Finite Group Databasebeta

← #61615

Subgroups — #61615

Order 256.

1022 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3487C211yesmaximal, characteristic, complemented
3#3333C211yesmaximal, characteristic, complemented
4#3326C211yesmaximal, characteristic, complemented
5#3317C211yesmaximal, characteristic, complemented
6#3316C211yesmaximal, characteristic, complemented
7#3313C211yesmaximal, characteristic, complemented
8#3309C211yesmaximal, characteristic, complemented
9#3304C211yesmaximal, characteristic, complemented
10#3300C211yesmaximal, characteristic, complemented
11#3285C211yesmaximal, characteristic, complemented
12#3284C211yesmaximal, characteristic, complemented
13#3278C211yesmaximal, characteristic, complemented
14#3277C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3271C211yesmaximal, characteristic, complemented
17#3270C211yesmaximal, characteristic, complemented
18#3269C211yesmaximal, characteristic, complemented
19#3224C211yesmaximal, characteristic, complemented
20#3222C211yesmaximal, characteristic, complemented
21#3200C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3197C211yesmaximal, characteristic, complemented
24#3190C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3011C211yesmaximal, characteristic, complemented
29#3007C211yesmaximal, characteristic, complemented
30#3002C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic
33C22×#41C2211yescharacteristic
34C2×#137C2211yescharacteristic
35C2×#137C2211yescharacteristic
36C2×#137C2211yescharacteristic, complemented
37C2×#137C2211yescharacteristic, complemented
38C2×#135C2211yescharacteristic
39C2×#135C2211yescharacteristic
40C2×#135C2211yescharacteristic, complemented
41C22×Q16C2211yescharacteristic, complemented
42#563—21no—
43#562—21no—
44#556C2211yescharacteristic, complemented
45#554—21no—
46#554C2211yescharacteristic, complemented
47#553—21no—
48#553C2211yescharacteristic, complemented
49#552C2211yescharacteristic, complemented
50#550—21no—
51#550—21no—
52#550C2211yescharacteristic
53#550C2211yescharacteristic
54#550C2211yescharacteristic
55#550C2211yescharacteristic
56D4×Q8C2211yescharacteristic, complemented
57#548—21no—
58#548—21no—
59#548C2211yescharacteristic
60#548C2211yescharacteristic
61#548C2211yescharacteristic
62#548C2211yescharacteristic
63#548C2211yescharacteristic, complemented
64#548C2211yescharacteristic, complemented
65#547C2211yescharacteristic, complemented
66#542—21no—
67#542C2211yescharacteristic
68#541C2211yescharacteristic
69#539—21no—
70#538—21no—
71#538—21no—
72#537C2211yescharacteristic
73#536C2211yescharacteristic
74#535—21no—
75#535—21no—
76#535C2211yescharacteristic
77#535C2211yescharacteristic
78#525—21no—
79#525—21no—
80#525C2211yescharacteristic
81#525C2211yescharacteristic
82#525C2211yescharacteristic
83C2×C22⋊Q8C2211yescharacteristic
84#519C2211yescharacteristic
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic, complemented
89#490C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#486C2211yescharacteristic, complemented
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic, complemented
103#480C2211yescharacteristic, 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#468C2211yescharacteristic, complemented
113#468C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#468C2211yescharacteristic, complemented
116#468C2211yescharacteristic, complemented
117#467C2211yescharacteristic, complemented
118#467C2211yescharacteristic, complemented
119#466C2211yescharacteristic, complemented
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#465C2211yescharacteristic, complemented
124#465C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#463C2211yescharacteristic, complemented
131#462C2211yescharacteristic, complemented
132#462C2211yescharacteristic, complemented
133#460C2211yescharacteristic, complemented
134#460C2211yescharacteristic, complemented
135#460C2211yescharacteristic, complemented
136#459C2211yescharacteristic, complemented
137#452C2211yescharacteristic
138#452C2211yescharacteristic
139#452C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic
143#452C2211yescharacteristic
144#452C2211yescharacteristic
145#452C2211yescharacteristic
146#452C2211yescharacteristic, complemented
147#452C2211yescharacteristic, complemented
148#452C2211yescharacteristic, complemented
149#452C2211yescharacteristic, complemented
150#451C2211yescharacteristic
151#451C2211yescharacteristic
152#451C2211yescharacteristic
153#451C2211yescharacteristic, complemented
154#451C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#450C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#448C2211yescharacteristic, complemented
171#448C2211yescharacteristic, complemented
172#447C2211yescharacteristic
173#441C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×Q16C2211yescharacteristic, 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
190#433C2211yescharacteristic
191#419C2211yescharacteristic, complemented
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic
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—42no—
211C2×#41—42no—
212C2×#41C2311yescharacteristic
213C2×#41C2311yescharacteristic
214C2×#41C2311yescharacteristic
215C2×#41C2311yescharacteristic
216C2×#41C2311yescharacteristic
217C2×#41C2311yescharacteristic
218C2×#41C2311yescharacteristic
219C2×#41C2311yescharacteristic
220C2×#41C2311yescharacteristic
221C2×#41C2311yescharacteristic
222C22×Q8—21no—
223C22×Q8C2311yescharacteristic
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×Q8C2311yescharacteristic
227C22×Q8C2311yescharacteristic
228C22×D4—21no—
229C22×D4C2311yescharacteristic
230C23×C4—21no—
231C23×C4C2311yescharacteristic
232#137—42no—
233#137—42no—
234#137—42no—
235#137—42no—
236#135—42no—
237#135—42no—
238#135—42no—
239C2×Q16—42no—
240C2×Q16C2311yescharacteristic
241C2×Q16C2311yescharacteristic
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×Q16C2311yescharacteristic
246C2×Q16C2311yescharacteristic
247C2×Q16C2311yescharacteristic
248C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
262C2×D8C2311yescharacteristic
263C2×D8C2311yescharacteristic
264C2×M16C2311yescharacteristic
265C2×M16C2311yescharacteristic
266C2×M16C2311yescharacteristic
267C2×M16C2311yescharacteristic
268C22×C8C2311yescharacteristic
269C22×C8C2311yescharacteristic
270C22×C8C2311yescharacteristic
271C22×C8C2311yescharacteristic
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8C2311yescharacteristic
275C4⋊Q8C2311yescharacteristic
276#127—21no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127C2311yescharacteristic
282#127C2311yescharacteristic
283#126—21no—
284#126—21no—
285#126—21no—
286#126—21no—
287#126—21no—
288#126—21no—
289#126—21no—
290#125—21no—
291#125—21no—
292#125—21no—
293#125—21no—
294#125C2311yescharacteristic
295#124—21no—
296#124—21no—
297#124—21no—
298#124—21no—
299#124—21no—
300#124—21no—
301#124—21no—
302#124—21no—
303#124—21no—
304#124—21no—
305#124C2311yescharacteristic
306#124C2311yescharacteristic
307#124C2311yescharacteristic
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#123D411yescharacteristic
318#123D411yescharacteristic
319C22⋊Q8—21no—
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⋊Q8D411yescharacteristic
334C22⋊Q8D411yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
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#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121D411yescharacteristic
368#121D411yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#121C2311yescharacteristic
373#121C2311yescharacteristic
374#121C2311yescharacteristic
375#121C2311yescharacteristic
376#121C2311yescharacteristic
377#121C2311yescharacteristic
378#120—21no—
379#120—21no—
380#120—21no—
381#120—21no—
382#120—21no—
383#120—21no—
384#120D411yescharacteristic
385#120D411yescharacteristic
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C2311yescharacteristic
390C4×Q8C2311yescharacteristic
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×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C2311yescharacteristic
414C4×D4C2311yescharacteristic
415C4×D4C2311yescharacteristic
416C4×D4C2311yescharacteristic
417C4×D4C2311yescharacteristic
418#117—21no—
419#117—21no—
420#117—21no—
421#117C2311yescharacteristic
422#117C2311yescharacteristic
423#117C2311yescharacteristic
424#117C2311yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4C2311yescharacteristic
428C2×C4⋊C4C2311yescharacteristic
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#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—
491C24C2×D411yescharacteristic
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—41no—
499#41—41no—
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—44no—
509#41—44no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—44no—
534C2×Q8C2×D411yescharacteristic
535C2×Q8C2411yescharacteristic
536C2×Q8C2411yescharacteristic
537C2×Q8C2411yescharacteristic
538C2×Q8C2411yescharacteristic
539C2×Q8C2411yescharacteristic
540C2×Q8C2411yescharacteristic
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—41no—
565C2×D4—41no—
566C2×D4—44no—
567C2×D4C2×D411yescharacteristic
568C2×D4C2×D411yescharacteristic
569C2×D4C2×D411yescharacteristic
570C2×D4C2×D411yescharacteristic
571C2×D4C2×D411yescharacteristic
572C2×D4C2×D411yescharacteristic
573C2×D4C2×D411yescharacteristic
574C2×D4C2411yescharacteristic
575C2×D4C2411yescharacteristic
576C2×D4C2411yescharacteristic
577C2×D4C2411yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
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—41no—
596C22×C4—41no—
597C22×C4—44no—
598C22×C4C2×D411yescharacteristic
599C22×C4C2×D411yescharacteristic
600C22×C4C2×D411yescharacteristic
601C22×C4C2411yescharacteristic
602C22×C4C2411yescharacteristic
603C22×C4C2411yescharacteristic
604C22×C4C2411yescharacteristic
605C22×C4C2411yescharacteristic
606Q16—22no—
607Q16—22no—
608Q16—22no—
609Q16—22no—
610Q16—22no—
611Q16—22no—
612Q16—41no—
613Q16—41no—
614Q16—41no—
615SD16—22no—
616SD16—22no—
617SD16—41no—
618SD16—41no—
619SD16—41no—
620SD16—41no—
621SD16—41no—
622SD16—41no—
623SD16—41no—
624SD16—41no—
625SD16—41no—
626SD16—41no—
627D8—41no—
628D8—41no—
629D8—41no—
630M16—41no—
631M16—41no—
632M16—41no—
633M16—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8C2411yescharacteristic
639C2×C8C2411yescharacteristic
640C2×C8C2411yescharacteristic
641C2×C8C2411yescharacteristic
642C2×C8C2411yescharacteristic
643C2×C8C2411yescharacteristic
644C2×C8C2411yescharacteristic
645C2×C8C2411yescharacteristic
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
672C4⋊C4C2×D411yescharacteristic
673C4⋊C4C2×D411yescharacteristic
674C4⋊C4C2×D411yescharacteristic
675C4⋊C4C2×D411yescharacteristic
676C4⋊C4C2×D411yescharacteristic
677C4⋊C4C2411yescharacteristic
678C4⋊C4C2411yescharacteristic
679C4⋊C4C2411yescharacteristic
680C4⋊C4C2411yescharacteristic
681C4⋊C4C2411yescharacteristic
682C4⋊C4C2411yescharacteristic
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
714C22⋊C4C2×D411yescharacteristic
715C22⋊C4C2×D411yescharacteristic
716C22⋊C4C2×D411yescharacteristic
717C22⋊C4C2×D411yescharacteristic
718C22⋊C4C2×D411yescharacteristic
719C22⋊C4C2×D411yescharacteristic
720C22⋊C4C2×D411yescharacteristic
721C22⋊C4C2×D411yescharacteristic
722C22⋊C4C2×D411yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42C2411yescharacteristic
734C42C2411yescharacteristic
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—81no—
744C23—81no—
745C23C22×D411yescharacteristic
746C23C22×D411yescharacteristic
747C23C22×D411yescharacteristic
748C23C22×D411yescharacteristic
749C23C22×D411yescharacteristic
750Q8—24no—
751Q8—21no—
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—21no—
761Q8—41no—
762Q8—42no—
763Q8—42no—
764Q8—81no—
765Q8—81no—
766Q8—81no—
767Q8H(5,𝔽2)12yes—
768Q8H(5,𝔽2)12yes—
769D4—21no—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—21no—
775D4—21no—
776D4—21no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—42no—
785D4—42no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—42no—
793D4—81no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—24no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
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—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4C22×D411yescharacteristic
850C2×C4C22×D411yescharacteristic
851C2×C4C22×D411yescharacteristic
852C2×C4C22×D411yescharacteristic
853C2×C4C22×D411yescharacteristic
854C2×C4C22×D411yescharacteristic
855C2×C4C22×D411yescharacteristic
856C2×C4C22×D411yescharacteristic
857C2×C4C22×D411yescharacteristic
858C2×C4C2511yescharacteristic
859C8—21no—
860C8—21no—
861C8—21no—
862C8—21no—
863C8—21no—
864C8—21no—
865C8—21no—
866C8—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—82no—
895C22—84no—
896C22C23×D411yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—22no—
902C4—22no—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4C2×H(5,𝔽2)11yescharacteristic
919C4C2×H(5,𝔽2)11yescharacteristic
920C2—41no—
921C2—41no—
922C2—41no—
923C2—41no—
924C2—41no—
925C2—81no—
926C2—81no—
927C2—81no—
928C2—81no—
929C2#348411yescharacteristic
930C2#358411yescharacteristic
931C2#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. #3541C2semidirect
2. #3487C2semidirect
3. #3333C2semidirect
4. #3326C2semidirect
5. #3317C2semidirect
6. #3316C2semidirect
7. #3313C2semidirect
8. #3309C2semidirect
9. #3304C2semidirect
10. #3300C2semidirect
11. #3285C2semidirect
12. #3284C2semidirect
13. #3278C2semidirect
14. #3277C2semidirect
15. #3271C2semidirect
16. #3271C2semidirect
17. #3270C2semidirect
18. #3269C2semidirect
19. #3224C2semidirect
20. #3222C2semidirect
21. #3200C2semidirect
22. #3198C2semidirect
23. #3197C2semidirect
24. #3190C2semidirect
25. #3127C2semidirect
26. #3121C2semidirect
27. #3013C2semidirect
28. #3011C2semidirect
29. #3007C2semidirect
30. #3002C2semidirect
31. #2976C2semidirect
36. C2×#137C22semidirect
37. C2×#137C22semidirect
40. C2×#135C22semidirect
41. C22×Q16C22semidirect
44. #556C22semidirect
46. #554C22semidirect
48. #553C22semidirect
49. #552C22semidirect
56. D4×Q8C22semidirect
63. #548C22semidirect
64. #548C22semidirect
65. #547C22semidirect
85. #497C22semidirect
86. #496C22semidirect
87. #495C22semidirect
88. #492C22semidirect
89. #490C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #486C22semidirect
96. #485C22semidirect
97. #483C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #481C22semidirect
103. #480C22semidirect
104. #480C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #477C22semidirect
108. #475C22semidirect
109. #470C22semidirect
110. #469C22semidirect
111. #469C22semidirect
112. #468C22semidirect
113. #468C22semidirect
114. #468C22semidirect
115. #468C22semidirect
116. #468C22semidirect
117. #467C22semidirect
118. #467C22semidirect
119. #466C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #465C22semidirect
124. #465C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #463C22semidirect
131. #462C22semidirect
132. #462C22semidirect
133. #460C22semidirect
134. #460C22semidirect
135. #460C22semidirect
136. #459C22semidirect
146. #452C22semidirect
147. #452C22semidirect
148. #452C22semidirect
149. #452C22semidirect
153. #451C22semidirect
154. #451C22semidirect
155. #451C22semidirect
156. #451C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #449C22semidirect
166. #449C22semidirect
168. #448C22semidirect
169. #448C22semidirect
170. #448C22semidirect
171. #448C22semidirect
173. #441C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×Q16C22semidirect
180. C4×SD16C22semidirect
181. #436C22semidirect
182. #436C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
187. C8×D4C22semidirect
188. C8×D4C22semidirect
191. #419C22semidirect
194. #417C22semidirect
197. #416C22semidirect
198. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#34872
#33332
#33262
#33172
#33162
#33132
#33092
#33042
#33002
#32852
#32842
#32782
#32772
#32712
#32702
#32692
#32242
#32222
#32002
#31982
#31972
#31902
#31272
#31212
#30132
#30112
#30072
#30022
#29762