Finite Group Databasebeta

← #687732

Subgroups — #687732

Order 512.

3754 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic
5C2×#2363C211yesmaximal, characteristic
6C2×#2310C211yesmaximal, characteristic, complemented
7#16295C214yesmaximal, complemented
8#15383C214yesmaximal, complemented
9#15300C214yesmaximal, complemented
10#15243C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15188C211yesmaximal, characteristic, complemented
13#15184C211yesmaximal, characteristic, complemented
14#14770C214yesmaximal, complemented
15#14155C211yesmaximal, characteristic, complemented
16#14138C211yesmaximal, characteristic, complemented
17#14027C211yesmaximal, characteristic, complemented
18#14000C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2620—28no—
32#2547—28no—
33#2436—28no—
34#2434—28no—
35C2×#397C2214yes—
36C2×#396C2214yes—
37C2×#395C2212yes—
38C2×#395C2212yes—
39C2×#394C2214yes—
40C2×#393C2214yes—
41#2363—28no—
42#2310—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2214yes—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2212yes—
58C2×#389C2211yescharacteristic
59C2×#388C2212yes—
60C2×#386C2212yes—
61C2×#386C2214yes—
62C2×#385C2212yes—
63C2×#385C2212yes—
64C2×#384C2211yescharacteristic
65C2×#381C2214yes—
66C2×#380C2214yes—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2211yescharacteristic
73#1445C2214yes—
74#1444C2212yes—
75#1442C2212yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1440C2214yes—
82#1440C2214yes—
83#1440C2214yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1436C2214yes—
90#1436C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2214yes—
94C22⋊#95C2214yes—
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×Q8C2312yes—
108C23×D4C2311yescharacteristic
109C23×D4C2312yes—
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124—24no—
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—42no—
126C2×#124—42no—
127C2×#124—42no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121D418yes—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4—42no—
137C2×#117—24no—
138C2×#117—24no—
139C2×#117—24no—
140C2×#117—24no—
141C2×#117—42no—
142C2×#117—42no—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2314yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179#397—216no—
180#396—216no—
181#395—28no—
182#395—28no—
183#394—216no—
184#393—216no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—24no—
193#391—24no—
194#391—216no—
195#391—42no—
196#391D418yescomplemented
197#390—24no—
198#390—28no—
199#390—24no—
200#389—24no—
201#388—28no—
202#386—216no—
203#386—28no—
204#385—28no—
205#385—28no—
206#384—24no—
207#381—216no—
208#380—216no—
209C4×C4⋊C4—24no—
210C4×C4⋊C4—24no—
211C4×C4⋊C4—42no—
212C4×C22⋊C4—24no—
213C4×C22⋊C4—28no—
214C4×C22⋊C4D418yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2314yes—
241C25C2412yes—
242C25C2411yescharacteristic
243C22×Q8—232no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—24no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—24no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
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—42no—
269C22×Q8—42no—
270C22×Q8—416no—
271C22×Q8—416no—
272C22×Q8—416no—
273C22×Q8—416no—
274C22×Q8—416no—
275C22×Q8—416no—
276C22×Q8C2×D414yes—
277C22×Q8#4114yes—
278C22×D4—24no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—44no—
287C22×D4—44no—
288C22×D4C2×D414yes—
289C22×D4C2×D418yes—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—28no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—44no—
306C23×C4C2×D414yes—
307C23×C4C2×D414yes—
308C23×C4#4114yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C4⋊Q8—416no—
327C4⋊Q8—416no—
328#124—416no—
329#124—416no—
330#124—416no—
331C22⋊Q8—416no—
332#121—232no—
333C4×D4—416no—
334#117—416no—
335#117—416no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
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—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4C2×D418yes—
413C2×C22⋊C4C2×D414yes—
414C2×C22⋊C4C2×D414yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—42no—
434C2×C42—44no—
435C2×C42C2×D414yes—
436C2×C42C2×D414yes—
437C2×C42C2×D414yes—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—24no—
454#95—24no—
455#95—44no—
456#95—42no—
457#95—42no—
458#95—44no—
459#95—42no—
460#95—44no—
461#95C2×D414yes—
462#95C2×D414yes—
463#95C2×D4116yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—24no—
482C24C22×D414yes—
483C24C22×D412yes—
484C24C22×D412yes—
485C24C2×#4112yes—
486C24C2511yescharacteristic
487C2×Q8—216no—
488C2×Q8—28no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—48no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—48no—
498C2×Q8—48no—
499C2×Q8—4128no—
500C2×Q8—48no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×D4—216no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—416no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—84no—
526C2×D4—84no—
527C2×D4—88no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
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—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
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—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—48no—
618C22×C4—416no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—84no—
627C22×C4—88no—
628C22×C4#121116yes—
629C22×C4C22×D414yes—
630C22×C4C22×D414yes—
631C22×C4C22×D412yes—
632C22×C4C22×D414yes—
633C22×C4C22×D414yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4H(5,𝔽2)12yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C42−1+414yes—
649C22×C42−1+414yes—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—44no—
660C4⋊C4—48no—
661C4⋊C4—44no—
662C4⋊C4—88no—
663C4⋊C4—84no—
664C22⋊C4—216no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—416no—
671C22⋊C4—416no—
672C22⋊C4—416no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—84no—
677C22⋊C4—88no—
678C42—28no—
679C42—28no—
680C42—28no—
681C42—48no—
682C42—44no—
683C42—44no—
684C42—44no—
685C42—84no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—28no—
704C23—28no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23C2×#12114yes—
732C23C23×D411yescharacteristic
733C23C23×D411yescharacteristic
734C23C23×D411yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4111yescharacteristic
737C23C2×H(5,𝔽2)11yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×2−1+412yes—
740C23C2×2−1+412yes—
741C23#58512yes—
742C23#58512yes—
743Q8—432no—
744Q8—416no—
745Q8—416no—
746Q8—88no—
747D4—416no—
748D4—816no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—232no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—432no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
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—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—816no—
845C2×C4C2×#12114yes—
846C2×C4C2×#12114yes—
847C2×C4#52514yes—
848C2×C4#53614yes—
849C2×C4#53614yes—
850C2×C4#53814yes—
851C2×C4D4214yes—
852C2×C4D4214yes—
853C2×C4#54614yes—
854C2×C4#54614yes—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—44no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22—42no—
864C22—42no—
865C22—44no—
866C22—44no—
867C22—48no—
868C22—48no—
869C22—44no—
870C22—44no—
871C22—82no—
872C22—82no—
873C22—84no—
874C22—82no—
875C22—82no—
876C22—84no—
877C22C22×#12111yescharacteristic
878C22C2×#52511yescharacteristic
879C22C2×#53611yescharacteristic
880C22C2×#53611yescharacteristic
881C22C2×#53811yescharacteristic
882C22C2×D4211yescharacteristic
883C22C2×D4211yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×#54611yescharacteristic
886C22#348512yes—
887C22#348912yes—
888C22#349712yes—
889C22#349912yes—
890C22#350011yescharacteristic
891C22#350011yescharacteristic
892C22#350912yes—
893C22#351012yes—
894C22#351612yes—
895C22#351812yes—
896C22#354112yes—
897C22#354712yes—
898C22#355412yes—
899C22#356112yes—
900C4—24no—
901C4—24no—
902C4—24no—
903C4—44no—
904C4—44no—
905C4—44no—
906C4—42no—
907C4—44no—
908C4—44no—
909C4—42no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C4#242418yes—
917C2—44no—
918C2—84no—
919C2C2×#242411yescharacteristic
920C2#3531611yescharacteristic
921C2#3561711yescharacteristic
922C2#3581712yes—
923C2#3767611yescharacteristic
924C2#3808511yescharacteristic
925C2#3895811yescharacteristic
926C2#3936311yescharacteristic
927C2#4294012yes—
928C2#4509112yes—
929C2#4509512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2547C2semidirect
3. C2×#2434C2semidirect
6. C2×#2310C2semidirect
7. #16295C2semidirect
8. #15383C2semidirect
9. #15300C2semidirect
10. #15243C2semidirect
11. #15217C2semidirect
12. #15188C2semidirect
13. #15184C2semidirect
14. #14770C2semidirect
15. #14155C2semidirect
16. #14138C2semidirect
17. #14027C2semidirect
18. #14000C2semidirect
19. #13844C2semidirect
196. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#24362
C2×#24342
C2×#26202
C2×#23632
C2×#23102
#162952
#153832
#153002
#152432
#152172
#151882
#151842
#147702
#141552
#141382
#140272
#140002
#138442