Finite Group Databasebeta

← #62048

Subgroups — #62048

Order 256.

898 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3561C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3402C211yesmaximal, characteristic, complemented
4#3393C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3360C211yesmaximal, characteristic, complemented
7#3328C211yesmaximal, characteristic, complemented
8#3327C211yesmaximal, characteristic, complemented
9#3322C211yesmaximal, characteristic, complemented
10#3320C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3300C211yesmaximal, characteristic, complemented
13#3282C211yesmaximal, characteristic, complemented
14#3276C211yesmaximal, characteristic, complemented
15#3275C211yesmaximal, characteristic, complemented
16#3273C211yesmaximal, characteristic, complemented
17#3267C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3252C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3223C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3107C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30#3040C211yesmaximal, characteristic, complemented
31#2993C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic, complemented
34C2×AGL(1,ℤ/8)C2211yescharacteristic
35C2×AGL(1,ℤ/8)C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C22×SD16C2211yescharacteristic, complemented
38#563—21no—
39#562—21no—
40#556C2211yescharacteristic
41#556C2211yescharacteristic, complemented
42#556C2211yescharacteristic, complemented
43#556C2211yescharacteristic, complemented
44#554C2211yescharacteristic, complemented
45#553—21no—
46#553C2211yescharacteristic
47#552—21no—
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51#551—21no—
52#551—21no—
53D4×Q8C2211yescharacteristic
54D4×Q8C2211yescharacteristic, complemented
55#548C2211yescharacteristic
56#548C2211yescharacteristic
57#547C2211yescharacteristic
58#546C2211yescharacteristic
59#546C2211yescharacteristic
60#546C2211yescharacteristic, complemented
61#546C2211yescharacteristic, complemented
62#543—21no—
63#542—21no—
64#542—21no—
65#542C2211yescharacteristic
66#542C2211yescharacteristic, complemented
67#542C2211yescharacteristic, complemented
68#541C2211yescharacteristic, complemented
69#539—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic
73#536C2211yescharacteristic, complemented
74#533C2211yescharacteristic, complemented
75#529—21no—
76#529C2211yescharacteristic
77#529C2211yescharacteristic
78C2×#126—21no—
79C2×#124C2211yescharacteristic, complemented
80#520C2211yescharacteristic, complemented
81#518C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic
83#497C2211yescharacteristic, complemented
84#497C2211yescharacteristic, complemented
85#495C2211yescharacteristic
86#495C2211yescharacteristic
87#495C2211yescharacteristic
88#494C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#480C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, 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#470C2211yescharacteristic, complemented
113#470C2211yescharacteristic, complemented
114#470C2211yescharacteristic, complemented
115#469C2211yescharacteristic
116#468C2211yescharacteristic
117#468C2211yescharacteristic
118#468C2211yescharacteristic
119#467C2211yescharacteristic, complemented
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
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#463C2211yescharacteristic
137#463C2211yescharacteristic
138#463C2211yescharacteristic
139#463C2211yescharacteristic
140#463C2211yescharacteristic
141#463C2211yescharacteristic
142#463C2211yescharacteristic
143#462C2211yescharacteristic, complemented
144#462C2211yescharacteristic, complemented
145#462C2211yescharacteristic, complemented
146#462C2211yescharacteristic, complemented
147#461C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#461C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#461C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#451C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#450C2211yescharacteristic, complemented
164#450C2211yescharacteristic, complemented
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#448C2211yescharacteristic
168#448C2211yescharacteristic, complemented
169#447C2211yescharacteristic
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#440C2211yescharacteristic, complemented
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×Q16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×D8C2211yescharacteristic
184C4×D8C2211yescharacteristic
185#436C2211yescharacteristic
186#436C2211yescharacteristic, complemented
187#436C2211yescharacteristic, complemented
188#435C2211yescharacteristic
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#419C2211yescharacteristic, complemented
199#418C2211yescharacteristic, complemented
200#417C2211yescharacteristic, complemented
201#416C2211yescharacteristic
202C2×#103C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213#137—42no—
214AGL(1,ℤ/8)—42no—
215AGL(1,ℤ/8)—42no—
216#135—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×SD16—42no—
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×D8C2311yescharacteristic
239C2×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C2×M16C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256#126—21no—
257#126—21no—
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#126—21no—
270#126—21no—
271#126—21no—
272#126D411yescharacteristic
273#126D411yescharacteristic
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125D411yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124D411yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
297#124C2311yescharacteristic
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#123D411yescharacteristic
315#123D411yescharacteristic
316C22⋊Q8—21no—
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⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8D411yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#120—21no—
359#120—21no—
360#120—21no—
361#120—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
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×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117C2311yescharacteristic
405#117C2311yescharacteristic
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C2311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
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#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
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—
486#41—22no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—41no—
500C2×Q8—41no—
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×Q8C2411yescharacteristic
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—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4C2×D411yescharacteristic
550C22×C4C2×D411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554Q16—41no—
555Q16—41no—
556Q16—41no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561Q16—41no—
562SD16—22no—
563SD16—22no—
564SD16—22no—
565SD16—22no—
566SD16—41no—
567SD16—41no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574D8—22no—
575D8—22no—
576D8—41no—
577D8—41no—
578M16—41no—
579M16—41no—
580M16—41no—
581M16—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C2×C8C2411yescharacteristic
590C2×C8C2411yescharacteristic
591C2×C8C2411yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D411yescharacteristic
624C4⋊C4C2×D411yescharacteristic
625C4⋊C4C2×D411yescharacteristic
626C4⋊C4C2×D411yescharacteristic
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2411yescharacteristic
634C4⋊C4C2411yescharacteristic
635C4⋊C4C2411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
678C22⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42C2×D411yescharacteristic
698C42C2×D411yescharacteristic
699C42C2411yescharacteristic
700C42C2411yescharacteristic
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—42no—
708C23—42no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23C22×D411yescharacteristic
714C23C22×D411yescharacteristic
715C23C22×D411yescharacteristic
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—41no—
729Q8—81no—
730Q8—81no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4H(5,𝔽2)12yes—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C2511yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—162no—
833C22—162no—
834C22C23×D411yescharacteristic
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4C2×H(5,𝔽2)11yescharacteristic
859C4#58511yescharacteristic
860C2—41no—
861C2—41no—
862C2—41no—
863C2—42no—
864C2—81no—
865C2—81no—
866C2—81no—
867C2#348811yescharacteristic
868C2#358411yescharacteristic
869C2#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. #3561C2semidirect
2. #3521C2semidirect
3. #3402C2semidirect
4. #3393C2semidirect
5. #3376C2semidirect
6. #3360C2semidirect
7. #3328C2semidirect
8. #3327C2semidirect
9. #3322C2semidirect
10. #3320C2semidirect
11. #3311C2semidirect
12. #3300C2semidirect
13. #3282C2semidirect
14. #3276C2semidirect
15. #3275C2semidirect
16. #3273C2semidirect
17. #3267C2semidirect
18. #3266C2semidirect
19. #3263C2semidirect
20. #3258C2semidirect
21. #3252C2semidirect
22. #3225C2semidirect
23. #3223C2semidirect
24. #3211C2semidirect
25. #3124C2semidirect
26. #3118C2semidirect
27. #3107C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. #3040C2semidirect
31. #2993C2semidirect
33. C2×#137C22semidirect
37. C22×SD16C22semidirect
41. #556C22semidirect
42. #556C22semidirect
43. #556C22semidirect
44. #554C22semidirect
48. #552C22semidirect
54. D4×Q8C22semidirect
60. #546C22semidirect
61. #546C22semidirect
66. #542C22semidirect
67. #542C22semidirect
68. #541C22semidirect
73. #536C22semidirect
74. #533C22semidirect
79. C2×#124C22semidirect
80. #520C22semidirect
81. #518C22semidirect
83. #497C22semidirect
84. #497C22semidirect
88. #494C22semidirect
89. #491C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #488C22semidirect
93. #488C22semidirect
94. #487C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #484C22semidirect
100. #480C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #477C22semidirect
106. #476C22semidirect
107. #476C22semidirect
108. #475C22semidirect
109. #475C22semidirect
110. #474C22semidirect
111. #470C22semidirect
112. #470C22semidirect
113. #470C22semidirect
114. #470C22semidirect
119. #467C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
132. #464C22semidirect
143. #462C22semidirect
144. #462C22semidirect
145. #462C22semidirect
146. #462C22semidirect
147. #461C22semidirect
148. #461C22semidirect
149. #461C22semidirect
150. #461C22semidirect
151. #461C22semidirect
152. #461C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #451C22semidirect
160. #451C22semidirect
161. #451C22semidirect
162. #451C22semidirect
163. #450C22semidirect
164. #450C22semidirect
168. #448C22semidirect
171. #446C22semidirect
172. C8×Q8C22semidirect
174. #440C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×Q16C22semidirect
180. C4×SD16C22semidirect
181. C4×SD16C22semidirect
182. C4×SD16C22semidirect
186. #436C22semidirect
187. #436C22semidirect
189. #435C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #431C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. #423C22semidirect
197. #419C22semidirect
198. #419C22semidirect
199. #418C22semidirect
200. #417C22semidirect
202. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35612
#35212
#34022
#33932
#33762
#33602
#33282
#33272
#33222
#33202
#33112
#33002
#32822
#32762
#32752
#32732
#32672
#32662
#32632
#32582
#32522
#32252
#32232
#32112
#31242
#31182
#31072
#30462
#30422
#30402
#29932