Finite Group Databasebeta

← #764796

Subgroups — #764796

Order 512.

3584 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2565C211yesmaximal, characteristic, complemented
4C2×#2323C211yesmaximal, characteristic
5#16104C214yesmaximal, complemented
6#16102C214yesmaximal
7#15912C214yesmaximal
8#15848C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic
10#15182C211yesmaximal, characteristic
11#15178C211yesmaximal, characteristic
12#15178C211yesmaximal, characteristic
13#14160C211yesmaximal, characteristic, complemented
14#14155C211yesmaximal, characteristic, complemented
15#14024C211yesmaximal, characteristic, complemented
16#14024C211yesmaximal, characteristic, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19#13852C211yesmaximal, characteristic
20C2×#541—28no—
21C2×#541—28no—
22C2×#541—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126C2212yes—
27C22×#126C2212yes—
28C22×#125C2212yes—
29C22×#125C2212yes—
30C22×#125C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2565—28no—
39#2546—28no—
40C2×#398C2214yes—
41C2×#398C2214yes—
42#2323—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2212yes—
54C2×#389C2214yes—
55C2×#388C2212yes—
56C2×#388C2212yes—
57C2×#387C2212yes—
58C2×#387C2214yes—
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1440C2214yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C24×C4C2311yescharacteristic
101#541—2128no—
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—42no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8D418yes—
111C2×#126—28no—
112C2×#126—28no—
113C2×#126—28no—
114C2×#126—28no—
115C2×#126—28no—
116C2×#126—28no—
117C2×#125—28no—
118C2×#125—28no—
119C2×#125—28no—
120C2×#125—28no—
121C2×#125—28no—
122C2×#125—28no—
123C2×#125—24no—
124C2×#125—24no—
125C2×#125D418yes—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—24no—
143C2×C4×Q8—24no—
144C2×#117—24no—
145C2×#117—24no—
146C2×#117D418yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2314yes—
158C22×C4⋊C4C2314yes—
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C42C2312yes—
179C22×C42C2312yes—
180C22×C42C2312yes—
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186C22×C42C2312yes—
187C22×C42C2311yescharacteristic
188#398—216no—
189#398—216no—
190#391—24no—
191#391—24no—
192#391—24no—
193#391—24no—
194#391—24no—
195#391—24no—
196#391—24no—
197#391—42no—
198#391—42no—
199#389—28no—
200#389—216no—
201#389—24no—
202#388—28no—
203#388—28no—
204#387—216no—
205#387—28no—
206#384—24no—
207#382—24no—
208#380—24no—
209C4×C4⋊C4—24no—
210C4×C4⋊C4—24no—
211C4×C4⋊C4—24no—
212C4×C22⋊C4—42no—
213C4×C22⋊C4—42no—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C25C2411yescharacteristic
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×Q8—22no—
259C22×Q8C2×D414yes—
260C22×Q8C2×D414yes—
261C22×Q8#4114yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4C2×D414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C4⋊Q8—232no—
288C4⋊Q8—416no—
289C4⋊Q8—416no—
290#126—264no—
291#126—264no—
292#125—264no—
293#125—264no—
294#125—232no—
295C22⋊Q8—232no—
296C22⋊Q8—232no—
297C22⋊Q8—232no—
298C4×Q8—232no—
299C4×Q8—232no—
300C4×Q8—416no—
301#117—232no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2×D418yes—
366C2×C4⋊C4C2×D418yes—
367C2×C4⋊C4C2×D418yes—
368C2×C4⋊C4C2×D418yes—
369C2×C4⋊C4#4114yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×D414yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—44no—
418C2×C42C2×D414yes—
419C2×C42C2×D414yes—
420C2×C42C2×D414yes—
421C2×C42C2×D414yes—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—24no—
428#95—24no—
429#95—28no—
430#95—28no—
431#95—24no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—24no—
437#95—28no—
438#95—24no—
439#95—24no—
440#95—28no—
441#95—44no—
442#95—42no—
443#95—44no—
444#95—42no—
445#95—42no—
446#95—44no—
447#95—44no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—22no—
458C24C22×D412yes—
459C24C2511yescharacteristic
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D412yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C42−1+414yes—
593C22×C42−1+414yes—
594C22×C42−1+414yes—
595C22×C42−1+412yes—
596C4⋊C4—216no—
597C4⋊C4—216no—
598C4⋊C4—216no—
599C4⋊C4—216no—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—28no—
611C4⋊C4—48no—
612C4⋊C4—416no—
613C4⋊C4—416no—
614C4⋊C4—416no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—84no—
619C22⋊C4—216no—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—84no—
627C42—216no—
628C42—216no—
629C42—28no—
630C42—48no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—84no—
636C42#120116yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23C23×D411yescharacteristic
661C23C23×D411yescharacteristic
662C23C23×D411yescharacteristic
663C23C22×#4111yescharacteristic
664C23C22×#4111yescharacteristic
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23C2×2−1+412yes—
668C23C2×2−1+412yes—
669C23C2×2−1+412yes—
670C23#58512yes—
671Q8—416no—
672Q8—416no—
673Q8—416no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
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—28no—
707C2×C4—22no—
708C2×C4—28no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
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—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
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—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—416no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4C2×#12014yes—
775C2×C4C2×#12014yes—
776C2×C4C2×#12014yes—
777C2×C4#52514yes—
778C2×C4#53714yes—
779C2×C4#54614yes—
780C2×C4#54714yes—
781C2×C4#54814yes—
782C2×C4#55014yes—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C22×#12011yescharacteristic
795C22C2×#52511yescharacteristic
796C22C2×#53711yescharacteristic
797C22C2×#54611yescharacteristic
798C22C2×#54711yescharacteristic
799C22C2×#54811yescharacteristic
800C22C2×#55011yescharacteristic
801C22#348612yes—
802C22#348912yes—
803C22#349712yes—
804C22#349911yescharacteristic
805C22#349911yescharacteristic
806C22#349911yescharacteristic
807C22#349912yes—
808C22#350011yescharacteristic
809C22#351512yes—
810C22#351612yes—
811C22#352312yes—
812C22#352312yes—
813C22#353812yes—
814C22#354112yes—
815C22#355512yes—
816C22#355612yes—
817C4—24no—
818C4—24no—
819C4—44no—
820C4—42no—
821C4—44no—
822C4—42no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—44no—
830C4—44no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4#240718yes—
835C2—82no—
836C2C2×#240711yescharacteristic
837C2#3562211yescharacteristic
838C2#3566011yescharacteristic
839C2#3566611yescharacteristic
840C2#3567011yescharacteristic
841C2#3738711yescharacteristic
842C2#3738911yescharacteristic
843C2#4521712yes—
844C2#4524912yes—
845C2#4532412yes—
846C2#4534312yes—
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
3. C2×#2565C2semidirect
5. #16104C2semidirect
8. #15848C2semidirect
13. #14160C2semidirect
14. #14155C2semidirect
15. #14024C2semidirect
16. #14024C2semidirect
17. #13978C2semidirect
18. #13976C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5412
C2×#25462
C2×#25652
C2×#23232
#161042
#161022
#159122
#158482
#152362
#151822
#151782
#141602
#141552
#140242
#139782
#139762
#138522