Finite Group Databasebeta

← #617373

Subgroups — #617373

Order 512.

3086 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2621C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic
5C2×#2323C211yesmaximal, characteristic
6C2×#2296C211yesmaximal, characteristic
7#15618C214yesmaximal, complemented
8#15472C214yesmaximal
9#15347C214yesmaximal, complemented
10#15290C214yesmaximal
11#15237C211yesmaximal, characteristic, complemented
12#15184C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#15180C211yesmaximal, characteristic, complemented
15#14702C211yesmaximal, characteristic
16#14258C211yesmaximal, characteristic
17#14155C211yesmaximal, characteristic, complemented
18#13942C211yesmaximal, characteristic, complemented
19#13909C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857—28no—
31#2621—28no—
32#2621—28no—
33#2546—28no—
34C2×#398C2212yes—
35C2×#398C2214yes—
36C2×#398C2214yes—
37C2×#398C2212yes—
38C2×#397C2212yes—
39C2×#397C2214yes—
40C2×#397C2212yes—
41#2323—28no—
42#2296—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#389C2212yes—
55C2×#389C2212yes—
56C2×#389C2214yes—
57C2×#389C2211yescharacteristic
58C2×#389C2214yes—
59C2×#389C2212yes—
60C2×#388C2212yes—
61C2×#388C2212yes—
62C2×#387C2212yes—
63C2×#385C2212yes—
64C2×#385C2212yes—
65C2×#384C2211yescharacteristic
66C2×#382C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2214yes—
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75#1445C2214yes—
76#1443C2214yes—
77#1442C2214yes—
78#1442C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1441C2214yes—
86#1441C2214yes—
87#1440C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95#1434C2214yes—
96C22⋊#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8—42no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8D418yes—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—42no—
128C2×#117D418yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42—24no—
159C22×C42—24no—
160C22×C42—42no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170#398—216no—
171#398—28no—
172#398—28no—
173#398—216no—
174#397—216no—
175#397—28no—
176#397—28no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—42no—
187#391—42no—
188#389—28no—
189#389—216no—
190#389—216no—
191#389—28no—
192#389—24no—
193#389—28no—
194#388—28no—
195#388—28no—
196#387—28no—
197#385—28no—
198#385—28no—
199#384—24no—
200#382—24no—
201#382—24no—
202#380—24no—
203#380—216no—
204C4×C4⋊C4—24no—
205C4×C4⋊C4—24no—
206C4×C4⋊C4—24no—
207C4×C4⋊C4—24no—
208C4×C4⋊C4D418yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C25C2411yescharacteristic
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8C2×D414yes—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4#4114yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C4⋊Q8—416no—
292C4⋊Q8—416no—
293C4⋊Q8—416no—
294C22⋊Q8—232no—
295C22⋊Q8—416no—
296C22⋊Q8—416no—
297C4×Q8—416no—
298#117—232no—
299#117—416no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D418yes—
364C2×C4⋊C4C2×D418yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4C2×D418yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—416no—
404C2×C42—42no—
405C2×C42—44no—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—28no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95C2×D418yes—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C2×#4112yes—
451C24C2511yescharacteristic
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—216no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4#121116yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C42−1+414yes—
592C22×C42−1+414yes—
593C22×C42−1+414yes—
594C22×C42−1+412yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—216no—
599C4⋊C4—216no—
600C4⋊C4—416no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—416no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—84no—
617C22⋊C4—216no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—84no—
624C42—28no—
625C42—28no—
626C42—28no—
627C42—48no—
628C42—48no—
629C42—44no—
630C42—44no—
631C42—84no—
632C42#121116yes—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×#12114yes—
656C23C23×D411yescharacteristic
657C23C23×D411yescharacteristic
658C23C23×D411yescharacteristic
659C23C22×#4111yescharacteristic
660C23C22×#4111yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×2−1+412yes—
663C23C2×2−1+412yes—
664C23C2×2−1+411yescharacteristic
665C23C2×2−1+412yes—
666C23#58512yes—
667Q8—416no—
668Q8—88no—
669Q8—88no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—232no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—432no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4C2×#12114yes—
770C2×C4C2×#12114yes—
771C2×C4C2×#12114yes—
772C2×C4C2×#12114yes—
773C2×C4C2×#12114yes—
774C2×C4#53618yes—
775C2×C4#53714yes—
776C2×C4D4214yes—
777C2×C4#54714yes—
778C2×C4#54814yes—
779C2×C4#55314yes—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22C22×#12111yescharacteristic
792C22C22×#12111yescharacteristic
793C22C2×#53612yes—
794C22C2×#53711yescharacteristic
795C22#346112yes—
796C22C2×D4211yescharacteristic
797C22C2×#54711yescharacteristic
798C22C2×#54811yescharacteristic
799C22C2×#55311yescharacteristic
800C22#348612yes—
801C22#348912yes—
802C22#348912yes—
803C22#349911yescharacteristic
804C22#349911yescharacteristic
805C22#349911yescharacteristic
806C22#350011yescharacteristic
807C22#350712yes—
808C22#350912yes—
809C22#350912yes—
810C22#353812yes—
811C22#354112yes—
812C22#355512yes—
813C22#355612yes—
814C4—28no—
815C4—24no—
816C4—24no—
817C4—24no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#241618yes—
832C2—44no—
833C2C2×#241611yescharacteristic
834C2#3530811yescharacteristic
835C2#3531611yescharacteristic
836C2#3562111yescharacteristic
837C2#3566711yescharacteristic
838C2#3738711yescharacteristic
839C2#3738911yescharacteristic
840C2#3765112yes—
841C2#3779312yes—
842C2#3972412yes—
843C2#3981912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2546C2semidirect
7. #15618C2semidirect
9. #15347C2semidirect
11. #15237C2semidirect
12. #15184C2semidirect
13. #15180C2semidirect
14. #15180C2semidirect
17. #14155C2semidirect
18. #13942C2semidirect
19. #13909C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25462
C2×#26212
C2×#23232
C2×#22962
#156182
#154722
#153472
#152902
#152372
#151842
#151802
#147022
#142582
#141552
#139422
#139092