×C4—84no—
868C2×C4—816no—
869C2×C4C23×D414yes—
870C2×C4C23×D414yes—
871C2×C4C23×D414yes—
872C2×C4C23×D414yes—
873C2×C4C23×D412yes—
874C2×C4C23×D412yes—
875C2×C4C22×#4118yes—
876C2×C4#58514yes—
877C22—28no—
878C22—28no—
879C22—28no—
880C22—22no—
881C22—24no—
882C22—22no—
883C22—24no—
884C22—216no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—28no—
889C22—416no—
890C22—48no—
891C22—48no—
892C22—44no—
893C22—44no—
894C22—416no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—88no—
899C22—816no—
900C22—816no—
901C22—816no—
902C22C2×#52514yes—
903C22C2×#52518yes—
904C22C24×D411yescharacteristic
905C22C23×#4112yes—
906C22C2×#58512yes—
907C22H(7,𝔽2)12yes—
908C4—22no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—24no—
913C4—28no—
914C4—416no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4—44no—
919C4—44no—
920C4#348514yes—
921C2—24no—
922C2—28no—
923C2—48no—
924C2—44no—
925C2—84no—
926C2C22×#52511yescharacteristic
927C2C2×#348511yescharacteristic
928C2#6285211yescharacteristic
929C2#6299214yes—
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. C22×#553C2semidirect
2. C2×C4×H(5,𝔽2)C2semidirect
3. #36361C2semidirect
4. #36157C2semidirect
5. #36032C2semidirect
6. #35840C2semidirect
7. #35454C2semidirect
8. #35354C2semidirect
9. #35351C2semidirect
10. #35347C2semidirect
11. #35138C2semidirect
12. #35076C2semidirect
13. #35000C2semidirect
14. #34963C2semidirect
15. #34809C2semidirect
16. C2×#2487C2semidirect
17. #34264C2semidirect
18. #34185C2semidirect
21. C2×#553C22semidirect
22. C2×#553C22semidirect
24. C22×#126C22semidirect
25. C22×#125C22semidirect
26. C22×#123C22semidirect
28. C22×#121C22semidirect
29. C22×#121C22semidirect
32. C2×#520C22semidirect
36. C2×#518C22semidirect
38. C2×C4×#41C22semidirect
42. C22×C4×D4C22semidirect
43. C22×C4×D4C22semidirect
44. C22×C4×D4C22semidirect
45. C22×#117C22semidirect
46. C23×C4⋊C4C22semidirect
47. #2854C22semidirect
48. #2854C22semidirect
49. #2851C22semidirect
50. #2847C22semidirect
51. #2847C22semidirect
52. #2635C22semidirect
53. #2634C22semidirect
54. #2633C22semidirect
55. #2618C22semidirect
56. #2617C22semidirect
57. #2611C22semidirect
58. #2598C22semidirect
59. #2591C22semidirect
60. #2584C22semidirect
61. #2580C22semidirect
62. #2562C22semidirect
63. #2543C22semidirect
64. #2539C22semidirect
65. #2535C22semidirect
66. #2534C22semidirect
67. #2487C22semidirect
68. #2487C22semidirect
69. #2487C22semidirect
70. #2487C22semidirect
71. #2487C22semidirect
72. #2486C22semidirect
73. #2485C22semidirect
74. #2484C22semidirect
75. #2484C22semidirect
76. #2483C22semidirect
77. #2482C22semidirect
78. #2482C22semidirect
79. #2481C22semidirect
80. #2479C22semidirect
81. #2470C22semidirect
82. #2469C22semidirect
83. #2467C22semidirect
84. #2457C22semidirect
85. #2455C22semidirect
86. #2444C22semidirect
87. #2443C22semidirect
88. #2430C22semidirect
89. #2418C22semidirect
90. #2416C22semidirect
91. #2414C22semidirect
92. #2410C22semidirect
93. #2408C22semidirect
96. #2405C22semidirect
99. #2398C22semidirect
100. #2397C22semidirect
101. #2395C22semidirect
102. C2×#400C22semidirect
103. C2×#399C22semidirect
104. #2364C22semidirect
105. #2361C22semidirect
106. #2359C22semidirect
107. #2358C22semidirect
108. #2353C22semidirect
109. #2352C22semidirect
110. #2322C22semidirect
111. #2321C22semidirect
112. #2313C22semidirect
113. #2312C22semidirect
115. #2308C22semidirect
116. C4×#123C22semidirect
117. C4×#121C22semidirect
118. C4×#120C22semidirect
119. #2296C22semidirect
120. C2×#389C22semidirect
122. C2×#385C22semidirect
123. #2283C22semidirect
124. #2280C22semidirect
125. #2280C22semidirect
126. C2×#380C22semidirect
127. C2×#380C22semidirect
128. #2273C22semidirect
188. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5532
C2×C4×H(5,𝔽2)2
#363612
#361572
#360322
#358402
#354542
#353542
#353512
#353472
#351382
#350762
#350002
#349632
#348092
C2×#24872
#342642
#341852