Finite Group Databasebeta

← #61612

Subgroups — #61612

Order 256.

1011 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3486C211yesmaximal, characteristic, complemented
3#3328C211yesmaximal, characteristic, complemented
4#3327C211yesmaximal, characteristic, complemented
5#3320C211yesmaximal, characteristic, complemented
6#3316C211yesmaximal, characteristic, complemented
7#3313C211yesmaximal, characteristic, complemented
8#3312C211yesmaximal, characteristic, complemented
9#3301C211yesmaximal, characteristic, complemented
10#3299C211yesmaximal, characteristic, complemented
11D4×Q16C211yesmaximal, characteristic, complemented
12#3285C211yesmaximal, characteristic, complemented
13#3277C211yesmaximal, characteristic, complemented
14#3276C211yesmaximal, characteristic, complemented
15#3270C211yesmaximal, characteristic, complemented
16#3270C211yesmaximal, characteristic, complemented
17#3270C211yesmaximal, characteristic, complemented
18#3269C211yesmaximal, characteristic, complemented
19#3225C211yesmaximal, characteristic, complemented
20#3223C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3196C211yesmaximal, characteristic, complemented
24#3191C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3011C211yesmaximal, characteristic, complemented
29#3004C211yesmaximal, characteristic, complemented
30C2×#451C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic
33C23×Q8C2211yescharacteristic
34C2×#137C2211yescharacteristic
35C2×#137C2211yescharacteristic
36C2×#137C2211yescharacteristic, complemented
37C2×#137C2211yescharacteristic, complemented
38C2×#135C2211yescharacteristic, complemented
39C22×Q16C2211yescharacteristic
40C22×Q16C2211yescharacteristic
41C22×Q16C2211yescharacteristic, complemented
42#563—21no—
43#562—21no—
44#556C2211yescharacteristic
45#554—21no—
46#554C2211yescharacteristic
47#553—21no—
48#553C2211yescharacteristic
49#552C2211yescharacteristic
50D4×Q8—21no—
51D4×Q8—21no—
52D4×Q8C2211yescharacteristic
53D4×Q8C2211yescharacteristic
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic
56D4×Q8C2211yescharacteristic
57#548—21no—
58#548—21no—
59#548C2211yescharacteristic
60#548C2211yescharacteristic
61#548C2211yescharacteristic
62#548C2211yescharacteristic
63#548C2211yescharacteristic
64#548C2211yescharacteristic
65#547C2211yescharacteristic
66#542—21no—
67#542C2211yescharacteristic
68#541C2211yescharacteristic
69#539—21no—
70#538—21no—
71#538—21no—
72#537C2211yescharacteristic
73#536—21no—
74#536—21no—
75#536C2211yescharacteristic
76#536C2211yescharacteristic
77#536C2211yescharacteristic
78#525—21no—
79#525—21no—
80#525C2211yescharacteristic
81#525C2211yescharacteristic
82#525C2211yescharacteristic
83C2×C22⋊Q8C2211yescharacteristic
84#519C2211yescharacteristic
85#497C2211yescharacteristic, complemented
86#497C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#494C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#487C2211yescharacteristic, complemented
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic, complemented
98#485C2211yescharacteristic, complemented
99#484C2211yescharacteristic
100#484C2211yescharacteristic, complemented
101#483C2211yescharacteristic, complemented
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#481C2211yescharacteristic
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#477C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#470C2211yescharacteristic
110#470C2211yescharacteristic
111#470C2211yescharacteristic, complemented
112#470C2211yescharacteristic, complemented
113#470C2211yescharacteristic, complemented
114#468C2211yescharacteristic
115#468C2211yescharacteristic
116#468C2211yescharacteristic, complemented
117#467C2211yescharacteristic
118#467C2211yescharacteristic, complemented
119#467C2211yescharacteristic, complemented
120#467C2211yescharacteristic, complemented
121#466C2211yescharacteristic
122#465C2211yescharacteristic
123#465C2211yescharacteristic
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#462C2211yescharacteristic, complemented
134#462C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#461C2211yescharacteristic, complemented
137#452C2211yescharacteristic
138#452C2211yescharacteristic
139#452C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic, complemented
142#452C2211yescharacteristic, complemented
143#452C2211yescharacteristic, complemented
144#452C2211yescharacteristic, complemented
145#452C2211yescharacteristic, complemented
146#451C2211yescharacteristic
147#451C2211yescharacteristic
148#451C2211yescharacteristic
149#451C2211yescharacteristic
150#451C2211yescharacteristic
151#451C2211yescharacteristic
152#451C2211yescharacteristic
153#451C2211yescharacteristic
154#451C2211yescharacteristic
155#451C2211yescharacteristic
156#451C2211yescharacteristic
157#451C2211yescharacteristic
158#451C2211yescharacteristic
159#451C2211yescharacteristic, complemented
160#451C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#451C2211yescharacteristic, complemented
164#449C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic
168#448C2211yescharacteristic
169#448C2211yescharacteristic
170#448C2211yescharacteristic
171#448C2211yescharacteristic
172#448C2211yescharacteristic, complemented
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
182#436C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic
185#435C2211yescharacteristic
186#435C2211yescharacteristic
187C8×D4C2211yescharacteristic
188C8×D4C2211yescharacteristic
189#433C2211yescharacteristic
190#433C2211yescharacteristic
191#419C2211yescharacteristic
192#419C2211yescharacteristic
193#419C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#103C2211yescharacteristic
197C2×#103C2211yescharacteristic
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×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C2×#41C2311yescharacteristic
212C2×#41C2311yescharacteristic
213C2×#41C2311yescharacteristic
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8C2311yescharacteristic
221C22×Q8C2311yescharacteristic
222C22×Q8C2311yescharacteristic
223C22×Q8C2311yescharacteristic
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×Q8C2311yescharacteristic
227C22×Q8C2311yescharacteristic
228C22×Q8C2311yescharacteristic
229C22×Q8C2311yescharacteristic
230C23×C4—21no—
231C23×C4C2311yescharacteristic
232#137—42no—
233#137—42no—
234#137—42no—
235#137—42no—
236#135—42no—
237C2×Q16—42no—
238C2×Q16—42no—
239C2×Q16—42no—
240C2×Q16C2311yescharacteristic
241C2×Q16C2311yescharacteristic
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×Q16C2311yescharacteristic
246C2×Q16C2311yescharacteristic
247C2×Q16C2311yescharacteristic
248C2×Q16C2311yescharacteristic
249C2×Q16C2311yescharacteristic
250C2×Q16C2311yescharacteristic
251C2×Q16C2311yescharacteristic
252C2×Q16C2311yescharacteristic
253C2×Q16C2311yescharacteristic
254C2×Q16C2311yescharacteristic
255C2×SD16C2311yescharacteristic
256C2×SD16C2311yescharacteristic
257C2×SD16C2311yescharacteristic
258C2×SD16C2311yescharacteristic
259C2×SD16C2311yescharacteristic
260C2×SD16C2311yescharacteristic
261C2×SD16C2311yescharacteristic
262C2×SD16C2311yescharacteristic
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⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8C2311yescharacteristic
280C4⋊Q8C2311yescharacteristic
281C4⋊Q8C2311yescharacteristic
282C4⋊Q8C2311yescharacteristic
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#123—21no—
318#123—21no—
319#123—21no—
320#123—21no—
321#123D411yescharacteristic
322#123D411yescharacteristic
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⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8D411yescharacteristic
348C22⋊Q8D411yescharacteristic
349C22⋊Q8C2311yescharacteristic
350C22⋊Q8C2311yescharacteristic
351C22⋊Q8C2311yescharacteristic
352C22⋊Q8C2311yescharacteristic
353C22⋊Q8C2311yescharacteristic
354C22⋊Q8C2311yescharacteristic
355C22⋊Q8C2311yescharacteristic
356C22⋊Q8C2311yescharacteristic
357C22⋊Q8C2311yescharacteristic
358C22⋊Q8C2311yescharacteristic
359C22⋊Q8C2311yescharacteristic
360C22⋊Q8C2311yescharacteristic
361C22⋊Q8C2311yescharacteristic
362C22⋊Q8C2311yescharacteristic
363C22⋊Q8C2311yescharacteristic
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121D411yescharacteristic
376#121D411yescharacteristic
377#121C2311yescharacteristic
378#121C2311yescharacteristic
379#121C2311yescharacteristic
380#121C2311yescharacteristic
381#121C2311yescharacteristic
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#103C2311yescharacteristic
461#103C2311yescharacteristic
462#103C2311yescharacteristic
463#103C2311yescharacteristic
464#103C2311yescharacteristic
465#103C2311yescharacteristic
466#103C2311yescharacteristic
467#103C2311yescharacteristic
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
490C24C2×D411yescharacteristic
491#41—22no—
492#41—22no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—44no—
500#41—44no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—44no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
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—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—44no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8C2×D411yescharacteristic
542C2×Q8C2411yescharacteristic
543C2×Q8C2411yescharacteristic
544C2×Q8C2411yescharacteristic
545C2×Q8C2411yescharacteristic
546C2×Q8C2411yescharacteristic
547C2×Q8C2411yescharacteristic
548C2×Q8C2411yescharacteristic
549C2×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
561C2×D4C2×D411yescharacteristic
562C2×D4C2×D411yescharacteristic
563C2×D4C2×D411yescharacteristic
564C2×D4C2×D411yescharacteristic
565C2×D4C2×D411yescharacteristic
566C2×D4C2×D411yescharacteristic
567C2×D4C2411yescharacteristic
568C2×D4C2411yescharacteristic
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
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—41no—
588C22×C4—41no—
589C22×C4—44no—
590C22×C4C2×D411yescharacteristic
591C22×C4C2×D411yescharacteristic
592C22×C4C2×D411yescharacteristic
593C22×C4C2411yescharacteristic
594C22×C4C2411yescharacteristic
595C22×C4C2411yescharacteristic
596C22×C4C2411yescharacteristic
597C22×C4C2411yescharacteristic
598Q16—22no—
599Q16—22no—
600Q16—22no—
601Q16—22no—
602Q16—22no—
603Q16—22no—
604Q16—41no—
605Q16—41no—
606Q16—41no—
607Q16—41no—
608Q16—41no—
609Q16—41no—
610Q16—41no—
611Q16—41no—
612Q16—41no—
613SD16—22no—
614SD16—22no—
615SD16—41no—
616SD16—41no—
617SD16—41no—
618SD16—41no—
619SD16—41no—
620SD16—41no—
621D8—41no—
622M16—41no—
623M16—41no—
624M16—41no—
625M16—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8C2411yescharacteristic
631C2×C8C2411yescharacteristic
632C2×C8C2411yescharacteristic
633C2×C8C2411yescharacteristic
634C2×C8C2411yescharacteristic
635C2×C8C2411yescharacteristic
636C2×C8C2411yescharacteristic
637C2×C8C2411yescharacteristic
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
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—22no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—41no—
740C23C22×D411yescharacteristic
741C23C22×D411yescharacteristic
742C23C22×D411yescharacteristic
743C23C22×D411yescharacteristic
744C23C22×D411yescharacteristic
745Q8—24no—
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—41no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—81no—
769Q8—81no—
770Q8—81no—
771Q8H(5,𝔽2)12yes—
772Q8H(5,𝔽2)12yes—
773D4—22no—
774D4—22no—
775D4—21no—
776D4—21no—
777D4—21no—
778D4—21no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—42no—
785D4—42no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—81no—
791D4—81no—
792D4—81no—
793D4—81no—
794C2×C4—24no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
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—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4C22×D411yescharacteristic
840C2×C4C22×D411yescharacteristic
841C2×C4C22×D411yescharacteristic
842C2×C4C22×D411yescharacteristic
843C2×C4C22×D411yescharacteristic
844C2×C4C22×D411yescharacteristic
845C2×C4C22×D411yescharacteristic
846C2×C4C22×D411yescharacteristic
847C2×C4C22×D411yescharacteristic
848C2×C4C2511yescharacteristic
849C8—21no—
850C8—21no—
851C8—21no—
852C8—21no—
853C8—21no—
854C8—21no—
855C8—21no—
856C8—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—44no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22#57812yes—
879C22C23×D411yescharacteristic
880C4—21no—
881C4—21no—
882C4—22no—
883C4—22no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—41no—
903C4C2×H(5,𝔽2)11yescharacteristic
904C4C2×H(5,𝔽2)11yescharacteristic
905C2—22no—
906C2—41no—
907C2—41no—
908C2—41no—
909C2—41no—
910C2—81no—
911C2—81no—
912C2#348411yescharacteristic
913C2C2×#57811yescharacteristic
914C2#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. #3486C2semidirect
3. #3328C2semidirect
4. #3327C2semidirect
5. #3320C2semidirect
6. #3316C2semidirect
7. #3313C2semidirect
8. #3312C2semidirect
9. #3301C2semidirect
10. #3299C2semidirect
11. D4×Q16C2semidirect
12. #3285C2semidirect
13. #3277C2semidirect
14. #3276C2semidirect
15. #3270C2semidirect
16. #3270C2semidirect
17. #3270C2semidirect
18. #3269C2semidirect
19. #3225C2semidirect
20. #3223C2semidirect
21. #3202C2semidirect
22. #3201C2semidirect
23. #3196C2semidirect
24. #3191C2semidirect
25. #3127C2semidirect
26. #3121C2semidirect
27. #3013C2semidirect
28. #3011C2semidirect
29. #3004C2semidirect
30. C2×#451C2semidirect
31. #2976C2semidirect
36. C2×#137C22semidirect
37. C2×#137C22semidirect
38. C2×#135C22semidirect
41. C22×Q16C22semidirect
85. #497C22semidirect
86. #497C22semidirect
87. #495C22semidirect
88. #494C22semidirect
89. #491C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #487C22semidirect
97. #485C22semidirect
98. #485C22semidirect
100. #484C22semidirect
101. #483C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #477C22semidirect
108. #475C22semidirect
111. #470C22semidirect
112. #470C22semidirect
113. #470C22semidirect
116. #468C22semidirect
118. #467C22semidirect
119. #467C22semidirect
120. #467C22semidirect
124. #465C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #463C22semidirect
131. #462C22semidirect
132. #462C22semidirect
133. #462C22semidirect
134. #462C22semidirect
135. #462C22semidirect
136. #461C22semidirect
141. #452C22semidirect
142. #452C22semidirect
143. #452C22semidirect
144. #452C22semidirect
145. #452C22semidirect
159. #451C22semidirect
160. #451C22semidirect
161. #451C22semidirect
162. #451C22semidirect
163. #451C22semidirect
166. #449C22semidirect
172. #448C22semidirect
173. #441C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×Q16C22semidirect
180. C4×SD16C22semidirect
193. #419C22semidirect
194. #417C22semidirect
195. #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
#34862
#33282
#33272
#33202
#33162
#33132
#33122
#33012
#32992
D4×Q162
#32852
#32772
#32762
#32702
#32692
#32252
#32232
#32022
#32012
#31962
#31912
#31272
#31212
#30132
#30112
#30042
C2×#4512
#29762