Finite Group Databasebeta

← #7608449

Subgroups — #7608449

Order 512.

1799 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45116C211yesmaximal, characteristic, complemented
2#44874C211yesmaximal, characteristic
3#32186C211yesmaximal, characteristic, complemented
4#32064C211yesmaximal, characteristic, complemented
5#31543C211yesmaximal, characteristic, complemented
6#31012C211yesmaximal, characteristic, complemented
7#29099C211yesmaximal, characteristic, complemented
8#28981C211yesmaximal, characteristic, complemented
9#28935C211yesmaximal, characteristic, complemented
10#28881C211yesmaximal, characteristic, complemented
11#28436C211yesmaximal, characteristic, complemented
12#28330C211yesmaximal, characteristic, complemented
13#27591C211yesmaximal, characteristic, complemented
14#27281C211yesmaximal, characteristic, complemented
15#27224C211yesmaximal, characteristic, complemented
16#27203C211yesmaximal, characteristic, complemented
17#27074C211yesmaximal, characteristic, complemented
18#26933C211yesmaximal, characteristic, complemented
19#26343C211yesmaximal, characteristic, complemented
20#26133C211yesmaximal, characteristic, complemented
21#25118C211yesmaximal, characteristic, complemented
22#24357C211yesmaximal, characteristic, complemented
23#23946C211yesmaximal, characteristic, complemented
24#23849C211yesmaximal, characteristic
25#23103C211yesmaximal, characteristic, complemented
26#22865C211yesmaximal, characteristic, complemented
27#22854C211yesmaximal, characteristic, complemented
28#22423C211yesmaximal, characteristic
29#21568C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#21231C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×D42C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#489C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#467C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic, complemented
41C2×#451C2211yescharacteristic, complemented
42C2×#448C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#440C2211yescharacteristic, complemented
46C2×#435C2211yescharacteristic
47C2×#427C2211yescharacteristic, complemented
48C2×#419C2211yescharacteristic, complemented
49C2×#418C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C2×#405C2211yescharacteristic, complemented
52#2799—21no—
53#2758—21no—
54#2743—21no—
55#2739—21no—
56#2697—21no—
57#2685—21no—
58#2684—21no—
59#2681—21no—
60#2607—21no—
61#2572—21no—
62#2568C2211yescharacteristic, complemented
63#2559—21no—
64#2544C2211yescharacteristic
65#2527—21no—
66#2527—21no—
67#2514C2211yescharacteristic, complemented
68#2511C2211yescharacteristic, complemented
69#2503C2211yescharacteristic, complemented
70#2492C2211yescharacteristic, complemented
71#2491C2211yescharacteristic
72#2472—21no—
73#2452C2211yescharacteristic
74#2445C2211yescharacteristic
75#2439C2211yescharacteristic, complemented
76#2435—21no—
77#2435C2211yescharacteristic
78#2435C2211yescharacteristic
79#2426C2211yescharacteristic
80#2423C2211yescharacteristic, complemented
81#2415C2211yescharacteristic
82#2409C2211yescharacteristic
83#2405—21no—
84#2395C2211yescharacteristic
85#2367C2211yescharacteristic
86#2363C2211yescharacteristic
87#2360C2211yescharacteristic, complemented
88#2356C2211yescharacteristic, complemented
89#2352C2211yescharacteristic
90Q8×C22⋊C4C2211yescharacteristic, complemented
91D4×C22⋊C4C2211yescharacteristic
92#2314C2211yescharacteristic, complemented
93#2310C2211yescharacteristic, complemented
94#2309C2211yescharacteristic
95#2097C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic, complemented
98#2092C2211yescharacteristic, complemented
99#2088C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2024C2211yescharacteristic, complemented
116#2024C2211yescharacteristic, complemented
117#2023C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic, complemented
120#2015C2211yescharacteristic, complemented
121#2015C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2001C2211yescharacteristic, complemented
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#1993C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic, complemented
133#1973C2211yescharacteristic, complemented
134#1971C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic, complemented
138#1968C2211yescharacteristic, complemented
139#1968C2211yescharacteristic, complemented
140#1961C2211yescharacteristic
141#1959C2211yescharacteristic, complemented
142#1958C2211yescharacteristic
143#1958C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1924C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic, complemented
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic, complemented
166#1892C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1874C2211yescharacteristic
179#1873C2211yescharacteristic, complemented
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1852C2211yescharacteristic, complemented
186#1850C2211yescharacteristic, complemented
187#1818C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1771C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202C8×C22⋊C4C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16—24no—
210C22×SD16—42no—
211C22×SD16—42no—
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221D42—24no—
222D42—42no—
223#542—24no—
224#542—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4—21no—
259#489—42no—
260#483—42no—
261#476—42no—
262#467—42no—
263#464—24no—
264#464—42no—
265#451—42no—
266#450—24no—
267#450—42no—
268#448—24no—
269#440—42no—
270#435—42no—
271#427—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#419—42no—
284#418—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
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×#102—42no—
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323#405—42no—
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#401—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400D411yescharacteristic
341#399—21no—
342#399D411yescharacteristic
343#398—21no—
344#398D411yescharacteristic
345#397—21no—
346#397D411yescharacteristic
347#397D411yescharacteristic
348#397D411yescharacteristic
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394D411yescharacteristic
365#394D411yescharacteristic
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
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#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#383—21no—
441#383—21no—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381—21no—
446#381—21no—
447#381—21no—
448#381—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457#379—21no—
458#379—21no—
459#379—21no—
460#379—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475#376—21no—
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C25—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—44no—
535C22×D4—82no—
536C22×D4—82no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—416no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16#4114yes—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—41no—
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594#127—22no—
595#127—41no—
596#126—44no—
597#124—22no—
598#124—22no—
599#124—41no—
600#124—41no—
601#124—41no—
602#124—41no—
603#124—44no—
604#124—82no—
605#123—44no—
606#123—82no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—44no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—82no—
617#121—22no—
618#121—22no—
619#121—44no—
620#121—41no—
621#121#4114yes—
622#120—44no—
623#120—44no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638#117—22no—
639#117—22no—
640#117—41no—
641#117—41no—
642#117—41no—
643#117—41no—
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—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
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—82no—
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—41no—
740#107—41no—
741#107—41no—
742#107—41no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—41no—
787#97—22no—
788#97—41no—
789#97—41no—
790#97—41no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
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#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—21no—
841C24—21no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24—81no—
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859C2×Q8—21no—
860C2×Q8—21no—
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—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—44no—
880C2×Q8—44no—
881C2×Q8—42no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8—81no—
885C2×Q8—81no—
886C2×Q8—81no—
887C2×Q8—82no—
888C2×Q8—82no—
889C2×Q8C2×#4112yes—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
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—21no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—41no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—82no—
923C2×D4—82no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—816no—
936C2×D4C2×#4112yes—
937C2×D4C2×#4112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C2×#4112yes—
989C22×C4H(5,𝔽2)12yes—
990C22×C4C2511yescharacteristic
991Q16—82no—
992Q16—82no—
993SD16—44no—
994SD16—44no—
995SD16—44no—
996SD16—44no—
997SD16—44no—
998SD16—82no—
999M16—44no—
1000C2×C8—28no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—82no—
1023C2×C8C2×#4112yes—
1024C2×C8H(5,𝔽2)12yes—
1025C2×C8H(5,𝔽2)12yes—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4C2×#4112yes—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—24no—
1075C22⋊C4—22no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—42no—
1125C42—42no—
1126C42—81no—
1127C42—81no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—84no—
1167C23—84no—
1168C23—84no—
1169C23—84no—
1170C23—84no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23#54612yes—
1181C23#57712yes—
1182C23C23×D411yescharacteristic
1183Q8—22no—
1184Q8—22no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—84no—
1196Q8—162no—
1197Q8—162no—
1198D4—22no—
1199D4—22no—
1200D4—22no—
1201D4—22no—
1202D4—44no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—84no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215D4—84no—
1216D4—162no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
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—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
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—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4#54612yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C22×#4111yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—22no—
1312C8—22no—
1313C8—22no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—168no—
1355C22—168no—
1356C22C2×#54611yescharacteristic
1357C22D4×#4111yescharacteristic
1358C22#349811yescharacteristic
1359C22C2×#57711yescharacteristic
1360C22#358411yescharacteristic
1361C22#358511yescharacteristic
1362C22#358611yescharacteristic
1363C4—22no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—41no—
1376C4—41no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4#348111yescharacteristic
1389C4#349011yescharacteristic
1390C4#351411yescharacteristic
1391C4#353411yescharacteristic
1392C2—42no—
1393C2—42no—
1394C2—82no—
1395C2—82no—
1396C2—161no—
1397C2#5980011yescharacteristic
1398C2#6118411yescharacteristic
1399C2#6120711yescharacteristic
1400C2#6152011yescharacteristic
1401C2#6152711yescharacteristic
1402C2#6243511yescharacteristic
1403C2#6244611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45116C2semidirect
3. #32186C2semidirect
4. #32064C2semidirect
5. #31543C2semidirect
6. #31012C2semidirect
7. #29099C2semidirect
8. #28981C2semidirect
9. #28935C2semidirect
10. #28881C2semidirect
11. #28436C2semidirect
12. #28330C2semidirect
13. #27591C2semidirect
14. #27281C2semidirect
15. #27224C2semidirect
16. #27203C2semidirect
17. #27074C2semidirect
18. #26933C2semidirect
19. #26343C2semidirect
20. #26133C2semidirect
21. #25118C2semidirect
22. #24357C2semidirect
23. #23946C2semidirect
25. #23103C2semidirect
26. #22865C2semidirect
27. #22854C2semidirect
29. #21568C2semidirect
30. #21412C2semidirect
31. #21231C2semidirect
35. C2×#489C22semidirect
36. C2×#483C22semidirect
37. C2×#476C22semidirect
38. C2×#467C22semidirect
40. C2×#464C22semidirect
41. C2×#451C22semidirect
45. C2×#440C22semidirect
47. C2×#427C22semidirect
48. C2×#419C22semidirect
51. C2×#405C22semidirect
62. #2568C22semidirect
67. #2514C22semidirect
68. #2511C22semidirect
69. #2503C22semidirect
70. #2492C22semidirect
75. #2439C22semidirect
80. #2423C22semidirect
87. #2360C22semidirect
88. #2356C22semidirect
90. Q8×C22⋊C4C22semidirect
92. #2314C22semidirect
93. #2310C22semidirect
95. #2097C22semidirect
97. #2092C22semidirect
98. #2092C22semidirect
99. #2088C22semidirect
100. #2085C22semidirect
101. #2077C22semidirect
102. #2073C22semidirect
104. #2071C22semidirect
105. #2068C22semidirect
106. #2067C22semidirect
107. #2057C22semidirect
108. #2056C22semidirect
110. #2055C22semidirect
112. #2042C22semidirect
113. #2036C22semidirect
114. #2035C22semidirect
115. #2024C22semidirect
116. #2024C22semidirect
119. #2015C22semidirect
120. #2015C22semidirect
121. #2015C22semidirect
124. #2001C22semidirect
127. #1993C22semidirect
128. #1990C22semidirect
132. #1973C22semidirect
133. #1973C22semidirect
134. #1971C22semidirect
137. #1968C22semidirect
138. #1968C22semidirect
139. #1968C22semidirect
141. #1959C22semidirect
143. #1958C22semidirect
144. #1949C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1934C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
152. #1926C22semidirect
154. #1925C22semidirect
155. #1924C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1917C22semidirect
160. #1916C22semidirect
162. #1894C22semidirect
165. #1892C22semidirect
166. #1892C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
174. #1877C22semidirect
175. #1877C22semidirect
176. #1877C22semidirect
179. #1873C22semidirect
181. #1865C22semidirect
182. #1862C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
185. #1852C22semidirect
186. #1850C22semidirect
187. #1818C22semidirect
192. #1771C22semidirect
193. #1770C22semidirect
194. #1763C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect
201. #1752C22semidirect
202. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#451162
#448742
#321862
#320642
#315432
#310122
#290992
#289812
#289352
#288812
#284362
#283302
#275912
#272812
#272242
#272032
#270742
#269332
#263432
#261332
#251182
#243572
#239462
#238492
#231032
#228652
#228542
#224232
#215682
#214122
#212312