Finite Group Databasebeta

← #7674222

Subgroups — #7674222

Order 512.

6946 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C2×#3506C211yesmaximal, characteristic
3#45313C218yesmaximal, complemented
4#45270C214yesmaximal, complemented
5#44937C214yesmaximal, complemented
6#39174C214yesmaximal, complemented
7#39168C214yesmaximal, complemented
8#39164C214yesmaximal, complemented
9#39162C214yesmaximal, complemented
10#37753C218yesmaximal, complemented
11#37707C218yesmaximal, complemented
12#35677C212yesmaximal, complemented
13#35532C212yesmaximal, complemented
14#35264C212yesmaximal, complemented
15#35178C211yesmaximal, characteristic, complemented
16#35172C211yesmaximal, characteristic, complemented
17#34637C211yesmaximal, characteristic, complemented
18#34276C212yesmaximal, complemented
19#34074C211yesmaximal, characteristic, complemented
20C2×#2326C211yesmaximal, characteristic, complemented
21#3506—216no—
22#3502—216no—
23C2×#559C2214yes—
24C2×Q82C2212yescomplemented
25C2×Q82C2212yescomplemented
26C2×#557C2214yescomplemented
27C2×#557C2214yescomplemented
28C2×#557C2212yescomplemented
29C2×#557C2212yescomplemented
30C2×#556C2212yes—
31C2×#555C2212yes—
32C2×#553C2214yes—
33C2×#550C2212yes—
34C2×#547C2212yes—
35C2×#544C2214yes—
36C2×#544C2212yes—
37C2×#538C2214yes—
38C2×#536C2212yes—
39C2×#535C2212yes—
40C2×#533C2214yes—
41C2×#533C2211yescharacteristic
42C2×#533C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C22×#124C2211yescharacteristic
45C2×#525C2214yes—
46C2×#520C2212yes—
47C2×#519C2212yes—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50#2861C2214yes—
51#2858C2214yes—
52#2854C2214yes—
53#2848C2214yes—
54#2731C22116yescomplemented
55#2729C22116yescomplemented
56#2725C22116yescomplemented
57#2711C22116yescomplemented
58#2711C22116yescomplemented
59#2707C22116yescomplemented
60#2674C22116yescomplemented
61#2674C22116yescomplemented
62#2642C2212yescomplemented
63#2641C2214yes—
64#2641C2212yescomplemented
65#2640C2214yes—
66#2640C2212yescomplemented
67#2640C2212yescomplemented
68#2639C2214yes—
69#2639C2214yes—
70#2626C2214yes—
71#2618C2214yes—
72#2580C2214yes—
73#2567C2214yescomplemented
74#2566C2214yes—
75#2566C2214yescomplemented
76#2565C2214yescomplemented
77#2563C2212yes—
78#2548C2214yes—
79#2548C2214yes—
80#2548C2212yescomplemented
81#2546C2212yescomplemented
82#2545C2214yes—
83#2545C2214yes—
84#2545C2214yescomplemented
85#2542C2212yes—
86#2542C2214yescomplemented
87#2538C2214yes—
88#2538C2214yescomplemented
89#2536C2214yescomplemented
90#2491C2218yes—
91#2490C2218yes—
92#2475C22116yescomplemented
93#2472C22116yes—
94#2469C22116yescomplemented
95#2460C22116yescomplemented
96#2458C22116yescomplemented
97#2452C22116yescomplemented
98#2449C22116yes—
99#2448C22116yescomplemented
100#2441C2218yescomplemented
101#2440C2218yescomplemented
102#2432C22116yescomplemented
103#2426C2218yes—
104#2426C2218yes—
105#2426C22116yescomplemented
106#2411C22116yes—
107#2398C2214yescomplemented
108#2398C2214yescomplemented
109#2362C2218yescomplemented
110#2360C2218yescomplemented
111#2359C22116yes—
112#2331C2212yescomplemented
113#2331C2212yescomplemented
114#2330C2214yescomplemented
115#2329C2214yes—
116#2329C2214yes—
117#2327C2214yescomplemented
118#2326C2214yes—
119#2326C2214yes—
120#2326C2214yes—
121#2326C2214yes—
122#2326C2214yescomplemented
123#2317C2212yes—
124#2311C2212yes—
125#2309C2212yes—
126C4×C4⋊Q8C2214yescomplemented
127C4×#124C2214yescomplemented
128#2297C2212yes—
129#2297C2212yes—
130#2296C2212yes—
131#2295C2214yescomplemented
132#2295C2214yescomplemented
133C2×#391C2211yescharacteristic
134C2×#390C2211yescharacteristic
135C2×#388C2214yes—
136C2×#385C2214yes—
137#2285C2211yescharacteristic
138C2×#384C2211yescharacteristic
139C4×#117C2212yes—
140C2×#376C2211yescharacteristic
141C22×#41C2312yes—
142C22×#41C2314yes—
143C23×Q8C2311yescharacteristic
144C23×D4C2311yescharacteristic
145C24×C4C2312yes—
146#559—232no—
147Q82—216no—
148Q82—216no—
149#557—216no—
150#557—232no—
151#557—232no—
152#557—216no—
153#556—216no—
154#555—216no—
155#553—232no—
156#550—216no—
157#547—216no—
158#544—232no—
159#544—216no—
160#538—232no—
161#536—216no—
162#535—216no—
163#533—232no—
164#533—28no—
165#533D4116yes—
166#532—28no—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2318yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2318yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2311yescharacteristic
178C2×C4⋊Q8C2311yescharacteristic
179C2×#127C2314yes—
180C2×#127C2311yescharacteristic
181C2×#126C2318yes—
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2318yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#125C2318yes—
188C2×#125C2312yes—
189C2×#124—28no—
190C2×#124C2314yes—
191C2×#124C2314yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194C2×#124C2312yes—
195C2×#124C2318yes—
196C2×#124C23116yes—
197#525—232no—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×C22⋊Q8C23116yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#120C2318yes—
217#520—216no—
218#519—216no—
219C2×C4×Q8—28no—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2318yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×D4—28no—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2318yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2318yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2312yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2314yes—
260C22×C42C2312yes—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#400C2318yes—
265#400C2318yes—
266#399C2318yes—
267#399C23116yes—
268#398C23116yes—
269#398C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C23116yes—
273#396C23116yes—
274#396C23116yes—
275#396C23116yes—
276#396C23116yes—
277#396C23116yes—
278#395C23116yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C23116yes—
283#394C23116yes—
284#394C23116yes—
285#394C23116yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C23116yes—
290#391C2312yes—
291#391C2314yes—
292#391C2312yes—
293#391C2314yes—
294#391C2312yes—
295#391C2314yes—
296#391C2312yes—
297#391C2318yes—
298#391C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2318yes—
302#390C2312yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2312yes—
307#390C2318yes—
308#390C23116yes—
309#390C2312yes—
310#390C2312yes—
311#390C23116yes—
312#390C23116yes—
313#389C23116yes—
314#389C23116yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#388C23116yes—
322#388C23116yes—
323#388C23116yes—
324#388C23116yes—
325#388C23116yes—
326#388C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C23116yes—
330#387C23116yes—
331#387C23116yes—
332#387C23116yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#385C23116yes—
341#385C23116yes—
342#385C2318yes—
343#385C23116yes—
344#385C23116yes—
345#385C23116yes—
346#385C2318yes—
347#384C2314yes—
348#384C2314yes—
349#384C2314yes—
350#384C2312yes—
351#382C2314yes—
352#382C2312yes—
353#380C2318yes—
354#380C2318yes—
355#380C2312yes—
356#380C2312yes—
357#379C2318yes—
358C4×C4⋊C4C23116yes—
359C4×C4⋊C4C2312yes—
360C4×C4⋊C4C2314yes—
361C4×C4⋊C4C2312yes—
362C4×C4⋊C4C2314yes—
363C4×C4⋊C4C2314yes—
364C4×C4⋊C4C2314yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C23116yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369#376C2312yes—
370#376C2312yes—
371#376C2312yes—
372#376C2312yes—
373#376C2314yes—
374C2×#95C2312yes—
375C2×#95C2312yes—
376C2×#95C2314yes—
377C43C2314yes—
378C25C2412yes—
379C2×#41—216no—
380C2×#41—28no—
381C2×#41—28no—
382C2×#41—28no—
383C2×#41—88no—
384C22×Q8—24no—
385C22×Q8—24no—
386C22×Q8#4118yescomplemented
387C22×Q8C2412yes—
388C22×Q8C2412yes—
389C22×Q8C2412yes—
390C22×Q8C2412yes—
391C22×Q8C2412yes—
392C22×Q8C2418yes—
393C22×Q8C2412yes—
394C22×Q8C2412yes—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4C2414yes—
399C22×D4C2412yes—
400C22×D4C2412yes—
401C22×D4C2412yes—
402C22×D4C2418yes—
403C22×D4C2412yes—
404C22×D4C2412yes—
405C22×D4C2418yes—
406C23×C4—28no—
407C23×C4—84no—
408C23×C4C2414yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2418yes—
415C23×C4C2414yes—
416C23×C4C2414yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C4⋊Q8—216no—
421C4⋊Q8—232no—
422C4⋊Q8—216no—
423C4⋊Q8—216no—
424C4⋊Q8—232no—
425C4⋊Q8—216no—
426C4⋊Q8—24no—
427C4⋊Q8—24no—
428C4⋊Q8—24no—
429C4⋊Q8—216no—
430C4⋊Q8C2×D418yes—
431C4⋊Q8C2×D418yes—
432#127—24no—
433#127—216no—
434#126—232no—
435#125—232no—
436#125—232no—
437#125—232no—
438#125—216no—
439#125—28no—
440#125—216no—
441#125C2×D4116yes—
442#124—232no—
443#124—216no—
444#124—216no—
445#124—216no—
446#124—28no—
447#124—216no—
448#124—816no—
449#123—232no—
450#123—232no—
451#123—232no—
452C22⋊Q8—216no—
453C22⋊Q8—232no—
454C22⋊Q8—28no—
455C22⋊Q8—28no—
456C22⋊Q8—232no—
457C22⋊Q8—816no—
458C22⋊Q8—88no—
459C22⋊Q8C2×D4116yes—
460C22⋊Q8C2×D4116yes—
461#121—28no—
462#121—28no—
463#121—216no—
464#121—216no—
465#121—216no—
466#121—232no—
467#120—232no—
468C4×Q8—216no—
469C4×Q8—216no—
470C4×Q8—216no—
471C4×Q8—232no—
472C4×Q8—216no—
473C4×Q8—28no—
474C4×Q8—28no—
475C4×Q8—28no—
476C4×Q8—28no—
477C4×Q8—216no—
478C4×Q8—216no—
479C4×Q8—216no—
480C4×Q8—28no—
481C4×Q8—28no—
482C4×Q8C2×D4116yes—
483C4×Q8C2×D4116yes—
484C4×D4—232no—
485C4×D4—232no—
486C4×D4—28no—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—216no—
491C4×D4—28no—
492C4×D4—28no—
493#117—28no—
494#117—28no—
495#117—216no—
496#117—216no—
497#117—232no—
498#117C2×D4116yes—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—28no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—216no—
503C2×C4⋊C4—84no—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C24116yes—
526C2×C4⋊C4C24116yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C24116yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C22⋊C4—28no—
539C2×C22⋊C4—216no—
540C2×C22⋊C4—84no—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C24116yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C24116yes—
552C2×C22⋊C4C24116yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C24116yes—
555C2×C22⋊C4C24116yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C24116yes—
560C2×C22⋊C4C2414yes—
561C2×C42—28no—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42C2×D418yes—
565C2×C42C2418yes—
566C2×C42C2414yes—
567C2×C42C2418yes—
568C2×C42C2418yes—
569C2×C42C2414yes—
570C2×C42C2414yes—
571C2×C42C2414yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2418yes—
577C2×C42C2418yes—
578C2×C42C2414yes—
579C2×C42C2411yescharacteristic
580C2×C42C2411yescharacteristic
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2414yes—
587#95C24116yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C24116yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2414yes—
597#95C2418yes—
598#95C2418yes—
599#95C24116yes—
600C24—24no—
601C24—24no—
602C24—24no—
603C24—44no—
604C24—44no—
605C24C2514yes—
606C24C2514yes—
607C24C2511yescharacteristic
608#41—432no—
609#41—832no—
610C2×Q8—232no—
611C2×Q8—24no—
612C2×Q8—24no—
613C2×Q8—24no—
614C2×Q8—24no—
615C2×Q8—24no—
616C2×Q8—216no—
617C2×Q8—24no—
618C2×Q8—24no—
619C2×Q8—24no—
620C2×Q8—24no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—416no—
626C2×Q8C22×D418yes—
627C2×Q8C22×D418yes—
628C2×Q8C2×#4118yes—
629C2×Q8C2×#4118yes—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—216no—
638C2×D4—24no—
639C2×D4—216no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—44no—
647C2×D4—416no—
648C2×D4—416no—
649C2×D4—44no—
650C2×D4—416no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—216no—
662C22×C4—28no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—48no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—48no—
672C22×C4—416no—
673C22×C4—42no—
674C22×C4—816no—
675C22×C4C22×D414yes—
676C22×C4C22×D414yes—
677C22×C4C22×D414yes—
678C22×C4C2×#4118yes—
679C22×C4C2×#4114yes—
680C22×C42−1+414yes—
681C22×C4C2514yes—
682C22×C4C2514yes—
683C22×C4C2514yes—
684C22×C4C2518yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2514yes—
692C22×C4C2511yescharacteristic
693C22×C4C2514yes—
694C22×C4C2511yescharacteristic
695C22×C4C2514yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—216no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—216no—
707C4⋊C4—24no—
708C4⋊C4—216no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—28no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—216no—
717C4⋊C4—216no—
718C4⋊C4—28no—
719C4⋊C4—232no—
720C4⋊C4—416no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C4⋊C4—48no—
724C4⋊C4—44no—
725C4⋊C4—416no—
726C4⋊C4C22×D418yes—
727C4⋊C4C22×D418yes—
728C4⋊C4C22×D418yes—
729C4⋊C4C22×D4116yes—
730C4⋊C4C22×D4116yes—
731C4⋊C4C22×D418yes—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—216no—
737C22⋊C4—216no—
738C22⋊C4—28no—
739C22⋊C4—216no—
740C22⋊C4—28no—
741C22⋊C4—232no—
742C22⋊C4—232no—
743C22⋊C4—416no—
744C22⋊C4—48no—
745C22⋊C4—416no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—416no—
749C22⋊C4—416no—
750C22⋊C4—48no—
751C22⋊C4C22×D4116yes—
752C42—28no—
753C42—28no—
754C42—216no—
755C42—216no—
756C42—216no—
757C42—28no—
758C42—24no—
759C42—24no—
760C42—28no—
761C42—24no—
762C42—24no—
763C42—48no—
764C42—48no—
765C42C22×D414yes—
766C42C22×D414yes—
767C42C22×D414yes—
768C42C22×D414yes—
769C42C22×D4116yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—28no—
782C23—416no—
783C23—48no—
784C23—84no—
785C23—84no—
786C23—88no—
787C23C23×D412yes—
788C23C22×#4112yes—
789C23C2×2−1+412yes—
790C23C2611yescharacteristic
791Q8—216no—
792Q8—216no—
793Q8—48no—
794Q8—48no—
795Q8—48no—
796Q8—48no—
797Q8—84no—
798Q8—816no—
799D4—48no—
800D4—416no—
801D4—48no—
802D4—48no—
803D4—48no—
804D4—84no—
805D4—816no—
806D4—816no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—28no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—416no—
839C2×C4—48no—
840C2×C4—416no—
841C2×C4—88no—
842C2×C4—816no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4—84no—
846C2×C4#548116yes—
847C2×C4C23×D412yes—
848C2×C4C23×D412yes—
849C2×C4C23×D418yes—
850C2×C4C23×D418yes—
851C2×C4C23×D412yes—
852C2×C4C23×D412yes—
853C2×C4C23×D412yes—
854C2×C4C23×D412yes—
855C2×C4C22×#4118yes—
856C2×C4C22×#4112yes—
857C2×C4C22×#4112yes—
858C2×C4C2×2−1+412yes—
859C2×C4C2×2−1+412yes—
860C22—24no—
861C22—22no—
862C22—22no—
863C22—24no—
864C22—48no—
865C22—48no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—48no—
871C22—48no—
872C22—44no—
873C22—44no—
874C22—816no—
875C22C2×#54814yes—
876C22C24×D411yescharacteristic
877C22C23×#4111yescharacteristic
878C22C22×2−1+411yescharacteristic
879C22H(7,𝔽2)12yes—
880C222−1+612yes—
881C4—22no—
882C4—22no—
883C4—28no—
884C4—22no—
885C4—22no—
886C4—28no—
887C4—28no—
888C4—48no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4C2×#54814yes—
897C4C2×#54814yes—
898C2—24no—
899C2—84no—
900C2—84no—
901C2C22×#54811yescharacteristic
902C2#6285112yes—
903C2#6285211yescharacteristic
904C2#6285911yescharacteristic
905C2#6287912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3506C2
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×#3502C2semidirect
3. #45313C2semidirect
4. #45270C2semidirect
5. #44937C2semidirect
6. #39174C2semidirect
7. #39168C2semidirect
8. #39164C2semidirect
9. #39162C2semidirect
10. #37753C2semidirect
11. #37707C2semidirect
12. #35677C2semidirect
13. #35532C2semidirect
14. #35264C2semidirect
15. #35178C2semidirect
16. #35172C2semidirect
17. #34637C2semidirect
18. #34276C2semidirect
19. #34074C2semidirect
20. C2×#2326C2semidirect
24. C2×Q82C22semidirect
25. C2×Q82C22semidirect
26. C2×#557C22semidirect
27. C2×#557C22semidirect
28. C2×#557C22semidirect
29. C2×#557C22semidirect
54. #2731C22semidirect
55. #2729C22semidirect
56. #2725C22semidirect
57. #2711C22semidirect
58. #2711C22semidirect
59. #2707C22semidirect
60. #2674C22semidirect
61. #2674C22semidirect
62. #2642C22semidirect
64. #2641C22semidirect
66. #2640C22semidirect
67. #2640C22semidirect
73. #2567C22semidirect
75. #2566C22semidirect
76. #2565C22semidirect
80. #2548C22semidirect
81. #2546C22semidirect
84. #2545C22semidirect
86. #2542C22semidirect
88. #2538C22semidirect
89. #2536C22semidirect
92. #2475C22semidirect
94. #2469C22semidirect
95. #2460C22semidirect
96. #2458C22semidirect
97. #2452C22semidirect
99. #2448C22semidirect
100. #2441C22semidirect
101. #2440C22semidirect
102. #2432C22semidirect
105. #2426C22semidirect
107. #2398C22semidirect
108. #2398C22semidirect
109. #2362C22semidirect
110. #2360C22semidirect
112. #2331C22semidirect
113. #2331C22semidirect
114. #2330C22semidirect
117. #2327C22semidirect
122. #2326C22semidirect
126. C4×C4⋊Q8C22semidirect
127. C4×#124C22semidirect
131. #2295C22semidirect
132. #2295C22semidirect
386. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#35062
#453132
#452702
#449372
#391742
#391682
#391642
#391622
#377532
#377072
#356772
#355322
#352642
#351782
#351722
#346372
#342762
#340742
C2×#23262