Finite Group Databasebeta

← #6611326

Subgroups — #6611326

Order 512.

1852 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36189C211yesmaximal, characteristic
2D4×C4⋊Q8C211yesmaximal, characteristic
3#33232C211yesmaximal, characteristic, complemented
4#33049C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#29144C211yesmaximal, characteristic, complemented
7#28748C211yesmaximal, characteristic, complemented
8#27975C211yesmaximal, characteristic, complemented
9#27972C211yesmaximal, characteristic, complemented
10#27762C214yesmaximal, complemented
11#27283C214yesmaximal, complemented
12#27268C214yesmaximal, complemented
13#25856C211yesmaximal, characteristic, complemented
14#25856C211yesmaximal, characteristic, complemented
15#22425C214yesmaximal
16#21647C211yesmaximal, characteristic, complemented
17#21202C211yesmaximal, characteristic, complemented
18C2×#1956C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×D4×Q8C2212yes—
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#491C2214yes—
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#435C2212yes—
28C2×#419C2214yes—
29C22×#103C2214yes—
30C2×C4×M16C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2868C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2570C2212yes—
39#2551—21no—
40#2551—21no—
41#2546C2212yes—
42#2511—21no—
43#2507—21no—
44#2497—21no—
45#2487—21no—
46#2442C2212yes—
47#2441C2212yes—
48#2440—21no—
49#2440—21no—
50#2440—21no—
51#2440—21no—
52#2434C2212yes—
53#2434C2212yes—
54#2423—21no—
55#2417—21no—
56#2360—21no—
57#2352C2212yes—
58D4×C4⋊C4—21no—
59D4×C4⋊C4—21no—
60#2345—21no—
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63#2285C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C42×D4C2211yescharacteristic
66#2074C2214yes—
67#2072C2214yes—
68#2043C2214yes—
69#2043C2214yes—
70#2043C2214yes—
71#2026C2214yes—
72#1990C2211yescharacteristic
73#1981C2214yes—
74#1960C2214yes—
75#1960C2214yes—
76#1956C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2214yes—
85#1956C2211yescharacteristic
86#1935C2214yes—
87#1935C2214yes—
88#1933C2214yes—
89#1894C2214yes—
90#1892C2214yes—
91#1873C2214yes—
92#1872C2214yes—
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1805C2214yes—
97#1787C2214yes—
98#1787C2214yes—
99#1771C2212yes—
100C4×C4⋊C8C2211yescharacteristic
101#1763C2214yes—
102#1753C2212yes—
103#1752C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C23×Q8C2312yes—
108C23×Q8C2312yes—
109C22×M16C2312yes—
110C23×C8C2312yes—
111D4×Q8—216no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×C4⋊Q8C2312yes—
125C2×C4⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×#125C2312yes—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—22no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8C2312yes—
135C2×C22⋊Q8C2312yes—
136C2×C4×Q8—21no—
137C2×C4×Q8C2312yes—
138C2×C4×D4—22no—
139C2×C4×D4D411yescharacteristic
140C2×C4×D4D411yescharacteristic
141C2×C4×D4C2311yescharacteristic
142C2×#117C2312yes—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#491—48no—
153#487—24no—
154#487—42no—
155#487—42no—
156#435—28no—
157C2×C4⋊C8C2312yes—
158#419—48no—
159C2×#103—48no—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C4×M16—42no—
175C2×#97C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8—42no—
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2312yes—
184#400—22no—
185#400—22no—
186#399—22no—
187#398—22no—
188#398—22no—
189#398—22no—
190#398—22no—
191#396—22no—
192#395—22no—
193#395—22no—
194#395—22no—
195#395—22no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#389—22no—
203#389—22no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384—21no—
236#384—21no—
237#384—21no—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2312yes—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382C2312yes—
244#382C2312yes—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—22no—
254#380C2312yes—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4—22no—
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—24no—
284C22×Q8—24no—
285C22×Q8—28no—
286C22×Q8—28no—
287C22×Q8—42no—
288C22×Q8—42no—
289C22×Q8—44no—
290C22×Q8—44no—
291C22×Q8C2412yes—
292C22×Q8C2412yes—
293C22×Q8C2412yes—
294C22×D4C2×D411yescharacteristic
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—42no—
307C22×C8—24no—
308C22×C8—24no—
309C22×C8—42no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—24no—
315C4⋊Q8—24no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—28no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—44no—
325C4⋊Q8—44no—
326C4⋊Q8—44no—
327C4⋊Q8—44no—
328C4⋊Q8—42no—
329C4⋊Q8—42no—
330C4⋊Q8—44no—
331C4⋊Q8—48no—
332C4⋊Q8#4114yes—
333#125—44no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—44no—
337C22⋊Q8—48no—
338C22⋊Q8—48no—
339C22⋊Q8—82no—
340C4×Q8—28no—
341C4×Q8—82no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—48no—
345C4×D4#4118yes—
346#117—44no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C4⋊C8—24no—
428#103—28no—
429#103—28no—
430#103—28no—
431#103—28no—
432#103—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442#97—24no—
443#97—24no—
444#97—42no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8—42no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—416no—
488C2×Q8—416no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—82no—
495C2×Q8—82no—
496C2×Q8—88no—
497C2×Q8—88no—
498C2×Q8C2×#4114yes—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4#12414yes—
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—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—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4#13714yes—
536C22×C4#13714yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C2×#4114yes—
550C22×C4C2×#4114yes—
551C22×C4C2511yescharacteristic
552M16—48no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—48no—
565C2×C8H(5,𝔽2)14yes—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4#12414yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4#12414yes—
619C22⋊C4#12414yes—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—22no—
632C42—21no—
633C42—44no—
634C42—82no—
635C42—82no—
636C42C2×#4114yes—
637C42C2×#4112yes—
638C42H(5,𝔽2)12yes—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23C2×#12412yes—
650C23C2×#12412yes—
651C23C2×#13712yes—
652C23C2×#13712yes—
653C23C23×D411yescharacteristic
654Q8—28no—
655Q8—44no—
656Q8—44no—
657Q8—44no—
658Q8—44no—
659Q8—44no—
660Q8—88no—
661Q8—88no—
662Q8—84no—
663D4—28no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
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—88no—
721C2×C4—88no—
722C2×C4—164no—
723C2×C4C2×#12412yes—
724C2×C4C2×#12412yes—
725C2×C4C2×#12412yes—
726C2×C4C2×#12412yes—
727C2×C4#54612yes—
728C2×C4#54612yes—
729C2×C4C2×#13712yes—
730C2×C4C2×#13712yes—
731C2×C4C2×#13712yes—
732C2×C4C2×#13712yes—
733C2×C4#57712yes—
734C2×C4#57812yes—
735C2×C4C22×#4111yescharacteristic
736C2×C4C22×#4112yes—
737C2×C4C2×H(5,𝔽2)12yes—
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C8—24no—
740C8—42no—
741C8—42no—
742C8—42no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22#313914yes—
757C22C22×#12411yescharacteristic
758C22C2×#54611yescharacteristic
759C22#349811yescharacteristic
760C22C22×#13711yescharacteristic
761C22C22×#13711yescharacteristic
762C22C2×#57711yescharacteristic
763C22C2×#57811yescharacteristic
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—44no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4#331214yes—
783C4#332014yes—
784C4#348112yes—
785C4#351912yes—
786C2—24no—
787C2—42no—
788C2#3628911yescharacteristic
789C2C2×#313911yescharacteristic
790C2#6062311yescharacteristic
791C2C2×#331211yescharacteristic
792C2C2×#332011yescharacteristic
793C2#6242211yescharacteristic
794C2#6242411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33232C2semidirect
4. #33049C2semidirect
5. #33043C2semidirect
6. #29144C2semidirect
7. #28748C2semidirect
8. #27975C2semidirect
9. #27972C2semidirect
10. #27762C2semidirect
11. #27283C2semidirect
12. #27268C2semidirect
13. #25856C2semidirect
14. #25856C2semidirect
16. #21647C2semidirect
17. #21202C2semidirect
18. C2×#1956C2semidirect

Maximal subgroups

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

subgroupindex
#361892
D4×C4⋊Q82
#332322
#330492
#330432
#291442
#287482
#279752
#279722
#277622
#272832
#272682
#258562
#224252
#216472
#212022
C2×#19562
C4×#4352