Finite Group Databasebeta

← #480212

Subgroups — #480212

Order 512.

789 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60239C211yesmaximal, characteristic
2#33488C211yesmaximal, characteristic, complemented
3#33487C211yesmaximal, characteristic, complemented
4#11492C211yesmaximal, characteristic, complemented
5#11491C211yesmaximal, characteristic, complemented
6#11470C211yesmaximal, characteristic, complemented
7#11470C211yesmaximal, characteristic, complemented
8#11469C211yesmaximal, characteristic, complemented
9#11468C211yesmaximal, characteristic, complemented
10#11464C211yesmaximal, characteristic, complemented
11#11463C211yesmaximal, characteristic, complemented
12#11422C211yesmaximal, characteristic, complemented
13#11422C211yesmaximal, characteristic, complemented
14#11421C211yesmaximal, characteristic, complemented
15C2×#1315C211yesmaximal, characteristic, complemented
16D4×#41C411yescharacteristic
17#2981—21no—
18#2979—21no—
19#2977—21no—
20#2977—21no—
21#2976—21no—
22#2976—21no—
23#2974—21no—
24#2972—21no—
25#2935C411yescharacteristic
26D4×M16C411yescharacteristic
27#2933C411yescharacteristic
28#2933C411yescharacteristic
29#2931C2211yescharacteristic
30#2929C2211yescharacteristic
31#2929C2211yescharacteristic
32C2×C8×D4C2211yescharacteristic
33#2925C411yescharacteristic
34#2922C2211yescharacteristic
35#2880C411yescharacteristic
36#2880C411yescharacteristic
37C2×#408C2211yescharacteristic
38C2×#408C2211yescharacteristic
39#2169—21no—
40#2168—21no—
41#2168—21no—
42#2168—21no—
43#2168—21no—
44#2168—21no—
45#2168—21no—
46D4×C16—21no—
47#2163C2211yescharacteristic, complemented
48#2163C2211yescharacteristic, complemented
49#2163C2211yescharacteristic, complemented
50#2162C2211yescharacteristic, complemented
51#2112C2211yescharacteristic, complemented
52#2112C2211yescharacteristic, complemented
53#2112C2211yescharacteristic, complemented
54#2112C2211yescharacteristic, complemented
55C2×C22⋊C16C2211yescharacteristic, complemented
56C2×C22⋊C16C2211yescharacteristic, complemented
57C2×C22⋊C16C2211yescharacteristic, complemented
58C2×C22⋊C16C2211yescharacteristic, complemented
59#1323C2211yescharacteristic, complemented
60#1323C2211yescharacteristic, complemented
61#1323C2211yescharacteristic, complemented
62#1323C2211yescharacteristic, complemented
63#1315C2211yescharacteristic
64#1315C2211yescharacteristic
65#1315C2211yescharacteristic
66#1315C2211yescharacteristic
67#1315C2211yescharacteristic, complemented
68#1315C2211yescharacteristic, complemented
69#1315C2211yescharacteristic, complemented
70#1315C2211yescharacteristic, complemented
71#1315C2211yescharacteristic, complemented
72#1315C2211yescharacteristic, complemented
73#1315C2211yescharacteristic, complemented
74#1315C2211yescharacteristic, complemented
75C22×#41C2×C411yescharacteristic
76C22×#41C2×C411yescharacteristic
77C2×#131C2×C411yescharacteristic
78C2×#131C2×C411yescharacteristic
79C2×#131C2×C411yescharacteristic
80C2×#131C2×C411yescharacteristic
81C22×M16C2×C411yescharacteristic
82C22×M16C2×C411yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85#550C811yescharacteristic
86D4×Q8C811yescharacteristic
87#548C811yescharacteristic
88#548C811yescharacteristic
89#547—21no—
90#547C811yescharacteristic
91#546—21no—
92#546—21no—
93#546C811yescharacteristic
94#546C811yescharacteristic
95D42—21no—
96D42C811yescharacteristic
97#532—21no—
98#532C2×C411yescharacteristic
99#525—21no—
100#525—21no—
101#525C2×C411yescharacteristic
102#525C2×C411yescharacteristic
103C4×#41C2×C411yescharacteristic
104C2×C4×D4—21no—
105C2×C4×D4C2×C411yescharacteristic
106C2×M32—21no—
107C2×M32—21no—
108C2×M32—21no—
109C2×M32—21no—
110C22×C16—21no—
111C22×C16—21no—
112C22×C16—21no—
113C22×C16—21no—
114#436—21no—
115#436—21no—
116#436—21no—
117#436—21no—
118#436—21no—
119#436—21no—
120#435—21no—
121#435—21no—
122#435—21no—
123#435—21no—
124#435—21no—
125#435—21no—
126#435—21no—
127#435—21no—
128#435—21no—
129#435—21no—
130#435—21no—
131#435—21no—
132C8×D4—21no—
133C8×D4—21no—
134C8×D4—21no—
135C8×D4—21no—
136C8×D4—21no—
137C8×D4—21no—
138C8×D4—21no—
139C8×D4—21no—
140C8×D4—21no—
141C8×D4—21no—
142C8×D4D411yescharacteristic
143C8×D4D411yescharacteristic
144C8×D4D411yescharacteristic
145C8×D4D411yescharacteristic
146C8×D4D411yescharacteristic
147C8×D4D411yescharacteristic
148C8×D4D411yescharacteristic
149C8×D4D411yescharacteristic
150#433—21no—
151#433—21no—
152#433—21no—
153#433—21no—
154#432—21no—
155#431—21no—
156#431—21no—
157#431—21no—
158#424C2×C411yescharacteristic
159#424C2311yescharacteristic
160#423C2×C411yescharacteristic
161C2×C4⋊C8C2×C411yescharacteristic
162#408—21no—
163#408—21no—
164#408—21no—
165#408—21no—
166#408—21no—
167#408—21no—
168#408—21no—
169#408—21no—
170#408C2×C411yescharacteristic
171#408C2×C411yescharacteristic
172#408C2×C411yescharacteristic
173#408C2×C411yescharacteristic
174#408C2×C411yescharacteristic
175#408C2311yescharacteristic
176#408C2311yescharacteristic
177#408C2311yescharacteristic
178#407—21no—
179#407—21no—
180#407C2×C411yescharacteristic
181#407C2×C411yescharacteristic
182C2×C22⋊C8—21no—
183C2×C22⋊C8—21no—
184C2×C22⋊C8—21no—
185C2×C22⋊C8—21no—
186C2×C22⋊C8—21no—
187C2×C22⋊C8—21no—
188C2×C22⋊C8C2×C411yescharacteristic
189C2×C22⋊C8C2×C411yescharacteristic
190#405C2×C411yescharacteristic
191#405C2×C411yescharacteristic
192C4×M16C2×C411yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C4⋊C16—21no—
195C4⋊C16—21no—
196C4⋊C16—21no—
197C4⋊C16—21no—
198C22⋊C16—21no—
199C22⋊C16—21no—
200C22⋊C16—21no—
201C22⋊C16—21no—
202C22⋊C16—21no—
203C22⋊C16—21no—
204C22⋊C16—21no—
205C22⋊C16—21no—
206C22⋊C16C2311yescharacteristic
207C22⋊C16C2311yescharacteristic
208C22⋊C16C2311yescharacteristic
209C22⋊C16C2311yescharacteristic
210C22⋊C16C2311yescharacteristic
211C22⋊C16C2311yescharacteristic
212C22⋊C16C2311yescharacteristic
213C22⋊C16C2311yescharacteristic
214#346—21no—
215#346—21no—
216#346—21no—
217C4×C16—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—21no—
222C2×#41—81no—
223C2×#41—81no—
224C2×#41—81no—
225C2×#41—81no—
226C2×#41C2×C811yescharacteristic
227C2×#41C2×C811yescharacteristic
228C2×#41C2×C811yescharacteristic
229C2×#41C2×C811yescharacteristic
230C2×#41C22×C411yescharacteristic
231C2×#41C22×C411yescharacteristic
232C2×#41C22×C411yescharacteristic
233C22×Q8C2×C811yescharacteristic
234C22×Q8C2×C811yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×C811yescharacteristic
239C22×D4C2×C811yescharacteristic
240C22×D4M1611yescharacteristic
241C23×C4—21no—
242C23×C4—21no—
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245#131—81no—
246#131—81no—
247#131—81no—
248#131—81no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—81no—
256C2×M16—81no—
257C2×M16C22×C411yescharacteristic
258C2×M16C22×C411yescharacteristic
259C2×M16C22×C411yescharacteristic
260C2×M16C22×C411yescharacteristic
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—81no—
268C22×C8—81no—
269C22×C8C22×C411yescharacteristic
270C22×C8C22×C411yescharacteristic
271C22×C8C22×C411yescharacteristic
272C22×C8C2×D411yescharacteristic
273C22×C8C2×D411yescharacteristic
274C22×C8C2×D411yescharacteristic
275C22×C8C2×D411yescharacteristic
276C22×C8C2×D411yescharacteristic
277C22×C8C2×D411yescharacteristic
278C22×C8C2×D411yescharacteristic
279C22×C8C2×D411yescharacteristic
280C22×C8C2411yescharacteristic
281C4⋊Q8—21no—
282C4⋊Q8C2×C811yescharacteristic
283#127—21no—
284#127C2×C811yescharacteristic
285#124—21no—
286#124—21no—
287#124C2×C811yescharacteristic
288#124C2×C811yescharacteristic
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8C2×C811yescharacteristic
300C22⋊Q8C2×C811yescharacteristic
301C22⋊Q8C2×C811yescharacteristic
302C22⋊Q8C2×C811yescharacteristic
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121C2×C811yescharacteristic
314#121C2×C811yescharacteristic
315#121C2×C811yescharacteristic
316#121C2×C811yescharacteristic
317#120—21no—
318#120—21no—
319#120—21no—
320#120—21no—
321#120—21no—
322#120—21no—
323C4×Q8C2×C811yescharacteristic
324C4×Q8C2×C811yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4C22⋊C411yescharacteristic
338C4×D4C22⋊C411yescharacteristic
339C4×D4C22⋊C411yescharacteristic
340C4×D4C22⋊C411yescharacteristic
341C4×D4C2×C811yescharacteristic
342C4×D4C2×C811yescharacteristic
343C4×D4C2×C811yescharacteristic
344C4×D4C2×C811yescharacteristic
345C4×D4C2×C811yescharacteristic
346C4×D4C2×C811yescharacteristic
347#117—21no—
348#117C22×C411yescharacteristic
349C2×C4⋊C4—21no—
350C2×C4⋊C4M1611yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4M1611yescharacteristic
354C2×C22⋊C4M1611yescharacteristic
355C2×C42—21no—
356C2×C42C22×C411yescharacteristic
357M32—81no—
358M32—81no—
359M32—81no—
360M32—81no—
361C2×C16—21no—
362C2×C16—21no—
363C2×C16—21no—
364C2×C16—21no—
365C2×C16—21no—
366C2×C16—21no—
367C2×C16—21no—
368C2×C16—21no—
369C2×C16—81no—
370C2×C16—81no—
371C2×C16—81no—
372C2×C16—81no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8C22⋊C411yescharacteristic
380C4⋊C8C22⋊C411yescharacteristic
381C4⋊C8C22⋊C411yescharacteristic
382C4⋊C8C22⋊C411yescharacteristic
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8C22⋊C411yescharacteristic
404C22⋊C8C22⋊C411yescharacteristic
405C22⋊C8C22⋊C411yescharacteristic
406C22⋊C8C22⋊C411yescharacteristic
407C22⋊C8C22⋊C411yescharacteristic
408C22⋊C8C22⋊C411yescharacteristic
409C22⋊C8C22⋊C411yescharacteristic
410C22⋊C8C22⋊C411yescharacteristic
411#97—21no—
412#97—21no—
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C2×D411yescharacteristic
418C4×C8C2×D411yescharacteristic
419C4×C8C2×D411yescharacteristic
420C4×C8C2×D411yescharacteristic
421C24—21no—
422C24—21no—
423C24C2×M1611yescharacteristic
424C24C2×M1611yescharacteristic
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—81no—
432#41—81no—
433#41—81no—
434#41—81no—
435#41—82no—
436#41—82no—
437#41—81no—
438#41—81no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—81no—
444C2×Q8—81no—
445C2×Q8C22×C811yescharacteristic
446C2×Q8C22×C811yescharacteristic
447C2×Q8C22×C811yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—44no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4—82no—
468C2×D4—82no—
469C2×D4C22⋊C811yescharacteristic
470C2×D4C22⋊C811yescharacteristic
471C2×D4C22⋊C811yescharacteristic
472C2×D4C22⋊C811yescharacteristic
473C2×D4C22×C811yescharacteristic
474C2×D4C22×C811yescharacteristic
475C2×D4C22×C811yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C22×C811yescharacteristic
500C22×C4C22×C811yescharacteristic
501C22×C4C22×C811yescharacteristic
502C22×C4C22×C811yescharacteristic
503C22×C4C2×M1611yescharacteristic
504C22×C4C2×M1611yescharacteristic
505C22×C4C2×M1611yescharacteristic
506C22×C4C2×M1611yescharacteristic
507C22×C4C23×C411yescharacteristic
508M16—41no—
509M16—41no—
510M16—41no—
511M16—41no—
512M16—81no—
513M16—81no—
514M16—81no—
515M16—81no—
516M16—81no—
517M16—81no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—81no—
535C2×C8—81no—
536C2×C8—81no—
537C2×C8—81no—
538C2×C8—81no—
539C2×C8—81no—
540C2×C8C2×C22⋊C411yescharacteristic
541C2×C8C2×C22⋊C411yescharacteristic
542C2×C8C2×C22⋊C411yescharacteristic
543C2×C8C2×C22⋊C411yescharacteristic
544C2×C8C2×C22⋊C411yescharacteristic
545C2×C8C2×C22⋊C411yescharacteristic
546C2×C8C22×D411yescharacteristic
547C2×C8C22×D411yescharacteristic
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4C22⋊C811yescharacteristic
557C4⋊C4C22⋊C811yescharacteristic
558C4⋊C4C22⋊C811yescharacteristic
559C4⋊C4C22⋊C811yescharacteristic
560C4⋊C4C22×C811yescharacteristic
561C4⋊C4C22×C811yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4C22⋊C811yescharacteristic
578C22⋊C4C22⋊C811yescharacteristic
579C22⋊C4C22⋊C811yescharacteristic
580C22⋊C4C22⋊C811yescharacteristic
581C22⋊C4C22⋊C811yescharacteristic
582C22⋊C4C22⋊C811yescharacteristic
583C22⋊C4C22⋊C811yescharacteristic
584C22⋊C4C22⋊C811yescharacteristic
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×C22⋊C411yescharacteristic
589C42C2×C22⋊C411yescharacteristic
590C42C22×C811yescharacteristic
591C42C22×C811yescharacteristic
592C16—41no—
593C16—41no—
594C16—41no—
595C16—41no—
596C16—41no—
597C16—41no—
598C16—41no—
599C16—41no—
600C23—22no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23C2×C22⋊C811yescharacteristic
616C23C2×C22⋊C811yescharacteristic
617C23C2×C22⋊C811yescharacteristic
618C23C2×C22⋊C811yescharacteristic
619C23C22×M1611yescharacteristic
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—81no—
624Q8—81no—
625D4—22no—
626D4—22no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—42no—
633D4—42no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—81no—
639D4—81no—
640D4—81no—
641D4—81no—
642D4—81no—
643D4—81no—
644D4—81no—
645D4—81no—
646D4—81no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4C2×C22⋊C811yescharacteristic
685C2×C4C2×C22⋊C811yescharacteristic
686C2×C4C2×C22⋊C811yescharacteristic
687C2×C4C2×C22⋊C811yescharacteristic
688C2×C4C2×C22⋊C811yescharacteristic
689C2×C4C2×C22⋊C811yescharacteristic
690C2×C4C2×C22⋊C811yescharacteristic
691C2×C4C2×C22⋊C811yescharacteristic
692C2×C4C22×C22⋊C411yescharacteristic
693C2×C4C23×C811yescharacteristic
694C8—21no—
695C8—21no—
696C8—21no—
697C8—21no—
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—82no—
730C22—82no—
731C22—162no—
732C22—162no—
733C22#211712yes—
734C22C22×C22⋊C811yescharacteristic
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—21no—
741C4—21no—
742C4—21no—
743C4—21no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4#288311yescharacteristic
750C4#288811yescharacteristic
751C2—22no—
752C2—41no—
753C2—41no—
754C2—41no—
755C2—41no—
756C2—81no—
757C2—81no—
758C2—81no—
759C2#1735011yescharacteristic
760C2C2×#211711yescharacteristic
761C2#3334011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC2×C4C23×C8
Frattini, cosocleC22×C8C24
socleC22C22×C22⋊C8
prime radicalD4×#41C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33488C2semidirect
3. #33487C2semidirect
4. #11492C2semidirect
5. #11491C2semidirect
6. #11470C2semidirect
7. #11470C2semidirect
8. #11469C2semidirect
9. #11468C2semidirect
10. #11464C2semidirect
11. #11463C2semidirect
12. #11422C2semidirect
13. #11422C2semidirect
14. #11421C2semidirect
15. C2×#1315C2semidirect
47. #2163C22semidirect
48. #2163C22semidirect
49. #2163C22semidirect
50. #2162C22semidirect
51. #2112C22semidirect
52. #2112C22semidirect
53. #2112C22semidirect
54. #2112C22semidirect
55. C2×C22⋊C16C22semidirect
56. C2×C22⋊C16C22semidirect
57. C2×C22⋊C16C22semidirect
58. C2×C22⋊C16C22semidirect
59. #1323C22semidirect
60. #1323C22semidirect
61. #1323C22semidirect
62. #1323C22semidirect
67. #1315C22semidirect
68. #1315C22semidirect
69. #1315C22semidirect
70. #1315C22semidirect
71. #1315C22semidirect
72. #1315C22semidirect
73. #1315C22semidirect
74. #1315C22semidirect

Maximal subgroups

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

subgroupindex
#602392
#334882
#334872
#114922
#114912
#114702
#114692
#114682
#114642
#114632
#114222
#114212
C2×#13152