Finite Group Databasebeta

← #687730

Subgroups — #687730

Order 512.

3526 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2434C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic
5C2×#2362C211yesmaximal, characteristic
6C2×#2310C211yesmaximal, characteristic
7#16293C214yesmaximal, complemented
8#15398C214yesmaximal
9#15298C214yesmaximal
10#15237C211yesmaximal, characteristic, complemented
11#15190C211yesmaximal, characteristic, complemented
12#15188C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#14816C214yesmaximal, complemented
15#14155C211yesmaximal, characteristic, complemented
16#14138C211yesmaximal, characteristic
17#14024C211yesmaximal, characteristic, complemented
18#14003C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2621—28no—
32#2546—28no—
33#2434—28no—
34#2434—28no—
35C2×#398C2214yes—
36C2×#398C2214yes—
37C2×#397C2214yes—
38C2×#395C2212yes—
39C2×#395C2214yes—
40C2×#395C2212yes—
41#2362—28no—
42#2310—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2214yes—
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#389C2214yes—
58C2×#389C2211yescharacteristic
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#387C2212yes—
62C2×#385C2212yes—
63C2×#385C2214yes—
64C2×#385C2212yes—
65C2×#382C2211yescharacteristic
66C2×#381C2214yes—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2212yes—
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73#1445C2214yes—
74#1444C2212yes—
75#1444C2214yes—
76#1444C2214yes—
77#1443C2214yes—
78#1443C2214yes—
79#1442C2212yes—
80#1442C2214yes—
81#1442C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1441C2214yes—
86#1440C2214yes—
87#1439C2212yes—
88#1439C2212yes—
89#1436C2214yes—
90#1436C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2214yes—
94#1434C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—24no—
101C23×Q8—24no—
102C23×Q8—42no—
103C23×Q8—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×Q8C2311yescharacteristic
108C23×Q8C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8—42no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8D418yes—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—42no—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117—24no—
138C2×#117—24no—
139C2×#117—42no—
140C2×#117—42no—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#398—216no—
176#398—216no—
177#397—216no—
178#395—216no—
179#395—28no—
180#395—28no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—216no—
193#391—42no—
194#391D418yes—
195#389—24no—
196#389—216no—
197#388—28no—
198#388—28no—
199#387—28no—
200#385—216no—
201#385—28no—
202#385—28no—
203#382—24no—
204#381—216no—
205C4×C4⋊C4—24no—
206C4×C4⋊C4—24no—
207C4×C4⋊C4—28no—
208C4×C4⋊C4—42no—
209C4×C22⋊C4—24no—
210C4×C22⋊C4D418yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2314yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2314yes—
241C25C2411yescharacteristic
242C22×Q8—232no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—24no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8—416no—
276C22×Q8—416no—
277C22×Q8—416no—
278C22×Q8—416no—
279C22×Q8—416no—
280C22×Q8—416no—
281C22×Q8C2×D414yes—
282C22×Q8C2×D414yes—
283C22×Q8#4114yes—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4#4114yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C4⋊Q8—416no—
317C4⋊Q8—416no—
318C4⋊Q8—416no—
319C4⋊Q8—416no—
320C4⋊Q8—416no—
321C22⋊Q8—232no—
322C22⋊Q8—416no—
323C4×Q8—416no—
324#117—416no—
325#117—416no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D418yes—
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—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4C2×D418yes—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4C2×D414yes—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—28no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42C2×D414yes—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—28no—
441#95—28no—
442#95—28no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—28no—
447#95—24no—
448#95—28no—
449#95—42no—
450#95—44no—
451#95C2×D414yes—
452#95C2×D414yes—
453#95C2×D4116yes—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C2×#4112yes—
465C24C2511yescharacteristic
466C2×Q8—216no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—4128no—
482C2×Q8—48no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
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—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4#121116yes—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C22×D414yes—
608C22×C4C22×D414yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C42−1+414yes—
623C22×C42−1+414yes—
624C22×C42−1+414yes—
625C22×C42−1+414yes—
626C4⋊C4—216no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—48no—
637C4⋊C4—416no—
638C4⋊C4—48no—
639C4⋊C4—416no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C42—28no—
652C42—28no—
653C42—28no—
654C42—48no—
655C42—48no—
656C42—48no—
657C42—44no—
658C42—44no—
659C42—44no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23C2×#12114yes—
683C23C23×D411yescharacteristic
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4111yescharacteristic
688C23C2×H(5,𝔽2)11yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×2−1+412yes—
691C23C2×2−1+412yes—
692C23C2×2−1+412yes—
693C23C2×2−1+412yes—
694Q8—432no—
695Q8—416no—
696Q8—416no—
697Q8—416no—
698Q8—88no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—232no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—28no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—432no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
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—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
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—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4C2×#12114yes—
802C2×C4C2×#12114yes—
803C2×C4#52514yes—
804C2×C4#53614yes—
805C2×C4#53614yes—
806C2×C4#53814yes—
807C2×C4D4214yes—
808C2×C4D4214yes—
809C2×C4#54614yes—
810C2×C4#54614yes—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—44no—
815C22—44no—
816C22—42no—
817C22—42no—
818C22—44no—
819C22—44no—
820C22—42no—
821C22—42no—
822C22C22×#12111yescharacteristic
823C22C2×#52511yescharacteristic
824C22C2×#53611yescharacteristic
825C22C2×#53611yescharacteristic
826C22C2×#53811yescharacteristic
827C22C2×D4211yescharacteristic
828C22C2×D4211yescharacteristic
829C22C2×#54611yescharacteristic
830C22C2×#54611yescharacteristic
831C22#348612yes—
832C22#348612yes—
833C22#349912yes—
834C22#349912yes—
835C22#349911yescharacteristic
836C22#349911yescharacteristic
837C22#350912yes—
838C22#350912yes—
839C22#352312yes—
840C22#352312yes—
841C22#353812yes—
842C22#355012yes—
843C22#355212yes—
844C22#355212yes—
845C4—24no—
846C4—24no—
847C4—24no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—42no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—42no—
856C4—44no—
857C4—44no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4#242418yes—
863C2—44no—
864C2C2×#242411yescharacteristic
865C2#3531611yescharacteristic
866C2#3566711yescharacteristic
867C2#3574912yes—
868C2#3767511yescharacteristic
869C2#3808111yescharacteristic
870C2#3895411yescharacteristic
871C2#3936011yescharacteristic
872C2#4294112yes—
873C2#4532112yes—
874C2#4532212yes—
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
1. C2×#2546C2semidirect
7. #16293C2semidirect
10. #15237C2semidirect
11. #15190C2semidirect
12. #15188C2semidirect
13. #15180C2semidirect
14. #14816C2semidirect
15. #14155C2semidirect
17. #14024C2semidirect
18. #14003C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24342
C2×#26212
C2×#23622
C2×#23102
#162932
#153982
#152982
#152372
#151902
#151882
#151802
#148162
#141552
#141382
#140242
#140032
#138442