Finite Group Databasebeta

← #7672696

Subgroups — #7672696

Order 512.

5188 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59225C218yesmaximal, complemented
2#59203C218yesmaximal, complemented
3#38943C214yesmaximal, complemented
4#38940C214yesmaximal, complemented
5#37955C218yesmaximal, complemented
6C2×#2857C211yesmaximal, characteristic, complemented
7#36315C214yesmaximal, complemented
8#36288C214yesmaximal, complemented
9#36209C214yesmaximal, complemented
10#36194C214yesmaximal, complemented
11#35661C212yesmaximal
12#35644C212yesmaximal, complemented
13#35316C211yesmaximal, characteristic, complemented
14#35312C212yesmaximal, complemented
15#35275C211yesmaximal, characteristic, complemented
16#34254C212yesmaximal, complemented
17#34209C211yesmaximal, characteristic, complemented
18#34188C211yesmaximal, characteristic, complemented
19C4×#525C211yesmaximal, characteristic
20#34012C211yesmaximal, characteristic, complemented
21C2×#544C2212yes—
22C2×#536C2212yes—
23C22×C4⋊Q8C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C2×#519C2212yes—
27C2×C4×#41C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2868C2212yescomplemented
30#2862C2214yescomplemented
31#2861C2214yescomplemented
32#2859C2212yescomplemented
33#2857C2214yes—
34#2857C2214yes—
35#2857C2214yes—
36#2857C2214yes—
37#2857C2212yescomplemented
38#2857C2212yescomplemented
39#2775C22116yescomplemented
40#2769C22116yescomplemented
41#2744C22116yes—
42#2737C22116yes—
43#2660C2214yescomplemented
44#2642C2214yescomplemented
45#2640C2214yescomplemented
46#2621C2214yescomplemented
47#2612C22116yescomplemented
48#2574C22116yes—
49#2571C2218yescomplemented
50#2563C2218yes—
51#2561C2218yes—
52#2552C2214yescomplemented
53#2551C2214yescomplemented
54#2547C2214yescomplemented
55#2546C2214yescomplemented
56#2538C2218yes—
57#2536C2218yes—
58#2531C22116yes—
59#2529C22116yescomplemented
60#2508C2218yescomplemented
61#2508C2218yescomplemented
62#2503C2218yes—
63#2497C2218yes—
64#2497C2218yescomplemented
65#2495C2218yes—
66#2495C2218yescomplemented
67#2492C2218yes—
68#2492C2218yes—
69#2492C2218yescomplemented
70#2489C2218yes—
71#2489C2218yes—
72#2489C2218yescomplemented
73#2488C22116yes—
74#2486C2218yes—
75#2485C2218yes—
76#2485C2218yes—
77#2440C2218yes—
78#2439C2218yes—
79#2439C2218yescomplemented
80#2429C2218yes—
81#2426C2218yes—
82#2413C2218yes—
83#2411C2218yes—
84#2369C2218yescomplemented
85#2365C2214yescomplemented
86#2365C2214yescomplemented
87#2356C2218yescomplemented
88#2355C2214yescomplemented
89#2355C2218yescomplemented
90#2354C2218yes—
91#2354C2214yescomplemented
92#2352C2218yes—
93#2346C2218yes—
94#2346C2218yescomplemented
95#2344C2218yes—
96#2343C22116yes—
97#2327C2214yescomplemented
98#2320C2218yescomplemented
99#2317C2212yes—
100#2314C2214yescomplemented
101#2311C2212yes—
102#2310C2212yes—
103#2310C2212yes—
104C4×C4⋊Q8C2214yescomplemented
105C4×C22⋊Q8C2212yes—
106C4×C22⋊Q8C2212yes—
107C4×#123C2214yes—
108C4×#121C2212yes—
109C4×#121C2212yes—
110C4×#120C2214yes—
111#2297C2211yescharacteristic
112#2296C2211yescharacteristic
113#2295C2218yescomplemented
114C2×#391C2212yes—
115C2×#389C2214yes—
116#2290C2214yes—
117#2285C2212yes—
118#2285C2212yes—
119#2285C2211yescharacteristic
120#2285C2211yescharacteristic
121#2285C2214yescomplemented
122C2×#384C2211yescharacteristic
123#2283C2214yes—
124#2283C2214yes—
125#2283C2214yes—
126#2280C2211yescharacteristic
127#2280C2212yes—
128#2280C2214yes—
129C2×#380C2214yes—
130#2274C2212yes—
131C42×D4C2214yes—
132C4×#117C2211yescharacteristic
133C4×#117C2214yes—
134C4×#117C2212yes—
135C22×#41C2311yescharacteristic
136C23×Q8C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139#544—48no—
140#536—48no—
141C2×C4⋊Q8—28no—
142C2×C4⋊Q8C2312yes—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2314yes—
145C2×C4⋊Q8C2318yes—
146C2×C4⋊Q8C2314yes—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2314yes—
149C2×#125C2314yes—
150C2×#125C2314yes—
151C2×#124C2314yes—
152#525—28no—
153C2×#123C2312yes—
154C2×#123C2318yes—
155C2×C22⋊Q8—48no—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2318yes—
158C2×C22⋊Q8C2318yes—
159C2×C22⋊Q8C2318yes—
160C2×C22⋊Q8C2314yes—
161C2×C22⋊Q8C2314yes—
162C2×#121C2312yes—
163C2×#120C2312yes—
164#519—216no—
165C4×#41—28no—
166C2×C4×Q8C2318yes—
167C2×C4×Q8C2318yes—
168C2×C4×Q8C2312yes—
169C2×C4×D4C2314yes—
170C2×C4×D4C2314yes—
171C2×C4×D4C2312yes—
172C2×C4×D4C2314yes—
173C2×C4×D4C2314yes—
174C2×#117C2311yescharacteristic
175C2×#117C2311yescharacteristic
176C2×#117C2312yes—
177C2×#117C2312yes—
178C2×#117C2312yes—
179C2×#117C2318yes—
180C2×#117C2314yes—
181C2×#117C2318yes—
182C2×#117C2314yes—
183C2×#117C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2314yes—
186C22×C4⋊C4C2314yes—
187C22×C4⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C42—28no—
190C22×C42C2312yes—
191C22×C42C2312yes—
192C22×C42C2312yes—
193C22×C42C2312yes—
194C22×C42C2312yes—
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198#400C23116yes—
199#400C23116yes—
200#400C23116yes—
201#400C23116yes—
202#398C23116yes—
203#398C23116yes—
204#398C23116yes—
205#397C23116yes—
206#397C23116yes—
207#397C23116yes—
208#396C23116yes—
209#396C23116yes—
210#395C23116yes—
211#394C23116yes—
212#393C23116yes—
213#393C23116yes—
214#391C2318yes—
215#391C2318yes—
216#391C2314yes—
217#391C2314yes—
218#391C2314yes—
219#391C2314yes—
220#391C2314yes—
221#391C23116yes—
222#391C2314yes—
223#391C2314yes—
224#391C2318yes—
225#391C2311yescharacteristic
226#391C23116yes—
227#391C2311yescharacteristic
228#390C23116yes—
229#390C2314yes—
230#390C2311yescharacteristic
231#390C2311yescharacteristic
232#389C2318yes—
233#389C2318yes—
234#389C2318yes—
235#389C2318yes—
236#389C23116yes—
237#389C2318yes—
238#389C2312yes—
239#389C2318yes—
240#389C2318yes—
241#389C2318yes—
242#389C2318yes—
243#389C2318yes—
244#389C2318yes—
245#389C2312yes—
246#388C23116yes—
247#388C23116yes—
248#388C23116yes—
249#388C23116yes—
250#388C23116yes—
251#388C23116yes—
252#388C23116yes—
253#388C2314yes—
254#388C2314yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#387C23116yes—
261#387C23116yes—
262#387C2314yes—
263#387C2314yes—
264#386C2318yes—
265#386C2314yes—
266#386C2314yes—
267#386C2314yes—
268#385C2318yes—
269#385C2314yes—
270#385C2314yes—
271#385C2314yes—
272#384C2312yes—
273#384C2312yes—
274#384C2318yes—
275#384C2314yes—
276#384C2312yes—
277#384C2314yes—
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#383C23116yes—
281#383C2318yes—
282#382C23116yes—
283#382C2312yes—
284#382C2314yes—
285#382C2318yes—
286#382C2314yes—
287#382C23116yes—
288#382C23116yes—
289#382C2312yes—
290#382C2314yes—
291#381C2318yes—
292#381C2318yes—
293#381C2314yes—
294#381C2318yes—
295#381C2312yes—
296#380C2314yes—
297#380C2318yes—
298#380C2318yes—
299#380C2318yes—
300#380C2318yes—
301#380C2318yes—
302#380C2314yes—
303#380C2318yes—
304#380C2318yes—
305#380C2318yes—
306#380C2314yes—
307#380C2314yes—
308#380C2312yes—
309#380C2314yes—
310#380C2312yes—
311#380C2314yes—
312#379C2312yes—
313#379C2314yes—
314C4×C4⋊C4C2318yes—
315C4×C4⋊C4C2318yes—
316C4×C4⋊C4C2318yes—
317C4×C4⋊C4C2314yes—
318C4×C4⋊C4C23116yes—
319C4×C4⋊C4C2318yes—
320C4×C4⋊C4C2318yes—
321C4×C4⋊C4C2314yes—
322C4×C4⋊C4C2314yes—
323C4×C4⋊C4C2314yes—
324C4×C4⋊C4C2314yes—
325C4×C4⋊C4C2314yes—
326C4×C4⋊C4C2312yes—
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C22⋊C4C2318yes—
332C4×C22⋊C4C2318yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2318yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342#376C2314yes—
343#376C2312yes—
344#376C23116yes—
345#376C2318yes—
346C2×#95C2318yes—
347C43C2312yes—
348C43C2314yes—
349C25C2411yescharacteristic
350C2×#41—24no—
351C2×#41—24no—
352C2×#41—24no—
353C22×Q8—28no—
354C22×Q8—28no—
355C22×Q8—28no—
356C22×Q8C2414yes—
357C22×Q8C2414yes—
358C22×Q8C2411yescharacteristic
359C22×Q8C2418yes—
360C22×D4C2412yes—
361C22×D4C2411yescharacteristic
362C22×D4C2414yes—
363C23×C4—24no—
364C23×C4—28no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—28no—
368C23×C4—44no—
369C23×C4C2414yes—
370C23×C4C2411yescharacteristic
371C23×C4C2414yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2414yes—
382C23×C4C2411yescharacteristic
383C4⋊Q8—28no—
384C4⋊Q8—28no—
385C4⋊Q8—216no—
386C4⋊Q8—416no—
387C4⋊Q8—48no—
388C4⋊Q8—48no—
389C4⋊Q8—48no—
390#125—48no—
391#125—48no—
392#124—48no—
393#123—28no—
394#123—416no—
395C22⋊Q8—28no—
396C22⋊Q8—416no—
397C22⋊Q8—416no—
398C22⋊Q8—416no—
399C22⋊Q8—48no—
400C22⋊Q8—48no—
401#121—28no—
402#120—28no—
403C4×Q8—232no—
404C4×Q8—28no—
405C4×Q8—232no—
406C4×D4—216no—
407C4×D4—216no—
408C4×D4—28no—
409C4×D4—216no—
410C4×D4—48no—
411#117—24no—
412#117—28no—
413#117—28no—
414#117—24no—
415#117—216no—
416#117—232no—
417#117—28no—
418#117—416no—
419#117—48no—
420#117#4118yes—
421C2×C4⋊C4—216no—
422C2×C4⋊C4—28no—
423C2×C4⋊C4—48no—
424C2×C4⋊C4—48no—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2414yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C24116yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C24116yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C24116yes—
453C2×C4⋊C4C2412yes—
454C2×C22⋊C4—48no—
455C2×C22⋊C4C2414yes—
456C2×C22⋊C4C2412yes—
457C2×C22⋊C4C2414yes—
458C2×C22⋊C4C2412yes—
459C2×C22⋊C4C2414yes—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C2414yes—
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C24116yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C24116yes—
468C2×C22⋊C4C2414yes—
469C2×C22⋊C4C2414yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2412yes—
473C2×C42—28no—
474C2×C42—24no—
475C2×C42—28no—
476C2×C42—28no—
477C2×C42—28no—
478C2×C42—28no—
479C2×C42—28no—
480C2×C42#4118yes—
481C2×C42C2412yes—
482C2×C42C2414yes—
483C2×C42C24116yes—
484C2×C42C2414yes—
485C2×C42C2412yes—
486C2×C42C2418yes—
487C2×C42C2414yes—
488C2×C42C2414yes—
489C2×C42C2414yes—
490C2×C42C2411yescharacteristic
491C2×C42C2412yes—
492C2×C42C2411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2412yes—
495C2×C42C2412yes—
496C2×C42C2412yes—
497C2×C42C2418yes—
498C2×C42C24116yes—
499C2×C42C2411yescharacteristic
500C2×C42C2412yes—
501C2×C42C2412yes—
502C2×C42C2411yescharacteristic
503#95C24116yes—
504#95C24116yes—
505#95C2414yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2414yes—
513#95C2414yes—
514#95C24116yes—
515#95C24116yes—
516#95C2414yes—
517#95C2414yes—
518#95C2414yes—
519#95C2414yes—
520#95C2414yes—
521#95C24116yes—
522#95C24116yes—
523#95C24116yes—
524#95C24116yes—
525#95C24116yes—
526C24—22no—
527C24—24no—
528C24—22no—
529C24—22no—
530C24—42no—
531C24C2512yes—
532C24C2512yes—
533C24C2511yescharacteristic
534#41—416no—
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—28no—
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—22no—
544C2×Q8—48no—
545C2×Q8—416no—
546C2×Q8—432no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—28no—
551C2×D4—22no—
552C2×D4—28no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—44no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—28no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—28no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—28no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—28no—
587C22×C4—24no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—432no—
592C22×C4—48no—
593C22×C4—416no—
594C22×C4C2×#4118yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4H(5,𝔽2)14yes—
598C22×C42−1+418yes—
599C22×C4C2512yes—
600C22×C4C2514yes—
601C22×C4C2518yes—
602C22×C4C2514yes—
603C22×C4C2512yes—
604C22×C4C2512yes—
605C22×C4C2512yes—
606C22×C4C2518yes—
607C22×C4C2512yes—
608C22×C4C2514yes—
609C22×C4C2518yes—
610C22×C4C2512yes—
611C22×C4C2514yes—
612C22×C4C2512yes—
613C22×C4C2511yescharacteristic
614C22×C4C2511yescharacteristic
615C22×C4C2512yes—
616C4⋊C4—216no—
617C4⋊C4—216no—
618C4⋊C4—24no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—232no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—216no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—48no—
636C4⋊C4—416no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—416no—
644C4⋊C4C2×#4118yes—
645C22⋊C4—28no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—28no—
649C22⋊C4—216no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—416no—
656C22⋊C4—416no—
657C22⋊C4—48no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4C2×#4118yes—
663C42—22no—
664C42—24no—
665C42—24no—
666C42—24no—
667C42—24no—
668C42—22no—
669C42—24no—
670C42—24no—
671C42—28no—
672C42—28no—
673C42—232no—
674C42—28no—
675C42—24no—
676C42—216no—
677C42—28no—
678C42—28no—
679C42—48no—
680C42—416no—
681C42C2×#4114yes—
682C42C2×#4114yes—
683C42C2×#4118yes—
684C42C2×#4118yes—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—48no—
700C23—48no—
701C23—44no—
702C23—44no—
703C23C22×#4112yes—
704C23C22×#4112yes—
705C23C2×H(5,𝔽2)12yes—
706C23C2×2−1+414yes—
707C23C2611yescharacteristic
708Q8—416no—
709Q8—416no—
710Q8—44no—
711Q8—168no—
712D4—416no—
713D4—48no—
714D4—44no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—216no—
722C2×C4—216no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—216no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—44no—
755C2×C4—416no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—416no—
760C2×C4—48no—
761C2×C4—88no—
762C2×C4#555116yes—
763C2×C4C22×#4118yes—
764C2×C4C22×#4114yes—
765C2×C4C22×#4112yes—
766C2×C4C22×#4112yes—
767C2×C4C22×#4112yes—
768C2×C4C22×#4112yes—
769C2×C4C22×#4114yes—
770C2×C4C2×H(5,𝔽2)12yes—
771C2×C4C2×H(5,𝔽2)12yes—
772C2×C4C2×2−1+414yes—
773C2×C4C2×2−1+414yes—
774C2×C4#58514yes—
775C22—24no—
776C22—24no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—416no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×#55514yes—
793C22C23×#4111yescharacteristic
794C22C23×#4111yescharacteristic
795C22C22×H(5,𝔽2)11yescharacteristic
796C22C22×2−1+412yes—
797C22C2×#58512yes—
798C4—24no—
799C4—24no—
800C4—28no—
801C4—44no—
802C4—42no—
803C4—48no—
804C4—44no—
805C4—42no—
806C4—48no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—48no—
812C4C2×#55514yes—
813C4C2×#55514yes—
814C4#349518yes—
815C2—24no—
816C2—44no—
817C2—82no—
818C2C22×#55511yescharacteristic
819C2C2×#349512yes—
820C2#6280512yes—
821C2#6283311yescharacteristic
822C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59225C2semidirect
2. #59203C2semidirect
3. #38943C2semidirect
4. #38940C2semidirect
5. #37955C2semidirect
6. C2×#2857C2semidirect
7. #36315C2semidirect
8. #36288C2semidirect
9. #36209C2semidirect
10. #36194C2semidirect
12. #35644C2semidirect
13. #35316C2semidirect
14. #35312C2semidirect
15. #35275C2semidirect
16. #34254C2semidirect
17. #34209C2semidirect
18. #34188C2semidirect
20. #34012C2semidirect
29. #2868C22semidirect
30. #2862C22semidirect
31. #2861C22semidirect
32. #2859C22semidirect
37. #2857C22semidirect
38. #2857C22semidirect
39. #2775C22semidirect
40. #2769C22semidirect
43. #2660C22semidirect
44. #2642C22semidirect
45. #2640C22semidirect
46. #2621C22semidirect
47. #2612C22semidirect
49. #2571C22semidirect
52. #2552C22semidirect
53. #2551C22semidirect
54. #2547C22semidirect
55. #2546C22semidirect
59. #2529C22semidirect
60. #2508C22semidirect
61. #2508C22semidirect
64. #2497C22semidirect
66. #2495C22semidirect
69. #2492C22semidirect
72. #2489C22semidirect
79. #2439C22semidirect
84. #2369C22semidirect
85. #2365C22semidirect
86. #2365C22semidirect
87. #2356C22semidirect
88. #2355C22semidirect
89. #2355C22semidirect
91. #2354C22semidirect
94. #2346C22semidirect
97. #2327C22semidirect
98. #2320C22semidirect
100. #2314C22semidirect
104. C4×C4⋊Q8C22semidirect
113. #2295C22semidirect
121. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#592252
#592032
#389432
#389402
#379552
C2×#28572
#363152
#362882
#362092
#361942
#356612
#356442
#353162
#353122
#352752
#342542
#342092
#341882
C4×#5252
#340122