Finite Group Databasebeta

← #62008

Subgroups — #62008

Order 256.

919 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3400C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3372C211yesmaximal, characteristic, complemented
7#3320C211yesmaximal, characteristic, complemented
8#3312C211yesmaximal, characteristic, complemented
9#3308C211yesmaximal, characteristic, complemented
10#3307C211yesmaximal, characteristic, complemented
11#3300C211yesmaximal, characteristic, complemented
12#3298C211yesmaximal, characteristic, complemented
13#3282C211yesmaximal, characteristic, complemented
14D4×SD16C211yesmaximal, characteristic, complemented
15#3267C211yesmaximal, characteristic, complemented
16#3266C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3250C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3221C211yesmaximal, characteristic, complemented
24#3218C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30C2×#461C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C22×SD16C2211yescharacteristic
36C22×SD16C2211yescharacteristic
37C22×SD16C2211yescharacteristic
38#563—21no—
39#563—21no—
40#559C2211yescharacteristic
41#557C2211yescharacteristic, complemented
42#556C2211yescharacteristic, complemented
43#554—21no—
44#554C2211yescharacteristic
45#553—21no—
46#553—21no—
47#553C2211yescharacteristic
48#552C2211yescharacteristic
49#551—21no—
50#551—21no—
51D4×Q8C2211yescharacteristic
52D4×Q8C2211yescharacteristic, complemented
53D4×Q8C2211yescharacteristic, complemented
54#548C2211yescharacteristic
55#548C2211yescharacteristic, complemented
56#547C2211yescharacteristic
57#547C2211yescharacteristic, complemented
58#546—21no—
59#546C2211yescharacteristic
60#546C2211yescharacteristic
61D42C2211yescharacteristic
62#544—21no—
63#542—21no—
64#542C2211yescharacteristic
65#541C2211yescharacteristic, complemented
66#541C2211yescharacteristic, complemented
67#540C2211yescharacteristic
68#539—21no—
69#539—21no—
70#539—21no—
71#538—21no—
72#536C2211yescharacteristic, complemented
73#536C2211yescharacteristic, complemented
74C2×C4⋊Q8C2211yescharacteristic, complemented
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77#529C2211yescharacteristic, complemented
78#525—21no—
79C2×#123—21no—
80#520C2211yescharacteristic
81#518C2211yescharacteristic
82C2×C4×D4C2211yescharacteristic
83#497C2211yescharacteristic, complemented
84#497C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#491C2211yescharacteristic, complemented
91#491C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#480C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#478C2211yescharacteristic
106#478C2211yescharacteristic, complemented
107#478C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#475C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#468C2211yescharacteristic
113#468C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic, complemented
116#467C2211yescharacteristic, complemented
117#466C2211yescharacteristic
118#465C2211yescharacteristic
119#465C2211yescharacteristic
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#463C2211yescharacteristic
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic, complemented
132#463C2211yescharacteristic, complemented
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#461C2211yescharacteristic
139#461C2211yescharacteristic
140#461C2211yescharacteristic
141#461C2211yescharacteristic
142#461C2211yescharacteristic
143#461C2211yescharacteristic
144#461C2211yescharacteristic, complemented
145#461C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#461C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#461C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic
152#460C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#451C2211yescharacteristic, complemented
159#450C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic
166#448C2211yescharacteristic
167#448C2211yescharacteristic
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic
183C4×SD16C2211yescharacteristic
184C4×SD16C2211yescharacteristic, complemented
185#435C2211yescharacteristic
186#435C2211yescharacteristic, complemented
187#435C2211yescharacteristic, complemented
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#417C2211yescharacteristic, complemented
199#416C2211yescharacteristic, complemented
200C2×#103C2211yescharacteristic, complemented
201C2×#103C2211yescharacteristic, complemented
202C2×#103C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4—21no—
215#137—42no—
216AGL(1,ℤ/8)—42no—
217#135—42no—
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×SD16—42no—
224C2×SD16—42no—
225C2×SD16—42no—
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×SD16C2311yescharacteristic
239C2×SD16C2311yescharacteristic
240C2×SD16C2311yescharacteristic
241C2×SD16C2311yescharacteristic
242C2×D8C2311yescharacteristic
243C2×D8C2311yescharacteristic
244C2×D8C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C2×M16C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258C4⋊Q8C2311yescharacteristic
259C4⋊Q8C2311yescharacteristic
260C4⋊Q8C2311yescharacteristic
261C4⋊Q8C2311yescharacteristic
262C4⋊Q8C2311yescharacteristic
263#127C2311yescharacteristic
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#126—21no—
271#126—21no—
272#126—21no—
273#126—21no—
274#126—21no—
275#126D411yescharacteristic
276#126D411yescharacteristic
277#125—21no—
278#125—21no—
279#125—21no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125—21no—
285#125D411yescharacteristic
286#125C2311yescharacteristic
287#125C2311yescharacteristic
288#125C2311yescharacteristic
289#124—21no—
290#124—21no—
291#124—21no—
292#124—21no—
293#124D411yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
297#124C2311yescharacteristic
298#124C2311yescharacteristic
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
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⋊Q8—21no—
338C22⋊Q8D411yescharacteristic
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#121D411yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#121C2311yescharacteristic
361#120—21no—
362#120—21no—
363#120—21no—
364#120—21no—
365C4×Q8—21no—
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4C2311yescharacteristic
415C2×C4⋊C4C2311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C42C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
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
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478#97C2311yescharacteristic
479#97C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486#41—22no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—82no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8C2×D411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×Q8C2411yescharacteristic
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—82no—
530C2×D4C2×D411yescharacteristic
531C2×D4C2×D411yescharacteristic
532C2×D4C2×D411yescharacteristic
533C2×D4C2411yescharacteristic
534C2×D4C2411yescharacteristic
535C2×D4C2411yescharacteristic
536C2×D4C2411yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—82no—
556C22×C4C2×D411yescharacteristic
557C22×C4C2×D411yescharacteristic
558C22×C4C2411yescharacteristic
559C22×C4C2411yescharacteristic
560C22×C4C2411yescharacteristic
561Q16—41no—
562Q16—41no—
563Q16—41no—
564Q16—41no—
565Q16—41no—
566SD16—22no—
567SD16—22no—
568SD16—22no—
569SD16—22no—
570SD16—22no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582D8—22no—
583D8—41no—
584D8—41no—
585M16—41no—
586M16—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8C2411yescharacteristic
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
594C2×C8C2411yescharacteristic
595C2×C8C2411yescharacteristic
596C2×C8C2411yescharacteristic
597C2×C8C2411yescharacteristic
598C2×C8C2411yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2×D411yescharacteristic
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42C2×D411yescharacteristic
701C42C2×D411yescharacteristic
702C42C2411yescharacteristic
703C42C2411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23C22×D411yescharacteristic
717C23C22×D411yescharacteristic
718C23C22×D411yescharacteristic
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—41no—
732Q8—81no—
733Q8—81no—
734Q8—81no—
735Q8—81no—
736Q8—81no—
737D4—22no—
738D4—22no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—41no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4H(5,𝔽2)12yes—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C22×D411yescharacteristic
803C2×C4C22×D411yescharacteristic
804C2×C4C22×D411yescharacteristic
805C2×C4C22×D411yescharacteristic
806C2×C4C22×D411yescharacteristic
807C2×C4C22×D411yescharacteristic
808C2×C4C22×D411yescharacteristic
809C2×C4C2511yescharacteristic
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—22no—
825C22—21no—
826C22—21no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—84no—
839C22—162no—
840C22#57712yes—
841C22C23×D411yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4C2×H(5,𝔽2)11yescharacteristic
866C4#58511yescharacteristic
867C2—22no—
868C2—41no—
869C2—41no—
870C2—42no—
871C2—81no—
872C2—81no—
873C2—81no—
874C2#348811yescharacteristic
875C2C2×#57711yescharacteristic
876C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3552C2semidirect
2. #3513C2semidirect
3. #3401C2semidirect
4. #3400C2semidirect
5. #3376C2semidirect
6. #3372C2semidirect
7. #3320C2semidirect
8. #3312C2semidirect
9. #3308C2semidirect
10. #3307C2semidirect
11. #3300C2semidirect
12. #3298C2semidirect
13. #3282C2semidirect
14. D4×SD16C2semidirect
15. #3267C2semidirect
16. #3266C2semidirect
17. #3266C2semidirect
18. #3265C2semidirect
19. #3260C2semidirect
20. #3258C2semidirect
21. #3250C2semidirect
22. #3225C2semidirect
23. #3221C2semidirect
24. #3218C2semidirect
25. #3123C2semidirect
26. #3120C2semidirect
27. #3114C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. C2×#461C2semidirect
31. #2992C2semidirect
41. #557C22semidirect
42. #556C22semidirect
52. D4×Q8C22semidirect
53. D4×Q8C22semidirect
55. #548C22semidirect
57. #547C22semidirect
65. #541C22semidirect
66. #541C22semidirect
72. #536C22semidirect
73. #536C22semidirect
74. C2×C4⋊Q8C22semidirect
77. #529C22semidirect
83. #497C22semidirect
84. #497C22semidirect
85. #497C22semidirect
87. #495C22semidirect
89. #491C22semidirect
90. #491C22semidirect
91. #491C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #487C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
98. #483C22semidirect
99. #483C22semidirect
100. #480C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #475C22semidirect
111. #470C22semidirect
113. #468C22semidirect
114. #468C22semidirect
115. #467C22semidirect
116. #467C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
131. #463C22semidirect
132. #463C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #462C22semidirect
136. #462C22semidirect
137. #462C22semidirect
144. #461C22semidirect
145. #461C22semidirect
146. #461C22semidirect
147. #461C22semidirect
148. #461C22semidirect
149. #461C22semidirect
150. #461C22semidirect
155. #452C22semidirect
156. #451C22semidirect
157. #451C22semidirect
158. #451C22semidirect
163. #449C22semidirect
164. #449C22semidirect
168. #448C22semidirect
169. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
174. #442C22semidirect
175. #441C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
184. C4×SD16C22semidirect
186. #435C22semidirect
187. #435C22semidirect
188. #435C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #432C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
197. #419C22semidirect
198. #417C22semidirect
199. #416C22semidirect
200. C2×#103C22semidirect
201. C2×#103C22semidirect
202. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35522
#35132
#34012
#34002
#33762
#33722
#33202
#33122
#33082
#33072
#33002
#32982
#32822
D4×SD162
#32672
#32662
#32652
#32602
#32582
#32502
#32252
#32212
#32182
#31232
#31202
#31142
#30462
#30422
C2×#4612
#29922