Finite Group Databasebeta

← #497477

Subgroups — #497477

Order 512.

827 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60215C211yesmaximal, characteristic
2D4×M32C211yesmaximal, characteristic, complemented
3C2×#2168C211yesmaximal, characteristic, complemented
4#13267C211yesmaximal, characteristic, complemented
5#13265C211yesmaximal, characteristic, complemented
6#12984C211yesmaximal, characteristic, complemented
7#12983C211yesmaximal, characteristic, complemented
8#12978C211yesmaximal, characteristic, complemented
9#12978C211yesmaximal, characteristic, complemented
10#12848C211yesmaximal, characteristic, complemented
11#12848C211yesmaximal, characteristic, complemented
12#12787C211yesmaximal, characteristic, complemented
13#12604C211yesmaximal, characteristic, complemented
14#12554C211yesmaximal, characteristic, complemented
15C2×#1379C211yesmaximal, characteristic, complemented
16#3475C411yescharacteristic
17C22×M32C2211yescharacteristic
18C22×M32C2211yescharacteristic
19C22×M32C2211yescharacteristic
20C23×C16C2211yescharacteristic
21#2970—21no—
22#2969—21no—
23#2968—21no—
24#2968—21no—
25#2966—21no—
26#2966—21no—
27#2966—21no—
28C8×#41—21no—
29#2962C411yescharacteristic
30#2960C2211yescharacteristic
31D4×M16C411yescharacteristic
32#2933C411yescharacteristic
33#2933C411yescharacteristic
34#2929C2211yescharacteristic
35#2929C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37#2925C411yescharacteristic
38#2924C411yescharacteristic
39#2924C411yescharacteristic
40C4×#131C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C2×#405C2211yescharacteristic
43#2169—21no—
44#2168—21no—
45#2168—21no—
46#2168—21no—
47#2168—21no—
48#2168—21no—
49#2168—21no—
50D4×C16—21no—
51#2150C2211yescharacteristic
52C2×C4⋊C16C2211yescharacteristic
53C2×#350C2211yescharacteristic
54C2×#350C2211yescharacteristic
55C2×#350C2211yescharacteristic
56C2×#350C2211yescharacteristic
57#2112C2211yescharacteristic
58#2112C2211yescharacteristic
59C2×C22⋊C16C2211yescharacteristic
60C2×C22⋊C16C2211yescharacteristic
61C4×M32C2211yescharacteristic
62C2×#346C2211yescharacteristic
63#1379C2211yescharacteristic
64#1379C2211yescharacteristic
65#1379C2211yescharacteristic
66#1379C2211yescharacteristic
67#1379C2211yescharacteristic
68#1379C2211yescharacteristic
69#1379C2211yescharacteristic
70#1379C2211yescharacteristic
71#1379C2211yescharacteristic
72#1379C2211yescharacteristic
73#1379C2211yescharacteristic
74#1379C2211yescharacteristic
75C2×#131C2×C411yescharacteristic
76C2×#131C2311yescharacteristic
77C22×M16C2×C411yescharacteristic
78C22×M16C2×C411yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81#556C811yescharacteristic
82#555C811yescharacteristic
83#554C811yescharacteristic
84#553C811yescharacteristic
85#553C811yescharacteristic
86#552—21no—
87#552C811yescharacteristic
88#552C811yescharacteristic
89#551—21no—
90#551—21no—
91#547C811yescharacteristic
92#546—21no—
93#533C2×C411yescharacteristic
94#529—21no—
95#529—21no—
96#529—21no—
97#525C2×C411yescharacteristic
98#525C2×C411yescharacteristic
99C4×#41—21no—
100C4×#41C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×#117C2×C411yescharacteristic
103C2×#117C2×C411yescharacteristic
104C2×M32—21no—
105C2×M32—21no—
106C2×M32—21no—
107C2×M32—21no—
108C2×M32—22no—
109C2×M32—22no—
110C2×M32—22no—
111C2×M32—41no—
112C2×M32—41no—
113C2×M32—41no—
114C2×M32C2311yescharacteristic
115C2×M32C2311yescharacteristic
116C2×M32C2311yescharacteristic
117C2×M32C2311yescharacteristic
118C22×C16—21no—
119C22×C16—21no—
120C22×C16—21no—
121C22×C16—21no—
122C22×C16—22no—
123C22×C16—41no—
124C22×C16C2311yescharacteristic
125C22×C16C2311yescharacteristic
126C22×C16C2311yescharacteristic
127C22×C16C2311yescharacteristic
128#446—21no—
129#446—21no—
130#446—21no—
131#446—21no—
132#446—21no—
133C8×Q8—21no—
134C8×Q8—21no—
135C8×Q8—21no—
136#436—21no—
137#436—21no—
138#436—21no—
139#435—21no—
140#435—21no—
141#435—21no—
142#435—21no—
143#435—21no—
144#435—21no—
145#435—21no—
146#435—21no—
147#435—21no—
148#435—21no—
149C8×D4—21no—
150C8×D4—21no—
151C8×D4—21no—
152C8×D4—21no—
153C8×D4—21no—
154C8×D4—21no—
155C8×D4—21no—
156C8×D4D411yescharacteristic
157C8×D4D411yescharacteristic
158C8×D4D411yescharacteristic
159C8×D4D411yescharacteristic
160C8×D4D411yescharacteristic
161C8×D4D411yescharacteristic
162C8×D4D411yescharacteristic
163C8×D4D411yescharacteristic
164#433—21no—
165#433—21no—
166#433—21no—
167#433—21no—
168#433—21no—
169#433—21no—
170#432—21no—
171#432—21no—
172#432—21no—
173#431—21no—
174#431—21no—
175#431—21no—
176#424C2×C411yescharacteristic
177#424C2×C411yescharacteristic
178#424C2×C411yescharacteristic
179#424C2×C411yescharacteristic
180#423C2×C411yescharacteristic
181C2×C4⋊C8C2×C411yescharacteristic
182#408C2×C411yescharacteristic
183#408C2×C411yescharacteristic
184#407C2×C411yescharacteristic
185#407C2×C411yescharacteristic
186C2×C22⋊C8C2×C411yescharacteristic
187C2×C22⋊C8C2×C411yescharacteristic
188#405—21no—
189#405—21no—
190#405—21no—
191#405—21no—
192#405—21no—
193#405—21no—
194#405C2×C411yescharacteristic
195#405C2×C411yescharacteristic
196#405C2×C411yescharacteristic
197#405C2×C411yescharacteristic
198#405C2×C411yescharacteristic
199#405C2311yescharacteristic
200#405C2311yescharacteristic
201#405C2311yescharacteristic
202C4×M16—21no—
203C4×M16C2×C411yescharacteristic
204C2×#97—21no—
205C2×#97—21no—
206C2×C4×C8—21no—
207C2×C4×C8—21no—
208C2×C4×C8—21no—
209C2×C4×C8C2311yescharacteristic
210C4⋊C16—21no—
211C4⋊C16—21no—
212C4⋊C16—21no—
213C4⋊C16—21no—
214#350—22no—
215#350—22no—
216#350—41no—
217#350—41no—
218C22⋊C16—21no—
219C22⋊C16—21no—
220C22⋊C16—21no—
221C22⋊C16—21no—
222C22⋊C16—21no—
223C22⋊C16—21no—
224C22⋊C16—21no—
225C22⋊C16—21no—
226#346—21no—
227#346—21no—
228#346—21no—
229C4×C16—21no—
230C2×#41—21no—
231C2×#41C22×C411yescharacteristic
232C22×D4M1611yescharacteristic
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C411yescharacteristic
235#131—22no—
236#131—21no—
237#131—21no—
238#131—21no—
239#131—21no—
240#131—41no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—41no—
248C2×M16—41no—
249C2×M16C22×C411yescharacteristic
250C2×M16C22×C411yescharacteristic
251C2×M16C22×C411yescharacteristic
252C2×M16C22×C411yescharacteristic
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8C22×C411yescharacteristic
266C22×C8C22×C411yescharacteristic
267C22×C8C22×C411yescharacteristic
268C22×C8C2×D411yescharacteristic
269C22×C8C2×D411yescharacteristic
270C22×C8C2×D411yescharacteristic
271C22×C8C2×D411yescharacteristic
272C22×C8C2×D411yescharacteristic
273C22×C8C2×D411yescharacteristic
274C22×C8C2×D411yescharacteristic
275C22×C8C2×D411yescharacteristic
276C22×C8C2411yescharacteristic
277C4⋊Q8C2×C811yescharacteristic
278C4⋊Q8C2×C811yescharacteristic
279#126—21no—
280#126—21no—
281#126—21no—
282#126—21no—
283#126—21no—
284#126—21no—
285#125—21no—
286#125—21no—
287#125—21no—
288#125C2×C811yescharacteristic
289#125C2×C811yescharacteristic
290#124—21no—
291#124—21no—
292#124—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8C2×C811yescharacteristic
307C22⋊Q8C2×C811yescharacteristic
308C22⋊Q8C2×C811yescharacteristic
309C22⋊Q8C2×C811yescharacteristic
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—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8C2×C811yescharacteristic
323C4×Q8C2×C811yescharacteristic
324C4×D4—21no—
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×D4C22⋊C411yescharacteristic
334C4×D4C22⋊C411yescharacteristic
335C4×D4C22⋊C411yescharacteristic
336C4×D4C22⋊C411yescharacteristic
337C4×D4C2×C811yescharacteristic
338C4×D4C2×C811yescharacteristic
339C4×D4C2×C811yescharacteristic
340C4×D4C2×C811yescharacteristic
341C4×D4C2×C811yescharacteristic
342C4×D4C2×C811yescharacteristic
343#117—21no—
344#117—21no—
345#117—21no—
346#117—21no—
347#117—21no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117C2×C811yescharacteristic
352#117C2×C811yescharacteristic
353#117C2×C811yescharacteristic
354#117C2×C811yescharacteristic
355#117C22×C411yescharacteristic
356#117C22×C411yescharacteristic
357#117C22×C411yescharacteristic
358C2×C4⋊C4C2×C811yescharacteristic
359C2×C4⋊C4C2×C811yescharacteristic
360C2×C4⋊C4C2×C811yescharacteristic
361C2×C4⋊C4C2×C811yescharacteristic
362C2×C4⋊C4M1611yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4M1611yescharacteristic
366C2×C22⋊C4M1611yescharacteristic
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42C22×C411yescharacteristic
371M32—21no—
372M32—21no—
373M32—21no—
374M32—21no—
375M32—21no—
376M32—21no—
377M32—21no—
378M32—42no—
379M32—42no—
380M32—42no—
381M32—42no—
382M32#4112yescomplemented
383C2×C16—21no—
384C2×C16—21no—
385C2×C16—21no—
386C2×C16—21no—
387C2×C16—21no—
388C2×C16—21no—
389C2×C16—21no—
390C2×C16—21no—
391C2×C16—21no—
392C2×C16—21no—
393C2×C16—21no—
394C2×C16—21no—
395C2×C16—21no—
396C2×C16—21no—
397C2×C16—21no—
398C2×C16—42no—
399C2×C16—42no—
400C2×C16—42no—
401C2×C16—42no—
402C2×C16#4112yescomplemented
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C22⋊C411yescharacteristic
414C4⋊C8C22⋊C411yescharacteristic
415C4⋊C8C22⋊C411yescharacteristic
416C4⋊C8C22⋊C411yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8C22⋊C411yescharacteristic
426C22⋊C8C22⋊C411yescharacteristic
427C22⋊C8C22⋊C411yescharacteristic
428C22⋊C8C22⋊C411yescharacteristic
429C22⋊C8C22⋊C411yescharacteristic
430C22⋊C8C22⋊C411yescharacteristic
431C22⋊C8C22⋊C411yescharacteristic
432C22⋊C8C22⋊C411yescharacteristic
433#97—21no—
434#97—21no—
435#97—21no—
436#97—21no—
437#97—21no—
438#97—21no—
439#97—21no—
440#97—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8—21no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8C2×D411yescharacteristic
452C4×C8C2×D411yescharacteristic
453C4×C8C2×D411yescharacteristic
454C4×C8C2×D411yescharacteristic
455C24C2×M1611yescharacteristic
456C24C2×M1611yescharacteristic
457#41—21no—
458#41—21no—
459#41—21no—
460#41—21no—
461#41—44no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C22×C811yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—42no—
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—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C22×C811yescharacteristic
496C22×C4C22×C811yescharacteristic
497C22×C4C22×C811yescharacteristic
498C22×C4C22×C811yescharacteristic
499C22×C4C2×M1611yescharacteristic
500C22×C4C2×M1611yescharacteristic
501C22×C4C2×M1611yescharacteristic
502C22×C4C2×M1611yescharacteristic
503C22×C4C23×C411yescharacteristic
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16—42no—
512M16—42no—
513M16—42no—
514M16—41no—
515M16—41no—
516M16#13112yes—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8C2×C22⋊C411yescharacteristic
549C2×C8C2×C22⋊C411yescharacteristic
550C2×C8C2×C22⋊C411yescharacteristic
551C2×C8C2×C22⋊C411yescharacteristic
552C2×C8C2×C22⋊C411yescharacteristic
553C2×C8C2×C22⋊C411yescharacteristic
554C2×C8C22×D411yescharacteristic
555C2×C8C22×D411yescharacteristic
556C2×C8C2×#4111yescharacteristic
557C2×C8C2×#4111yescharacteristic
558C2×C8H(5,𝔽2)11yescharacteristic
559C2×C82−1+411yescharacteristic
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4C22⋊C811yescharacteristic
577C4⋊C4C22⋊C811yescharacteristic
578C4⋊C4C22⋊C811yescharacteristic
579C4⋊C4C22⋊C811yescharacteristic
580C4⋊C4C22×C811yescharacteristic
581C4⋊C4C22×C811yescharacteristic
582C4⋊C4C22×C811yescharacteristic
583C4⋊C4C22×C811yescharacteristic
584C4⋊C4C22×C811yescharacteristic
585C4⋊C4C22×C811yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4C22⋊C811yescharacteristic
604C22⋊C4C22⋊C811yescharacteristic
605C22⋊C4C22⋊C811yescharacteristic
606C22⋊C4C22⋊C811yescharacteristic
607C22⋊C4C22⋊C811yescharacteristic
608C22⋊C4C22⋊C811yescharacteristic
609C22⋊C4C22⋊C811yescharacteristic
610C22⋊C4C22⋊C811yescharacteristic
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42C2×C22⋊C411yescharacteristic
621C42C2×C22⋊C411yescharacteristic
622C42C22×C811yescharacteristic
623C42C22×C811yescharacteristic
624C16—22no—
625C16—22no—
626C16—41no—
627C16—41no—
628C16—41no—
629C16—41no—
630C16—41no—
631C16—41no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23C2×C22⋊C811yescharacteristic
642C23C2×C22⋊C811yescharacteristic
643C23C2×C22⋊C811yescharacteristic
644C23C2×C22⋊C811yescharacteristic
645C23C22×M1611yescharacteristic
646Q8—21no—
647Q8—21no—
648Q8—42no—
649Q8—81no—
650D4—22no—
651D4—22no—
652D4—21no—
653D4—21no—
654D4—41no—
655D4—41no—
656D4—42no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—81no—
661D4—81no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4C2×C22⋊C811yescharacteristic
700C2×C4C2×C22⋊C811yescharacteristic
701C2×C4C2×C22⋊C811yescharacteristic
702C2×C4C2×C22⋊C811yescharacteristic
703C2×C4C2×C22⋊C811yescharacteristic
704C2×C4C2×C22⋊C811yescharacteristic
705C2×C4C2×C22⋊C811yescharacteristic
706C2×C4C2×C22⋊C811yescharacteristic
707C2×C4C22×C22⋊C411yescharacteristic
708C2×C4C4×#4111yescharacteristic
709C2×C4#52011yescharacteristic
710C2×C4C23×C811yescharacteristic
711C2×C4C2×#13111yescharacteristic
712C2×C4#56811yescharacteristic
713C8—21no—
714C8—21no—
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8#54611yescharacteristic
724C8#54611yescharacteristic
725C8#54711yescharacteristic
726C8#54711yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22#211712yes—
748C22C22×C22⋊C811yescharacteristic
749C22#297011yescharacteristic
750C22#299011yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4#233911yescharacteristic
767C4#288011yescharacteristic
768C4C8×#4111yescharacteristic
769C4#298811yescharacteristic
770C2—21no—
771C2—21no—
772C2—22no—
773C2—41no—
774C2—41no—
775C2—41no—
776C2—81no—
777C2#2246911yescharacteristic
778C2C2×#211711yescharacteristic
779C2#3334011yescharacteristic
subgroupG/H
centerC2×C8C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC22×C8C24
socleC22C22×C22⋊C8
prime radical#3475C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C2×C8×D4 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. D4×M32C2semidirect
3. C2×#2168C2semidirect
4. #13267C2semidirect
5. #13265C2semidirect
6. #12984C2semidirect
7. #12983C2semidirect
8. #12978C2semidirect
9. #12978C2semidirect
10. #12848C2semidirect
11. #12848C2semidirect
12. #12787C2semidirect
13. #12604C2semidirect
14. #12554C2semidirect
15. C2×#1379C2semidirect
382. M32#41semidirect
402. C2×C16#41semidirect

Maximal subgroups

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

subgroupindex
#602152
D4×M322
C2×#21682
#132672
#132652
#129842
#129832
#129782
#128482
#127872
#126042
#125542
C2×#13792