Finite Group Databasebeta

← #5955561

Subgroups — #5955561

Order 512.

2598 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15249C211yesmaximal, characteristic, complemented
2#15169C212yesmaximal, complemented
3#15167C211yesmaximal, characteristic, complemented
4#15065C212yesmaximal, complemented
5#15058C212yesmaximal, complemented
6#14905C212yesmaximal, complemented
7#14887C211yesmaximal, characteristic, complemented
8#14886C211yesmaximal, characteristic
9#14865C212yesmaximal, complemented
10#14832C212yesmaximal, complemented
11#14830C212yesmaximal, complemented
12#14795C212yesmaximal
13#14745C212yesmaximal, complemented
14#14743C212yesmaximal, complemented
15#13793C211yesmaximal, characteristic, complemented
16#13791C211yesmaximal, characteristic, complemented
17#13788C212yesmaximal, complemented
18C4×#386C212yesmaximal, complemented
19#13756C211yesmaximal, characteristic, complemented
20C22×C4×D4C2212yes—
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#400C2212yes—
25C2×#399C2212yes—
26C2×#397C2212yes—
27C2×#397C2212yes—
28C2×#397C2212yes—
29C2×#395C2211yescharacteristic
30C2×#394C2211yescharacteristic
31C2×#393C2211yescharacteristic
32C2×#393C2212yes—
33C2×#392C2211yescharacteristic
34C2×#391C2212yes—
35C2×#391C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×C4×C22⋊C4C2212yes—
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2212yes—
45#1445C2212yes—
46#1445C2212yes—
47#1445C2212yes—
48#1445C2212yes—
49#1445C2212yes—
50#1443C2212yes—
51#1443C2212yes—
52#1442C2212yes—
53#1442C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1441C2211yescharacteristic
57#1441C2211yescharacteristic
58#1440C2212yes—
59#1439C2212yes—
60#1439C2212yes—
61#1439C2212yes—
62#1439C2211yescharacteristic
63#1439C2211yescharacteristic
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1438C2212yes—
68#1438C2212yes—
69#1438C2212yes—
70#1438C2212yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88#1434C2212yes—
89#1434C2211yescharacteristic
90#1434C2211yescharacteristic
91#1434C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C4×#95C2211yescharacteristic
102C4×#95C2211yescharacteristic
103C4×#95C2211yescharacteristic
104C4×#95C2211yescharacteristic
105C4×#95C2212yes—
106C4×#95C2212yes—
107C23×Q8C2311yescharacteristic
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×C4×D4—28no—
114C2×C4×D4—44no—
115C2×C4×D4—44no—
116C2×#117—24no—
117C2×#117—24no—
118C2×#117—42no—
119C2×#117—42no—
120C2×#117—42no—
121C2×#117—42no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C42—24no—
150C22×C42—42no—
151C22×C42—42no—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162#400—44no—
163#399—44no—
164#397—44no—
165#397—44no—
166#397—44no—
167#395—42no—
168#394—42no—
169#393—44no—
170#393—42no—
171#392—42no—
172#391—24no—
173#391—28no—
174#390—24no—
175#388—28no—
176#388—28no—
177#386—28no—
178#386—28no—
179#386—28no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—44no—
182C4×C22⋊C4—44no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C25C2412yes—
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—24no—
231C22×Q8—42no—
232C22×Q8—41no—
233C22×Q8—41no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—41no—
245C22×D4—41no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4#4114yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C4×D4—432no—
285#117—416no—
286#117—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4#4118yes—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—41no—
375C2×C42—41no—
376C2×C42—41no—
377C2×C42—41no—
378C2×C42—41no—
379C2×C42—41no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—41no—
385C2×C42—41no—
386C2×C42—42no—
387C2×C42—41no—
388C2×C42—41no—
389C2×C42—416no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42#4114yes—
395C2×C42#4118yes—
396C2×C42#4114yes—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—41no—
429#95—42no—
430#95—42no—
431#95—41no—
432#95—41no—
433#95—41no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C2×#4114yes—
464C24C2×#4112yes—
465C24H(5,𝔽2)12yes—
466C242−1+412yes—
467C24C2511yescharacteristic
468C2×Q8—28no—
469C2×Q8—84no—
470C2×Q8—82no—
471C2×Q8—82no—
472C2×Q8—84no—
473C2×D4—216no—
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—82no—
482C2×D4—82no—
483C2×D4—84no—
484C2×D4—84no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
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—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
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—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
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—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4C2×#4114yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)14yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—82no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—82no—
625C4⋊C4—84no—
626C22⋊C4—216no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—44no—
645C42—44no—
646C42—48no—
647C42—48no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—84no—
653C42—84no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23#53914yes—
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4112yes—
716C23C22×#4112yes—
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)12yes—
721C23C2×2−1+411yescharacteristic
722C23#58512yes—
723Q8—88no—
724D4—432no—
725D4—88no—
726C2×C4—232no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—432no—
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—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
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—41no—
787C2×C4—42no—
788C2×C4—41no—
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—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
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—41no—
820C2×C4—42no—
821C2×C4—41no—
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—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—816no—
837C2×C4#52918yes—
838C2×C4#52914yes—
839C2×C4#53814yes—
840C22—24no—
841C22—28no—
842C22—44no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22C2×#52912yes—
867C22C2×#52911yescharacteristic
868C22#344411yescharacteristic
869C22#344411yescharacteristic
870C22#344412yes—
871C22C2×#53811yescharacteristic
872C22C2×#53911yescharacteristic
873C22#346012yes—
874C22#349011yescharacteristic
875C22#349012yes—
876C22#349011yescharacteristic
877C22#349211yescharacteristic
878C22#349211yescharacteristic
879C22#349412yes—
880C22#349512yes—
881C22#350612yes—
882C22#350811yescharacteristic
883C22#350812yes—
884C22#351011yescharacteristic
885C22#351312yes—
886C22#351412yes—
887C22#351912yes—
888C22#352012yes—
889C4—28no—
890C4—24no—
891C4—24no—
892C4—44no—
893C4—42no—
894C4—44no—
895C4—42no—
896C4—44no—
897C4—44no—
898C4—82no—
899C4—81no—
900C4—82no—
901C4—81no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C2—44no—
907C2—84no—
908C2#3455111yescharacteristic
909C2#3499711yescharacteristic
910C2#3504412yes—
911C2#3505412yes—
912C2#3526811yescharacteristic
913C2#3537512yes—
914C2#3540811yescharacteristic
915C2#3541911yescharacteristic
916C2#3543811yescharacteristic
917C2#3544511yescharacteristic
918C2#3555312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #15249C2semidirect
2. #15169C2semidirect
3. #15167C2semidirect
4. #15065C2semidirect
5. #15058C2semidirect
6. #14905C2semidirect
7. #14887C2semidirect
9. #14865C2semidirect
10. #14832C2semidirect
11. #14830C2semidirect
13. #14745C2semidirect
14. #14743C2semidirect
15. #13793C2semidirect
16. #13791C2semidirect
17. #13788C2semidirect
18. C4×#386C2semidirect
19. #13756C2semidirect

Maximal subgroups

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

subgroupindex
#152492
#151692
#151672
#150652
#150582
#149052
#148872
#148862
#148652
#148322
#148302
#147952
#147452
#147432
#137932
#137912
#137882
C4×#3862
#137562