Finite Group Databasebeta

← #666230

Subgroups — #666230

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16227C212yesmaximal
2#16137C212yesmaximal
3#16130C212yesmaximal
4#16041C212yesmaximal
5#15196C211yesmaximal, characteristic
6#15191C211yesmaximal, characteristic
7#15187C211yesmaximal, characteristic
8#15185C211yesmaximal, characteristic
9#15119C212yesmaximal
10#15034C212yesmaximal
11#14703C211yesmaximal, characteristic
12#14142C211yesmaximal, characteristic
13#14142C211yesmaximal, characteristic
14#14065C212yesmaximal
15#14059C212yesmaximal
16#14053C211yesmaximal, characteristic
17#14053C211yesmaximal, characteristic
18#14021C211yesmaximal, characteristic
19#14021C211yesmaximal, characteristic
20#13936C211yesmaximal, characteristic
21C4⋊C42C211yesmaximal, characteristic
22C4×#387C211yesmaximal, characteristic
23#13755C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C2×#391C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#387C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#384C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2212yes—
47C2×#376C2212yes—
48C2×C43C2211yescharacteristic
49#1446C2212yes—
50#1446C2212yes—
51#1446C2212yes—
52#1446C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1444C2212yes—
57#1444C2212yes—
58#1443C2212yes—
59#1443C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1436C2211yescharacteristic
80#1436C2212yes—
81#1436C2211yescharacteristic
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2211yescharacteristic
90#1436C2212yes—
91#1436C2211yescharacteristic
92#1436C2212yes—
93C4⋊#95C2212yes—
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2211yescharacteristic
106#1434C2212yes—
107#1434C2212yes—
108#1434C2212yes—
109#1434C2212yes—
110#1434C2212yes—
111#1434C2211yescharacteristic
112#1434C2212yes—
113#1434C2212yes—
114#1434C2212yes—
115#1434C2211yescharacteristic
116#1434C2212yes—
117#1434C2212yes—
118C4×#95C2211yescharacteristic
119C4×#95C2211yescharacteristic
120C4×#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2212yes—
123C23×Q8C2311yescharacteristic
124C23×Q8C2312yes—
125C2×C4⋊Q8—24no—
126C2×C4⋊Q8—24no—
127C2×C4⋊Q8—42no—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—28no—
166#391—44no—
167#391—42no—
168#391—42no—
169#389—42no—
170#389—42no—
171#389—42no—
172#387—24no—
173#387Q818yescomplemented
174#384—24no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—24no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—24no—
181C4×C4⋊C4—44no—
182#376—44no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2311yescharacteristic
186C2×#95C2311yescharacteristic
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C43—24no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—42no—
260C22×Q8—42no—
261C22×Q8—42no—
262C22×Q8—42no—
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C4⋊Q8—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4C2×Q814yes—
334C2×C4⋊C4C2×Q814yes—
335C2×C4⋊C4#4114yes—
336C2×C4⋊C4#4114yes—
337C2×C4⋊C4#4114yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—41no—
375C2×C42—41no—
376C2×C42—41no—
377C2×C42—41no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42C2×Q814yes—
381C2×C42#4114yes—
382C2×C42#4114yes—
383#95—22no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—24no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—24no—
395#95—24no—
396#95—24no—
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—22no—
409#95—24no—
410#95—22no—
411#95—41no—
412#95—42no—
413#95—41no—
414#95—41no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—41no—
420#95—42no—
421#95—42no—
422#95—41no—
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—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95C2×Q814yes—
444#95C2×Q814yes—
445#95C2×Q814yes—
446#95C2×Q814yes—
447#95#4114yes—
448C24C2511yescharacteristic
449C2×Q8—48no—
450C2×Q8—48no—
451C2×Q8—48no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—84no—
460C2×Q8—84no—
461C2×Q8—84no—
462C2×Q8—84no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
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—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
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—21no—
569C22×C4—22no—
570C22×C4—22no—
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—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4C22×Q812yes—
599C22×C4C22×Q812yes—
600C22×C4C22×Q812yes—
601C22×C4C22×Q812yes—
602C22×C4C22×Q812yes—
603C22×C4C22×Q812yes—
604C22×C4C22×Q812yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C42−1+412yes—
623C22×C42−1+412yes—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4—84no—
641C42—28no—
642C42—28no—
643C42—28no—
644C42—48no—
645C42—48no—
646C42—48no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—84no—
656C23C23×Q811yescharacteristic
657C23C22×#4111yescharacteristic
658C23C22×#4111yescharacteristic
659C23C22×#4111yescharacteristic
660C23C22×#4111yescharacteristic
661C23C22×#4111yescharacteristic
662C23C22×#4111yescharacteristic
663C23C2×H(5,𝔽2)11yescharacteristic
664C23C2×H(5,𝔽2)11yescharacteristic
665C23C2×2−1+411yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23#58511yescharacteristic
668C23#58511yescharacteristic
669C23#58511yescharacteristic
670C23#58511yescharacteristic
671Q8—816no—
672Q8—88no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4#52914yes—
826C2×C4#52914yes—
827C2×C4#53314yes—
828C2×C4#54214yes—
829C2×C4#55114yes—
830C2×C4#55214yes—
831C2×C4#55414yes—
832C2×C4#55514yes—
833C2×C4#55614yes—
834C22C2×#52911yescharacteristic
835C22C2×#52911yescharacteristic
836C22C2×#53311yescharacteristic
837C22C2×#54211yescharacteristic
838C22#346011yescharacteristic
839C22C2×#55111yescharacteristic
840C22C2×#55211yescharacteristic
841C22C2×#55411yescharacteristic
842C22C2×#55511yescharacteristic
843C22C2×#55611yescharacteristic
844C22#347511yescharacteristic
845C22#347511yescharacteristic
846C22Q8×#4111yescharacteristic
847C22Q8×#4111yescharacteristic
848C22Q8×#4111yescharacteristic
849C22#348111yescharacteristic
850C22#348211yescharacteristic
851C22#349311yescharacteristic
852C22#349511yescharacteristic
853C22#349511yescharacteristic
854C22#350211yescharacteristic
855C22#350311yescharacteristic
856C22#350711yescharacteristic
857C22#351011yescharacteristic
858C22#351311yescharacteristic
859C22#351311yescharacteristic
860C22#351411yescharacteristic
861C22#351611yescharacteristic
862C22#351811yescharacteristic
863C22#352111yescharacteristic
864C22#352411yescharacteristic
865C22#354611yescharacteristic
866C22#355011yescharacteristic
867C22#355711yescharacteristic
868C22#356211yescharacteristic
869C4—24no—
870C4—24no—
871C4—44no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—44no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4#253218yes—
892C2#3477211yescharacteristic
893C2C2×#253211yescharacteristic
894C2#3564811yescharacteristic
895C2#3628611yescharacteristic
896C2#3628811yescharacteristic
897C2#3631011yescharacteristic
898C2#3655311yescharacteristic
899C2#3824011yescharacteristic
900C2#3829011yescharacteristic
901C2#3960911yescharacteristic
902C2#3993011yescharacteristic
903C2#5947711yescharacteristic
904C2#5948811yescharacteristic
905C2#5993411yescharacteristic
906C2#5996011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
173. #387Q8semidirect

Maximal subgroups

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

subgroupindex
#162272
#161372
#161302
#160412
#151962
#151912
#151872
#151852
#151192
#150342
#147032
#141422
#140652
#140592
#140532
#140212
#139362
C4⋊C422
C4×#3872
#137552