Finite Group Databasebeta

← #7643347

Subgroups — #7643347

Order 512.

5644 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39771C214yesmaximal, complemented
2#39387C214yesmaximal, complemented
3#39201C214yesmaximal, complemented
4#38985C214yesmaximal, complemented
5#38110C218yesmaximal, complemented
6#37696C218yesmaximal, complemented
7#37322C214yesmaximal, complemented
8#37321C214yesmaximal, complemented
9#36645C211yesmaximal, characteristic, complemented
10C2×#2858C211yesmaximal, characteristic, complemented
11#35558C212yesmaximal, complemented
12#35556C212yesmaximal, complemented
13#35541C212yesmaximal, complemented
14#35515C212yesmaximal, complemented
15#35288C214yesmaximal, complemented
16#35279C211yesmaximal, characteristic, complemented
17#35277C214yesmaximal, complemented
18#35272C211yesmaximal, characteristic
19#34216C211yesmaximal, characteristic, complemented
20#34210C211yesmaximal, characteristic, complemented
21#34026C211yesmaximal, characteristic, complemented
22C2×#542C2218yescomplemented
23C2×#535C2212yes—
24C2×#533C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#124C2214yes—
28C2×#518C2212yes—
29C2×C4×#41C2211yescharacteristic
30#2868C2212yescomplemented
31#2862C2212yescomplemented
32#2859C2212yescomplemented
33#2859C2212yescomplemented
34#2858C2214yes—
35#2858C2214yes—
36#2858C2212yes—
37#2858C2212yes—
38#2858C2212yes—
39#2858C2212yes—
40#2857C2214yes—
41#2857C2214yes—
42#2857C2214yescomplemented
43#2856C2214yes—
44#2796C22116yescomplemented
45#2751C22116yescomplemented
46#2730C22116yescomplemented
47#2715C22116yescomplemented
48#2712C22116yescomplemented
49#2710C22116yescomplemented
50#2705C22116yescomplemented
51#2700C22116yescomplemented
52#2644C2218yescomplemented
53#2640C2218yescomplemented
54#2628C2214yescomplemented
55#2624C2218yescomplemented
56#2620C2218yescomplemented
57#2619C2214yes—
58#2592C2218yescomplemented
59#2580C2218yescomplemented
60#2568C2212yescomplemented
61#2567C2212yescomplemented
62#2563C2212yescomplemented
63#2548C2212yes—
64#2548C2212yes—
65#2548C2218yescomplemented
66#2542C2212yescomplemented
67#2541C2212yes—
68#2541C2212yes—
69#2538C2218yescomplemented
70#2513C2218yescomplemented
71#2513C2218yescomplemented
72#2512C2218yescomplemented
73#2512C2218yescomplemented
74#2512C2218yescomplemented
75#2491C2218yescomplemented
76#2491C2218yescomplemented
77#2490C2218yescomplemented
78#2487C2214yes—
79#2480C22116yes—
80#2472C22116yes—
81#2454C2218yescomplemented
82#2452C2218yescomplemented
83#2452C2218yescomplemented
84#2448C2218yescomplemented
85#2447C2218yescomplemented
86#2447C2218yescomplemented
87#2445C2218yescomplemented
88#2437C22116yes—
89#2427C2218yescomplemented
90#2426C2218yescomplemented
91#2422C2218yescomplemented
92#2422C2218yescomplemented
93#2420C2218yescomplemented
94#2412C22116yes—
95#2409C2214yes—
96#2408C2214yes—
97#2408C2214yes—
98#2369C2214yescomplemented
99#2366C2214yes—
100#2366C2214yes—
101#2365C2214yescomplemented
102#2345C2214yes—
103Q8×C22⋊C4C2214yes—
104D4×C22⋊C4C2214yes—
105D4×C22⋊C4C2214yes—
106#2331C2214yescomplemented
107#2328C2214yes—
108#2326C2218yescomplemented
109#2324C2218yescomplemented
110#2319C2218yescomplemented
111#2317C2212yes—
112#2316C2212yes—
113#2311C2212yes—
114#2309C2212yes—
115#2309C2212yes—
116C4×C4⋊Q8C2214yescomplemented
117C4×C4⋊Q8C2214yescomplemented
118C4×C4⋊Q8C2214yescomplemented
119C4×#127C2214yes—
120#2298C2212yescomplemented
121#2298C2212yescomplemented
122#2297C2211yescharacteristic
123#2297C2211yescharacteristic
124#2296C2211yescharacteristic
125#2296C2211yescharacteristic
126#2295C2212yescomplemented
127#2295C2212yescomplemented
128#2293C2212yescomplemented
129#2293C2212yescomplemented
130C2×#390C2212yes—
131C2×#390C2212yes—
132C2×#390C2214yes—
133#2290C2214yes—
134#2290C2214yes—
135#2285C2211yescharacteristic
136#2285C2211yescharacteristic
137#2285C2212yes—
138#2274C2212yes—
139C4×#117C2211yescharacteristic
140C4×#117C2212yescomplemented
141C4×#117C2212yescomplemented
142C2×C43C2211yescharacteristic
143C22×#41C2311yescharacteristic
144C23×Q8C2312yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2312yes—
148#542—432no—
149#535—48no—
150#533—48no—
151C2×C4⋊Q8—28no—
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2314yes—
154C2×C4⋊Q8C2312yes—
155C2×C4⋊Q8C2312yes—
156C2×C4⋊Q8C2312yes—
157C2×C4⋊Q8C2314yes—
158C2×C4⋊Q8C2314yes—
159C2×#127—28no—
160C2×#127C2312yes—
161C2×#127C2312yes—
162C2×#127C2312yes—
163C2×#127C2312yes—
164C2×#127C2314yes—
165C2×#126C23116yes—
166C2×#125C2314yes—
167C2×#124—416no—
168C2×#124C2318yes—
169C2×#124C2314yes—
170C2×#124C2318yes—
171C2×#124C2318yes—
172C2×#124C2318yes—
173C2×#124C23116yes—
174C2×#123C23116yes—
175C2×C22⋊Q8C2318yes—
176C2×C22⋊Q8C2318yes—
177C2×C22⋊Q8C23116yes—
178C2×#121C2318yes—
179C2×#121C2318yes—
180C2×#121C2318yes—
181C2×#120C2318yes—
182#518—48no—
183C4×#41—28no—
184C2×C4×Q8C2311yescharacteristic
185C2×C4×Q8C2311yescharacteristic
186C2×C4×Q8C2318yes—
187C2×C4×Q8C2318yes—
188C2×C4×D4C2311yescharacteristic
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2311yescharacteristic
192C2×C4×D4C2318yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×#117C2311yescharacteristic
197C2×#117C2311yescharacteristic
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2312yes—
202C2×#117C2314yes—
203C2×#117C2314yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C22⋊C4C2318yes—
207C22×C22⋊C4C2318yes—
208C22×C22⋊C4C2318yes—
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215#400C2318yes—
216#399C23116yes—
217#399C2318yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#397C23116yes—
222#397C23116yes—
223#397C23116yes—
224#396C23116yes—
225#396C23116yes—
226#396C23116yes—
227#395C2318yes—
228#394C2318yes—
229#394C2318yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#394C23116yes—
234#393C2318yes—
235#393C23116yes—
236#393C23116yes—
237#392C2318yes—
238#392C2318yes—
239#391C2318yes—
240#391C2318yes—
241#391C2318yes—
242#391C2314yes—
243#391C2318yes—
244#391C23116yes—
245#391C2312yes—
246#391C2312yes—
247#390C2318yes—
248#390C2318yes—
249#390C2318yes—
250#390C2314yes—
251#390C2314yes—
252#390C2318yes—
253#390C2318yes—
254#390C2314yes—
255#390C2318yes—
256#390C2318yes—
257#390C23116yes—
258#390C2318yes—
259#390C2318yes—
260#390C2314yes—
261#390C2314yes—
262#390C2318yes—
263#390C2318yes—
264#390C2318yes—
265#390C2314yes—
266#390C2314yes—
267#390C2318yes—
268#390C2312yes—
269#390C2312yes—
270#389C2318yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2312yes—
285#388C23116yes—
286#388C23116yes—
287#388C23116yes—
288#388C23116yes—
289#388C23116yes—
290#388C2314yes—
291#388C2314yes—
292#388C2314yes—
293#388C2314yes—
294#387C23116yes—
295#387C2314yes—
296#387C2314yes—
297#387C2314yes—
298#387C2314yes—
299#386C2318yes—
300#386C23116yes—
301#386C23116yes—
302#386C23116yes—
303#386C2314yes—
304#386C2314yes—
305#385C2318yes—
306#385C23116yes—
307#385C23116yes—
308#385C23116yes—
309#385C2314yes—
310#385C2314yes—
311#384C2312yes—
312#384C2312yes—
313#384C2314yes—
314#384C2314yes—
315#384C2314yes—
316#384C2314yes—
317#382C2314yes—
318#382C2312yes—
319#382C2312yes—
320#382C2314yes—
321#381C23116yes—
322#380C2318yes—
323#380C2318yes—
324#380C2318yes—
325#380C23116yes—
326#380C2312yes—
327#380C2312yes—
328#380C2312yes—
329#380C2312yes—
330#380C2318yes—
331#379C2318yes—
332#379C2318yes—
333C4×C4⋊C4C2312yes—
334C4×C4⋊C4C2312yes—
335C4×C4⋊C4C2312yes—
336C4×C4⋊C4C2312yes—
337C4×C4⋊C4C2318yes—
338C4×C4⋊C4C2318yes—
339C4×C4⋊C4C2318yes—
340C4×C4⋊C4C2318yes—
341C4×C4⋊C4C2312yes—
342C4×C4⋊C4C2312yes—
343C4×C4⋊C4C2314yes—
344C4×C4⋊C4C2312yes—
345C4×C4⋊C4C2314yes—
346C4×C4⋊C4C2312yes—
347C4×C4⋊C4C2312yes—
348C4×C4⋊C4C2312yes—
349C4×C22⋊C4C2312yes—
350C4×C22⋊C4C2312yes—
351C4×C22⋊C4C2318yes—
352C4×C22⋊C4C2312yes—
353C4×C22⋊C4C2312yes—
354C4×C22⋊C4C2314yes—
355C4×C22⋊C4C2314yes—
356C4×C22⋊C4C2312yes—
357C4×C22⋊C4C2312yes—
358#376C2314yes—
359#376C2314yes—
360#376C2312yes—
361C43C2312yes—
362C43C2312yes—
363C43C2312yes—
364C43C2311yescharacteristic
365C43C2311yescharacteristic
366C43C2311yescharacteristic
367C43C2311yescharacteristic
368C25C2414yes—
369C2×#41—24no—
370C2×#41—24no—
371C2×#41—24no—
372C22×Q8—28no—
373C22×Q8—48no—
374C22×Q8C2414yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2418yes—
377C22×Q8C2414yes—
378C22×D4—28no—
379C22×D4—28no—
380C22×D4—28no—
381C22×D4—28no—
382C22×D4—28no—
383C22×D4—48no—
384C22×D4—48no—
385C22×D4C2412yes—
386C22×D4C2414yes—
387C22×D4C2414yes—
388C22×D4C2414yes—
389C22×D4C2414yes—
390C22×D4C2411yescharacteristic
391C22×D4C2414yes—
392C22×D4C2414yes—
393C22×D4C24116yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2414yes—
402C23×C4C24116yes—
403C23×C4C2411yescharacteristic
404C4⋊Q8—28no—
405C4⋊Q8—28no—
406C4⋊Q8—28no—
407C4⋊Q8—28no—
408C4⋊Q8—216no—
409C4⋊Q8—48no—
410C4⋊Q8—48no—
411#127—28no—
412#127—28no—
413#127—28no—
414#127—28no—
415#127—48no—
416#126—432no—
417#125—48no—
418#124—232no—
419#124—416no—
420#124—416no—
421#124—416no—
422#124—48no—
423#124—432no—
424#123—432no—
425C22⋊Q8—416no—
426C22⋊Q8—432no—
427C22⋊Q8—416no—
428#121—416no—
429#121—416no—
430#121—416no—
431#120—416no—
432C4×Q8—24no—
433C4×Q8—24no—
434C4×Q8—416no—
435C4×Q8—416no—
436C4×D4—28no—
437C4×D4—28no—
438C4×D4—24no—
439C4×D4—24no—
440C4×D4—416no—
441C4×D4—416no—
442C4×D4—416no—
443C4×D4—416no—
444#117—24no—
445#117—24no—
446#117—28no—
447#117—28no—
448#117—24no—
449#117—28no—
450#117—216no—
451#117—48no—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C24116yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C24116yes—
480C2×C4⋊C4C2418yes—
481C2×C22⋊C4—416no—
482C2×C22⋊C4—416no—
483C2×C22⋊C4—416no—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C2412yes—
489C2×C22⋊C4C2412yes—
490C2×C22⋊C4C2412yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2412yes—
495C2×C22⋊C4C24116yes—
496C2×C22⋊C4C24116yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C24116yes—
503C2×C22⋊C4C24116yes—
504C2×C22⋊C4C24116yes—
505C2×C22⋊C4C24116yes—
506C2×C42—24no—
507C2×C42—24no—
508C2×C42—28no—
509C2×C42—28no—
510C2×C42—44no—
511C2×C42#4118yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2414yes—
516C2×C42C2414yes—
517C2×C42C2414yes—
518C2×C42C2414yes—
519C2×C42C2412yes—
520C2×C42C2412yes—
521C2×C42C2412yes—
522C2×C42C2412yes—
523C2×C42C2412yes—
524C2×C42C2412yes—
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527C2×C42C2411yescharacteristic
528C2×C42C2412yes—
529C2×C42C2411yescharacteristic
530C2×C42C2411yescharacteristic
531C2×C42C2412yes—
532C2×C42C24116yes—
533C2×C42C2412yes—
534C2×C42C2412yes—
535C2×C42C2411yescharacteristic
536C2×C42C2411yescharacteristic
537C2×C42C2411yescharacteristic
538C2×C42C2411yescharacteristic
539C2×C42C2412yes—
540#95C2414yes—
541#95C2414yes—
542#95C2414yes—
543#95C2414yes—
544#95C2414yes—
545#95C2414yes—
546#95C2414yes—
547#95C2414yes—
548#95C2414yes—
549#95C2414yes—
550#95C24116yes—
551#95C24116yes—
552#95C2418yes—
553#95C2414yes—
554#95C2414yes—
555#95C2418yes—
556#95C2414yes—
557#95C2414yes—
558#95C24116yes—
559#95C24116yes—
560C24—28no—
561C24—28no—
562C24—28no—
563C24—48no—
564C24—48no—
565C24C2518yes—
566C24C2512yes—
567C24C2511yescharacteristic
568#41—416no—
569C2×Q8—22no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—216no—
573C2×Q8—22no—
574C2×Q8—216no—
575C2×Q8—22no—
576C2×Q8—48no—
577C2×Q8—48no—
578C2×Q8—48no—
579C2×Q8—816no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—28no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—216no—
593C2×D4—22no—
594C2×D4—28no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—216no—
598C2×D4—48no—
599C2×D4—48no—
600C2×D4—416no—
601C2×D4—416no—
602C2×D4—416no—
603C2×D4—432no—
604C2×D4—816no—
605C2×D4—816no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—28no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—28no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—28no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—48no—
623C22×C4—416no—
624C22×C4—416no—
625C22×C4—416no—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C42−1+414yes—
631C22×C4C2512yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2514yes—
635C22×C4C2514yes—
636C22×C4C2518yes—
637C22×C4C2518yes—
638C22×C4C2518yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2511yescharacteristic
642C22×C4C2511yescharacteristic
643C22×C4C2512yes—
644C22×C4C2512yes—
645C22×C4C2511yescharacteristic
646C22×C4C2511yescharacteristic
647C22×C4C2511yescharacteristic
648C22×C4C2511yescharacteristic
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—24no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—416no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—416no—
675C4⋊C4—48no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—232no—
684C22⋊C4—232no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—416no—
688C22⋊C4—416no—
689C22⋊C4—416no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—416no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C22⋊C4—416no—
696C22⋊C4—416no—
697C22⋊C4—416no—
698C42—24no—
699C42—24no—
700C42—24no—
701C42—24no—
702C42—24no—
703C42—24no—
704C42—24no—
705C42—22no—
706C42—22no—
707C42—24no—
708C42—28no—
709C42—28no—
710C42—28no—
711C42—22no—
712C42—24no—
713C42—22no—
714C42—24no—
715C42—24no—
716C42—24no—
717C42—28no—
718C42—42no—
719C42—42no—
720C42—416no—
721C42C2×#4114yes—
722C42C2×#4114yes—
723C42C2×#4114yes—
724C42C2×#4114yes—
725C42H(5,𝔽2)18yes—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—28no—
730C23—24no—
731C23—216no—
732C23—28no—
733C23—22no—
734C23—22no—
735C23—28no—
736C23—24no—
737C23—216no—
738C23—416no—
739C23—88no—
740C23—88no—
741C23—816no—
742C23—816no—
743C23C22×#4112yes—
744C23C2×H(5,𝔽2)12yes—
745C23C2×2−1+412yes—
746C23C2611yescharacteristic
747Q8—44no—
748Q8—416no—
749Q8—816no—
750Q8—88no—
751D4—48no—
752D4—416no—
753D4—416no—
754D4—44no—
755D4—416no—
756D4—416no—
757D4—88no—
758D4—88no—
759D4—1616no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—216no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—48no—
799C2×C4—48no—
800C2×C4—88no—
801C2×C4—1616no—
802C2×C4#542116yescomplemented
803C2×C4C22×#4112yes—
804C2×C4C22×#4112yes—
805C2×C4C22×#4112yes—
806C2×C4C22×#4112yes—
807C2×C4C22×#4112yes—
808C2×C4C22×#4112yes—
809C2×C4C2×H(5,𝔽2)14yes—
810C2×C4C2×H(5,𝔽2)14yes—
811C2×C4C2×H(5,𝔽2)12yes—
812C2×C4C2×H(5,𝔽2)12yes—
813C2×C4C2×H(5,𝔽2)14yes—
814C2×C4C2×2−1+412yes—
815C2×C4C2×2−1+412yes—
816C2×C4#58514yes—
817C22—22no—
818C22—22no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—48no—
823C22—42no—
824C22—48no—
825C22—416no—
826C22—44no—
827C22—44no—
828C22—416no—
829C22—42no—
830C22—48no—
831C22—1616no—
832C22C2×#54214yes—
833C22C23×#4111yescharacteristic
834C22C22×H(5,𝔽2)12yes—
835C22C22×H(5,𝔽2)11yescharacteristic
836C22C22×2−1+411yescharacteristic
837C22C2×#58512yes—
838C4—22no—
839C4—22no—
840C4—24no—
841C4—24no—
842C4—42no—
843C4—48no—
844C4—42no—
845C4—42no—
846C4—44no—
847C4—48no—
848C4—48no—
849C4—44no—
850C4—42no—
851C4—42no—
852C4C2×#54214yes—
853C4C2×#54214yes—
854C4#350814yes—
855C4#351014yes—
856C2—24no—
857C2—82no—
858C2—88no—
859C2C22×#54211yescharacteristic
860C2C2×#350811yescharacteristic
861C2C2×#351011yescharacteristic
862C2#6283412yes—
863C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35272C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39771C2semidirect
2. #39387C2semidirect
3. #39201C2semidirect
4. #38985C2semidirect
5. #38110C2semidirect
6. #37696C2semidirect
7. #37322C2semidirect
8. #37321C2semidirect
9. #36645C2semidirect
10. C2×#2858C2semidirect
11. #35558C2semidirect
12. #35556C2semidirect
13. #35541C2semidirect
14. #35515C2semidirect
15. #35288C2semidirect
16. #35279C2semidirect
17. #35277C2semidirect
19. #34216C2semidirect
20. #34210C2semidirect
21. #34026C2semidirect
22. C2×#542C22semidirect
30. #2868C22semidirect
31. #2862C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
42. #2857C22semidirect
44. #2796C22semidirect
45. #2751C22semidirect
46. #2730C22semidirect
47. #2715C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2705C22semidirect
51. #2700C22semidirect
52. #2644C22semidirect
53. #2640C22semidirect
54. #2628C22semidirect
55. #2624C22semidirect
56. #2620C22semidirect
58. #2592C22semidirect
59. #2580C22semidirect
60. #2568C22semidirect
61. #2567C22semidirect
62. #2563C22semidirect
65. #2548C22semidirect
66. #2542C22semidirect
69. #2538C22semidirect
70. #2513C22semidirect
71. #2513C22semidirect
72. #2512C22semidirect
73. #2512C22semidirect
74. #2512C22semidirect
75. #2491C22semidirect
76. #2491C22semidirect
77. #2490C22semidirect
81. #2454C22semidirect
82. #2452C22semidirect
83. #2452C22semidirect
84. #2448C22semidirect
85. #2447C22semidirect
86. #2447C22semidirect
87. #2445C22semidirect
89. #2427C22semidirect
90. #2426C22semidirect
91. #2422C22semidirect
92. #2422C22semidirect
93. #2420C22semidirect
98. #2369C22semidirect
101. #2365C22semidirect
106. #2331C22semidirect
108. #2326C22semidirect
109. #2324C22semidirect
110. #2319C22semidirect
116. C4×C4⋊Q8C22semidirect
117. C4×C4⋊Q8C22semidirect
118. C4×C4⋊Q8C22semidirect
120. #2298C22semidirect
121. #2298C22semidirect
126. #2295C22semidirect
127. #2295C22semidirect
128. #2293C22semidirect
129. #2293C22semidirect
140. C4×#117C22semidirect
141. C4×#117C22semidirect
802. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#397712
#393872
#392012
#389852
#381102
#376962
#373222
#373212
#366452
C2×#28582
#355582
#355562
#355412
#355152
#352882
#352792
#352772
#352722
#342162
#342102
#340262