Finite Group Databasebeta

← #7711927

Subgroups — #7711927

Order 512.

5432 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C212yesmaximal, complemented
2#59827C212yesmaximal, complemented
3#59823C212yesmaximal, complemented
4#59821C212yesmaximal, complemented
5#46014C214yesmaximal, complemented
6#46013C214yesmaximal, complemented
7#39736C214yesmaximal, complemented
8#39726C214yesmaximal, complemented
9#39470C214yesmaximal, complemented
10#39468C214yesmaximal, complemented
11#38985C214yesmaximal, complemented
12#38975C214yesmaximal, complemented
13#37640C212yesmaximal, complemented
14#37315C214yesmaximal, complemented
15#36645C211yesmaximal, characteristic, complemented
16#36644C211yesmaximal, characteristic
17#36595C212yesmaximal, complemented
18#36594C212yesmaximal, complemented
19#36563C212yesmaximal, complemented
20#36559C212yesmaximal, complemented
21#35288C214yesmaximal, complemented
22#34368C212yesmaximal, complemented
23C4×#533C211yesmaximal, characteristic, complemented
24C2×#559C2214yes—
25C2×#556C2214yes—
26C2×#554C2214yes—
27C2×#533C2211yescharacteristic
28C2×#533C2212yes—
29C2×#532C2212yes—
30C2×#532C2212yes—
31C2×#532C2212yes—
32#2868C2211yescharacteristic
33#2868C2211yescharacteristic
34#2868C2211yescharacteristic
35#2867C2211yescharacteristic
36#2862C2212yes—
37#2859C2212yes—
38#2859C2212yes—
39#2859C2214yes—
40#2858C2212yes—
41#2858C2212yes—
42#2858C2212yes—
43#2858C2214yes—
44#2857C2212yes—
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2856C2212yes—
49#2856C2212yes—
50#2856C2212yes—
51#2856C2212yes—
52#2820C2218yes—
53#2808C2218yes—
54#2761C22116yes—
55#2732C2218yes—
56#2727C2218yes—
57#2724C2218yes—
58#2715C22116yes—
59#2707C22116yes—
60#2700C22116yes—
61#2691C22116yes—
62#2681C22116yes—
63#2644C2218yes—
64#2624C2218yes—
65#2620C2218yes—
66#2616C2218yes—
67#2592C2218yes—
68#2582C2214yes—
69#2567C2214yes—
70#2566C2218yes—
71#2563C2214yes—
72#2552C2214yes—
73#2550C2218yes—
74#2548C2214yes—
75#2548C2214yes—
76#2548C2214yes—
77#2547C2214yes—
78#2547C2214yes—
79#2545C2218yes—
80#2544C2218yes—
81#2542C2214yes—
82#2538C2214yes—
83#2538C2214yes—
84#2538C2214yes—
85#2538C2214yes—
86#2538C2218yes—
87#2513C2218yes—
88#2512C2218yes—
89#2512C2218yes—
90#2512C2218yes—
91#2507C2218yes—
92#2490C2218yes—
93#2486C2218yes—
94#2485C2218yes—
95#2454C2218yes—
96#2452C2218yes—
97#2452C2218yes—
98#2451C2218yes—
99#2448C2218yes—
100#2447C2218yes—
101#2447C2218yes—
102#2445C2218yes—
103#2445C2218yes—
104#2427C2218yes—
105#2426C2218yes—
106#2420C2218yes—
107#2417C2218yes—
108#2415C2218yes—
109#2379C2218yes—
110#2369C2214yes—
111#2366C2214yes—
112#2366C2214yes—
113#2355C2214yes—
114#2354C2214yes—
115#2354C2214yes—
116#2354C2214yes—
117Q8×C4⋊C4C2214yes—
118D4×C4⋊C4C2214yes—
119D4×C4⋊C4C2214yes—
120D4×C4⋊C4C2214yes—
121#2324C2218yes—
122#2324C2218yes—
123#2319C2218yes—
124#2311C2218yes—
125C4×C4⋊Q8C2212yes—
126C4×C4⋊Q8C2212yes—
127C4×C4⋊Q8C2212yes—
128C4×C4⋊Q8C2212yes—
129C4×C4⋊Q8C2211yescharacteristic
130C4×C4⋊Q8C2211yescharacteristic
131C4×C4⋊Q8C2211yescharacteristic
132C4×C4⋊Q8C2214yes—
133C4×C4⋊Q8C2211yescharacteristic
134C4×#127C2212yes—
135C4×#127C2212yes—
136C4×#127C2212yes—
137C4×#127C2212yes—
138C4×#127C2214yes—
139C4×#125C2212yes—
140C4×#125C2212yes—
141C4×C22⋊Q8C2212yes—
142C4×C22⋊Q8C2212yes—
143C4×C22⋊Q8C2212yes—
144C4×C22⋊Q8C2212yes—
145#2296C2212yes—
146#2295C2212yes—
147#2295C2212yes—
148#2285C2212yes—
149#2285C2212yes—
150#2285C2211yescharacteristic
151C42×Q8C2212yes—
152C42×Q8C2212yes—
153C4×#117C2212yes—
154C2×C43C2211yescharacteristic
155C22×#41C2314yes—
156#559—416no—
157#556—416no—
158#554—416no—
159#533—28no—
160#533—48no—
161#532—216no—
162#532—48no—
163#532—48no—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2311yescharacteristic
166C2×C4⋊Q8C2311yescharacteristic
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×#127C2312yes—
176C2×#127C2312yes—
177C2×#127C2312yes—
178C2×#127C2312yes—
179C2×#127C2312yes—
180C2×#127C2312yes—
181C2×#127C2312yes—
182C2×#126C23116yes—
183C2×#125C2312yes—
184C2×#125C2318yes—
185C2×#125C2314yes—
186C2×#124C2314yes—
187C2×#124C2318yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2318yes—
191C2×#124C2318yes—
192C2×#123C23116yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C23116yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2318yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yes—
225C2×#117C2312yes—
226C2×#117C2318yes—
227C2×#117C2312yes—
228C2×#117C2314yes—
229C22×C4⋊C4C2318yes—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#399C23116yes—
238#398C23116yes—
239#398C23116yes—
240#397C23116yes—
241#397C23116yes—
242#397C23116yes—
243#397C23116yes—
244#397C23116yes—
245#396C23116yes—
246#396C23116yes—
247#396C23116yes—
248#396C23116yes—
249#396C23116yes—
250#395C23116yes—
251#394C23116yes—
252#394C23116yes—
253#394C23116yes—
254#394C23116yes—
255#394C23116yes—
256#393C23116yes—
257#391C2318yes—
258#391C2312yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2312yes—
264#391C2312yes—
265#391C2312yes—
266#391C23116yes—
267#391C2318yes—
268#390C2318yes—
269#390C2314yes—
270#390C2314yes—
271#390C2314yes—
272#390C2314yes—
273#390C2314yes—
274#390C2314yes—
275#390C2314yes—
276#390C2314yes—
277#390C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2314yes—
281#390C2318yes—
282#390C2318yes—
283#390C23116yes—
284#390C2318yes—
285#390C2318yes—
286#390C2318yes—
287#390C2318yes—
288#390C2318yes—
289#390C2318yes—
290#389C2312yes—
291#389C2312yes—
292#389C2312yes—
293#389C2312yes—
294#389C2318yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2312yes—
305#389C2312yes—
306#389C2312yes—
307#389C2312yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C23116yes—
314#388C23116yes—
315#388C23116yes—
316#388C23116yes—
317#388C23116yes—
318#388C23116yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C23116yes—
324#386C23116yes—
325#386C23116yes—
326#386C23116yes—
327#385C23116yes—
328#385C23116yes—
329#385C23116yes—
330#385C2314yes—
331#385C2314yes—
332#384C2312yes—
333#384C2312yes—
334#384C2312yes—
335#384C2312yes—
336#384C2312yes—
337#384C2311yescharacteristic
338#384C2311yescharacteristic
339#384C2312yes—
340#384C2312yes—
341#384C2312yes—
342#384C2312yes—
343#384C2318yes—
344#384C2312yes—
345#384C2312yes—
346#384C2312yes—
347#382C2312yes—
348#382C2318yes—
349#382C2314yes—
350#382C2314yes—
351#381C23116yes—
352#380C2318yes—
353#380C2318yes—
354#380C2312yes—
355#380C2314yes—
356#380C2318yes—
357#380C23116yes—
358#380C2312yes—
359#380C2314yes—
360#380C2314yes—
361#380C2314yes—
362#380C2318yes—
363C4×C4⋊C4C2312yes—
364C4×C4⋊C4C2312yes—
365C4×C4⋊C4C2312yes—
366C4×C4⋊C4C2312yes—
367C4×C4⋊C4C2314yes—
368C4×C4⋊C4C2314yes—
369C4×C4⋊C4C2314yes—
370C4×C4⋊C4C2314yes—
371C4×C4⋊C4C2314yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2314yes—
375C4×C4⋊C4C2312yes—
376C4×C4⋊C4C2318yes—
377C4×C4⋊C4C2312yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2312yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2312yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2314yes—
386C4×C22⋊C4C2314yes—
387C4×C22⋊C4C2314yes—
388#376C2314yes—
389C43C2311yescharacteristic
390C43C2311yescharacteristic
391C43C2311yescharacteristic
392C43C2311yescharacteristic
393C43C2311yescharacteristic
394C43C2311yescharacteristic
395C43C2314yes—
396C43C2311yescharacteristic
397C43C2311yescharacteristic
398C2×#41—216no—
399C2×#41—48no—
400C2×#41—48no—
401C22×Q8C2412yes—
402C22×Q8C2414yes—
403C22×Q8C2412yes—
404C22×Q8C2414yes—
405C22×Q8C2414yes—
406C22×D4C2414yes—
407C22×D4C2414yes—
408C22×D4C2414yes—
409C22×D4C2414yes—
410C22×D4C2414yes—
411C22×D4C2414yes—
412C22×D4C2418yes—
413C22×D4C2414yes—
414C23×C4C2418yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C24116yes—
423C4⋊Q8—28no—
424C4⋊Q8—24no—
425C4⋊Q8—24no—
426C4⋊Q8—28no—
427C4⋊Q8—28no—
428C4⋊Q8—28no—
429C4⋊Q8—44no—
430C4⋊Q8—44no—
431C4⋊Q8—44no—
432C4⋊Q8—44no—
433C4⋊Q8—44no—
434#127—28no—
435#127—28no—
436#127—28no—
437#127—28no—
438#127—44no—
439#127—44no—
440#127—44no—
441#126—432no—
442#125—28no—
443#125—48no—
444#125—416no—
445#124—216no—
446#124—48no—
447#124—48no—
448#124—416no—
449#124—416no—
450#124—416no—
451#123—432no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C22⋊Q8—432no—
455C22⋊Q8—48no—
456C22⋊Q8—48no—
457C22⋊Q8—416no—
458C22⋊Q8—416no—
459#121—216no—
460#121—216no—
461#121—48no—
462#121—48no—
463#121—48no—
464#121—48no—
465C4×Q8—28no—
466C4×Q8—28no—
467C4×Q8—216no—
468C4×Q8—28no—
469C4×Q8—28no—
470C4×Q8—28no—
471C4×Q8—28no—
472C4×Q8—48no—
473C4×Q8—416no—
474C4×D4—216no—
475C4×D4—216no—
476C4×D4—216no—
477C4×D4—216no—
478C4×D4—416no—
479C4×D4—416no—
480C4×D4—416no—
481C4×D4—416no—
482C4×D4—48no—
483C4×D4—48no—
484#117—28no—
485#117—44no—
486#117—48no—
487#117—416no—
488C2×C4⋊C4—416no—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C24116yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C24116yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C24116yes—
527C2×C4⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C24116yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C24116yes—
539C2×C22⋊C4C24116yes—
540C2×C22⋊C4C24116yes—
541C2×C22⋊C4C24116yes—
542C2×C22⋊C4C24116yes—
543C2×C22⋊C4C24116yes—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42#4118yes—
551C2×C42C2414yes—
552C2×C42C2418yes—
553C2×C42C2414yes—
554C2×C42C2411yescharacteristic
555C2×C42C2411yescharacteristic
556C2×C42C2414yes—
557C2×C42C2414yes—
558C2×C42C2411yescharacteristic
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2411yescharacteristic
562C2×C42C2411yescharacteristic
563C2×C42C2411yescharacteristic
564C2×C42C2411yescharacteristic
565C2×C42C2411yescharacteristic
566C2×C42C2411yescharacteristic
567C2×C42C2411yescharacteristic
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2411yescharacteristic
573C2×C42C2411yescharacteristic
574C2×C42C2411yescharacteristic
575C2×C42C24116yes—
576C2×C42C2411yescharacteristic
577C2×C42C2411yescharacteristic
578C2×C42C2411yescharacteristic
579C2×C42C2411yescharacteristic
580C2×C42C2411yescharacteristic
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C2×C42C2411yescharacteristic
586C2×C42C2411yescharacteristic
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C24116yes—
598#95C2418yes—
599#95C2418yes—
600#95C24116yes—
601#95C2418yes—
602#95C2418yes—
603#95C24116yes—
604#95C24116yes—
605C24C2518yes—
606C24C2511yescharacteristic
607#41—832no—
608C2×Q8—24no—
609C2×Q8—24no—
610C2×Q8—28no—
611C2×Q8—24no—
612C2×Q8—24no—
613C2×Q8—28no—
614C2×Q8—24no—
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—24no—
618C2×Q8—28no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×D4—216no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—44no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—216no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—216no—
661C22×C4—216no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—416no—
669C22×C4—416no—
670C22×C4—416no—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C22×C4C2×#4114yes—
674C22×C4C2511yescharacteristic
675C22×C4C2514yes—
676C22×C4C2514yes—
677C22×C4C2514yes—
678C22×C4C2511yescharacteristic
679C22×C4C2518yes—
680C22×C4C2518yes—
681C22×C4C2518yes—
682C22×C4C2514yes—
683C22×C4C2511yescharacteristic
684C22×C4C2511yescharacteristic
685C22×C4C2511yescharacteristic
686C22×C4C2511yescharacteristic
687C22×C4C2511yescharacteristic
688C22×C4C2511yescharacteristic
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2511yescharacteristic
692C22×C4C2511yescharacteristic
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—28no—
705C4⋊C4—24no—
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—216no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—416no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—48no—
730C4⋊C4—416no—
731C4⋊C4—44no—
732C4⋊C4—416no—
733C4⋊C4—44no—
734C22⋊C4—28no—
735C22⋊C4—216no—
736C22⋊C4—216no—
737C22⋊C4—216no—
738C22⋊C4—216no—
739C22⋊C4—44no—
740C22⋊C4—48no—
741C22⋊C4—416no—
742C22⋊C4—416no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—416no—
746C22⋊C4—416no—
747C22⋊C4—416no—
748C22⋊C4—416no—
749C22⋊C4—416no—
750C42—28no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—22no—
758C42—22no—
759C42—22no—
760C42—216no—
761C42—28no—
762C42—28no—
763C42—28no—
764C42—22no—
765C42—22no—
766C42—22no—
767C42—22no—
768C42—22no—
769C42—22no—
770C42—28no—
771C42—22no—
772C42—22no—
773C42—28no—
774C42—41no—
775C42—41no—
776C42—416no—
777C42C2×#4114yes—
778C42C2×#4114yes—
779C42C2×#4114yes—
780C42C2×#4114yes—
781C42H(5,𝔽2)14yes—
782C42H(5,𝔽2)14yes—
783C42H(5,𝔽2)14yes—
784C422−1+414yes—
785C422−1+414yes—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—28no—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23C22×#4112yes—
800C23C2611yescharacteristic
801Q8—48no—
802Q8—48no—
803Q8—416no—
804Q8—88no—
805Q8—88no—
806D4—416no—
807D4—416no—
808D4—416no—
809D4—416no—
810D4—88no—
811D4—88no—
812D4—88no—
813D4—816no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—28no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—432no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—1616no—
864C2×C4C22×#4112yes—
865C2×C4C22×#4112yes—
866C2×C4C22×#4112yes—
867C2×C4C22×#4112yes—
868C2×C4C22×#4112yes—
869C2×C4C22×#4112yes—
870C2×C4C2×H(5,𝔽2)12yes—
871C2×C4C2×H(5,𝔽2)12yes—
872C2×C4C2×H(5,𝔽2)12yes—
873C2×C4C2×H(5,𝔽2)12yes—
874C2×C4C2×H(5,𝔽2)12yes—
875C2×C4C2×H(5,𝔽2)12yes—
876C2×C4C2×H(5,𝔽2)12yes—
877C2×C4C2×H(5,𝔽2)12yes—
878C2×C4C2×H(5,𝔽2)12yes—
879C2×C4C2×2−1+412yes—
880C2×C4C2×2−1+412yes—
881C2×C4C2×2−1+412yes—
882C2×C4C2×2−1+412yes—
883C2×C4C2×2−1+412yes—
884C2×C4C2×2−1+412yes—
885C2×C4#58512yes—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—48no—
894C22—48no—
895C22—48no—
896C22—48no—
897C22—48no—
898C22—48no—
899C22—48no—
900C22C23×#4111yescharacteristic
901C22C22×H(5,𝔽2)11yescharacteristic
902C22C22×H(5,𝔽2)11yescharacteristic
903C22C22×H(5,𝔽2)11yescharacteristic
904C22C22×2−1+411yescharacteristic
905C22C22×2−1+411yescharacteristic
906C22C2×#58511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—22no—
913C4—22no—
914C4—41no—
915C4—48no—
916C4—41no—
917C4—48no—
918C4—44no—
919C4—44no—
920C4—44no—
921C4—48no—
922C4—44no—
923C4#350714yes—
924C4#350814yes—
925C4#351114yes—
926C4#354814yes—
927C4#355014yes—
928C2—42no—
929C2—88no—
930C2C2×#354811yescharacteristic
931C2C2×#355011yescharacteristic
932C2C2×#350711yescharacteristic
933C2C2×#350811yescharacteristic
934C2C2×#351111yescharacteristic
935C2#6283411yescharacteristic
936C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36644C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59827C2semidirect
3. #59823C2semidirect
4. #59821C2semidirect
5. #46014C2semidirect
6. #46013C2semidirect
7. #39736C2semidirect
8. #39726C2semidirect
9. #39470C2semidirect
10. #39468C2semidirect
11. #38985C2semidirect
12. #38975C2semidirect
13. #37640C2semidirect
14. #37315C2semidirect
15. #36645C2semidirect
17. #36595C2semidirect
18. #36594C2semidirect
19. #36563C2semidirect
20. #36559C2semidirect
21. #35288C2semidirect
22. #34368C2semidirect
23. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#598272
#598232
#598212
#460142
#460132
#397362
#397262
#394702
#394682
#389852
#389752
#376402
#373152
#366452
#366442
#365952
#365942
#365632
#365592
#352882
#343682
C4×#5332