Finite Group Databasebeta

← #477144

Subgroups — #477144

Order 512.

1080 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2088C211yesmaximal, characteristic
2C2×#2066C211yesmaximal, characteristic
3C2×#2058C211yesmaximal, characteristic
4C2×#2024C211yesmaximal, characteristic
5#15193C211yesmaximal, characteristic
6#15128C211yesmaximal, characteristic
7#11327C211yesmaximal, characteristic
8#11316C211yesmaximal, characteristic
9#11257C211yesmaximal, characteristic
10#11220C211yesmaximal, characteristic
11#11202C211yesmaximal, characteristic
12#11190C211yesmaximal, characteristic
13#11122C211yesmaximal, characteristic
14#11122C211yesmaximal, characteristic
15#11067C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C2×#395—21no—
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34#2088—24no—
35#2066—24no—
36#2058—24no—
37#2024—24no—
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1446—21no—
53#1445—21no—
54#1445—21no—
55#1445—21no—
56#1444—21no—
57#1444—21no—
58#1441—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C23×Q8—21no—
64C23×Q8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—41no—
72C2×C4⋊Q8—41no—
73C2×C4⋊Q8—41no—
74C2×C4⋊Q8—41no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4D411yescharacteristic
81C22×C4⋊C4D411yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×#106—22no—
93C2×#106—22no—
94C2×#106—22no—
95C2×#106—22no—
96C2×#106—22no—
97C2×#106—41no—
98C2×#106—41no—
99C2×#106—41no—
100C2×#106—41no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—41no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—41no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103Q814yescomplemented
116#395—44no—
117#391—22no—
118#391—22no—
119#391—41no—
120#391—41no—
121#391—41no—
122#391—41no—
123#389—22no—
124#389—22no—
125#389—22no—
126#389—22no—
127#389—41no—
128#389—41no—
129#389—41no—
130#389—41no—
131C4×C4⋊C4—41no—
132C4×C4⋊C4—41no—
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×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95D411yescharacteristic
152C2×#95D411yescharacteristic
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340D414yes—
161#340D414yes—
162#336—22no—
163#336—22no—
164#336—41no—
165#336—41no—
166#336—41no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—42no—
181C22×Q8—42no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—42no—
185C22×Q8—81no—
186C22×Q8—81no—
187C22×Q8C2×Q812yes—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2411yescharacteristic
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×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C2×D412yes—
229C22×C8C2×D412yes—
230C22×C8C2×Q812yes—
231C4⋊Q8—44no—
232C4⋊Q8—44no—
233C4⋊Q8—44no—
234C4⋊Q8—44no—
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—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
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—22no—
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—21no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
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—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4SD1614yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4C2×D412yes—
294C2×C4⋊C4C2×D412yes—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4C2×Q812yes—
297C2×C4⋊C4#4112yes—
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—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316#106—44no—
317#106—44no—
318#106—44no—
319C4⋊C8—44no—
320#103—44no—
321#103—44no—
322#103—44no—
323#103—44no—
324#95—41no—
325#95—41no—
326#95—42no—
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—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—81no—
342#95—81no—
343#95—81no—
344C24C22×D411yescharacteristic
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—48no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—84no—
375C2×Q8—84no—
376C2×Q8—84no—
377C2×Q8—84no—
378C2×Q8—84no—
379C2×Q8—84no—
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—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
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×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4C2×SD1612yes—
475C22×C4C2×SD1612yes—
476C22×C4C2×SD1612yes—
477C22×C4#13712yes—
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C22×Q811yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C4H(5,𝔽2)11yescharacteristic
486C22×C4H(5,𝔽2)11yescharacteristic
487C22×C42−1+411yescharacteristic
488C22×C42−1+411yescharacteristic
489C22×C42−1+411yescharacteristic
490C22×C42−1+411yescharacteristic
491C22×C42−1+411yescharacteristic
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
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—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—48no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—84no—
552C4⋊C4—84no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C23#53411yescharacteristic
568C23#53611yescharacteristic
569C23#53711yescharacteristic
570C23D4211yescharacteristic
571C23D4211yescharacteristic
572C23#54811yescharacteristic
573C23D4×Q811yescharacteristic
574C23C22×SD1611yescharacteristic
575C23C2×#13711yescharacteristic
576C23#57511yescharacteristic
577C23#57511yescharacteristic
578C23#57711yescharacteristic
579C23#57711yescharacteristic
580C23#57711yescharacteristic
581C23#57811yescharacteristic
582Q8—42no—
583Q8—42no—
584Q8—42no—
585Q8—42no—
586Q8—816no—
587Q8—81no—
588Q8—81no—
589Q8—81no—
590Q8—81no—
591C2×C4—22no—
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—41no—
604C2×C4—41no—
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—41no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
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—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4#53511yescharacteristic
690C2×C4#53511yescharacteristic
691C2×C4#53611yescharacteristic
692C2×C4#53611yescharacteristic
693C2×C4#53611yescharacteristic
694C2×C4#53711yescharacteristic
695C2×C4#53911yescharacteristic
696C2×C4#54211yescharacteristic
697C2×C4#54211yescharacteristic
698C2×C4#54311yescharacteristic
699C2×C4#54411yescharacteristic
700C2×C4#54411yescharacteristic
701C2×C4D4211yescharacteristic
702C2×C4#54611yescharacteristic
703C2×C4#54711yescharacteristic
704C2×C4D4×Q811yescharacteristic
705C2×C4D4×Q811yescharacteristic
706C2×C4#55411yescharacteristic
707C2×C4#56011yescharacteristic
708C2×C4#56211yescharacteristic
709C2×C4#56211yescharacteristic
710C2×C4#56211yescharacteristic
711C2×C4#56311yescharacteristic
712C2×C4#56311yescharacteristic
713C2×C4#56311yescharacteristic
714C2×C4#56311yescharacteristic
715C2×C4#56311yescharacteristic
716C2×C4#56311yescharacteristic
717C8—42no—
718C8—42no—
719C8—42no—
720C8—81no—
721C22#266911yescharacteristic
722C22#267411yescharacteristic
723C22#267711yescharacteristic
724C22#268111yescharacteristic
725C22#268311yescharacteristic
726C22#272911yescharacteristic
727C22#281411yescharacteristic
728C22#318711yescharacteristic
729C22#319611yescharacteristic
730C22#320011yescharacteristic
731C22#320111yescharacteristic
732C22#322911yescharacteristic
733C22#324011yescharacteristic
734C22#324211yescharacteristic
735C22#324411yescharacteristic
736C22#324611yescharacteristic
737C22#325211yescharacteristic
738C22#325811yescharacteristic
739C22#326311yescharacteristic
740C22#326611yescharacteristic
741C22#326711yescharacteristic
742C22#326711yescharacteristic
743C22#327011yescharacteristic
744C22#327511yescharacteristic
745C22#327711yescharacteristic
746C22D4×SD1611yescharacteristic
747C22D4×SD1611yescharacteristic
748C22#335911yescharacteristic
749C22#336911yescharacteristic
750C22#337111yescharacteristic
751C22#337611yescharacteristic
752C22Q8×SD1611yescharacteristic
753C22#338711yescharacteristic
754C22#338811yescharacteristic
755C22#339011yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—82no—
761C4—82no—
762C4—82no—
763C4—81no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4—81no—
769C4—161no—
770C4#267211yescharacteristic
771C4#267711yescharacteristic
772C4#269211yescharacteristic
773C4#272011yescharacteristic
774C4#282011yescharacteristic
775C4#282111yescharacteristic
776C4#283811yescharacteristic
777C4#284111yescharacteristic
778C2#1710411yescharacteristic
779C2#3050011yescharacteristic
780C2#3051811yescharacteristic
781C2#3080811yescharacteristic
782C2#3082311yescharacteristic
783C2#3094911yescharacteristic
784C2#3096411yescharacteristic
785C2#3115911yescharacteristic
786C2#3117811yescharacteristic
787C2#3124011yescharacteristic
788C2#3125311yescharacteristic
789C2#3256611yescharacteristic
790C2#3258211yescharacteristic
791C2#3274011yescharacteristic
792C2#3275211yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
115. C2×#103Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#20882
C2×#20662
C2×#20582
C2×#20242
#151932
#151282
#113272
#113162
#112572
#112202
#112022
#111902
#111222
#110672