Finite Group Databasebeta

← #62049

Subgroups — #62049

Order 256.

927 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558C211yesmaximal, characteristic, complemented
2#3524C211yesmaximal, characteristic, complemented
3#3403C211yesmaximal, characteristic, complemented
4#3396C211yesmaximal, characteristic, complemented
5#3371C211yesmaximal, characteristic, complemented
6#3365C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3325C211yesmaximal, characteristic, complemented
9#3322C211yesmaximal, characteristic, complemented
10#3321C211yesmaximal, characteristic, complemented
11#3310C211yesmaximal, characteristic, complemented
12#3297C211yesmaximal, characteristic, complemented
13#3282C211yesmaximal, characteristic, complemented
14#3277C211yesmaximal, characteristic, complemented
15#3275C211yesmaximal, characteristic, complemented
16#3274C211yesmaximal, characteristic, complemented
17#3271C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3251C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3220C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3106C211yesmaximal, characteristic, complemented
28#3045C211yesmaximal, characteristic, complemented
29#3043C211yesmaximal, characteristic, complemented
30#3040C211yesmaximal, characteristic, complemented
31#2993C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×#137C2211yescharacteristic, complemented
34C2×AGL(1,ℤ/8)C2211yescharacteristic
35C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
36C2×#135C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic, complemented
38#562—21no—
39H(3,𝔽4)—21no—
40#559—21no—
41#559C2211yescharacteristic
42#559C2211yescharacteristic
43#559C2211yescharacteristic, complemented
44#557C2211yescharacteristic, complemented
45#555—21no—
46#555C2211yescharacteristic, complemented
47#553—21no—
48#553C2211yescharacteristic, complemented
49#552—21no—
50#552C2211yescharacteristic, complemented
51#550C2211yescharacteristic, complemented
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic, complemented
55#548C2211yescharacteristic, complemented
56#546—21no—
57#546—21no—
58#546C2211yescharacteristic
59#546C2211yescharacteristic
60D42C2211yescharacteristic
61D42C2211yescharacteristic
62#542—21no—
63#542C2211yescharacteristic
64#542C2211yescharacteristic
65#542C2211yescharacteristic, complemented
66#540—21no—
67#540C2211yescharacteristic, complemented
68#538—21no—
69#538—21no—
70#538—21no—
71#535C2211yescharacteristic
72#535C2211yescharacteristic
73#534—21no—
74#532C2211yescharacteristic
75#529—21no—
76#529—21no—
77#529C2211yescharacteristic
78#529C2211yescharacteristic, complemented
79C2×#124C2211yescharacteristic
80#520C2211yescharacteristic, complemented
81#519C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic, complemented
83#496C2211yescharacteristic
84#496C2211yescharacteristic, complemented
85#495C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#493C2211yescharacteristic
89#490C2211yescharacteristic
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#486C2211yescharacteristic
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#482C2211yescharacteristic
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#480C2211yescharacteristic
101#479C2211yescharacteristic, complemented
102#478C2211yescharacteristic, complemented
103#478C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#477C2211yescharacteristic, complemented
106#476C2211yescharacteristic, complemented
107#476C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#475C2211yescharacteristic, complemented
110#474C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#469C2211yescharacteristic
113#469C2211yescharacteristic
114#469C2211yescharacteristic, complemented
115#469C2211yescharacteristic, complemented
116#468C2211yescharacteristic, complemented
117#468C2211yescharacteristic, complemented
118#468C2211yescharacteristic, complemented
119#466C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#464C2211yescharacteristic, complemented
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#463C2211yescharacteristic, complemented
136#463C2211yescharacteristic, complemented
137#463C2211yescharacteristic, complemented
138#463C2211yescharacteristic, complemented
139#463C2211yescharacteristic, complemented
140#463C2211yescharacteristic, complemented
141#463C2211yescharacteristic, complemented
142#463C2211yescharacteristic, complemented
143#460C2211yescharacteristic
144#460C2211yescharacteristic
145#460C2211yescharacteristic
146#460C2211yescharacteristic, complemented
147#460C2211yescharacteristic, complemented
148#460C2211yescharacteristic, complemented
149#459C2211yescharacteristic
150#459C2211yescharacteristic, complemented
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#450C2211yescharacteristic
158#450C2211yescharacteristic, complemented
159#449C2211yescharacteristic
160#449C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic
166#448C2211yescharacteristic, complemented
167#447C2211yescharacteristic
168#447C2211yescharacteristic, complemented
169#447C2211yescharacteristic, complemented
170#447C2211yescharacteristic, complemented
171#446C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182C4×D8C2211yescharacteristic, complemented
183C4×D8C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic, complemented
185#436C2211yescharacteristic, complemented
186#436C2211yescharacteristic, complemented
187#436C2211yescharacteristic, complemented
188#435C2211yescharacteristic, complemented
189#435C2211yescharacteristic, complemented
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#431C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#418C2211yescharacteristic
199#418C2211yescharacteristic, complemented
200#417C2211yescharacteristic, complemented
201#416C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215#137—42no—
216#137—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×D8C2311yescharacteristic
238C2×D8C2311yescharacteristic
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
254#127—21no—
255#127C2311yescharacteristic
256#127C2311yescharacteristic
257#127C2311yescharacteristic
258#127C2311yescharacteristic
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126D411yescharacteristic
266#126D411yescharacteristic
267#125—21no—
268#125—21no—
269#125—21no—
270#125D411yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#124—21no—
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#124—21no—
287#124—21no—
288#124D411yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
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#123D411yescharacteristic
314#123D411yescharacteristic
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8D411yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121D411yescharacteristic
347#121C2311yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#120—21no—
356#120—21no—
357#120—21no—
358#120—21no—
359#120—21no—
360#120—21no—
361#120—21no—
362#120—21no—
363#120—21no—
364#120—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×Q8C2311yescharacteristic
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×D4—21no—
391C4×D4—21no—
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#117—21no—
408#117—21no—
409#117—21no—
410#117C2311yescharacteristic
411#117C2311yescharacteristic
412#117C2311yescharacteristic
413#117C2311yescharacteristic
414C2×C4⋊C4—21no—
415C2×C4⋊C4C2311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C42—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#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
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
480C4×C8C2311yescharacteristic
481C4×C8C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487#41—22no—
488#41—22no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—82no—
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×Q8C2×D411yescharacteristic
505C2×Q8C2411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
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—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4C2×D411yescharacteristic
541C2×D4C2×D411yescharacteristic
542C2×D4C2×D411yescharacteristic
543C2×D4C2411yescharacteristic
544C2×D4C2411yescharacteristic
545C2×D4C2411yescharacteristic
546C2×D4C2411yescharacteristic
547C2×D4C2411yescharacteristic
548C2×D4C2411yescharacteristic
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—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4C2×D411yescharacteristic
565C22×C4C2×D411yescharacteristic
566C22×C4C2411yescharacteristic
567C22×C4C2411yescharacteristic
568C22×C4C2411yescharacteristic
569Q16—22no—
570Q16—22no—
571Q16—41no—
572Q16—41no—
573SD16—22no—
574SD16—22no—
575SD16—22no—
576SD16—22no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585D8—41no—
586D8—41no—
587D8—41no—
588D8—41no—
589D8—41no—
590D8—41no—
591D8—41no—
592D8—41no—
593M16—41no—
594M16—41no—
595M16—41no—
596M16—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8C2411yescharacteristic
600C2×C8C2411yescharacteristic
601C2×C8C2411yescharacteristic
602C2×C8C2411yescharacteristic
603C2×C8C2411yescharacteristic
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
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⋊C4—21no—
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C42—21no—
691C42—21no—
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—21no—
711C23—21no—
712C23—42no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23C22×D411yescharacteristic
722C23C22×D411yescharacteristic
723C23C22×D411yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—41no—
732Q8—42no—
733Q8—81no—
734Q8—81no—
735Q8—81no—
736Q8H(5,𝔽2)12yes—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—41no—
750D4—41no—
751D4—41no—
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—
765D4—81no—
766D4—81no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
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—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4C22×D411yescharacteristic
809C2×C4C22×D411yescharacteristic
810C2×C4C22×D411yescharacteristic
811C2×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C22×D411yescharacteristic
815C2×C4C22×D411yescharacteristic
816C2×C4C22×D411yescharacteristic
817C2×C4C22×D411yescharacteristic
818C2×C4C22×D411yescharacteristic
819C2×C4C2511yescharacteristic
820C8—21no—
821C8—21no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—162no—
856C22—162no—
857C22—162no—
858C22C23×D411yescharacteristic
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4C2×H(5,𝔽2)11yescharacteristic
881C4#58511yescharacteristic
882C2—41no—
883C2—41no—
884C2—41no—
885C2—81no—
886C2—81no—
887C2—81no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2#348811yescharacteristic
892C2#358411yescharacteristic
893C2#358511yescharacteristic
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. #3558C2semidirect
2. #3524C2semidirect
3. #3403C2semidirect
4. #3396C2semidirect
5. #3371C2semidirect
6. #3365C2semidirect
7. #3327C2semidirect
8. #3325C2semidirect
9. #3322C2semidirect
10. #3321C2semidirect
11. #3310C2semidirect
12. #3297C2semidirect
13. #3282C2semidirect
14. #3277C2semidirect
15. #3275C2semidirect
16. #3274C2semidirect
17. #3271C2semidirect
18. #3265C2semidirect
19. #3263C2semidirect
20. #3257C2semidirect
21. #3251C2semidirect
22. #3224C2semidirect
23. #3220C2semidirect
24. #3211C2semidirect
25. #3124C2semidirect
26. #3121C2semidirect
27. #3106C2semidirect
28. #3045C2semidirect
29. #3043C2semidirect
30. #3040C2semidirect
31. #2993C2semidirect
32. C2×#137C22semidirect
33. C2×#137C22semidirect
35. C2×AGL(1,ℤ/8)C22semidirect
36. C2×#135C22semidirect
37. C22×SD16C22semidirect
43. #559C22semidirect
44. #557C22semidirect
46. #555C22semidirect
48. #553C22semidirect
50. #552C22semidirect
51. #550C22semidirect
54. #548C22semidirect
55. #548C22semidirect
65. #542C22semidirect
67. #540C22semidirect
78. #529C22semidirect
80. #520C22semidirect
81. #519C22semidirect
82. C4×#41C22semidirect
84. #496C22semidirect
85. #495C22semidirect
86. #495C22semidirect
87. #495C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #488C22semidirect
93. #488C22semidirect
95. #485C22semidirect
96. #484C22semidirect
98. #482C22semidirect
99. #482C22semidirect
101. #479C22semidirect
102. #478C22semidirect
103. #478C22semidirect
104. #478C22semidirect
105. #477C22semidirect
106. #476C22semidirect
107. #476C22semidirect
108. #475C22semidirect
109. #475C22semidirect
110. #474C22semidirect
111. #470C22semidirect
114. #469C22semidirect
115. #469C22semidirect
116. #468C22semidirect
117. #468C22semidirect
118. #468C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
132. #464C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #463C22semidirect
136. #463C22semidirect
137. #463C22semidirect
138. #463C22semidirect
139. #463C22semidirect
140. #463C22semidirect
141. #463C22semidirect
142. #463C22semidirect
146. #460C22semidirect
147. #460C22semidirect
148. #460C22semidirect
150. #459C22semidirect
151. #459C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #451C22semidirect
156. #451C22semidirect
158. #450C22semidirect
160. #449C22semidirect
161. #449C22semidirect
162. #449C22semidirect
163. #449C22semidirect
164. #449C22semidirect
166. #448C22semidirect
168. #447C22semidirect
169. #447C22semidirect
170. #447C22semidirect
171. #446C22semidirect
172. C8×Q8C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. C4×SD16C22semidirect
182. C4×D8C22semidirect
183. C4×D8C22semidirect
184. C4×D8C22semidirect
185. #436C22semidirect
186. #436C22semidirect
187. #436C22semidirect
188. #435C22semidirect
189. #435C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #431C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. #423C22semidirect
197. #419C22semidirect
199. #418C22semidirect
200. #417C22semidirect
201. #416C22semidirect
202. C2×#102C22semidirect

Maximal subgroups

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

subgroupindex
#35582
#35242
#34032
#33962
#33712
#33652
#33272
#33252
#33222
#33212
#33102
#32972
#32822
#32772
#32752
#32742
#32712
#32652
#32632
#32572
#32512
#32242
#32202
#32112
#31242
#31212
#31062
#30452
#30432
#30402
#29932