Finite Group Databasebeta

← #802770

Subgroups — #802770

Order 512.

2318 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2421C211yesmaximal, characteristic
2C2×#2343C211yesmaximal, characteristic
3#17048C211yesmaximal, characteristic, complemented
4#17005C211yesmaximal, characteristic
5#15929C212yesmaximal
6#15720C212yesmaximal, complemented
7#15681C212yesmaximal, complemented
8#15298C212yesmaximal
9#15206C211yesmaximal, characteristic, complemented
10#15119C211yesmaximal, characteristic, complemented
11#15012C211yesmaximal, characteristic, complemented
12#14934C211yesmaximal, characteristic
13#14901C211yesmaximal, characteristic, complemented
14#14878C211yesmaximal, characteristic, complemented
15#14763C211yesmaximal, characteristic
16#14133C212yesmaximal, complemented
17#14072C212yesmaximal
18#14014C212yesmaximal, complemented
19#13983C212yesmaximal
20#13965C211yesmaximal, characteristic
21#13963C211yesmaximal, characteristic, complemented
22C4×#395C211yesmaximal, characteristic, complemented
23#13816C211yesmaximal, characteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2421—28no—
28C2×#400C2212yes—
29C2×#398C2212yes—
30C2×#397C2212yes—
31C2×#395C2211yescharacteristic
32#2343—28no—
33C2×#391C2211yescharacteristic
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#387C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#387C2212yes—
42C2×#387C2211yescharacteristic
43C2×#387C2211yescharacteristic
44C2×#387C2212yes—
45C2×#385C2211yescharacteristic
46C2×#385C2211yescharacteristic
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#383C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#381C2211yescharacteristic
53C2×#381C2212yes—
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×#376C2211yescharacteristic
61C2×#376C2211yescharacteristic
62C22×#95C2211yescharacteristic
63#1446C2211yescharacteristic
64#1446C2211yescharacteristic
65#1446C2211yescharacteristic
66#1445C2212yes—
67#1445C2212yes—
68#1444C2211yescharacteristic
69#1444C2211yescharacteristic
70#1444C2212yes—
71#1444C2211yescharacteristic
72#1444C2211yescharacteristic
73#1444C2211yescharacteristic
74#1443C2212yes—
75#1443C2212yes—
76#1443C2212yes—
77#1442C2211yescharacteristic
78#1442C2211yescharacteristic
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2211yescharacteristic
85#1442C2211yescharacteristic
86#1442C2212yes—
87#1442C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1441C2211yescharacteristic
91#1441C2211yescharacteristic
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2211yescharacteristic
97#1440C2212yes—
98#1440C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1437C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2212yes—
113C4⋊#95C2212yes—
114C4⋊#95C2212yes—
115C4⋊#95C2212yes—
116#1434C2212yes—
117#1434C2211yescharacteristic
118#1434C2212yes—
119#1434C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2211yescharacteristic
122C4×#95C2211yescharacteristic
123C4×#95C2212yes—
124C4×#95C2212yes—
125C23×Q8C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—44no—
131C2×C4×Q8—24no—
132C2×C4×Q8—44no—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#400—28no—
174#398—44no—
175#397—28no—
176#395—24no—
177#391—24no—
178#389—28no—
179#389—24no—
180#389—44no—
181#388—28no—
182#388—28no—
183#387—24no—
184#387—24no—
185#387—28no—
186#387—24no—
187#387—24no—
188#387—28no—
189#385—24no—
190#385—24no—
191#385—28no—
192#385—28no—
193#383—24no—
194#382—24no—
195#382—24no—
196#381—24no—
197#381—44no—
198#380—24no—
199C4×C4⋊C4—24no—
200C4×C4⋊C4—44no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4D418yes—
204#376—24no—
205#376—24no—
206C2×#95—24no—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2311yescharacteristic
238C2×#95C2312yes—
239C2×#95C2311yescharacteristic
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C25C2411yescharacteristic
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—24no—
269C22×Q8—22no—
270C22×Q8—42no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—41no—
284C23×C4—42no—
285C23×C4C2×D414yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C22⋊Q8—416no—
309C4×Q8—416no—
310#117—232no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
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—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4#4114yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4#4118yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—41no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42#4114yes—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—24no—
424#95—22no—
425#95—22no—
426#95—24no—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—22no—
435#95—22no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—22no—
453#95—24no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95C2×D414yes—
469#95C2×D414yes—
470#95#4114yes—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24C22×D412yes—
481C24C2×#4114yes—
482C24C2511yescharacteristic
483C2×Q8—28no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—44no—
487C2×Q8—44no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
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—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—28no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—82no—
612C22×C4—84no—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C42−1+412yes—
631C22×C42−1+412yes—
632C22×C42−1+414yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—216no—
656C22⋊C4—48no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—84no—
660C42—28no—
661C42—28no—
662C42—28no—
663C42—44no—
664C42—48no—
665C42—44no—
666C42—48no—
667C42—48no—
668C42—82no—
669C42—84no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23#53214yes—
693C23C23×D411yescharacteristic
694C23C22×#4111yescharacteristic
695C23C22×#4111yescharacteristic
696C23C22×#4112yes—
697C23C22×#4111yescharacteristic
698C23C2×H(5,𝔽2)12yes—
699C23C2×2−1+411yescharacteristic
700C23C2×2−1+412yes—
701C23C2×2−1+411yescharacteristic
702C23#58512yes—
703C23#58511yescharacteristic
704Q8—416no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—416no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—88no—
834C2×C4—88no—
835C2×C4#52514yes—
836C2×C4#54714yes—
837C2×C4#55218yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22C2×#52511yescharacteristic
850C22C2×#53211yescharacteristic
851C22#344911yescharacteristic
852C22C2×#54711yescharacteristic
853C22C2×#55212yes—
854C22#347512yes—
855C22#347512yes—
856C22#348011yescharacteristic
857C22#348211yescharacteristic
858C22#348411yescharacteristic
859C22#348911yescharacteristic
860C22#349911yescharacteristic
861C22#350911yescharacteristic
862C22#350912yes—
863C22#351112yes—
864C22#351312yes—
865C22#351412yes—
866C22#351811yescharacteristic
867C22#352012yes—
868C22#352012yes—
869C22#353512yes—
870C22#356312yes—
871C22#356512yes—
872C4—24no—
873C4—28no—
874C4—24no—
875C4—42no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—42no—
886C4—81no—
887C4—82no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4—82no—
894C2—44no—
895C2#3487711yescharacteristic
896C2#3574011yescharacteristic
897C2#3594011yescharacteristic
898C2#3618111yescharacteristic
899C2#3640511yescharacteristic
900C2#3891211yescharacteristic
901C2#4231611yescharacteristic
902C2#4399312yes—
903C2#4436612yes—
904C2#5949512yes—
905C2#5949712yes—
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
3. #17048C2semidirect
6. #15720C2semidirect
7. #15681C2semidirect
9. #15206C2semidirect
10. #15119C2semidirect
11. #15012C2semidirect
13. #14901C2semidirect
14. #14878C2semidirect
16. #14133C2semidirect
18. #14014C2semidirect
21. #13963C2semidirect
22. C4×#395C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24212
C2×#23432
#170482
#170052
#159292
#157202
#156812
#152982
#152062
#151192
#150122
#149342
#149012
#148782
#147632
#141332
#140722
#140142
#139832
#139652
#139632
C4×#3952
#138162