Finite Group Databasebeta

← #876090

Subgroups — #876090

Order 512.

2594 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2599C211yesmaximal, characteristic, complemented
2C2×#2482C211yesmaximal, characteristic
3#16779C212yesmaximal, complemented
4#16546C212yesmaximal, complemented
5#15907C212yesmaximal, complemented
6#15871C212yesmaximal, complemented
7#15579C211yesmaximal, characteristic, complemented
8#15568C211yesmaximal, characteristic, complemented
9#15480C211yesmaximal, characteristic
10#15467C211yesmaximal, characteristic
11#15117C212yesmaximal, complemented
12#15023C212yesmaximal, complemented
13#14837C212yesmaximal, complemented
14#14701C212yesmaximal, complemented
15#14542C212yesmaximal, complemented
16#14366C212yesmaximal
17#14188C212yesmaximal, complemented
18#13971C212yesmaximal
19#13761C211yesmaximal, characteristic, complemented
20C22×C4×Q8C2211yescharacteristic, complemented
21C22×#117C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2599—28no—
24#2482—28no—
25C2×#399C2212yes—
26C2×#398C2211yescharacteristic, complemented
27C2×#397C2211yescharacteristic
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#395C2211yescharacteristic, complemented
31C2×#393C2211yescharacteristic
32C2×#393C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#387C2212yescomplemented
40C2×#387C2212yescomplemented
41C2×#385C2212yes—
42C2×#385C2211yescharacteristic
43C2×#385C2211yescharacteristic
44C2×#383C2211yescharacteristic, complemented
45C2×#381C2211yescharacteristic
46C2×#379C2211yescharacteristic
47C2×#379C2212yes—
48C2×#379C2212yes—
49C2×#379C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×#376C2211yescharacteristic, complemented
52C2×C43C2211yescharacteristic, complemented
53#1446C2212yescomplemented
54#1445C2212yescomplemented
55#1443C2212yescomplemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2211yescharacteristic
91#1437C2212yes—
92#1437C2211yescharacteristic
93#1436C2212yescomplemented
94#1436C2211yescharacteristic, complemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2211yescharacteristic, complemented
103C4⋊#95C2212yescomplemented
104#1434C2212yescomplemented
105#1434C2212yescomplemented
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C4×#95C2212yescomplemented
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×C4×Q8—24no—
114C2×C4×Q8—42no—
115C2×C4×Q8—42no—
116C2×#117—42no—
117C2×#117—42no—
118C2×#117D418yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—24no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
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×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#399—28no—
163#398—24no—
164#397—28no—
165#397—24no—
166#397—28no—
167#395—24no—
168#393—24no—
169#393—28no—
170#388—28no—
171#388—28no—
172#388—28no—
173#388—28no—
174#388—44no—
175#388—44no—
176#387—28no—
177#387—28no—
178#385—28no—
179#385—24no—
180#385—24no—
181#383—24no—
182#381—24no—
183#379—24no—
184#379—24no—
185#379—28no—
186#379—28no—
187C4×C22⋊C4—28no—
188#376—42no—
189C2×#95C2311yescharacteristic
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
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×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
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—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2311yescharacteristic
232C43—42no—
233C25—22no—
234C25—24no—
235C25—24no—
236C25—41no—
237C25—41no—
238C25—42no—
239C25—42no—
240C25—42no—
241C25—42no—
242C25C2412yes—
243C25C2411yescharacteristic
244C22×Q8—22no—
245C22×Q8—24no—
246C22×Q8—41no—
247C22×Q8—41no—
248C22×Q8—42no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—42no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4C2×D414yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C4×Q8—416no—
277#117—416no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D414yes—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
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—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—416no—
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—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4C2×D414yes—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4#4118yes—
372C2×C22⋊C4#4118yes—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—41no—
387C2×C42—41no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—22no—
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—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—41no—
432#95—42no—
433#95—41no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—48no—
460C24—44no—
461C24—48no—
462C24—48no—
463C24—44no—
464C24—48no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—84no—
469C24—84no—
470C24—84no—
471C24—84no—
472C24—84no—
473C24—84no—
474C24—84no—
475C24—82no—
476C24—82no—
477C24—84no—
478C24—84no—
479C24—84no—
480C24C22×D412yes—
481C24C2×#4114yes—
482C24C2×#4114yes—
483C24C2511yescharacteristic
484C2×Q8—48no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—48no—
488C2×Q8—44no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
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—22no—
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—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—44no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—84no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—84no—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4114yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4—84no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C42—28no—
639C42—28no—
640C42—48no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—416no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
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—816no—
703C23—88no—
704C23—816no—
705C23—816no—
706C23—816no—
707C23—816no—
708C23—88no—
709C23—816no—
710C23#53214yes—
711C23C23×D411yescharacteristic
712C23C22×#4112yes—
713C23C22×#4112yes—
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23#58512yes—
717C23#58512yes—
718C23#58512yes—
719C23#58512yes—
720Q8—416no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—416no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
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—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—42no—
800C2×C4—42no—
801C2×C4—42no—
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—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—88no—
829C2×C4#53414yes—
830C22—28no—
831C22—24no—
832C22—44no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—832no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22C2×#53211yescharacteristic
856C22C2×#53411yescharacteristic
857C22#344911yescharacteristic
858C22#345912yes—
859C22D4×#4112yes—
860C22#347512yes—
861C22#347512yes—
862C22#348111yescharacteristic
863C22#349112yes—
864C22#350012yes—
865C22#351012yes—
866C22#351312yes—
867C22#351312yes—
868C22#352112yes—
869C22#352112yes—
870C22#352911yescharacteristic
871C22#354011yescharacteristic
872C22#354011yescharacteristic
873C22#355112yes—
874C22#356612yes—
875C22#356812yes—
876C4—24no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—44no—
881C4—42no—
882C4—42no—
883C4—44no—
884C4—44no—
885C4—42no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C2—44no—
894C2—84no—
895C2#3506411yescharacteristic
896C2#3626712yes—
897C2#3741911yescharacteristic
898C2#3835412yes—
899C2#3875212yes—
900C2#3994712yes—
901C2#4595012yes—
902C2#5216311yescharacteristic
903C2#6001412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2599C2semidirect
3. #16779C2semidirect
4. #16546C2semidirect
5. #15907C2semidirect
6. #15871C2semidirect
7. #15579C2semidirect
8. #15568C2semidirect
11. #15117C2semidirect
12. #15023C2semidirect
13. #14837C2semidirect
14. #14701C2semidirect
15. #14542C2semidirect
17. #14188C2semidirect
19. #13761C2semidirect
20. C22×C4×Q8C22semidirect
26. C2×#398C22semidirect
30. C2×#395C22semidirect
39. C2×#387C22semidirect
40. C2×#387C22semidirect
44. C2×#383C22semidirect
51. C2×#376C22semidirect
52. C2×C43C22semidirect
53. #1446C22semidirect
54. #1445C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. C4⋊#95C22semidirect
104. #1434C22semidirect
105. #1434C22semidirect
108. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25992
C2×#24822
#167792
#165462
#159072
#158712
#155792
#155682
#154802
#154672
#151172
#150232
#148372
#147012
#145422
#143662
#141882
#139712
#137612