Finite Group Databasebeta

← #61681

Subgroups — #61681

Order 256.

1018 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic, complemented
2#3497C211yesmaximal, characteristic, complemented
3#3327C211yesmaximal, characteristic, complemented
4#3326C211yesmaximal, characteristic, complemented
5#3320C211yesmaximal, characteristic, complemented
6#3317C211yesmaximal, characteristic, complemented
7#3312C211yesmaximal, characteristic, complemented
8#3309C211yesmaximal, characteristic, complemented
9#3301C211yesmaximal, characteristic, complemented
10#3300C211yesmaximal, characteristic, complemented
11#3285C211yesmaximal, characteristic, complemented
12#3282C211yesmaximal, characteristic, complemented
13#3277C211yesmaximal, characteristic, complemented
14#3275C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3270C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3219C211yesmaximal, characteristic, complemented
20#3212C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3117C211yesmaximal, characteristic, complemented
26#3108C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3013C211yesmaximal, characteristic, complemented
29#3011C211yesmaximal, characteristic, complemented
30#3010C211yesmaximal, characteristic, complemented
31#2981C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic
33C2×2−1+4C2211yescharacteristic, complemented
34C2×#137C2211yescharacteristic
35C2×#137C2211yescharacteristic
36C2×#137C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)C2211yescharacteristic
38C2×#135C2211yescharacteristic
39C2×#135C2211yescharacteristic
40C22×Q16C2211yescharacteristic, complemented
41C22×SD16C2211yescharacteristic
42#563—21no—
43#560—21no—
44#555—21no—
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#551—21no—
50#550—21no—
51#550C2211yescharacteristic
52#550C2211yescharacteristic, complemented
53D4×Q8—21no—
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic, complemented
56#548—21no—
57#548—21no—
58#548C2211yescharacteristic
59#548C2211yescharacteristic
60#548C2211yescharacteristic
61#548C2211yescharacteristic
62#548C2211yescharacteristic, complemented
63#548C2211yescharacteristic, complemented
64#546C2211yescharacteristic
65#546C2211yescharacteristic
66#540—21no—
67#540—21no—
68#538—21no—
69#538—21no—
70#537—21no—
71#537—21no—
72#537C2211yescharacteristic
73#537C2211yescharacteristic
74#537C2211yescharacteristic
75#537C2211yescharacteristic, complemented
76#536C2211yescharacteristic
77#535C2211yescharacteristic
78#532—21no—
79#532—21no—
80#532C2211yescharacteristic
81#532C2211yescharacteristic, complemented
82#529C2211yescharacteristic
83#529C2211yescharacteristic
84C2×C4×Q8C2211yescharacteristic, complemented
85#497C2211yescharacteristic
86#496C2211yescharacteristic
87#495C2211yescharacteristic
88#495C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#485C2211yescharacteristic
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic, complemented
101#481C2211yescharacteristic
102#481C2211yescharacteristic, complemented
103#480C2211yescharacteristic
104#480C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#470C2211yescharacteristic
110#470C2211yescharacteristic, complemented
111#469C2211yescharacteristic
112#469C2211yescharacteristic
113#468C2211yescharacteristic
114#468C2211yescharacteristic
115#468C2211yescharacteristic
116#468C2211yescharacteristic, complemented
117#467C2211yescharacteristic
118#467C2211yescharacteristic, complemented
119#466C2211yescharacteristic
120#466C2211yescharacteristic
121#465C2211yescharacteristic
122#465C2211yescharacteristic
123#465C2211yescharacteristic
124#465C2211yescharacteristic, complemented
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic
128#464C2211yescharacteristic
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#462C2211yescharacteristic, complemented
134#461C2211yescharacteristic
135#460C2211yescharacteristic, complemented
136#459C2211yescharacteristic
137#452C2211yescharacteristic
138#452C2211yescharacteristic
139#452C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic, complemented
142#452C2211yescharacteristic, complemented
143#452C2211yescharacteristic, complemented
144#452C2211yescharacteristic, complemented
145#452C2211yescharacteristic, complemented
146#452C2211yescharacteristic, complemented
147#451C2211yescharacteristic
148#451C2211yescharacteristic
149#451C2211yescharacteristic, complemented
150#451C2211yescharacteristic, complemented
151#451C2211yescharacteristic, complemented
152#451C2211yescharacteristic, complemented
153#451C2211yescharacteristic, complemented
154#450C2211yescharacteristic
155#449C2211yescharacteristic
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic
165#448C2211yescharacteristic
166#448C2211yescharacteristic
167#448C2211yescharacteristic
168#448C2211yescharacteristic
169#448C2211yescharacteristic
170#448C2211yescharacteristic
171#448C2211yescharacteristic, complemented
172#447C2211yescharacteristic
173#441C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#440C2211yescharacteristic
176#440C2211yescharacteristic
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic
180C4×SD16C2211yescharacteristic
181#436C2211yescharacteristic
182#436C2211yescharacteristic, complemented
183#435C2211yescharacteristic
184#435C2211yescharacteristic
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic
188C8×D4C2211yescharacteristic, complemented
189#432C2211yescharacteristic, complemented
190#431C2211yescharacteristic, complemented
191#419C2211yescharacteristic
192#419C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202#408C2211yescharacteristic, complemented
2032−1+4—42no—
2042−1+4—42no—
2052−1+4—42no—
2062−1+4—42no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41C2311yescharacteristic
214C2×#41C2311yescharacteristic
215C2×#41C2311yescharacteristic
216C2×#41C2311yescharacteristic
217C2×#41C2311yescharacteristic
218C2×#41C2311yescharacteristic
219C2×#41C2311yescharacteristic
220C2×#41C2311yescharacteristic
221C2×#41C2311yescharacteristic
222C2×#41C2311yescharacteristic
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8C2311yescharacteristic
226C22×Q8C2311yescharacteristic
227C22×Q8C2311yescharacteristic
228C22×Q8C2311yescharacteristic
229C22×Q8C2311yescharacteristic
230C22×Q8C2311yescharacteristic
231C22×D4C2311yescharacteristic
232#137—42no—
233#137—42no—
234#137—42no—
235AGL(1,ℤ/8)—42no—
236#135—42no—
237#135—42no—
238C2×Q16—42no—
239C2×Q16C2311yescharacteristic
240C2×Q16C2311yescharacteristic
241C2×Q16C2311yescharacteristic
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×Q16C2311yescharacteristic
246C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
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⋊Q8—21no—
275C4⋊Q8D411yescharacteristic
276C4⋊Q8C2311yescharacteristic
277#127—21no—
278#127—21no—
279#127—21no—
280#127D411yescharacteristic
281#127C2311yescharacteristic
282#126—21no—
283#126—21no—
284#126—21no—
285#126—21no—
286#126—21no—
287#126—21no—
288#125—21no—
289#125—21no—
290#125C2311yescharacteristic
291#125C2311yescharacteristic
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#124D411yescharacteristic
301#124D411yescharacteristic
302#124C2311yescharacteristic
303#124C2311yescharacteristic
304#124C2311yescharacteristic
305#124C2311yescharacteristic
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—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
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⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
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#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#121—21no—
368#121D411yescharacteristic
369#121D411yescharacteristic
370#121D411yescharacteristic
371#121D411yescharacteristic
372#121C2311yescharacteristic
373#121C2311yescharacteristic
374#121C2311yescharacteristic
375#121C2311yescharacteristic
376#121C2311yescharacteristic
377#121C2311yescharacteristic
378#121C2311yescharacteristic
379#121C2311yescharacteristic
380#121C2311yescharacteristic
381#121C2311yescharacteristic
382#120—21no—
383#120—21no—
384#120—21no—
385#120—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C2311yescharacteristic
389C4×Q8C2311yescharacteristic
390C4×Q8C2311yescharacteristic
391C4×Q8C2311yescharacteristic
392C4×Q8C2311yescharacteristic
393C4×Q8C2311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
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
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420#117C2311yescharacteristic
421#117C2311yescharacteristic
422C2×C4⋊C4—21no—
423C2×C4⋊C4C2311yescharacteristic
424C2×C4⋊C4C2311yescharacteristic
425C2×C4⋊C4C2311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42—21no—
429C2×C42C2311yescharacteristic
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#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—
491#41—22no—
492#41—22no—
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—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
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—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8C2×D411yescharacteristic
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—21no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4C2×D411yescharacteristic
569C2×D4C2×D411yescharacteristic
570C2×D4C2×D411yescharacteristic
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—21no—
601C22×C4C2×D411yescharacteristic
602C22×C4C2×D411yescharacteristic
603C22×C4C2411yescharacteristic
604C22×C4C2411yescharacteristic
605C22×C4C2411yescharacteristic
606C22×C4C2411yescharacteristic
607C22×C4C2411yescharacteristic
608Q16—22no—
609Q16—22no—
610Q16—22no—
611Q16—22no—
612Q16—41no—
613Q16—41no—
614Q16—41no—
615Q16—41no—
616SD16—22no—
617SD16—22no—
618SD16—22no—
619SD16—22no—
620SD16—41no—
621SD16—41no—
622SD16—41no—
623SD16—41no—
624SD16—41no—
625SD16—41no—
626SD16—41no—
627SD16—41no—
628D8—41no—
629D8—41no—
630D8—41no—
631D8—41no—
632M16—41no—
633M16—41no—
634M16—41no—
635M16—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8C2411yescharacteristic
641C2×C8C2411yescharacteristic
642C2×C8C2411yescharacteristic
643C2×C8C2411yescharacteristic
644C2×C8C2411yescharacteristic
645C2×C8C2411yescharacteristic
646C2×C8C2411yescharacteristic
647C2×C8C2411yescharacteristic
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⋊C4—21no—
672C4⋊C4—21no—
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⋊C4—21no—
714C22⋊C4—21no—
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—
731C42C2×D411yescharacteristic
732C42C2×D411yescharacteristic
733C42C2411yescharacteristic
734C42C2411yescharacteristic
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23C22×D411yescharacteristic
743C23C22×D411yescharacteristic
744C23C22×D411yescharacteristic
745C23C22×D411yescharacteristic
746C23C22×D411yescharacteristic
747Q8—24no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—41no—
759Q8—41no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—81no—
765Q8H(5,𝔽2)12yes—
766Q8H(5,𝔽2)12yes—
767D4—21no—
768D4—21no—
769D4—21no—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—21no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—81no—
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—
806C2×C4—24no—
807C2×C4—21no—
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—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
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—81no—
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—162no—
895C22C23×D411yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—22no—
902C4—21no—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—41no—
916C4—41no—
917C4C2×H(5,𝔽2)11yescharacteristic
918C4C2×H(5,𝔽2)11yescharacteristic
919C2—41no—
920C2—41no—
921C2—41no—
922C2—41no—
923C2—41no—
924C2—81no—
925C2—81no—
926C2—81no—
927C2—81no—
928C2#348411yescharacteristic
929C2#358411yescharacteristic
930C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3551C2semidirect
2. #3497C2semidirect
3. #3327C2semidirect
4. #3326C2semidirect
5. #3320C2semidirect
6. #3317C2semidirect
7. #3312C2semidirect
8. #3309C2semidirect
9. #3301C2semidirect
10. #3300C2semidirect
11. #3285C2semidirect
12. #3282C2semidirect
13. #3277C2semidirect
14. #3275C2semidirect
15. #3271C2semidirect
16. #3270C2semidirect
17. #3268C2semidirect
18. #3266C2semidirect
19. #3219C2semidirect
20. #3212C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3201C2semidirect
24. #3198C2semidirect
25. #3117C2semidirect
26. #3108C2semidirect
27. #3013C2semidirect
28. #3013C2semidirect
29. #3011C2semidirect
30. #3010C2semidirect
31. #2981C2semidirect
33. C2×2−1+4C22semidirect
36. C2×#137C22semidirect
40. C22×Q16C22semidirect
52. #550C22semidirect
55. D4×Q8C22semidirect
62. #548C22semidirect
63. #548C22semidirect
75. #537C22semidirect
81. #532C22semidirect
84. C2×C4×Q8C22semidirect
89. #491C22semidirect
90. #490C22semidirect
91. #488C22semidirect
92. #488C22semidirect
94. #485C22semidirect
95. #484C22semidirect
96. #484C22semidirect
97. #483C22semidirect
98. #483C22semidirect
100. #482C22semidirect
102. #481C22semidirect
104. #480C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
108. #479C22semidirect
110. #470C22semidirect
116. #468C22semidirect
118. #467C22semidirect
124. #465C22semidirect
129. #464C22semidirect
130. #464C22semidirect
133. #462C22semidirect
135. #460C22semidirect
141. #452C22semidirect
142. #452C22semidirect
143. #452C22semidirect
144. #452C22semidirect
145. #452C22semidirect
146. #452C22semidirect
149. #451C22semidirect
150. #451C22semidirect
151. #451C22semidirect
152. #451C22semidirect
153. #451C22semidirect
171. #448C22semidirect
173. #441C22semidirect
174. #441C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
182. #436C22semidirect
185. #435C22semidirect
186. #435C22semidirect
188. C8×D4C22semidirect
189. #432C22semidirect
190. #431C22semidirect
192. #419C22semidirect
193. #417C22semidirect
194. #417C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#103C22semidirect
201. #408C22semidirect
202. #408C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#34972
#33272
#33262
#33202
#33172
#33122
#33092
#33012
#33002
#32852
#32822
#32772
#32752
#32712
#32702
#32682
#32662
#32192
#32122
#32042
#32032
#32012
#31982
#31172
#31082
#30132
#30112
#30102
#29812