Finite Group Databasebeta

← #61611

Subgroups — #61611

Order 256.

1043 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3486C211yesmaximal, characteristic, complemented
3#3329C211yesmaximal, characteristic, complemented
4#3326C211yesmaximal, characteristic, complemented
5#3321C211yesmaximal, characteristic, complemented
6#3320C211yesmaximal, characteristic, complemented
7#3312C211yesmaximal, characteristic, complemented
8#3308C211yesmaximal, characteristic, complemented
9#3300C211yesmaximal, characteristic, complemented
10#3298C211yesmaximal, characteristic, complemented
11#3282C211yesmaximal, characteristic, complemented
12D4×SD16C211yesmaximal, characteristic, complemented
13#3278C211yesmaximal, characteristic, complemented
14#3275C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3266C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3225C211yesmaximal, characteristic, complemented
20#3221C211yesmaximal, characteristic, complemented
21#3201C211yesmaximal, characteristic, complemented
22#3200C211yesmaximal, characteristic, complemented
23#3194C211yesmaximal, characteristic, complemented
24#3191C211yesmaximal, characteristic, complemented
25#3126C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3010C211yesmaximal, characteristic, complemented
29#3004C211yesmaximal, characteristic, complemented
30C2×#448C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic, complemented
33C23×Q8C2211yescharacteristic, complemented
34C2×#137C2211yescharacteristic, complemented
35C2×#137C2211yescharacteristic, complemented
36C2×#137C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
38C2×#135C2211yescharacteristic, complemented
39C22×SD16C2211yescharacteristic
40C22×SD16C2211yescharacteristic
41C22×SD16C2211yescharacteristic, complemented
42#562—21no—
43#560—21no—
44#555C2211yescharacteristic
45#553C2211yescharacteristic
46#552C2211yescharacteristic
47#551—21no—
48#550C2211yescharacteristic
49D4×Q8—21no—
50D4×Q8—21no—
51D4×Q8C2211yescharacteristic
52D4×Q8C2211yescharacteristic, complemented
53D4×Q8C2211yescharacteristic, complemented
54D4×Q8C2211yescharacteristic, complemented
55#548—21no—
56#548—21no—
57#548C2211yescharacteristic
58#548C2211yescharacteristic, complemented
59#548C2211yescharacteristic, complemented
60#548C2211yescharacteristic, complemented
61#547C2211yescharacteristic
62#546—21no—
63#546C2211yescharacteristic
64#546C2211yescharacteristic
65D42C2211yescharacteristic
66#542C2211yescharacteristic
67#540—21no—
68#540C2211yescharacteristic
69#538—21no—
70#537C2211yescharacteristic
71#536—21no—
72#536—21no—
73#536C2211yescharacteristic, complemented
74#536C2211yescharacteristic, complemented
75#535—21no—
76#535C2211yescharacteristic
77#534—21no—
78#525—21no—
79#525—21no—
80#525C2211yescharacteristic
81#525C2211yescharacteristic
82#525C2211yescharacteristic, complemented
83C2×#121C2211yescharacteristic
84#519C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#487C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#480C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#477C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#470C2211yescharacteristic, complemented
110#469C2211yescharacteristic
111#469C2211yescharacteristic, complemented
112#468C2211yescharacteristic
113#468C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#468C2211yescharacteristic, complemented
116#468C2211yescharacteristic, complemented
117#467C2211yescharacteristic, complemented
118#467C2211yescharacteristic, complemented
119#466C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic, 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#462C2211yescharacteristic, complemented
132#461C2211yescharacteristic, complemented
133#461C2211yescharacteristic, complemented
134#461C2211yescharacteristic, complemented
135#460C2211yescharacteristic, complemented
136#460C2211yescharacteristic, complemented
137#452C2211yescharacteristic, complemented
138#452C2211yescharacteristic, complemented
139#452C2211yescharacteristic, complemented
140#452C2211yescharacteristic, complemented
141#452C2211yescharacteristic, complemented
142#451C2211yescharacteristic, complemented
143#451C2211yescharacteristic, complemented
144#451C2211yescharacteristic, complemented
145#451C2211yescharacteristic, complemented
146#451C2211yescharacteristic, complemented
147#450C2211yescharacteristic
148#450C2211yescharacteristic, complemented
149#450C2211yescharacteristic, complemented
150#449C2211yescharacteristic
151#449C2211yescharacteristic, complemented
152#449C2211yescharacteristic, complemented
153#449C2211yescharacteristic, complemented
154#449C2211yescharacteristic, complemented
155#449C2211yescharacteristic, complemented
156#449C2211yescharacteristic, complemented
157#448C2211yescharacteristic
158#448C2211yescharacteristic
159#448C2211yescharacteristic
160#448C2211yescharacteristic
161#448C2211yescharacteristic
162#448C2211yescharacteristic
163#448C2211yescharacteristic, complemented
164#448C2211yescharacteristic, complemented
165#448C2211yescharacteristic, complemented
166#448C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#448C2211yescharacteristic, complemented
171#448C2211yescharacteristic, complemented
172#447C2211yescharacteristic
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
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic
188C8×D4C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#433C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#419C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#103C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, 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×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C2×#41C2311yescharacteristic
212C2×#41C2311yescharacteristic
213C2×#41C2311yescharacteristic
214C2×#41C2311yescharacteristic
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—42no—
220C22×Q8—42no—
221C22×Q8C2311yescharacteristic
222C22×Q8C2311yescharacteristic
223C22×Q8C2311yescharacteristic
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×Q8C2311yescharacteristic
227C22×Q8C2311yescharacteristic
228C22×Q8C2311yescharacteristic
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C2311yescharacteristic
232C22×D4C2311yescharacteristic
233C23×C4—21no—
234C23×C4C2311yescharacteristic
235#137—42no—
236#137—42no—
237#137—42no—
238AGL(1,ℤ/8)—42no—
239#135—42no—
240C2×Q16C2311yescharacteristic
241C2×Q16C2311yescharacteristic
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×SD16—42no—
246C2×SD16—42no—
247C2×SD16—42no—
248C2×SD16C2311yescharacteristic
249C2×SD16C2311yescharacteristic
250C2×SD16C2311yescharacteristic
251C2×SD16C2311yescharacteristic
252C2×SD16C2311yescharacteristic
253C2×SD16C2311yescharacteristic
254C2×SD16C2311yescharacteristic
255C2×SD16C2311yescharacteristic
256C2×SD16C2311yescharacteristic
257C2×SD16C2311yescharacteristic
258C2×SD16C2311yescharacteristic
259C2×SD16C2311yescharacteristic
260C2×SD16C2311yescharacteristic
261C2×SD16C2311yescharacteristic
262C2×SD16C2311yescharacteristic
263C2×SD16C2311yescharacteristic
264C2×D8C2311yescharacteristic
265C2×D8C2311yescharacteristic
266C2×D8C2311yescharacteristic
267C2×M16C2311yescharacteristic
268C2×M16C2311yescharacteristic
269C2×M16C2311yescharacteristic
270C2×M16C2311yescharacteristic
271C22×C8C2311yescharacteristic
272C22×C8C2311yescharacteristic
273C22×C8C2311yescharacteristic
274C22×C8C2311yescharacteristic
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8C2311yescharacteristic
281C4⋊Q8C2311yescharacteristic
282C4⋊Q8C2311yescharacteristic
283#127—21no—
284#127—21no—
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#123—21no—
315#123—21no—
316#123—21no—
317#123—21no—
318#123D411yescharacteristic
319#123D411yescharacteristic
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8D411yescharacteristic
338C22⋊Q8D411yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
346C22⋊Q8C2311yescharacteristic
347C22⋊Q8C2311yescharacteristic
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#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121D411yescharacteristic
367#121D411yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#121C2311yescharacteristic
373#121C2311yescharacteristic
374#121C2311yescharacteristic
375#121C2311yescharacteristic
376#121C2311yescharacteristic
377#121C2311yescharacteristic
378#121C2311yescharacteristic
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#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
460#103C2311yescharacteristic
461#103C2311yescharacteristic
462#103C2311yescharacteristic
463#103C2311yescharacteristic
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—
492C24C2×D411yescharacteristic
493#41—22no—
494#41—22no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—44no—
502#41—44no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—44no—
508#41—82no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8C2×D411yescharacteristic
539C2×Q8C2411yescharacteristic
540C2×Q8C2411yescharacteristic
541C2×Q8C2411yescharacteristic
542C2×Q8C2411yescharacteristic
543C2×Q8C2411yescharacteristic
544C2×Q8C2411yescharacteristic
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—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4C2×D411yescharacteristic
572C2×D4C2×D411yescharacteristic
573C2×D4C2×D411yescharacteristic
574C2×D4C2×D411yescharacteristic
575C2×D4C2×D411yescharacteristic
576C2×D4C2×D411yescharacteristic
577C2×D4C2×D411yescharacteristic
578C2×D4C2411yescharacteristic
579C2×D4C2411yescharacteristic
580C2×D4C2411yescharacteristic
581C2×D4C2411yescharacteristic
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
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—41no—
601C22×C4—41no—
602C22×C4—44no—
603C22×C4C2×D411yescharacteristic
604C22×C4C2×D411yescharacteristic
605C22×C4C2×D411yescharacteristic
606C22×C4C2411yescharacteristic
607C22×C4C2411yescharacteristic
608C22×C4C2411yescharacteristic
609C22×C4C2411yescharacteristic
610C22×C4C2411yescharacteristic
611Q16—22no—
612Q16—22no—
613Q16—41no—
614Q16—41no—
615Q16—41no—
616SD16—22no—
617SD16—22no—
618SD16—22no—
619SD16—22no—
620SD16—22no—
621SD16—22no—
622SD16—41no—
623SD16—41no—
624SD16—41no—
625SD16—41no—
626SD16—41no—
627SD16—41no—
628SD16—41no—
629SD16—41no—
630SD16—41no—
631SD16—41no—
632D8—41no—
633D8—41no—
634D8—41no—
635M16—41no—
636M16—41no—
637M16—41no—
638M16—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8C2411yescharacteristic
644C2×C8C2411yescharacteristic
645C2×C8C2411yescharacteristic
646C2×C8C2411yescharacteristic
647C2×C8C2411yescharacteristic
648C2×C8C2411yescharacteristic
649C2×C8C2411yescharacteristic
650C2×C8C2411yescharacteristic
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
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—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23C22×D411yescharacteristic
752C23C22×D411yescharacteristic
753C23C22×D411yescharacteristic
754C23C22×D411yescharacteristic
755C23C22×D411yescharacteristic
756Q8—24no—
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—21no—
761Q8—21no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—41no—
768Q8—42no—
769Q8—42no—
770Q8—42no—
771Q8—42no—
772Q8—42no—
773Q8—42no—
774Q8—42no—
775Q8—81no—
776Q8H(5,𝔽2)12yes—
777Q8H(5,𝔽2)12yes—
778D4—22no—
779D4—22no—
780D4—21no—
781D4—21no—
782D4—21no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—21no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813C2×C4—24no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
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—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4C22×D411yescharacteristic
857C2×C4C22×D411yescharacteristic
858C2×C4C22×D411yescharacteristic
859C2×C4C22×D411yescharacteristic
860C2×C4C22×D411yescharacteristic
861C2×C4C22×D411yescharacteristic
862C2×C4C22×D411yescharacteristic
863C2×C4C22×D411yescharacteristic
864C2×C4C22×D411yescharacteristic
865C2×C4C2511yescharacteristic
866C8—21no—
867C8—21no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—21no—
872C8—21no—
873C8—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—162no—
902C22—162no—
903C22#57712yes—
904C22C23×D411yescharacteristic
905C4—21no—
906C4—21no—
907C4—22no—
908C4—22no—
909C4—21no—
910C4—21no—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×H(5,𝔽2)11yescharacteristic
927C4C2×H(5,𝔽2)11yescharacteristic
928C2—22no—
929C2—41no—
930C2—41no—
931C2—41no—
932C2—41no—
933C2—81no—
934C2—81no—
935C2—81no—
936C2—81no—
937C2#348411yescharacteristic
938C2C2×#57711yescharacteristic
939C2#358611yescharacteristic
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. #3486C2semidirect
3. #3329C2semidirect
4. #3326C2semidirect
5. #3321C2semidirect
6. #3320C2semidirect
7. #3312C2semidirect
8. #3308C2semidirect
9. #3300C2semidirect
10. #3298C2semidirect
11. #3282C2semidirect
12. D4×SD16C2semidirect
13. #3278C2semidirect
14. #3275C2semidirect
15. #3271C2semidirect
16. #3266C2semidirect
17. #3266C2semidirect
18. #3265C2semidirect
19. #3225C2semidirect
20. #3221C2semidirect
21. #3201C2semidirect
22. #3200C2semidirect
23. #3194C2semidirect
24. #3191C2semidirect
25. #3126C2semidirect
26. #3121C2semidirect
27. #3013C2semidirect
28. #3010C2semidirect
29. #3004C2semidirect
30. C2×#448C2semidirect
31. #2976C2semidirect
32. C2×2−1+4C22semidirect
33. C23×Q8C22semidirect
34. C2×#137C22semidirect
35. C2×#137C22semidirect
36. C2×#137C22semidirect
37. C2×AGL(1,ℤ/8)C22semidirect
38. C2×#135C22semidirect
41. C22×SD16C22semidirect
52. D4×Q8C22semidirect
53. D4×Q8C22semidirect
54. D4×Q8C22semidirect
58. #548C22semidirect
59. #548C22semidirect
60. #548C22semidirect
73. #536C22semidirect
74. #536C22semidirect
82. #525C22semidirect
84. #519C22semidirect
85. #497C22semidirect
86. #496C22semidirect
87. #495C22semidirect
88. #492C22semidirect
89. #491C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #487C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
98. #483C22semidirect
99. #483C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #480C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #477C22semidirect
108. #475C22semidirect
109. #470C22semidirect
111. #469C22semidirect
113. #468C22semidirect
114. #468C22semidirect
115. #468C22semidirect
116. #468C22semidirect
117. #467C22semidirect
118. #467C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #465C22semidirect
124. #465C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #463C22semidirect
129. #463C22semidirect
130. #463C22semidirect
131. #462C22semidirect
132. #461C22semidirect
133. #461C22semidirect
134. #461C22semidirect
135. #460C22semidirect
136. #460C22semidirect
137. #452C22semidirect
138. #452C22semidirect
139. #452C22semidirect
140. #452C22semidirect
141. #452C22semidirect
142. #451C22semidirect
143. #451C22semidirect
144. #451C22semidirect
145. #451C22semidirect
146. #451C22semidirect
148. #450C22semidirect
149. #450C22semidirect
151. #449C22semidirect
152. #449C22semidirect
153. #449C22semidirect
154. #449C22semidirect
155. #449C22semidirect
156. #449C22semidirect
163. #448C22semidirect
164. #448C22semidirect
165. #448C22semidirect
166. #448C22semidirect
167. #448C22semidirect
168. #448C22semidirect
169. #448C22semidirect
170. #448C22semidirect
171. #448C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. #436C22semidirect
182. #436C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
188. C8×D4C22semidirect
189. #433C22semidirect
190. #433C22semidirect
191. #419C22semidirect
192. #419C22semidirect
193. #419C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. C2×#103C22semidirect
197. C2×#103C22semidirect
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
#34862
#33292
#33262
#33212
#33202
#33122
#33082
#33002
#32982
#32822
D4×SD162
#32782
#32752
#32712
#32662
#32652
#32252
#32212
#32012
#32002
#31942
#31912
#31262
#31212
#30132
#30102
#30042
C2×#4482
#29762