Finite Group Databasebeta

← #61001

Subgroups — #61001

Order 256.

871 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3495C211yesmaximal, characteristic, complemented
2#3494C211yesmaximal, characteristic, complemented
3#3250C211yesmaximal, characteristic, complemented
4#3248C211yesmaximal, characteristic, complemented
5#3247C211yesmaximal, characteristic, complemented
6#3246C211yesmaximal, characteristic, complemented
7#3244C211yesmaximal, characteristic, complemented
8#3244C211yesmaximal, characteristic, complemented
9#3242C211yesmaximal, characteristic, complemented
10#3241C211yesmaximal, characteristic, complemented
11#3225C211yesmaximal, characteristic, complemented
12#3224C211yesmaximal, characteristic, complemented
13#3222C211yesmaximal, characteristic, complemented
14#3221C211yesmaximal, characteristic, complemented
15#3191C211yesmaximal, characteristic, complemented
16#3190C211yesmaximal, characteristic, complemented
17#3188C211yesmaximal, characteristic, complemented
18#3187C211yesmaximal, characteristic, complemented
19#3181C211yesmaximal, characteristic, complemented
20#3180C211yesmaximal, characteristic, complemented
21#3168C211yesmaximal, characteristic, complemented
22#3167C211yesmaximal, characteristic, complemented
23#3126C211yesmaximal, characteristic, complemented
24#3125C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3123C211yesmaximal, characteristic, complemented
27#3121C211yesmaximal, characteristic, complemented
28#3120C211yesmaximal, characteristic, complemented
29#3119C211yesmaximal, characteristic, complemented
30#3118C211yesmaximal, characteristic, complemented
31C2×#433C211yesmaximal, characteristic, complemented
32#556—21no—
33#555—21no—
34#554—21no—
35#553—21no—
36#553—21no—
37#552—21no—
38#552—21no—
39#552—21no—
40#552—21no—
41#551—21no—
42#551—21no—
43#551—21no—
44#551—21no—
45#547—21no—
46#546—21no—
47#546—21no—
48#544C2211yescharacteristic
49#544C2211yescharacteristic, complemented
50#542C2211yescharacteristic
51#542C2211yescharacteristic
52#542C2211yescharacteristic
53#542C2211yescharacteristic
54#541C2211yescharacteristic
55#541C2211yescharacteristic
56#540C2211yescharacteristic
57#540C2211yescharacteristic
58#536C2211yescharacteristic, complemented
59#535C2211yescharacteristic
60#533C2211yescharacteristic, complemented
61#533C2211yescharacteristic, complemented
62#532C2211yescharacteristic
63#532C2211yescharacteristic
64#529C2211yescharacteristic
65#529C2211yescharacteristic
66#529C2211yescharacteristic, complemented
67#529C2211yescharacteristic, complemented
68#525C2211yescharacteristic
69#525C2211yescharacteristic
70C2×C22⋊Q8C2211yescharacteristic
71C2×#121C2211yescharacteristic
72#520C2211yescharacteristic
73#520C2211yescharacteristic, complemented
74#519C2211yescharacteristic, complemented
75#518C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#497C2211yescharacteristic, complemented
82#496C2211yescharacteristic, complemented
83#495C2211yescharacteristic, complemented
84#492C2211yescharacteristic, complemented
85#491C2211yescharacteristic, complemented
86#490C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#487C2211yescharacteristic, complemented
92#486C2211yescharacteristic, complemented
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic
98#483C2211yescharacteristic
99#483C2211yescharacteristic
100#483C2211yescharacteristic, complemented
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic, complemented
105#481C2211yescharacteristic
106#481C2211yescharacteristic
107#481C2211yescharacteristic
108#480C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#478C2211yescharacteristic, complemented
114#478C2211yescharacteristic, complemented
115#478C2211yescharacteristic, complemented
116#478C2211yescharacteristic, complemented
117#477C2211yescharacteristic, complemented
118#476C2211yescharacteristic, complemented
119#476C2211yescharacteristic, complemented
120#476C2211yescharacteristic, complemented
121#475C2211yescharacteristic, complemented
122#475C2211yescharacteristic, complemented
123#475C2211yescharacteristic, complemented
124#474C2211yescharacteristic, complemented
125#467C2211yescharacteristic, complemented
126#467C2211yescharacteristic, complemented
127#467C2211yescharacteristic, complemented
128#466C2211yescharacteristic
129#466C2211yescharacteristic
130#466C2211yescharacteristic, complemented
131#465C2211yescharacteristic
132#465C2211yescharacteristic
133#465C2211yescharacteristic
134#465C2211yescharacteristic
135#465C2211yescharacteristic
136#465C2211yescharacteristic
137#465C2211yescharacteristic, complemented
138#465C2211yescharacteristic, complemented
139#465C2211yescharacteristic, complemented
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic, complemented
142#464C2211yescharacteristic, complemented
143#464C2211yescharacteristic, complemented
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic, complemented
146#463C2211yescharacteristic, complemented
147#463C2211yescharacteristic, complemented
148#463C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#461C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#460C2211yescharacteristic, complemented
155#460C2211yescharacteristic, complemented
156#459C2211yescharacteristic, complemented
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#450C2211yescharacteristic
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic
168#449C2211yescharacteristic, complemented
169#448C2211yescharacteristic
170#448C2211yescharacteristic
171#448C2211yescharacteristic, complemented
172#447C2211yescharacteristic
173#442C2211yescharacteristic, complemented
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×SD16C2211yescharacteristic, complemented
185C4×SD16C2211yescharacteristic, complemented
186C4×SD16C2211yescharacteristic, complemented
187C4×SD16C2211yescharacteristic, complemented
188C4×D8C2211yescharacteristic, complemented
189#433C2211yescharacteristic
190#433C2211yescharacteristic
191#433C2211yescharacteristic
192#433C2211yescharacteristic
193#433C2211yescharacteristic, complemented
194#433C2211yescharacteristic, complemented
195#433C2211yescharacteristic, complemented
196#433C2211yescharacteristic, complemented
197C2×C4⋊C8C2211yescharacteristic, complemented
198C2×C4⋊C8C2211yescharacteristic, complemented
199C2×C22⋊C8C2211yescharacteristic
200C2×C22⋊C8C2211yescharacteristic
201C2×#97C2211yescharacteristic, complemented
202C2×C4×C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×D8C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239#127C2311yescharacteristic
240#127C2311yescharacteristic
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124C2311yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#120—21no—
332#120—21no—
333#120—21no—
334#120—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117D411yescharacteristic
382#117D411yescharacteristic
383#117D411yescharacteristic
384#117D411yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D411yescharacteristic
395C2×C4⋊C4D411yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4D411yescharacteristic
403C2×C22⋊C4D411yescharacteristic
404C2×C42C2311yescharacteristic
405C2×C42C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24C2×D411yescharacteristic
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—82no—
485#41—82no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—82no—
515C2×D4C2411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C2×D4C2411yescharacteristic
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4C2×D411yescharacteristic
535C22×C4C2×D411yescharacteristic
536C22×C4C2×D411yescharacteristic
537C22×C4C2×D411yescharacteristic
538C22×C4C2×D411yescharacteristic
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544Q16—41no—
545Q16—41no—
546Q16—41no—
547SD16—41no—
548SD16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557D8—41no—
558D8—41no—
559D8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42C2×D411yescharacteristic
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—81no—
691C23—81no—
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—81no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C2511yescharacteristic
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—82no—
810C22—162no—
811C22#57712yes—
812C22C23×D411yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4#58511yescharacteristic
837C4#58511yescharacteristic
838C2—22no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2—81no—
845C2#344911yescharacteristic
846C2C2×#57711yescharacteristic
847C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#117 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3495C2semidirect
2. #3494C2semidirect
3. #3250C2semidirect
4. #3248C2semidirect
5. #3247C2semidirect
6. #3246C2semidirect
7. #3244C2semidirect
8. #3244C2semidirect
9. #3242C2semidirect
10. #3241C2semidirect
11. #3225C2semidirect
12. #3224C2semidirect
13. #3222C2semidirect
14. #3221C2semidirect
15. #3191C2semidirect
16. #3190C2semidirect
17. #3188C2semidirect
18. #3187C2semidirect
19. #3181C2semidirect
20. #3180C2semidirect
21. #3168C2semidirect
22. #3167C2semidirect
23. #3126C2semidirect
24. #3125C2semidirect
25. #3125C2semidirect
26. #3123C2semidirect
27. #3121C2semidirect
28. #3120C2semidirect
29. #3119C2semidirect
30. #3118C2semidirect
31. C2×#433C2semidirect
49. #544C22semidirect
58. #536C22semidirect
60. #533C22semidirect
61. #533C22semidirect
66. #529C22semidirect
67. #529C22semidirect
73. #520C22semidirect
74. #519C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #498C22semidirect
81. #497C22semidirect
82. #496C22semidirect
83. #495C22semidirect
84. #492C22semidirect
85. #491C22semidirect
86. #490C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #488C22semidirect
91. #487C22semidirect
92. #486C22semidirect
96. #485C22semidirect
100. #483C22semidirect
104. #482C22semidirect
108. #480C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #478C22semidirect
114. #478C22semidirect
115. #478C22semidirect
116. #478C22semidirect
117. #477C22semidirect
118. #476C22semidirect
119. #476C22semidirect
120. #476C22semidirect
121. #475C22semidirect
122. #475C22semidirect
123. #475C22semidirect
124. #474C22semidirect
125. #467C22semidirect
126. #467C22semidirect
127. #467C22semidirect
130. #466C22semidirect
137. #465C22semidirect
138. #465C22semidirect
139. #465C22semidirect
140. #465C22semidirect
141. #464C22semidirect
142. #464C22semidirect
143. #464C22semidirect
144. #464C22semidirect
145. #463C22semidirect
146. #463C22semidirect
147. #463C22semidirect
148. #463C22semidirect
149. #462C22semidirect
150. #461C22semidirect
151. #461C22semidirect
152. #461C22semidirect
153. #460C22semidirect
154. #460C22semidirect
155. #460C22semidirect
156. #459C22semidirect
160. #452C22semidirect
161. #451C22semidirect
168. #449C22semidirect
171. #448C22semidirect
173. #442C22semidirect
174. #442C22semidirect
175. #441C22semidirect
176. #441C22semidirect
177. #440C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
184. C4×SD16C22semidirect
185. C4×SD16C22semidirect
186. C4×SD16C22semidirect
187. C4×SD16C22semidirect
188. C4×D8C22semidirect
193. #433C22semidirect
194. #433C22semidirect
195. #433C22semidirect
196. #433C22semidirect
197. C2×C4⋊C8C22semidirect
198. C2×C4⋊C8C22semidirect
201. C2×#97C22semidirect
202. C2×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#34952
#34942
#32502
#32482
#32472
#32462
#32442
#32422
#32412
#32252
#32242
#32222
#32212
#31912
#31902
#31882
#31872
#31812
#31802
#31682
#31672
#31262
#31252
#31232
#31212
#31202
#31192
#31182
C2×#4332