Finite Group Databasebeta

← #61992

Subgroups — #61992

Order 256.

935 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3514C211yesmaximal, characteristic, complemented
2#3480C211yesmaximal, characteristic, complemented
3#3403C211yesmaximal, characteristic, complemented
4#3401C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3320C211yesmaximal, characteristic, complemented
8#3318C211yesmaximal, characteristic, complemented
9#3313C211yesmaximal, characteristic, complemented
10#3311C211yesmaximal, characteristic, complemented
11#3301C211yesmaximal, characteristic, complemented
12#3297C211yesmaximal, characteristic, complemented
13#3285C211yesmaximal, characteristic, complemented
14#3282C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3270C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3256C211yesmaximal, characteristic, complemented
20#3250C211yesmaximal, characteristic, complemented
21#3247C211yesmaximal, characteristic, complemented
22#3219C211yesmaximal, characteristic, complemented
23#3213C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3117C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3102C211yesmaximal, characteristic, complemented
28#3040C211yesmaximal, characteristic, complemented
29#3035C211yesmaximal, characteristic, complemented
30C2×#464C211yesmaximal, characteristic, complemented
31#2990C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic, complemented
35C2×#135C2211yescharacteristic, complemented
36C22×Q16C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic
38#559—21no—
39#559C2211yescharacteristic
40#559C2211yescharacteristic, complemented
41#557C2211yescharacteristic, complemented
42#556—21no—
43#556C2211yescharacteristic
44#556C2211yescharacteristic, complemented
45#555—21no—
46#553—21no—
47#553—21no—
48#553C2211yescharacteristic
49#553C2211yescharacteristic, complemented
50#551—21no—
51#551—21no—
52#550C2211yescharacteristic, complemented
53D4×Q8C2211yescharacteristic
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#548C2211yescharacteristic
57#548C2211yescharacteristic, complemented
58#546—21no—
59#546C2211yescharacteristic
60#546C2211yescharacteristic
61D42C2211yescharacteristic
62#542—21no—
63#538—21no—
64#538—21no—
65#532—21no—
66#532C2211yescharacteristic
67#532C2211yescharacteristic, complemented
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#529C2211yescharacteristic
73#529C2211yescharacteristic, complemented
74#529C2211yescharacteristic, complemented
75C2×#124C2211yescharacteristic
76C2×#124C2211yescharacteristic
77#518—21no—
78C4×#41—21no—
79C4×#41C2211yescharacteristic
80C4×#41C2211yescharacteristic, complemented
81C4×#41C2211yescharacteristic, complemented
82C2×C4×Q8C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#496C2211yescharacteristic
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic
88#495C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic
94#488C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#481C2211yescharacteristic
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#476C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#469C2211yescharacteristic
113#468C2211yescharacteristic
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic, complemented
116#466C2211yescharacteristic
117#466C2211yescharacteristic
118#466C2211yescharacteristic
119#465C2211yescharacteristic
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#464C2211yescharacteristic, complemented
133#464C2211yescharacteristic, complemented
134#464C2211yescharacteristic, complemented
135#464C2211yescharacteristic, complemented
136#464C2211yescharacteristic, complemented
137#463C2211yescharacteristic
138#463C2211yescharacteristic
139#463C2211yescharacteristic
140#463C2211yescharacteristic
141#463C2211yescharacteristic, complemented
142#463C2211yescharacteristic, complemented
143#463C2211yescharacteristic, complemented
144#463C2211yescharacteristic, complemented
145#463C2211yescharacteristic, complemented
146#463C2211yescharacteristic, complemented
147#462C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#460C2211yescharacteristic
150#460C2211yescharacteristic, complemented
151#459C2211yescharacteristic
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#451C2211yescharacteristic, complemented
159#450C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic, complemented
163#449C2211yescharacteristic, complemented
164#448C2211yescharacteristic
165#448C2211yescharacteristic, complemented
166#448C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#447C2211yescharacteristic
169#447C2211yescharacteristic
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic, complemented
185#435C2211yescharacteristic
186#435C2211yescharacteristic
187#435C2211yescharacteristic, complemented
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic, complemented
190C8×D4C2211yescharacteristic, complemented
191#432C2211yescharacteristic, complemented
192#432C2211yescharacteristic, complemented
193#431C2211yescharacteristic, complemented
194#423C2211yescharacteristic, complemented
195C2×C4⋊C8C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#418C2211yescharacteristic
199#416C2211yescharacteristic, complemented
200#416C2211yescharacteristic, complemented
201C2×#103C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41D411yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C22×D4—21no—
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215#137—42no—
216AGL(1,ℤ/8)—42no—
217#135—42no—
218#135—42no—
219C2×Q16—42no—
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×SD16—42no—
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×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
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⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255#127—21no—
256#127C2311yescharacteristic
257#127C2311yescharacteristic
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#125—21no—
270#125—21no—
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#125C2311yescharacteristic
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
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—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#121C2311yescharacteristic
340#121C2311yescharacteristic
341#120—21no—
342#120—21no—
343#120—21no—
344#120—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8D411yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
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×D4D411yescharacteristic
383C4×D4D411yescharacteristic
384C4×D4D411yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117D411yescharacteristic
404#117D411yescharacteristic
405#117D411yescharacteristic
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4C2311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C2311yescharacteristic
420C2×C42C2311yescharacteristic
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#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
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—22no—
488#41—42no—
489#41—41no—
490#41—41no—
491#41—44no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—22no—
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×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
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—21no—
528C2×D4—21no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—44no—
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2×D411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C2×D4C2411yescharacteristic
541C2×D4C2411yescharacteristic
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—21no—
556C22×C4—21no—
557C22×C4C2×D411yescharacteristic
558C22×C4C2×D411yescharacteristic
559C22×C4C2×D411yescharacteristic
560C22×C4C2×D411yescharacteristic
561C22×C4C2×D411yescharacteristic
562C22×C4C2×D411yescharacteristic
563C22×C4C2411yescharacteristic
564C22×C4C2411yescharacteristic
565C22×C4C2411yescharacteristic
566Q16—22no—
567Q16—22no—
568Q16—22no—
569Q16—41no—
570Q16—41no—
571Q16—41no—
572SD16—22no—
573SD16—22no—
574SD16—22no—
575SD16—41no—
576SD16—41no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584D8—41no—
585D8—41no—
586D8—41no—
587D8—41no—
588D8—41no—
589D8—41no—
590M16—41no—
591M16—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8C2411yescharacteristic
597C2×C8C2411yescharacteristic
598C2×C8C2411yescharacteristic
599C2×C8C2411yescharacteristic
600C2×C8C2411yescharacteristic
601C2×C8C2411yescharacteristic
602C2×C8C2411yescharacteristic
603C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2411yescharacteristic
635C4⋊C4C2411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42C2×D411yescharacteristic
697C42C2×D411yescharacteristic
698C42C2×D411yescharacteristic
699C42C2×D411yescharacteristic
700C42C2×D411yescharacteristic
701C42C2×D411yescharacteristic
702C42C2411yescharacteristic
703C42C2411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—42no—
712C23—42no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23C22×D411yescharacteristic
718C23C22×D411yescharacteristic
719C23C22×D411yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—41no—
730Q8—42no—
731Q8—42no—
732Q8—81no—
733Q8—81no—
734Q8H(5,𝔽2)12yes—
735D4—22no—
736D4—22no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—41no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765C2×C4—22no—
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—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4C22×D411yescharacteristic
804C2×C4C22×D411yescharacteristic
805C2×C4C22×D411yescharacteristic
806C2×C4C22×D411yescharacteristic
807C2×C4C22×D411yescharacteristic
808C2×C4C22×D411yescharacteristic
809C2×C4C22×D411yescharacteristic
810C2×C4C22×D411yescharacteristic
811C2×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C2511yescharacteristic
815C8—21no—
816C8—21no—
817C8—21no—
818C8—21no—
819C8—21no—
820C8—21no—
821C8—21no—
822C8—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—162no—
847C22—162no—
848C22#57512yes—
849C22C23×D411yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—22no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4C2×H(5,𝔽2)11yescharacteristic
873C4#58511yescharacteristic
874C2—22no—
875C2—41no—
876C2—41no—
877C2—81no—
878C2—81no—
879C2—81no—
880C2—81no—
881C2—81no—
882C2#348811yescharacteristic
883C2C2×#57511yescharacteristic
884C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3514C2semidirect
2. #3480C2semidirect
3. #3403C2semidirect
4. #3401C2semidirect
5. #3377C2semidirect
6. #3371C2semidirect
7. #3320C2semidirect
8. #3318C2semidirect
9. #3313C2semidirect
10. #3311C2semidirect
11. #3301C2semidirect
12. #3297C2semidirect
13. #3285C2semidirect
14. #3282C2semidirect
15. #3271C2semidirect
16. #3270C2semidirect
17. #3268C2semidirect
18. #3265C2semidirect
19. #3256C2semidirect
20. #3250C2semidirect
21. #3247C2semidirect
22. #3219C2semidirect
23. #3213C2semidirect
24. #3211C2semidirect
25. #3117C2semidirect
26. #3111C2semidirect
27. #3102C2semidirect
28. #3040C2semidirect
29. #3035C2semidirect
30. C2×#464C2semidirect
31. #2990C2semidirect
32. C2×#137C22semidirect
34. C2×#135C22semidirect
35. C2×#135C22semidirect
36. C22×Q16C22semidirect
40. #559C22semidirect
41. #557C22semidirect
44. #556C22semidirect
49. #553C22semidirect
52. #550C22semidirect
57. #548C22semidirect
67. #532C22semidirect
73. #529C22semidirect
74. #529C22semidirect
80. C4×#41C22semidirect
81. C4×#41C22semidirect
82. C2×C4×Q8C22semidirect
83. #497C22semidirect
86. #496C22semidirect
88. #495C22semidirect
89. #491C22semidirect
92. #489C22semidirect
94. #488C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #476C22semidirect
111. #470C22semidirect
114. #468C22semidirect
115. #467C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
132. #464C22semidirect
133. #464C22semidirect
134. #464C22semidirect
135. #464C22semidirect
136. #464C22semidirect
141. #463C22semidirect
142. #463C22semidirect
143. #463C22semidirect
144. #463C22semidirect
145. #463C22semidirect
146. #463C22semidirect
147. #462C22semidirect
148. #461C22semidirect
150. #460C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
158. #451C22semidirect
162. #449C22semidirect
163. #449C22semidirect
165. #448C22semidirect
166. #448C22semidirect
167. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #441C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
184. C4×D8C22semidirect
187. #435C22semidirect
188. #435C22semidirect
189. C8×D4C22semidirect
190. C8×D4C22semidirect
191. #432C22semidirect
192. #432C22semidirect
193. #431C22semidirect
194. #423C22semidirect
195. C2×C4⋊C8C22semidirect
196. C2×C4⋊C8C22semidirect
197. #419C22semidirect
199. #416C22semidirect
200. #416C22semidirect
201. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35142
#34802
#34032
#34012
#33772
#33712
#33202
#33182
#33132
#33112
#33012
#32972
#32852
#32822
#32712
#32702
#32682
#32652
#32562
#32502
#32472
#32192
#32132
#32112
#31172
#31112
#31022
#30402
#30352
C2×#4642
#29902