Finite Group Databasebeta

← #618032

Subgroups — #618032

Order 512.

3812 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#125C211yesmaximal, characteristic, complemented
2C2×#2579C211yesmaximal, characteristic
3C2×#2487C211yesmaximal, characteristic
4C2×#2322C211yesmaximal, characteristic
5#16104C214yesmaximal, complemented
6#15996C214yesmaximal, complemented
7#15847C214yesmaximal, complemented
8#15846C214yesmaximal, complemented
9#15092C211yesmaximal, characteristic, complemented
10#15092C211yesmaximal, characteristic, complemented
11#15091C211yesmaximal, characteristic
12#15091C211yesmaximal, characteristic
13#14706C211yesmaximal, characteristic
14#14705C211yesmaximal, characteristic, complemented
15#14339C211yesmaximal, characteristic, complemented
16#14263C211yesmaximal, characteristic, complemented
17#14256C211yesmaximal, characteristic
18#13924C211yesmaximal, characteristic, complemented
19#13923C211yesmaximal, characteristic, complemented
20C22×#125—28no—
21C22×#125—28no—
22C22×#125—28no—
23C22×#125C2214yes—
24C22×#125C2214yes—
25C22×#123C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2579—28no—
35#2487—28no—
36C2×#400C2212yes—
37C2×#399C2212yes—
38C2×#398C2212yes—
39C2×#396C2212yes—
40#2322—28no—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#388C2212yes—
44C2×#387C2212yes—
45C2×#387C2212yes—
46C2×#386C2211yescharacteristic
47C2×#386C2211yescharacteristic
48C2×#386C2211yescharacteristic
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#385C2212yes—
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2212yes—
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2214yes—
87C22⋊#95C2211yescharacteristic
88C22⋊#95C2211yescharacteristic
89C22⋊#95C2211yescharacteristic
90C22⋊#95C2211yescharacteristic
91C22⋊#95C2211yescharacteristic
92C22⋊#95C2211yescharacteristic
93C22⋊#95C2211yescharacteristic
94C22⋊#95C2211yescharacteristic
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2211yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C2×#125—2128no—
107C2×#125—216no—
108C2×#125—216no—
109C2×#125—216no—
110C2×#125—216no—
111C2×#125—216no—
112C2×#125—216no—
113C2×#123—24no—
114C2×#123—24no—
115C2×#123Q818yes—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4D418yes—
135C22×C4⋊C4D418yes—
136C22×C4⋊C4D418yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42C2314yes—
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175#400—28no—
176#399—28no—
177#398—28no—
178#396—28no—
179#389—28no—
180#389—28no—
181#388—28no—
182#387—28no—
183#387—28no—
184#386—24no—
185#386—24no—
186#386—24no—
187#386—24no—
188#386—24no—
189#385—24no—
190#385—24no—
191#385—24no—
192#385—24no—
193#385—24no—
194#385—28no—
195#385—28no—
196#381—24no—
197#381—24no—
198#381—24no—
199#380—24no—
200#380—24no—
201#380—28no—
202C4×C22⋊C4—24no—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C25C2411yescharacteristic
231C25C2411yescharacteristic
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4C2×Q814yes—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×Q814yes—
273C23×C4#4114yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291#125—2128no—
292#125—2128no—
293#123—232no—
294C4×D4—416no—
295C2×C4⋊C4—232no—
296C2×C4⋊C4—232no—
297C2×C4⋊C4—232no—
298C2×C4⋊C4—232no—
299C2×C4⋊C4—232no—
300C2×C4⋊C4—232no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C2×D418yes—
342C2×C4⋊C4C2×D418yes—
343C2×C4⋊C4C2×D418yes—
344C2×C4⋊C4C2×D418yes—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D418yes—
347C2×C4⋊C4C2×Q818yes—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4C2×Q814yes—
384C2×C22⋊C4C2×Q818yes—
385C2×C42—232no—
386C2×C42—28no—
387C2×C42—28no—
388C2×C42—28no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—44no—
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—24no—
409#95—28no—
410#95—28no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421C24—24no—
422C24—24no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—24no—
430C24—24no—
431C24C22×D412yes—
432C24C22×D412yes—
433C24C22×D412yes—
434C24C22×Q812yes—
435C24C22×Q812yes—
436C24C2×#4112yes—
437C242−1+412yes—
438C242−1+412yes—
439C24C2511yescharacteristic
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
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—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—44no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4#120116yes—
550C22×C4C22⋊Q8116yes—
551C22×C4C22×D414yes—
552C22×C4C22×D414yes—
553C22×C4C22×D414yes—
554C22×C4C22×D414yes—
555C22×C4C22×D414yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×Q814yes—
564C22×C4C22×Q812yes—
565C22×C4C22×Q814yes—
566C22×C4C2×#4114yes—
567C4⋊C4—232no—
568C4⋊C4—232no—
569C4⋊C4—232no—
570C4⋊C4—216no—
571C4⋊C4—216no—
572C4⋊C4—216no—
573C4⋊C4—216no—
574C4⋊C4—216no—
575C4⋊C4—216no—
576C4⋊C4—216no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C4⋊C4—84no—
583C4⋊C4—84no—
584C4⋊C4—84no—
585C22⋊C4—28no—
586C22⋊C4—216no—
587C22⋊C4—48no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C42—232no—
600C42—44no—
601C42—84no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—28no—
609C23—28no—
610C23—28no—
611C23—28no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—28no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23C2×#12014yes—
630C23C2×C22⋊Q814yes—
631C23#53614yes—
632C23#54814yes—
633C23#54814yes—
634C23D4×Q814yes—
635C23D4×Q814yes—
636C23C23×D411yescharacteristic
637C23C23×D411yescharacteristic
638C23C23×D411yescharacteristic
639C23C23×Q811yescharacteristic
640C23C22×#4111yescharacteristic
641C23C2×2−1+411yescharacteristic
642C23C2×2−1+411yescharacteristic
643C23#58514yes—
644C23#58514yes—
645D4—416no—
646C2×C4—24no—
647C2×C4—232no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—28no—
679C2×C4—416no—
680C2×C4—416no—
681C2×C4—416no—
682C2×C4—416no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—88no—
736C2×C4C2×#12014yes—
737C2×C4C2×#12014yes—
738C2×C4C2×C22⋊Q818yes—
739C22—28no—
740C22—24no—
741C22—28no—
742C22—28no—
743C22—28no—
744C22—24no—
745C22—28no—
746C22—28no—
747C22—44no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—82no—
752C22—81no—
753C22—82no—
754C22—82no—
755C22—81no—
756C22#240918yes—
757C22C22×#12011yescharacteristic
758C22C22×C22⋊Q811yescharacteristic
759C22C2×#53611yescharacteristic
760C22#344912yes—
761C22#344912yes—
762C22C2×#54811yescharacteristic
763C22C2×#54811yescharacteristic
764C22C2×D4×Q811yescharacteristic
765C22C2×D4×Q811yescharacteristic
766C22#348512yes—
767C22#348512yes—
768C22#348512yes—
769C22#348712yes—
770C22#350414yes—
771C22#351214yes—
772C22#355314yes—
773C22#355314yes—
774C4—24no—
775C4—24no—
776C4—28no—
777C4—44no—
778C4—44no—
779C4—44no—
780C4—44no—
781C4—44no—
782C4—44no—
783C4—42no—
784C4—82no—
785C4—81no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—81no—
791C2—28no—
792C2—82no—
793C2C2×#240911yescharacteristic
794C2#3508811yescharacteristic
795C2#3514911yescharacteristic
796C2#3563912yes—
797C2#3712012yes—
798C2#3958912yes—
799C2#3958912yes—
800C2#3971712yes—
801C2#3971712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#125C2semidirect
5. #16104C2semidirect
6. #15996C2semidirect
7. #15847C2semidirect
8. #15846C2semidirect
9. #15092C2semidirect
10. #15092C2semidirect
14. #14705C2semidirect
15. #14339C2semidirect
16. #14263C2semidirect
18. #13924C2semidirect
19. #13923C2semidirect

Maximal subgroups

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

subgroupindex
C23×#1252
C2×#25792
C2×#24872
C2×#23222
#161042
#159962
#158472
#158462
#150922
#150912
#147062
#147052
#143392
#142632
#142562
#139242
#139232