Finite Group Databasebeta

← #664693

Subgroups — #664693

Order 512.

2862 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic
2C2×#2360C211yesmaximal, characteristic
3#15624C214yesmaximal, complemented
4#15591C214yesmaximal, complemented
5#15237C211yesmaximal, characteristic, complemented
6#15234C211yesmaximal, characteristic, complemented
7#15191C211yesmaximal, characteristic, complemented
8#15153C211yesmaximal, characteristic, complemented
9#14738C214yesmaximal
10#14702C211yesmaximal, characteristic
11#14155C211yesmaximal, characteristic, complemented
12#14139C211yesmaximal, characteristic
13#14052C214yesmaximal
14#14050C211yesmaximal, characteristic, complemented
15#13978C211yesmaximal, characteristic, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13881C211yesmaximal, characteristic
18C4×#385C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2440—28no—
28C2×#400C2214yes—
29C2×#398C2212yes—
30C2×#395C2212yes—
31#2360—28no—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2214yes—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#387C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C22×#95C2214yes—
57#1446C2214yes—
58#1445C2214yes—
59#1445C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1436C2212yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2212yes—
75C4⋊#95C2214yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2312yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—42no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—216no—
106C2×C22⋊Q8Q818yescomplemented
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—42no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C42—24no—
141C22×C42—42no—
142C22×C42—42no—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152#400—48no—
153#398—28no—
154#395—28no—
155#391—24no—
156#391—24no—
157#391—48no—
158#391—42no—
159#391—42no—
160#391—42no—
161#389—24no—
162#389—24no—
163#389—24no—
164#389—28no—
165#387—28no—
166#385—28no—
167#385—28no—
168#385—28no—
169#384—24no—
170#382—24no—
171#382—42no—
172#380—24no—
173C4×C4⋊C4—24no—
174C4×C4⋊C4—42no—
175C4×C4⋊C4—42no—
176C4×C22⋊C4—24no—
177C4×C22⋊C4—28no—
178C4×C22⋊C4D418yes—
179C2×#95—48no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C25C2411yescharacteristic
213C22×Q8—22no—
214C22×Q8—24no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—28no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—42no—
223C22×Q8—44no—
224C22×Q8C2×Q814yes—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—28no—
237C23×C4—28no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4C2×D414yes—
247C23×C4C2×Q814yes—
248C23×C4#4114yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C4⋊Q8—416no—
268C22⋊Q8—232no—
269C22⋊Q8—432no—
270C4×Q8—416no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—416no—
312C2×C4⋊C4—416no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×Q814yes—
322C2×C4⋊C4C2×Q818yes—
323C2×C4⋊C4#4114yes—
324C2×C4⋊C4#4114yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4C2×D414yes—
334C2×C22⋊C4C2×D414yes—
335C2×C22⋊C4C2×Q818yes—
336C2×C22⋊C4#4118yes—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—24no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—416no—
361C2×C42—44no—
362C2×C42C2×D414yes—
363C2×C42C2×D414yes—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—44no—
383#95—44no—
384#95—42no—
385#95—42no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95C2×D414yes—
395#95C2×D414yes—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24C22×D412yes—
403C24C22×Q812yes—
404C24C2×#4112yes—
405C24C2×#4114yes—
406C242−1+414yes—
407C24C2511yescharacteristic
408C2×Q8—28no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—48no—
412C2×Q8—416no—
413C2×Q8—48no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—84no—
419C2×Q8—88no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—216no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
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—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—84no—
522C22×C4—84no—
523C22×C4—88no—
524C22×C4—88no—
525C22×C4C22⋊Q8116yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q812yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4114yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)14yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C42−1+414yes—
548C4⋊C4—28no—
549C4⋊C4—216no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—84no—
566C4⋊C4—84no—
567C22⋊C4—216no—
568C22⋊C4—28no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4#124116yes—
572C42—28no—
573C42—28no—
574C42—48no—
575C42—48no—
576C42—44no—
577C42—44no—
578C42—44no—
579C42—44no—
580C42—84no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23C2×C22⋊Q814yes—
600C23C2×#12414yes—
601C23#53614yes—
602C23#55618yes—
603C23#55718yes—
604C23C23×D411yescharacteristic
605C23C23×Q811yescharacteristic
606C23C22×#4111yescharacteristic
607C23C22×#4112yes—
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C2×H(5,𝔽2)11yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×H(5,𝔽2)12yes—
613C23C2×2−1+412yes—
614C23C2×2−1+412yes—
615Q8—416no—
616Q8—816no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—232no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—28no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—28no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—432no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—44no—
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—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—816no—
714C2×C4—816no—
715C2×C4C2×C22⋊Q814yes—
716C2×C4C2×C22⋊Q814yes—
717C2×C4C2×#12414yes—
718C2×C4C2×#12414yes—
719C2×C4#52914yes—
720C2×C4#53814yes—
721C2×C4#54614yes—
722C2×C4#54614yes—
723C2×C4#55414yes—
724C2×C4#55414yes—
725C22—28no—
726C22—28no—
727C22—24no—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—28no—
735C22#256818yes—
736C22C22×C22⋊Q811yescharacteristic
737C22C22×#12411yescharacteristic
738C22C2×#52911yescharacteristic
739C22C2×#53611yescharacteristic
740C22C2×#53811yescharacteristic
741C22C2×#54611yescharacteristic
742C22C2×#54611yescharacteristic
743C22C2×#55411yescharacteristic
744C22C2×#55411yescharacteristic
745C22C2×#55612yes—
746C22C2×#55712yes—
747C22#348112yes—
748C22#348212yes—
749C22#349212yes—
750C22#349811yescharacteristic
751C22#349911yescharacteristic
752C22#350312yes—
753C22#351912yes—
754C22#352012yes—
755C22#352012yes—
756C22#352312yes—
757C22#353612yes—
758C22#353812yes—
759C4—24no—
760C4—24no—
761C4—24no—
762C4—44no—
763C4—42no—
764C4—44no—
765C4—44no—
766C4—42no—
767C4—44no—
768C4—44no—
769C4—44no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4#245018yes—
777C2—28no—
778C2C2×#245011yescharacteristic
779C2C2×#256811yescharacteristic
780C2#3553211yescharacteristic
781C2#3628911yescharacteristic
782C2#3630311yescharacteristic
783C2#3648912yes—
784C2#3807811yescharacteristic
785C2#3808111yescharacteristic
786C2#3915412yes—
787C2#5966312yes—
788C2#5966412yes—
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
3. #15624C2semidirect
4. #15591C2semidirect
5. #15237C2semidirect
6. #15234C2semidirect
7. #15191C2semidirect
8. #15153C2semidirect
11. #14155C2semidirect
14. #14050C2semidirect
15. #13978C2semidirect
16. #13926C2semidirect
106. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#23602
#156242
#155912
#152372
#152342
#151912
#151532
#147382
#147022
#141552
#141392
#140522
#140502
#139782
#139262
#138812
C4×#3852
C2×C4⋊#952