Finite Group Databasebeta

← #61616

Subgroups — #61616

Order 256.

1054 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3487C211yesmaximal, characteristic, complemented
3#3332C211yesmaximal, characteristic, complemented
4#3327C211yesmaximal, characteristic, complemented
5#3321C211yesmaximal, characteristic, complemented
6#3317C211yesmaximal, characteristic, complemented
7#3309C211yesmaximal, characteristic, complemented
8#3308C211yesmaximal, characteristic, complemented
9#3305C211yesmaximal, characteristic, complemented
10#3301C211yesmaximal, characteristic, complemented
11#3287C211yesmaximal, characteristic, complemented
12#3282C211yesmaximal, characteristic, complemented
13#3275C211yesmaximal, characteristic, complemented
14#3274C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3268C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3224C211yesmaximal, characteristic, complemented
20#3220C211yesmaximal, characteristic, complemented
21#3199C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3197C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3126C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3010C211yesmaximal, characteristic, complemented
29#3006C211yesmaximal, characteristic, complemented
30#3002C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic, complemented
33C22×#41C2211yescharacteristic, complemented
34C2×#137C2211yescharacteristic, complemented
35C2×AGL(1,ℤ/8)C2211yescharacteristic
36C2×AGL(1,ℤ/8)C2211yescharacteristic
37C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
38C2×#135C2211yescharacteristic, complemented
39C2×#135C2211yescharacteristic, complemented
40C2×#135C2211yescharacteristic, complemented
41C22×SD16C2211yescharacteristic, complemented
42#562—21no—
43#560—21no—
44#555C2211yescharacteristic, complemented
45#553C2211yescharacteristic, complemented
46#552C2211yescharacteristic, complemented
47#551—21no—
48#550—21no—
49#550—21no—
50#550C2211yescharacteristic
51#550C2211yescharacteristic, complemented
52#550C2211yescharacteristic, complemented
53#550C2211yescharacteristic, complemented
54#550C2211yescharacteristic, complemented
55#548—21no—
56#548—21no—
57#548C2211yescharacteristic
58#548C2211yescharacteristic, complemented
59#548C2211yescharacteristic, complemented
60#548C2211yescharacteristic, complemented
61#547C2211yescharacteristic, complemented
62#546—21no—
63#546C2211yescharacteristic, complemented
64#546C2211yescharacteristic, complemented
65D42C2211yescharacteristic, complemented
66#542C2211yescharacteristic
67#540—21no—
68#540C2211yescharacteristic
69#538—21no—
70#537C2211yescharacteristic
71#535—21no—
72#535—21no—
73#535—21no—
74#535C2211yescharacteristic
75#535C2211yescharacteristic, complemented
76#535C2211yescharacteristic, complemented
77#534—21no—
78#525—21no—
79#525—21no—
80#525C2211yescharacteristic
81#525C2211yescharacteristic
82#525C2211yescharacteristic, complemented
83C2×#121C2211yescharacteristic
84#519C2211yescharacteristic, complemented
85#496C2211yescharacteristic, complemented
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#493C2211yescharacteristic, complemented
89#490C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#486C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#482C2211yescharacteristic
97#482C2211yescharacteristic, complemented
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic, complemented
103#481C2211yescharacteristic, complemented
104#480C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#477C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#470C2211yescharacteristic, complemented
110#469C2211yescharacteristic, complemented
111#469C2211yescharacteristic, complemented
112#469C2211yescharacteristic, complemented
113#469C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#468C2211yescharacteristic, complemented
116#468C2211yescharacteristic, complemented
117#466C2211yescharacteristic, complemented
118#466C2211yescharacteristic, complemented
119#466C2211yescharacteristic, complemented
120#466C2211yescharacteristic, complemented
121#466C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#465C2211yescharacteristic, complemented
124#465C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#463C2211yescharacteristic, complemented
129#463C2211yescharacteristic, complemented
130#463C2211yescharacteristic, complemented
131#460C2211yescharacteristic, complemented
132#460C2211yescharacteristic, complemented
133#460C2211yescharacteristic, complemented
134#459C2211yescharacteristic, complemented
135#459C2211yescharacteristic, complemented
136#459C2211yescharacteristic, complemented
137#452C2211yescharacteristic, complemented
138#452C2211yescharacteristic, complemented
139#452C2211yescharacteristic, complemented
140#452C2211yescharacteristic, complemented
141#452C2211yescharacteristic, complemented
142#451C2211yescharacteristic, complemented
143#451C2211yescharacteristic, complemented
144#450C2211yescharacteristic, complemented
145#450C2211yescharacteristic, complemented
146#449C2211yescharacteristic
147#449C2211yescharacteristic
148#449C2211yescharacteristic
149#449C2211yescharacteristic
150#449C2211yescharacteristic
151#449C2211yescharacteristic, complemented
152#449C2211yescharacteristic, complemented
153#449C2211yescharacteristic, complemented
154#449C2211yescharacteristic, complemented
155#449C2211yescharacteristic, complemented
156#449C2211yescharacteristic, complemented
157#449C2211yescharacteristic, complemented
158#449C2211yescharacteristic, complemented
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#448C2211yescharacteristic
162#448C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#448C2211yescharacteristic, complemented
165#448C2211yescharacteristic, complemented
166#448C2211yescharacteristic, complemented
167#447C2211yescharacteristic
168#447C2211yescharacteristic, complemented
169#447C2211yescharacteristic, complemented
170#447C2211yescharacteristic, complemented
171#447C2211yescharacteristic, complemented
172#447C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181#436C2211yescharacteristic, complemented
182#436C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic, complemented
188C8×D4C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#433C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201#407C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
2032−1+4—42no—
2042−1+4—42no—
205C2×#41—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—42no—
212C2×#41—42no—
213C2×#41C2311yescharacteristic
214C2×#41C2311yescharacteristic
215C2×#41C2311yescharacteristic
216C2×#41C2311yescharacteristic
217C2×#41C2311yescharacteristic
218C2×#41C2311yescharacteristic
219C2×#41C2311yescharacteristic
220C2×#41C2311yescharacteristic
221C2×#41C2311yescharacteristic
222C2×#41C2311yescharacteristic
223C22×Q8—21no—
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×Q8C2311yescharacteristic
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4C2311yescharacteristic
231C22×D4C2311yescharacteristic
232C22×D4C2311yescharacteristic
233C23×C4—21no—
234C23×C4C2311yescharacteristic
235#137—42no—
236AGL(1,ℤ/8)—42no—
237AGL(1,ℤ/8)—42no—
238AGL(1,ℤ/8)—42no—
239#135—42no—
240#135—42no—
241#135—42no—
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×SD16—42no—
246C2×SD16C2311yescharacteristic
247C2×SD16C2311yescharacteristic
248C2×SD16C2311yescharacteristic
249C2×SD16C2311yescharacteristic
250C2×SD16C2311yescharacteristic
251C2×SD16C2311yescharacteristic
252C2×SD16C2311yescharacteristic
253C2×SD16C2311yescharacteristic
254C2×SD16C2311yescharacteristic
255C2×SD16C2311yescharacteristic
256C2×SD16C2311yescharacteristic
257C2×SD16C2311yescharacteristic
258C2×D8C2311yescharacteristic
259C2×D8C2311yescharacteristic
260C2×D8C2311yescharacteristic
261C2×D8C2311yescharacteristic
262C2×D8C2311yescharacteristic
263C2×D8C2311yescharacteristic
264C2×D8C2311yescharacteristic
265C2×D8C2311yescharacteristic
266C2×D8C2311yescharacteristic
267C2×M16C2311yescharacteristic
268C2×M16C2311yescharacteristic
269C2×M16C2311yescharacteristic
270C2×M16C2311yescharacteristic
271C22×C8C2311yescharacteristic
272C22×C8C2311yescharacteristic
273C22×C8C2311yescharacteristic
274C22×C8C2311yescharacteristic
275C4⋊Q8C2311yescharacteristic
276#127—21no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127—21no—
282#127—21no—
283#127C2311yescharacteristic
284#127C2311yescharacteristic
285#127C2311yescharacteristic
286#126—21no—
287#126—21no—
288#126—21no—
289#125—21no—
290#125C2311yescharacteristic
291#124—21no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124—21no—
299#124—21no—
300#124C2311yescharacteristic
301#124C2311yescharacteristic
302#124C2311yescharacteristic
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123D411yescharacteristic
315#123D411yescharacteristic
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8D411yescharacteristic
324C22⋊Q8D411yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121D411yescharacteristic
359#121D411yescharacteristic
360#121C2311yescharacteristic
361#121C2311yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#121C2311yescharacteristic
367#121C2311yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#121C2311yescharacteristic
373#121C2311yescharacteristic
374#121C2311yescharacteristic
375#120—21no—
376#120—21no—
377#120—21no—
378#120—21no—
379#120—21no—
380#120—21no—
381#120—21no—
382#120—21no—
383#120—21no—
384#120—21no—
385#120—21no—
386#120—21no—
387#120D411yescharacteristic
388#120D411yescharacteristic
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C2311yescharacteristic
392C4×Q8C2311yescharacteristic
393C4×Q8C2311yescharacteristic
394C4×Q8C2311yescharacteristic
395C4×Q8C2311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4C2311yescharacteristic
411C4×D4C2311yescharacteristic
412C4×D4C2311yescharacteristic
413C4×D4C2311yescharacteristic
414C4×D4C2311yescharacteristic
415C4×D4C2311yescharacteristic
416C4×D4C2311yescharacteristic
417#117—21no—
418#117—21no—
419#117—21no—
420#117—21no—
421#117C2311yescharacteristic
422#117C2311yescharacteristic
423#117C2311yescharacteristic
424#117C2311yescharacteristic
425C2×C4⋊C4C2311yescharacteristic
426C2×C4⋊C4C2311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430#107C2311yescharacteristic
431#107C2311yescharacteristic
432#107C2311yescharacteristic
433#107C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436#106C2311yescharacteristic
437#106C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440C4⋊C8C2311yescharacteristic
441C4⋊C8C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472#102C2311yescharacteristic
473#102C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480C22⋊C8C2311yescharacteristic
481C22⋊C8C2311yescharacteristic
482C22⋊C8C2311yescharacteristic
483C22⋊C8C2311yescharacteristic
484C22⋊C8C2311yescharacteristic
485C22⋊C8C2311yescharacteristic
486#97C2311yescharacteristic
487#97C2311yescharacteristic
488C4×C8C2311yescharacteristic
489C4×C8C2311yescharacteristic
490C24—21no—
491C24—21no—
492C24—21no—
493C24C2×D411yescharacteristic
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—44no—
511#41—44no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516#41—44no—
517#41—44no—
518#41—44no—
519#41—82no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—44no—
531C2×Q8C2×D411yescharacteristic
532C2×Q8C2411yescharacteristic
533C2×Q8C2411yescharacteristic
534C2×Q8C2411yescharacteristic
535C2×Q8C2411yescharacteristic
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—44no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4C2×D411yescharacteristic
579C2×D4C2×D411yescharacteristic
580C2×D4C2×D411yescharacteristic
581C2×D4C2×D411yescharacteristic
582C2×D4C2×D411yescharacteristic
583C2×D4C2×D411yescharacteristic
584C2×D4C2×D411yescharacteristic
585C2×D4C2411yescharacteristic
586C2×D4C2411yescharacteristic
587C2×D4C2411yescharacteristic
588C2×D4C2411yescharacteristic
589C2×D4C2411yescharacteristic
590C2×D4C2411yescharacteristic
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×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—44no—
611C22×C4C2×D411yescharacteristic
612C22×C4C2×D411yescharacteristic
613C22×C4C2×D411yescharacteristic
614C22×C4C2411yescharacteristic
615C22×C4C2411yescharacteristic
616C22×C4C2411yescharacteristic
617C22×C4C2411yescharacteristic
618C22×C4C2411yescharacteristic
619Q16—22no—
620Q16—22no—
621Q16—41no—
622SD16—22no—
623SD16—22no—
624SD16—22no—
625SD16—22no—
626SD16—22no—
627SD16—22no—
628SD16—41no—
629SD16—41no—
630SD16—41no—
631SD16—41no—
632SD16—41no—
633SD16—41no—
634D8—41no—
635D8—41no—
636D8—41no—
637D8—41no—
638D8—41no—
639D8—41no—
640D8—41no—
641D8—41no—
642D8—41no—
643M16—41no—
644M16—41no—
645M16—41no—
646M16—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8C2411yescharacteristic
652C2×C8C2411yescharacteristic
653C2×C8C2411yescharacteristic
654C2×C8C2411yescharacteristic
655C2×C8C2411yescharacteristic
656C2×C8C2411yescharacteristic
657C2×C8C2411yescharacteristic
658C2×C8C2411yescharacteristic
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4C2×D411yescharacteristic
675C4⋊C4C2×D411yescharacteristic
676C4⋊C4C2×D411yescharacteristic
677C4⋊C4C2×D411yescharacteristic
678C4⋊C4C2×D411yescharacteristic
679C4⋊C4C2×D411yescharacteristic
680C4⋊C4C2411yescharacteristic
681C4⋊C4C2411yescharacteristic
682C4⋊C4C2411yescharacteristic
683C4⋊C4C2411yescharacteristic
684C4⋊C4C2411yescharacteristic
685C4⋊C4C2411yescharacteristic
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4C2×D411yescharacteristic
719C22⋊C4C2×D411yescharacteristic
720C22⋊C4C2×D411yescharacteristic
721C22⋊C4C2×D411yescharacteristic
722C22⋊C4C2×D411yescharacteristic
723C22⋊C4C2×D411yescharacteristic
724C22⋊C4C2×D411yescharacteristic
725C22⋊C4C2×D411yescharacteristic
726C22⋊C4C2×D411yescharacteristic
727C22⋊C4C2×D411yescharacteristic
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42C2411yescharacteristic
737C42C2411yescharacteristic
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—42no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23C22×D411yescharacteristic
757C23C22×D411yescharacteristic
758C23C22×D411yescharacteristic
759C23C22×D411yescharacteristic
760C23C22×D411yescharacteristic
761Q8—24no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—41no—
769Q8—42no—
770Q8—42no—
771Q8—81no—
772Q8H(5,𝔽2)12yes—
773Q8H(5,𝔽2)12yes—
774D4—21no—
775D4—21no—
776D4—21no—
777D4—21no—
778D4—21no—
779D4—21no—
780D4—21no—
781D4—21no—
782D4—21no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816D4—81no—
817D4—81no—
818D4—81no—
819D4—81no—
820D4—81no—
821D4—81no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826C2×C4—24no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4C22×D411yescharacteristic
867C2×C4C22×D411yescharacteristic
868C2×C4C22×D411yescharacteristic
869C2×C4C22×D411yescharacteristic
870C2×C4C22×D411yescharacteristic
871C2×C4C22×D411yescharacteristic
872C2×C4C22×D411yescharacteristic
873C2×C4C22×D411yescharacteristic
874C2×C4C22×D411yescharacteristic
875C2×C4C2511yescharacteristic
876C8—21no—
877C8—21no—
878C8—21no—
879C8—21no—
880C8—21no—
881C8—21no—
882C8—21no—
883C8—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—82no—
918C22—84no—
919C22—162no—
920C22—162no—
921C22C23×D411yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—22no—
927C4—22no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4C2×H(5,𝔽2)11yescharacteristic
942C4C2×H(5,𝔽2)11yescharacteristic
943C2—41no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2—81no—
953C2—81no—
954C2#348411yescharacteristic
955C2#358411yescharacteristic
956C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3542C2semidirect
2. #3487C2semidirect
3. #3332C2semidirect
4. #3327C2semidirect
5. #3321C2semidirect
6. #3317C2semidirect
7. #3309C2semidirect
8. #3308C2semidirect
9. #3305C2semidirect
10. #3301C2semidirect
11. #3287C2semidirect
12. #3282C2semidirect
13. #3275C2semidirect
14. #3274C2semidirect
15. #3271C2semidirect
16. #3268C2semidirect
17. #3268C2semidirect
18. #3265C2semidirect
19. #3224C2semidirect
20. #3220C2semidirect
21. #3199C2semidirect
22. #3198C2semidirect
23. #3197C2semidirect
24. #3188C2semidirect
25. #3126C2semidirect
26. #3121C2semidirect
27. #3013C2semidirect
28. #3010C2semidirect
29. #3006C2semidirect
30. #3002C2semidirect
31. #2976C2semidirect
32. C2×2−1+4C22semidirect
33. C22×#41C22semidirect
34. C2×#137C22semidirect
37. C2×AGL(1,ℤ/8)C22semidirect
38. C2×#135C22semidirect
39. C2×#135C22semidirect
40. C2×#135C22semidirect
41. C22×SD16C22semidirect
44. #555C22semidirect
45. #553C22semidirect
46. #552C22semidirect
51. #550C22semidirect
52. #550C22semidirect
53. #550C22semidirect
54. #550C22semidirect
58. #548C22semidirect
59. #548C22semidirect
60. #548C22semidirect
61. #547C22semidirect
63. #546C22semidirect
64. #546C22semidirect
65. D42C22semidirect
75. #535C22semidirect
76. #535C22semidirect
82. #525C22semidirect
84. #519C22semidirect
85. #496C22semidirect
86. #496C22semidirect
87. #495C22semidirect
88. #493C22semidirect
89. #490C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #486C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #484C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #481C22semidirect
103. #481C22semidirect
104. #480C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #477C22semidirect
108. #475C22semidirect
109. #470C22semidirect
110. #469C22semidirect
111. #469C22semidirect
112. #469C22semidirect
113. #469C22semidirect
114. #468C22semidirect
115. #468C22semidirect
116. #468C22semidirect
117. #466C22semidirect
118. #466C22semidirect
119. #466C22semidirect
120. #466C22semidirect
121. #466C22semidirect
122. #465C22semidirect
123. #465C22semidirect
124. #465C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #463C22semidirect
129. #463C22semidirect
130. #463C22semidirect
131. #460C22semidirect
132. #460C22semidirect
133. #460C22semidirect
134. #459C22semidirect
135. #459C22semidirect
136. #459C22semidirect
137. #452C22semidirect
138. #452C22semidirect
139. #452C22semidirect
140. #452C22semidirect
141. #452C22semidirect
142. #451C22semidirect
143. #451C22semidirect
144. #450C22semidirect
145. #450C22semidirect
151. #449C22semidirect
152. #449C22semidirect
153. #449C22semidirect
154. #449C22semidirect
155. #449C22semidirect
156. #449C22semidirect
157. #449C22semidirect
158. #449C22semidirect
159. #449C22semidirect
160. #449C22semidirect
162. #448C22semidirect
163. #448C22semidirect
164. #448C22semidirect
165. #448C22semidirect
166. #448C22semidirect
168. #447C22semidirect
169. #447C22semidirect
170. #447C22semidirect
171. #447C22semidirect
172. #447C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. #436C22semidirect
182. #436C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
187. C8×D4C22semidirect
188. C8×D4C22semidirect
189. #433C22semidirect
190. #433C22semidirect
191. #419C22semidirect
192. #417C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#103C22semidirect
199. #408C22semidirect
200. #408C22semidirect
201. #407C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35422
#34872
#33322
#33272
#33212
#33172
#33092
#33082
#33052
#33012
#32872
#32822
#32752
#32742
#32712
#32682
#32652
#32242
#32202
#31992
#31982
#31972
#31882
#31262
#31212
#30132
#30102
#30062
#30022
#29762