Finite Group Databasebeta

← #62084

Subgroups — #62084

Order 256.

921 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#3554C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3403C211yesmaximal, characteristic, complemented
4#3400C211yesmaximal, characteristic, complemented
5#3372C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3330C211yesmaximal, characteristic, complemented
8#3327C211yesmaximal, characteristic, complemented
9#3320C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3309C211yesmaximal, characteristic, complemented
12#3308C211yesmaximal, characteristic, complemented
13#3275C211yesmaximal, characteristic, complemented
14#3272C211yesmaximal, characteristic, complemented
15#3268C211yesmaximal, characteristic, complemented
16#3267C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3252C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3221C211yesmaximal, characteristic, complemented
24#3219C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3110C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30#3036C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×AGL(1,ℤ/8)C2211yescharacteristic
35C2×AGL(1,ℤ/8)C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C22×SD16C2211yescharacteristic
38#562—21no—
39#562—21no—
40#559—21no—
41#559C2211yescharacteristic
42#559C2211yescharacteristic, complemented
43#557C2211yescharacteristic, complemented
44#554—21no—
45#554C2211yescharacteristic
46#553—21no—
47#553C2211yescharacteristic
48#552C2211yescharacteristic
49#551—21no—
50#551—21no—
51#550C2211yescharacteristic, complemented
52D4×Q8C2211yescharacteristic, complemented
53#548C2211yescharacteristic
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic
56#547C2211yescharacteristic
57#547C2211yescharacteristic, complemented
58#546—21no—
59#546C2211yescharacteristic
60#546C2211yescharacteristic
61D42C2211yescharacteristic
62#542—21no—
63#542C2211yescharacteristic
64#542C2211yescharacteristic, complemented
65#542C2211yescharacteristic, complemented
66#540—21no—
67#540C2211yescharacteristic
68#539—21no—
69#539—21no—
70#539—21no—
71#538—21no—
72#536C2211yescharacteristic, complemented
73#536C2211yescharacteristic, complemented
74#533C2211yescharacteristic, complemented
75#532C2211yescharacteristic, complemented
76#529C2211yescharacteristic
77#529C2211yescharacteristic
78#525—21no—
79C2×#123—21no—
80#520C2211yescharacteristic
81#518C2211yescharacteristic
82C2×C4×D4C2211yescharacteristic
83#497C2211yescharacteristic, complemented
84#497C2211yescharacteristic, complemented
85#496C2211yescharacteristic
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#491C2211yescharacteristic, complemented
91#490C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#480C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#477C2211yescharacteristic, complemented
106#477C2211yescharacteristic, complemented
107#476C2211yescharacteristic, complemented
108#474C2211yescharacteristic
109#474C2211yescharacteristic, complemented
110#474C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#470C2211yescharacteristic, complemented
113#469C2211yescharacteristic, complemented
114#468C2211yescharacteristic
115#468C2211yescharacteristic
116#468C2211yescharacteristic
117#468C2211yescharacteristic, complemented
118#468C2211yescharacteristic, complemented
119#467C2211yescharacteristic, complemented
120#466C2211yescharacteristic
121#466C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#463C2211yescharacteristic, complemented
136#463C2211yescharacteristic, complemented
137#463C2211yescharacteristic, complemented
138#463C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#461C2211yescharacteristic
142#461C2211yescharacteristic
143#461C2211yescharacteristic
144#461C2211yescharacteristic
145#461C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#461C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#460C2211yescharacteristic
150#459C2211yescharacteristic
151#459C2211yescharacteristic
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#450C2211yescharacteristic
160#450C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#440C2211yescharacteristic
175#440C2211yescharacteristic
176#440C2211yescharacteristic
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic
183C4×D8C2211yescharacteristic
184C4×D8C2211yescharacteristic, complemented
185#436C2211yescharacteristic
186#436C2211yescharacteristic, complemented
187#435C2211yescharacteristic
188#435C2211yescharacteristic, complemented
189#435C2211yescharacteristic, complemented
190#435C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#417C2211yescharacteristic, complemented
199#417C2211yescharacteristic, complemented
200#417C2211yescharacteristic, complemented
201#416C2211yescharacteristic, complemented
202C2×#103C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4—21no—
215#137—42no—
216AGL(1,ℤ/8)—42no—
217AGL(1,ℤ/8)—42no—
218AGL(1,ℤ/8)—42no—
219#135—42no—
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×SD16—42no—
225C2×SD16C2311yescharacteristic
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×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×D8C2311yescharacteristic
243C2×D8C2311yescharacteristic
244C2×D8C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C2×M16C2311yescharacteristic
247C2×M16C2311yescharacteristic
248C2×M16C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258#127—21no—
259#127C2311yescharacteristic
260#127C2311yescharacteristic
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126D411yescharacteristic
268#126D411yescharacteristic
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125D411yescharacteristic
275#125C2311yescharacteristic
276#125C2311yescharacteristic
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124D411yescharacteristic
285#124C2311yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
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—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123D411yescharacteristic
316#123D411yescharacteristic
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⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8D411yescharacteristic
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#121D411yescharacteristic
355#121C2311yescharacteristic
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×Q8—21no—
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×D4—21no—
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402C4×D4C2311yescharacteristic
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
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#107C2311yescharacteristic
427#107C2311yescharacteristic
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#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—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—82no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2×D411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
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—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—82no—
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C2×D4C2411yescharacteristic
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—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—82no—
561C22×C4C2×D411yescharacteristic
562C22×C4C2×D411yescharacteristic
563C22×C4C2411yescharacteristic
564C22×C4C2411yescharacteristic
565C22×C4C2411yescharacteristic
566Q16—41no—
567Q16—41no—
568Q16—41no—
569Q16—41no—
570SD16—22no—
571SD16—22no—
572SD16—22no—
573SD16—22no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584D8—22no—
585D8—22no—
586D8—41no—
587D8—41no—
588D8—41no—
589D8—41no—
590M16—41no—
591M16—41no—
592M16—41no—
593M16—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⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
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⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
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
692C22⋊C4C2×D411yescharacteristic
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—21no—
711C23—42no—
712C23—42no—
713C23—42no—
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—21no—
730Q8—41no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734Q8—81no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—41no—
745D4—41no—
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—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4H(5,𝔽2)12yes—
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—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
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×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—21no—
832C22—22no—
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—41no—
847C22—84no—
848C22—162no—
849C22C23×D411yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—41no—
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—41no—
875C2—41no—
876C2—41no—
877C2—42no—
878C2—81no—
879C2—81no—
880C2—81no—
881C2—81no—
882C2#348811yescharacteristic
883C2#358511yescharacteristic
884C2#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. #3554C2semidirect
2. #3513C2semidirect
3. #3403C2semidirect
4. #3400C2semidirect
5. #3372C2semidirect
6. #3370C2semidirect
7. #3330C2semidirect
8. #3327C2semidirect
9. #3320C2semidirect
10. #3315C2semidirect
11. #3309C2semidirect
12. #3308C2semidirect
13. #3275C2semidirect
14. #3272C2semidirect
15. #3268C2semidirect
16. #3267C2semidirect
17. #3266C2semidirect
18. #3265C2semidirect
19. #3262C2semidirect
20. #3257C2semidirect
21. #3252C2semidirect
22. #3225C2semidirect
23. #3221C2semidirect
24. #3219C2semidirect
25. #3124C2semidirect
26. #3118C2semidirect
27. #3110C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. #3036C2semidirect
31. #2995C2semidirect
42. #559C22semidirect
43. #557C22semidirect
51. #550C22semidirect
52. D4×Q8C22semidirect
54. #548C22semidirect
57. #547C22semidirect
64. #542C22semidirect
65. #542C22semidirect
72. #536C22semidirect
73. #536C22semidirect
74. #533C22semidirect
75. #532C22semidirect
83. #497C22semidirect
84. #497C22semidirect
86. #496C22semidirect
87. #495C22semidirect
89. #491C22semidirect
90. #491C22semidirect
91. #490C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #487C22semidirect
95. #485C22semidirect
96. #484C22semidirect
97. #484C22semidirect
98. #484C22semidirect
99. #482C22semidirect
100. #480C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #477C22semidirect
106. #477C22semidirect
107. #476C22semidirect
109. #474C22semidirect
110. #474C22semidirect
111. #470C22semidirect
112. #470C22semidirect
113. #469C22semidirect
117. #468C22semidirect
118. #468C22semidirect
119. #467C22semidirect
121. #466C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #463C22semidirect
136. #463C22semidirect
137. #463C22semidirect
138. #463C22semidirect
139. #462C22semidirect
140. #462C22semidirect
145. #461C22semidirect
146. #461C22semidirect
147. #461C22semidirect
148. #461C22semidirect
152. #459C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
165. #449C22semidirect
166. #449C22semidirect
168. #448C22semidirect
169. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
177. #440C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
184. C4×D8C22semidirect
186. #436C22semidirect
188. #435C22semidirect
189. #435C22semidirect
190. #435C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #432C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. #423C22semidirect
197. #419C22semidirect
198. #417C22semidirect
199. #417C22semidirect
200. #417C22semidirect
201. #416C22semidirect
202. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35542
#35132
#34032
#34002
#33722
#33702
#33302
#33272
#33202
#33152
#33092
#33082
#32752
#32722
#32682
#32672
#32662
#32652
#32622
#32572
#32522
#32252
#32212
#32192
#31242
#31182
#31102
#30462
#30422
#30362
#29952