Finite Group Databasebeta

← #649308

Subgroups — #649308

Order 512.

2922 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic
2C2×#2423C211yesmaximal, characteristic
3C2×#2360C211yesmaximal, characteristic
4C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#15406C214yesmaximal
6#15363C214yesmaximal, complemented
7#15199C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic
9#15180C211yesmaximal, characteristic, complemented
10#15178C211yesmaximal, characteristic
11#14809C214yesmaximal, complemented
12#14712C211yesmaximal, characteristic, complemented
13#14112C214yesmaximal
14#14000C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13976C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2502—28no—
27#2423—28no—
28C2×#399C2212yes—
29C2×#398C2212yes—
30C2×#398C2214yes—
31#2360—28no—
32C4×C4⋊Q8—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2212yes—
42C2×#389C2214yes—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2214yes—
46C2×#389C2214yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#387C2212yes—
51C2×#385C2214yes—
52C2×#385C2212yes—
53C2×#385C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2214yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1444C2214yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2212yes—
83#1436C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C4×Q8—24no—
109C2×C4×Q8—24no—
110C2×C4×Q8—24no—
111C2×C4×Q8—24no—
112C2×C4×Q8—42no—
113C2×C4×Q8—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#399—28no—
158#398—28no—
159#398—216no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—42no—
167#391D418yes—
168#389—24no—
169#389—24no—
170#389—216no—
171#389—28no—
172#389—48no—
173#389—48no—
174#388—28no—
175#388Q8116yescomplemented
176#387—28no—
177#387—28no—
178#385—28no—
179#385—216no—
180#385—48no—
181#384—24no—
182#384—24no—
183#384—24no—
184#384—24no—
185#384—24no—
186#384—42no—
187#380—24no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—216no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4D418yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2311yescharacteristic
218C2×#95C2314yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2312yes—
222C43—24no—
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8C2×D414yes—
237C22×Q8#4114yes—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—42no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4C2×D414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C4⋊Q8—232no—
269C22⋊Q8—232no—
270C22⋊Q8—416no—
271C4×Q8—416no—
272C4×Q8—416no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—416no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
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⋊C4C2×D414yes—
334C2×C4⋊C4C2×Q818yes—
335C2×C4⋊C4#4114yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4C2×D414yes—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×Q818yes—
352C2×C22⋊C4C2×Q818yes—
353C2×C22⋊C4C2×Q818yes—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—44no—
381C2×C42C2×D414yes—
382C2×C42C2×D414yes—
383C2×C42C2×D414yes—
384C2×C42C2×Q818yes—
385C2×C42#4114yes—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—28no—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—24no—
404#95—42no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95C2×D414yes—
409#95C2×D414yes—
410#95C2×D4116yes—
411#95C2×Q818yes—
412#95C2×Q818yes—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—22no—
422C24C22×D412yes—
423C24C22×Q814yes—
424C24C2511yescharacteristic
425C2×Q8—28no—
426C2×Q8—28no—
427C2×Q8—28no—
428C2×Q8—28no—
429C2×Q8—28no—
430C2×Q8—28no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
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—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—88no—
529C22×C4—84no—
530C22×C4—88no—
531C22×C4C22×D412yes—
532C22×C4C22×D414yes—
533C22×C4C22×D412yes—
534C22×C4C22×D414yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D414yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×Q814yes—
542C22×C4C22×Q814yes—
543C22×C4C22×Q814yes—
544C22×C4C22×Q814yes—
545C22×C4C22×Q814yes—
546C22×C4C22×Q814yes—
547C22×C4C2×#4114yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4H(5,𝔽2)14yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C42−1+414yes—
556C22×C42−1+412yes—
557C4⋊C4—216no—
558C4⋊C4—232no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—216no—
562C4⋊C4—416no—
563C4⋊C4—416no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—88no—
574C4⋊C4—84no—
575C4⋊C4—88no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C4⋊C4—88no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—44no—
583C22⋊C4—48no—
584C22⋊C4—84no—
585C22⋊C4C4⋊Q8116yescomplemented
586C42—28no—
587C42—28no—
588C42—28no—
589C42—28no—
590C42—216no—
591C42—48no—
592C42—48no—
593C42—48no—
594C42—44no—
595C42—44no—
596C42—84no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C2×C4⋊Q814yes—
620C23C23×D411yescharacteristic
621C23C23×D411yescharacteristic
622C23C23×Q812yes—
623C23C22×#4111yescharacteristic
624C23C22×#4111yescharacteristic
625C23C22×#4111yescharacteristic
626C23C2×H(5,𝔽2)11yescharacteristic
627C23C2×H(5,𝔽2)12yes—
628C23C2×2−1+411yescharacteristic
629C23C2×2−1+412yes—
630C23#58512yes—
631Q8—416no—
632Q8—416no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—816no—
730C2×C4#52514yes—
731C2×C4#52514yes—
732C2×C4C2×C4⋊Q814yes—
733C2×C4C2×C4⋊Q814yes—
734C2×C4#53914yes—
735C2×C4D4214yes—
736C2×C4#54714yes—
737C2×C4#54714yes—
738C2×C4D4×Q818yes—
739C2×C4#55418yes—
740C2×C4#55914yes—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—44no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22C2×#52511yescharacteristic
753C22C2×#52511yescharacteristic
754C22C22×C4⋊Q811yescharacteristic
755C22#344911yescharacteristic
756C22C2×#53911yescharacteristic
757C22C2×D4211yescharacteristic
758C22C2×#54711yescharacteristic
759C22C2×#54711yescharacteristic
760C22C2×D4×Q812yes—
761C22C2×#55412yes—
762C22Q8×#4112yes—
763C22Q8×#4112yes—
764C22C2×#55911yescharacteristic
765C22#348812yes—
766C22#349811yescharacteristic
767C22#349911yescharacteristic
768C22#350312yes—
769C22#350312yes—
770C22#350712yes—
771C22#352012yes—
772C22#352212yes—
773C22#354612yes—
774C22#356312yes—
775C4—24no—
776C4—24no—
777C4—28no—
778C4—28no—
779C4—42no—
780C4—44no—
781C4—42no—
782C4—42no—
783C4—44no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4#245518yes—
793C2—44no—
794C2C2×#245511yescharacteristic
795C2#3495311yescharacteristic
796C2#3553511yescharacteristic
797C2D4×C4⋊Q811yescharacteristic
798C2#3618011yescharacteristic
799C2#3654412yes—
800C2#3768111yescharacteristic
801C2#3948411yescharacteristic
802C2#3966212yes—
803C2#5911312yes—
804C2#5964212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊Q8C2semidirect
6. #15363C2semidirect
7. #15199C2semidirect
9. #15180C2semidirect
11. #14809C2semidirect
12. #14712C2semidirect
14. #14000C2semidirect
15. #13976C2semidirect
16. #13976C2semidirect
17. #13910C2semidirect
175. #388Q8semidirect
585. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24232
C2×#23602
C2×C4×C4⋊Q82
#154062
#153632
#151992
#151822
#151802
#151782
#148092
#147122
#141122
#140002
#139762
#139102
#138802
C4×#3882