Finite Group Databasebeta

← #1080631

Subgroups — #1080631

Order 512.

2358 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17248C212yesmaximal, complemented
2#16742C212yesmaximal, complemented
3#16578C212yesmaximal, complemented
4#16318C211yesmaximal, characteristic, complemented
5#16297C211yesmaximal, characteristic
6#16057C212yesmaximal, complemented
7#15772C212yesmaximal, complemented
8#15282C212yesmaximal
9#15176C212yesmaximal, complemented
10#15045C211yesmaximal, characteristic, complemented
11#14979C212yesmaximal, complemented
12#14514C211yesmaximal, characteristic, complemented
13#14366C211yesmaximal, characteristic
14#14233C212yesmaximal, complemented
15#14086C212yesmaximal, complemented
16#14010C212yesmaximal, complemented
17#13991C211yesmaximal, characteristic
18#13991C212yesmaximal
19C4×#393C211yesmaximal, characteristic, complemented
20C22×C4×Q8C2211yescharacteristic, complemented
21C23×C22⋊C4C2211yescharacteristic
22C2×#397C2212yes—
23C2×#395C2212yescomplemented
24C2×#393C2211yescharacteristic
25C2×#393C2212yes—
26C2×#389C2211yescharacteristic, complemented
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#387C2212yescomplemented
34C2×#385C2211yescharacteristic
35C2×#385C2212yes—
36C2×#382C2212yescomplemented
37C2×#379C2211yescharacteristic
38C2×#379C2212yes—
39C2×#379C2211yescharacteristic
40C2×#379C2212yes—
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2211yescharacteristic
43#1446C2211yescharacteristic, complemented
44#1445C2212yescomplemented
45#1445C2212yescomplemented
46#1443C2212yescomplemented
47#1443C2212yescomplemented
48#1442C2212yescomplemented
49#1442C2211yescharacteristic, complemented
50#1442C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2211yescharacteristic, complemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2211yescharacteristic, complemented
58#1441C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1441C2212yescomplemented
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1439C2212yes—
69#1439C2211yescharacteristic
70#1439C2212yes—
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94C4⋊#95C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99#1434C2211yescharacteristic, complemented
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C4×#95C2212yescomplemented
105C4×#95C2212yescomplemented
106C4×#95C2211yescharacteristic, complemented
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×C4×Q8—42no—
112C2×C4×Q8—44no—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153#397—28no—
154#395—44no—
155#393—24no—
156#393—44no—
157#389—42no—
158#388—28no—
159#388—28no—
160#388—44no—
161#388—44no—
162#388—44no—
163#388—44no—
164#387—44no—
165#385—24no—
166#385—44no—
167#382—44no—
168#379—28no—
169#379—24no—
170#379—24no—
171#379—44no—
172C4×C22⋊C4—44no—
173C4×C22⋊C4—42no—
174C2×#95C2312yes—
175C2×#95C2311yescharacteristic
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
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×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C25—24no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—41no—
224C25—42no—
225C25—41no—
226C25—42no—
227C25—41no—
228C25—41no—
229C25—42no—
230C25C2412yes—
231C25C2411yescharacteristic
232C22×Q8—22no—
233C22×Q8—24no—
234C22×Q8—41no—
235C22×Q8—42no—
236C22×Q8—41no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—41no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—42no—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C4×Q8—416no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
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—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—416no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—41no—
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#4114yes—
357C2×C22⋊C4#4114yes—
358C2×C22⋊C4#4118yes—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—22no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—41no—
392#95—41no—
393#95—42no—
394#95—41no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—41no—
405#95—41no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—48no—
443C24—44no—
444C24—48no—
445C24—48no—
446C24—44no—
447C24—48no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—82no—
452C24—82no—
453C24—84no—
454C24—84no—
455C24—84no—
456C24—82no—
457C24—82no—
458C24—84no—
459C24—84no—
460C24—82no—
461C24—84no—
462C24—82no—
463C24—84no—
464C24—84no—
465C24C2×#4114yes—
466C24C2×#4112yes—
467C24C2×#4112yes—
468C242−1+412yes—
469C24C2511yescharacteristic
470C2×Q8—48no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—48no—
474C2×Q8—44no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
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—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
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—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
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—21no—
552C22×C4—22no—
553C22×C4—21no—
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—21no—
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—44no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—84no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—84no—
582C22×C4—82no—
583C22×C4—84no—
584C22×C4C2×#4112yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4114yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4112yes—
589C22×C4H(5,𝔽2)14yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)14yes—
592C4⋊C4—44no—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—48no—
596C4⋊C4—84no—
597C4⋊C4—84no—
598C4⋊C4—84no—
599C4⋊C4—84no—
600C4⋊C4—82no—
601C4⋊C4—84no—
602C22⋊C4—28no—
603C22⋊C4—48no—
604C22⋊C4—44no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—82no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C42—48no—
625C42—44no—
626C42—48no—
627C42—82no—
628C42—84no—
629C42—84no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—42no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—42no—
659C23—416no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
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—816no—
689C23—88no—
690C23—88no—
691C23—88no—
692C23—816no—
693C23—816no—
694C23—816no—
695C23—88no—
696C23—88no—
697C23—88no—
698C23#55214yes—
699C23C22×#4111yescharacteristic
700C23C22×#4112yes—
701C23C22×#4111yescharacteristic
702C23C2×H(5,𝔽2)11yescharacteristic
703C23C2×H(5,𝔽2)12yes—
704C23C2×H(5,𝔽2)12yes—
705C23C2×2−1+411yescharacteristic
706C23#58511yescharacteristic
707C23#58512yes—
708C23#58511yescharacteristic
709C23#58511yescharacteristic
710Q8—416no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
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—42no—
768C2×C4—42no—
769C2×C4—41no—
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—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—88no—
818C2×C4—88no—
819C2×C4H(3,𝔽4)14yes—
820C22—28no—
821C22—24no—
822C22—42no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—832no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22#346012yes—
848C22#346011yescharacteristic
849C22C2×#55211yescharacteristic
850C22#347512yes—
851C22#348111yescharacteristic
852C22#348112yes—
853C22#349311yescharacteristic
854C22#350512yes—
855C22#350511yescharacteristic
856C22#351011yescharacteristic
857C22#351412yes—
858C22#351912yes—
859C22#352012yes—
860C22#352112yes—
861C22C2×H(3,𝔽4)11yescharacteristic
862C22#353511yescharacteristic
863C22#353512yes—
864C22#353711yescharacteristic
865C22#354212yes—
866C22#354512yes—
867C22#354511yescharacteristic
868C22#356212yes—
869C22#356411yescharacteristic
870C4—24no—
871C4—44no—
872C4—44no—
873C4—42no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—82no—
878C4—82no—
879C4—81no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—81no—
885C4—82no—
886C4—81no—
887C2—44no—
888C2—84no—
889C2#3954311yescharacteristic
890C2#4034012yes—
891C2#4180812yes—
892C2#4187711yescharacteristic
893C2#4380011yescharacteristic
894C2#4383812yes—
895C2#4564511yescharacteristic
896C2#5229411yescharacteristic
897C2#5292511yescharacteristic
898C2#5949212yes—
899C2#5953811yescharacteristic
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. #17248C2semidirect
2. #16742C2semidirect
3. #16578C2semidirect
4. #16318C2semidirect
6. #16057C2semidirect
7. #15772C2semidirect
9. #15176C2semidirect
10. #15045C2semidirect
11. #14979C2semidirect
12. #14514C2semidirect
14. #14233C2semidirect
15. #14086C2semidirect
16. #14010C2semidirect
19. C4×#393C2semidirect
20. C22×C4×Q8C22semidirect
23. C2×#395C22semidirect
26. C2×#389C22semidirect
33. C2×#387C22semidirect
36. C2×#382C22semidirect
43. #1446C22semidirect
44. #1445C22semidirect
45. #1445C22semidirect
46. #1443C22semidirect
47. #1443C22semidirect
48. #1442C22semidirect
49. #1442C22semidirect
50. #1442C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. C4⋊#95C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect
99. #1434C22semidirect
104. C4×#95C22semidirect
105. C4×#95C22semidirect
106. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
#172482
#167422
#165782
#163182
#162972
#160572
#157722
#152822
#151762
#150452
#149792
#145142
#143662
#142332
#140862
#140102
#139912
C4×#3932