Finite Group Databasebeta

← #6828049

Subgroups — #6828049

Order 512.

1615 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40225C211yesmaximal, characteristic, complemented
2#39034C211yesmaximal, characteristic, complemented
3#33253C211yesmaximal, characteristic, complemented
4#32189C211yesmaximal, characteristic, complemented
5#32182C211yesmaximal, characteristic, complemented
6#31012C211yesmaximal, characteristic, complemented
7#31007C211yesmaximal, characteristic, complemented
8#30888C211yesmaximal, characteristic, complemented
9#30886C211yesmaximal, characteristic, complemented
10#30531C211yesmaximal, characteristic, complemented
11#30525C211yesmaximal, characteristic, complemented
12#30044C211yesmaximal, characteristic, complemented
13#30043C211yesmaximal, characteristic, complemented
14#28471C211yesmaximal, characteristic, complemented
15#28466C211yesmaximal, characteristic, complemented
16#28029C211yesmaximal, characteristic, complemented
17#27806C211yesmaximal, characteristic, complemented
18#26611C211yesmaximal, characteristic, complemented
19#26606C211yesmaximal, characteristic, complemented
20#26481C211yesmaximal, characteristic, complemented
21#26263C211yesmaximal, characteristic, complemented
22#25796C211yesmaximal, characteristic
23#25796C211yesmaximal, characteristic
24#25427C211yesmaximal, characteristic, complemented
25#25176C211yesmaximal, characteristic, complemented
26#25171C211yesmaximal, characteristic, complemented
27#25039C211yesmaximal, characteristic, complemented
28#23194C211yesmaximal, characteristic, complemented
29#22443C211yesmaximal, characteristic
30#21702C211yesmaximal, characteristic, complemented
31#21667C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#499C2211yescharacteristic, complemented
34C2×#497C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#495C2211yescharacteristic
38C2×#494C2211yescharacteristic, complemented
39C2×#488C2211yescharacteristic
40C2×#488C2211yescharacteristic, complemented
41C2×#470C2211yescharacteristic
42C2×#470C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#464C2211yescharacteristic, complemented
45C2×#462C2211yescharacteristic, complemented
46C2×#461C2211yescharacteristic
47C2×#452C2211yescharacteristic
48C2×#452C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#441C2211yescharacteristic, complemented
52C2×#441C2211yescharacteristic, complemented
53C2×#440C2211yescharacteristic
54C2×#440C2211yescharacteristic
55C2×C4×Q16C2211yescharacteristic, complemented
56C2×C4×SD16C2211yescharacteristic
57#2861C2211yescharacteristic
58#2861C2211yescharacteristic, complemented
59#2800—21no—
60#2781—21no—
61#2770—21no—
62#2768—21no—
63#2741—21no—
64#2735—21no—
65#2735—21no—
66#2727—21no—
67#2651—21no—
68#2649—21no—
69#2593—21no—
70#2587—21no—
71#2547C2211yescharacteristic
72#2546C2211yescharacteristic, complemented
73#2545C2211yescharacteristic
74#2545C2211yescharacteristic, complemented
75#2518—21no—
76#2513C2211yescharacteristic
77#2512C2211yescharacteristic, complemented
78#2489C2211yescharacteristic
79#2489C2211yescharacteristic
80#2480—21no—
81#2454C2211yescharacteristic
82#2453C2211yescharacteristic, complemented
83#2448C2211yescharacteristic
84#2448C2211yescharacteristic, complemented
85#2435C2211yescharacteristic
86#2435C2211yescharacteristic
87#2432C2211yescharacteristic
88#2432C2211yescharacteristic
89#2429C2211yescharacteristic
90#2429C2211yescharacteristic
91#2423C2211yescharacteristic
92#2421C2211yescharacteristic
93#2367C2211yescharacteristic
94#2365C2211yescharacteristic, complemented
95#2341C2211yescharacteristic
96D4×C22⋊C4C2211yescharacteristic
97#2334—21no—
98#2312—21no—
99C4×C4⋊Q8C2211yescharacteristic, complemented
100C4×#126C2211yescharacteristic
101C4×#124C2211yescharacteristic
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2016C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic, complemented
132#2013C2211yescharacteristic
133#2013C2211yescharacteristic
134#2013C2211yescharacteristic
135#2013C2211yescharacteristic, complemented
136#2012C2211yescharacteristic
137#2012C2211yescharacteristic
138#2012C2211yescharacteristic
139#2012C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#1983C2211yescharacteristic
143#1981C2211yescharacteristic, complemented
144#1973C2211yescharacteristic
145#1973C2211yescharacteristic
146#1973C2211yescharacteristic, complemented
147#1973C2211yescharacteristic, complemented
148#1972C2211yescharacteristic
149#1972C2211yescharacteristic
150#1972C2211yescharacteristic
151#1971C2211yescharacteristic, complemented
152#1971C2211yescharacteristic, complemented
153#1971C2211yescharacteristic, complemented
154#1970C2211yescharacteristic
155#1969C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1968C2211yescharacteristic
158#1968C2211yescharacteristic
159#1968C2211yescharacteristic
160#1960C2211yescharacteristic, complemented
161#1959C2211yescharacteristic
162#1941C2211yescharacteristic, complemented
163#1941C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic, complemented
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic
170#1923C2211yescharacteristic
171#1917C2211yescharacteristic, complemented
172#1917C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic, complemented
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1878C2211yescharacteristic, complemented
182#1878C2211yescharacteristic, complemented
183#1878C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1877C2211yescharacteristic
186#1865C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1847C2211yescharacteristic, complemented
191#1839C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×M16C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#126—21no—
230C2×#126D411yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C22×C22⋊C4—21no—
252#499—42no—
253#497—24no—
254#497—24no—
255#495—42no—
256#495—42no—
257#494—42no—
258#488—42no—
259#488—42no—
260#470—42no—
261#470—42no—
262#464—42no—
263#464—42no—
264#462—42no—
265#461—42no—
266#452—42no—
267#452—42no—
268#450—42no—
269#450—42no—
270#441—42no—
271#441—42no—
272#440—42no—
273#440—42no—
274C4×Q16—42no—
275C4×SD16—42no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#390—21no—
382#390—21no—
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#388D411yescharacteristic
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387D411yescharacteristic
443#387D411yescharacteristic
444#387D411yescharacteristic
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#383D411yescharacteristic
455#382—21no—
456#382—21no—
457#382C2311yescharacteristic
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#379—21no—
465#379—21no—
466#379—21no—
467#379—21no—
468#379—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4—21no—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4—21no—
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484C43C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532AGL(1,ℤ/8)—416no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16#4114yes—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—22no—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600#126—42no—
601#126—44no—
602#125—41no—
603#125—41no—
604#125—41no—
605#125—41no—
606#124—22no—
607#124—22no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749#107—22no—
750#107—41no—
751#107—41no—
752#107—41no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—41no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—41no—
795#97—22no—
796#97—22no—
797#97—22no—
798#97—22no—
799#97—41no—
800C4×C8—22no—
801C4×C8—22no—
802C4×C8—22no—
803C4×C8—22no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846C24—21no—
847C24—21no—
848C24—21no—
849C24—42no—
850C24—42no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24C22×D411yescharacteristic
857#41—44no—
858#41—82no—
859#41—82no—
860#41—82no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8C2×#4112yes—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—44no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4C2×#4112yes—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C2511yescharacteristic
961Q16—44no—
962Q16—44no—
963Q16—44no—
964Q16—82no—
965Q16—82no—
966Q16—82no—
967SD16—28no—
968SD16—44no—
969SD16—44no—
970SD16—82no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
974SD16—82no—
975D8—44no—
976D8—44no—
977M16—44no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8C2×#4112yes—
998C2×C8H(5,𝔽2)12yes—
999C2×C8H(5,𝔽2)12yes—
1000C2×C8H(5,𝔽2)12yes—
1001C2×C8H(5,𝔽2)12yes—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C22⋊C4—22no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—41no—
1111C42—41no—
1112C42—41no—
1113C42—41no—
1114C42—42no—
1115C42—81no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23C23×D411yescharacteristic
1158Q8—22no—
1159Q8—22no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178D4—22no—
1179D4—22no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4—84no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—84no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4#57512yes—
1277C2×C4C22×#4111yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—22no—
1284C8—22no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8#53814yes—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—42no—
1299C22—41no—
1300C22—41no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—168no—
1320C22D4×#4111yescharacteristic
1321C22#349811yescharacteristic
1322C22#349811yescharacteristic
1323C22C2×#57511yescharacteristic
1324C22#358411yescharacteristic
1325C22#358611yescharacteristic
1326C22#358611yescharacteristic
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4C2×#53811yescharacteristic
1354C4#351911yescharacteristic
1355C4#354611yescharacteristic
1356C4#355811yescharacteristic
1357C2—81no—
1358C2—82no—
1359C2—161no—
1360C2—161no—
1361C2#3940511yescharacteristic
1362C2#6146311yescharacteristic
1363C2#6155011yescharacteristic
1364C2#6242911yescharacteristic
1365C2#6244211yescharacteristic
1366C2#6245011yescharacteristic
1367C2#6246211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40225C2semidirect
2. #39034C2semidirect
3. #33253C2semidirect
4. #32189C2semidirect
5. #32182C2semidirect
6. #31012C2semidirect
7. #31007C2semidirect
8. #30888C2semidirect
9. #30886C2semidirect
10. #30531C2semidirect
11. #30525C2semidirect
12. #30044C2semidirect
13. #30043C2semidirect
14. #28471C2semidirect
15. #28466C2semidirect
16. #28029C2semidirect
17. #27806C2semidirect
18. #26611C2semidirect
19. #26606C2semidirect
20. #26481C2semidirect
21. #26263C2semidirect
24. #25427C2semidirect
25. #25176C2semidirect
26. #25171C2semidirect
27. #25039C2semidirect
28. #23194C2semidirect
30. #21702C2semidirect
31. #21667C2semidirect
33. C2×#499C22semidirect
38. C2×#494C22semidirect
40. C2×#488C22semidirect
44. C2×#464C22semidirect
45. C2×#462C22semidirect
51. C2×#441C22semidirect
52. C2×#441C22semidirect
55. C2×C4×Q16C22semidirect
58. #2861C22semidirect
72. #2546C22semidirect
74. #2545C22semidirect
77. #2512C22semidirect
82. #2453C22semidirect
84. #2448C22semidirect
94. #2365C22semidirect
99. C4×C4⋊Q8C22semidirect
102. #2074C22semidirect
103. #2073C22semidirect
104. #2072C22semidirect
106. #2068C22semidirect
109. #2065C22semidirect
111. #2055C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
115. #2042C22semidirect
120. #2026C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
124. #2016C22semidirect
125. #2016C22semidirect
131. #2015C22semidirect
135. #2013C22semidirect
143. #1981C22semidirect
146. #1973C22semidirect
147. #1973C22semidirect
151. #1971C22semidirect
152. #1971C22semidirect
153. #1971C22semidirect
155. #1969C22semidirect
156. #1969C22semidirect
160. #1960C22semidirect
162. #1941C22semidirect
163. #1941C22semidirect
164. #1928C22semidirect
165. #1928C22semidirect
167. #1925C22semidirect
171. #1917C22semidirect
172. #1917C22semidirect
173. #1916C22semidirect
178. #1880C22semidirect
181. #1878C22semidirect
182. #1878C22semidirect
183. #1878C22semidirect
184. #1878C22semidirect
186. #1865C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
190. #1847C22semidirect
191. #1839C22semidirect
195. #1776C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. C8×C4⋊C4C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#402252
#390342
#332532
#321892
#321822
#310122
#310072
#308882
#308862
#305312
#305252
#300442
#300432
#284712
#284662
#280292
#278062
#266112
#266062
#264812
#262632
#257962
#254272
#251762
#251712
#250392
#231942
#224432
#217022
#216672