Finite Group Databasebeta

← #398697

Subgroups — #398697

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1865C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15146C211yesmaximal, characteristic
4Q8×#95C211yesmaximal, characteristic
5#11378C211yesmaximal, characteristic
6#11316C211yesmaximal, characteristic
7#11315C211yesmaximal, characteristic
8#11292C211yesmaximal, characteristic
9#11267C211yesmaximal, characteristic
10#11255C211yesmaximal, characteristic
11#11231C211yesmaximal, characteristic
12#10789C211yesmaximal, characteristic
13#10789C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C2×#400—21no—
26C2×#389C2211yescharacteristic
27C2×#384C2211yescharacteristic
28#1865—24no—
29#1803—24no—
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46#1442—21no—
47#1442—21no—
48#1441—21no—
49C4⋊#95—21no—
50C4⋊#95—21no—
51C4⋊#95—21no—
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4×#95—21no—
60C4×#95C2211yescharacteristic
61C23×Q8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C2×C4×Q8—22no—
67C2×C4×Q8—22no—
68C2×C4×Q8—22no—
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—41no—
78C2×C4×Q8—41no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C2×C4×Q8—41no—
83C2×C4×Q8Q814yes—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C42—21no—
98C22×C42—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×#106—22no—
104C2×#106—22no—
105C2×#106—41no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—41no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—22no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103D414yes—
121#400—44no—
122#389—22no—
123#389—41no—
124#384—22no—
125#384—41no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#336—22no—
157#336—22no—
158#336—41no—
159#336—41no—
160#336—41no—
161C22×Q8—21no—
162C22×Q8—21no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8C2×D412yes—
169C22×Q8C2×Q812yes—
170C22×Q8#4112yes—
171C22×Q8#4112yes—
172C22×Q8#4112yes—
173C22×Q8#4112yes—
174C22×Q8#4112yes—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2411yescharacteristic
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8C2×D412yes—
218C4×Q8—28no—
219C4×Q8—44no—
220C4×Q8—44no—
221C4×Q8—44no—
222C4×Q8—44no—
223C4×Q8—44no—
224C4×Q8—44no—
225C4×Q8—44no—
226C4×Q8—44no—
227C4×Q8—44no—
228C4×Q8—44no—
229C4×Q8—44no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×Q812yes—
288C2×C4⋊C4#4112yes—
289C2×C4⋊C4#4112yes—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42C2×Q812yes—
316C2×C42#4112yes—
317#106—44no—
318C4⋊C8—44no—
319#103—28no—
320#103—44no—
321#103—44no—
322#103—44no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95—22no—
327#95—42no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—81no—
337#95—81no—
338#95—81no—
339#95—81no—
340#95—81no—
341#95—81no—
342C24C22×D411yescharacteristic
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8C22⋊Q814yes—
365C2×Q8#12314yes—
366C2×Q8#12414yes—
367C2×Q8#12514yes—
368C2×Q8#12514yes—
369C2×Q8#12614yes—
370C2×Q8#12614yes—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4C22⋊Q812yes—
464C22×C4C22⋊Q812yes—
465C22×C4#13512yes—
466C22×C4AGL(1,ℤ/8)12yes—
467C22×C4#13712yes—
468C22×C4#13712yes—
469C22×C4C22×D411yescharacteristic
470C22×C4C22×Q811yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4H(5,𝔽2)11yescharacteristic
480C22×C4H(5,𝔽2)11yescharacteristic
481C22×C4H(5,𝔽2)11yescharacteristic
482C22×C42−1+411yescharacteristic
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—48no—
520C4⋊C4—48no—
521C4⋊C4—48no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—84no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—48no—
550C42—48no—
551C42—48no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C23C2×C22⋊Q811yescharacteristic
561C23#52511yescharacteristic
562C23#52511yescharacteristic
563C23D4211yescharacteristic
564C23#54611yescharacteristic
565C23#54611yescharacteristic
566C23#54811yescharacteristic
567C23C2×#13511yescharacteristic
568C23C2×AGL(1,ℤ/8)11yescharacteristic
569C23C2×#13711yescharacteristic
570C23C2×#13711yescharacteristic
571C23#57711yescharacteristic
572C23#57711yescharacteristic
573C23#57711yescharacteristic
574C23#57811yescharacteristic
575Q8—24no—
576Q8—24no—
577Q8—24no—
578Q8—24no—
579Q8—24no—
580Q8—24no—
581Q8—24no—
582Q8#40018yescomplemented
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4#47914yes—
681C2×C4C2×C22⋊Q811yescharacteristic
682C2×C4C2×#12311yescharacteristic
683C2×C4C2×#12411yescharacteristic
684C2×C4C2×#12511yescharacteristic
685C2×C4C2×#12511yescharacteristic
686C2×C4C2×#12611yescharacteristic
687C2×C4C2×#12611yescharacteristic
688C2×C4#52911yescharacteristic
689C2×C4#52911yescharacteristic
690C2×C4#53311yescharacteristic
691C2×C4#53811yescharacteristic
692C2×C4#53811yescharacteristic
693C2×C4#53911yescharacteristic
694C2×C4#53911yescharacteristic
695C2×C4#54311yescharacteristic
696C2×C4#54411yescharacteristic
697C2×C4#54611yescharacteristic
698C2×C4#54611yescharacteristic
699C2×C4#54711yescharacteristic
700C2×C4#55111yescharacteristic
701C2×C4#55111yescharacteristic
702C2×C4#55111yescharacteristic
703C2×C4#55111yescharacteristic
704C2×C4#55211yescharacteristic
705C2×C4#55211yescharacteristic
706C2×C4#55311yescharacteristic
707C2×C4#55311yescharacteristic
708C2×C4#55311yescharacteristic
709C8—42no—
710C8—81no—
711C8—81no—
712C8—81no—
713C22#243711yescharacteristic
714C22#244211yescharacteristic
715C22#244311yescharacteristic
716C22#247211yescharacteristic
717C22#248011yescharacteristic
718C22#248111yescharacteristic
719C22#285111yescharacteristic
720C22C2×#47911yescharacteristic
721C22#307911yescharacteristic
722C22#308211yescharacteristic
723C22#308411yescharacteristic
724C22#310611yescharacteristic
725C22#310711yescharacteristic
726C22#311211yescharacteristic
727C22#311311yescharacteristic
728C22#312011yescharacteristic
729C22#312111yescharacteristic
730C22#312511yescharacteristic
731C22#312611yescharacteristic
732C22#326511yescharacteristic
733C22#327011yescharacteristic
734C22#327811yescharacteristic
735C22#328211yescharacteristic
736C22#330011yescharacteristic
737C22#330411yescharacteristic
738C22#330811yescharacteristic
739C22#331611yescharacteristic
740C22#331611yescharacteristic
741C22#332011yescharacteristic
742C22#332911yescharacteristic
743C22#333211yescharacteristic
744C22#336511yescharacteristic
745C22#336811yescharacteristic
746C22#336911yescharacteristic
747C22#337411yescharacteristic
748C4—24no—
749C4—28no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—82no—
754C4—81no—
755C4—82no—
756C4—82no—
757C4—81no—
758C4—82no—
759C4—161no—
760C4—161no—
761C4—161no—
762C4C2×#40011yescharacteristic
763C4#243811yescharacteristic
764C4#244411yescharacteristic
765C4#248811yescharacteristic
766C4#249311yescharacteristic
767C4#251011yescharacteristic
768C4#256911yescharacteristic
769C4#264611yescharacteristic
770C2#1476711yescharacteristic
771C2#2595711yescharacteristic
772C2#2596711yescharacteristic
773C2#2611311yescharacteristic
774C2#2612211yescharacteristic
775C2#2615911yescharacteristic
776C2#2618711yescharacteristic
777C2#2723311yescharacteristic
778C2#2723911yescharacteristic
779C2#2752711yescharacteristic
780C2#2753711yescharacteristic
781C2#2756111yescharacteristic
782C2#2756711yescharacteristic
783C2#3307311yescharacteristic
784C2#3307511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
582. Q8#400semidirect

Maximal subgroups

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

subgroupindex
C2×#18652
C2×#18032
#151462
Q8×#952
#113782
#113162
#113152
#112922
#112672
#112552
#112312
#107892