Finite Group Databasebeta

← #617549

Subgroups — #617549

Order 512.

3010 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2566C211yesmaximal, characteristic, complemented
2C2×#2629C211yesmaximal, characteristic, complemented
3C2×#2324C211yesmaximal, characteristic
4C2×#2296C211yesmaximal, characteristic, complemented
5#15677C214yesmaximal, complemented
6#15507C214yesmaximal, complemented
7#15324C214yesmaximal, complemented
8#15306C214yesmaximal, complemented
9#15234C211yesmaximal, characteristic, complemented
10#15222C211yesmaximal, characteristic, complemented
11#15222C211yesmaximal, characteristic, complemented
12#15151C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic
14#14682C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14257C211yesmaximal, characteristic
17#14160C211yesmaximal, characteristic, complemented
18#13911C211yesmaximal, characteristic, complemented
19#13906C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2629—28no—
27#2566—28no—
28C2×#398C2212yes—
29C2×#398C2212yes—
30C2×#398C2214yes—
31C2×#396C2212yes—
32C2×#396C2212yes—
33C2×#396C2214yes—
34#2324—28no—
35#2296—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#388C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2212yes—
51C2×#385C2214yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#1445C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C2×#125—24no—
101C2×#125—24no—
102C2×#125—24no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121Q818yes—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—42no—
114C2×#117D418yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—42no—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#398—28no—
163#398—28no—
164#398—48no—
165#396—216no—
166#396—28no—
167#396—28no—
168#390—28no—
169#390—24no—
170#390—24no—
171#390—24no—
172#390—42no—
173#390—42no—
174#389—28no—
175#389—24no—
176#389—24no—
177#389—24no—
178#389—28no—
179#388—28no—
180#386—28no—
181#386—48no—
182#385—28no—
183#385—28no—
184#385—216no—
185#385—28no—
186#384—24no—
187#384—24no—
188#382—24no—
189#382—42no—
190#382—42no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—48no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4D418yescomplemented
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C25C2412yes—
223C25C2411yescharacteristic
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4C2×Q814yes—
235C22×D4C2×Q818yes—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4C2×D414yes—
253C23×C4C2×Q814yes—
254C23×C4#4114yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272#125—416no—
273#121—232no—
274C4×D4—416no—
275#117—232no—
276#117—416no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
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—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
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—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D418yes—
337C2×C4⋊C4C2×Q814yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4C2×D414yes—
373C2×C22⋊C4C2×D414yes—
374C2×C22⋊C4C2×Q818yes—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—416no—
391C2×C42—42no—
392C2×C42—44no—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397C2×C42C2×D414yes—
398C2×C42#4114yes—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—28no—
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#95C2×D418yes—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—22no—
435C24—22no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24C22×D412yes—
440C24C22×Q814yes—
441C24C22×Q812yes—
442C24C2×#4112yes—
443C24C2511yescharacteristic
444C2×D4—216no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—416no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—88no—
454C2×D4—84no—
455C2×D4—84no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
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—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
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—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—416no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—88no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4C22⋊Q8116yes—
550C22×C4C22×D412yes—
551C22×C4C22×D414yes—
552C22×C4C22×D412yes—
553C22×C4C22×D414yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×Q814yes—
562C22×C4C22×Q812yes—
563C22×C4C22×Q812yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C42−1+412yes—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—84no—
589C4⋊C4—84no—
590C4⋊C4—88no—
591C4⋊C4—84no—
592C4⋊C4—84no—
593C4⋊C4—84no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—216no—
597C22⋊C4—48no—
598C22⋊C4—416no—
599C22⋊C4—48no—
600C22⋊C4—88no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C22⋊C4—88no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C22⋊C4—88no—
608C42—28no—
609C42—28no—
610C42—28no—
611C42—48no—
612C42—44no—
613C42—44no—
614C42—84no—
615C42#121116yes—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—28no—
634C23—28no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—42no—
648C23—42no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23C2×C22⋊Q814yes—
662C23C23×D411yescharacteristic
663C23C23×D411yescharacteristic
664C23C23×Q811yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4111yescharacteristic
667C23C2×H(5,𝔽2)11yescharacteristic
668C23C2×H(5,𝔽2)12yes—
669C23C2×2−1+411yescharacteristic
670C23#58512yes—
671C23#58512yes—
672C23#58512yes—
673D4—416no—
674D4—816no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—232no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—432no—
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—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—816no—
765C2×C4C2×#12114yes—
766C2×C4C2×#12114yes—
767C2×C4C2×#12114yes—
768C2×C4C2×C22⋊Q814yes—
769C2×C4C2×C22⋊Q814yes—
770C2×C4#53714yes—
771C2×C4#54614yes—
772C2×C4D4×Q814yes—
773C2×C4#55214yes—
774C2×C4#55414yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—48no—
787C22—44no—
788C22—44no—
789C22—48no—
790C22—44no—
791C22—82no—
792C22—82no—
793C22—84no—
794C22—82no—
795C22—82no—
796C22—84no—
797C22C22×#12111yescharacteristic
798C22C22×C22⋊Q811yescharacteristic
799C22C2×#53711yescharacteristic
800C22#344912yes—
801C22#346012yes—
802C22C2×#54611yescharacteristic
803C22C2×D4×Q811yescharacteristic
804C22C2×#55211yescharacteristic
805C22C2×#55411yescharacteristic
806C22#348812yes—
807C22#349312yes—
808C22#349412yes—
809C22#349811yescharacteristic
810C22#350011yescharacteristic
811C22#350011yescharacteristic
812C22#350011yescharacteristic
813C22#350112yes—
814C22#350412yes—
815C22#351212yes—
816C22#353912yes—
817C22#354212yes—
818C22#355412yes—
819C22#355712yes—
820C4—24no—
821C4—24no—
822C4—24no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4#241718yes—
837C2—44no—
838C2—84no—
839C2C2×#241711yescharacteristic
840C2#3525611yescharacteristic
841C2#3532811yescharacteristic
842C2#3552911yescharacteristic
843C2#3562011yescharacteristic
844C2#3730111yescharacteristic
845C2#3742011yescharacteristic
846C2#3784612yes—
847C2#3798712yes—
848C2#3959012yes—
849C2#3969212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2566C2semidirect
2. C2×#2629C2semidirect
4. C2×#2296C2semidirect
5. #15677C2semidirect
6. #15507C2semidirect
7. #15324C2semidirect
8. #15306C2semidirect
9. #15234C2semidirect
10. #15222C2semidirect
11. #15222C2semidirect
12. #15151C2semidirect
14. #14682C2semidirect
15. #14340C2semidirect
17. #14160C2semidirect
18. #13911C2semidirect
19. #13906C2semidirect
199. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25662
C2×#26292
C2×#23242
C2×#22962
#156772
#155072
#153242
#153062
#152342
#152222
#151512
#146982
#146822
#143402
#142572
#141602
#139112
#139062