Finite Group Databasebeta

← #7081809

Subgroups — #7081809

Order 512.

1651 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59103C211yesmaximal, characteristic
2#39604C211yesmaximal, characteristic, complemented
3#32105C211yesmaximal, characteristic, complemented
4#32074C211yesmaximal, characteristic, complemented
5#31922C211yesmaximal, characteristic, complemented
6#31586C211yesmaximal, characteristic, complemented
7#31534C211yesmaximal, characteristic, complemented
8#31302C211yesmaximal, characteristic, complemented
9#30635C211yesmaximal, characteristic, complemented
10#30600C211yesmaximal, characteristic, complemented
11#28957C211yesmaximal, characteristic, complemented
12#28419C211yesmaximal, characteristic, complemented
13#28342C211yesmaximal, characteristic, complemented
14#28078C211yesmaximal, characteristic, complemented
15#27274C211yesmaximal, characteristic, complemented
16#27088C211yesmaximal, characteristic, complemented
17#26544C211yesmaximal, characteristic, complemented
18#26359C211yesmaximal, characteristic, complemented
19#26148C211yesmaximal, characteristic, complemented
20#25958C211yesmaximal, characteristic, complemented
21#25505C211yesmaximal, characteristic, complemented
22#25098C211yesmaximal, characteristic, complemented
23#24901C211yesmaximal, characteristic, complemented
24#24791C211yesmaximal, characteristic, complemented
25#24511C211yesmaximal, characteristic, complemented
26#24452C211yesmaximal, characteristic
27#23734C211yesmaximal, characteristic, complemented
28#23035C211yesmaximal, characteristic, complemented
29#22912C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic
31#21867C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#470C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#462C2211yescharacteristic, complemented
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×#432C2211yescharacteristic, complemented
46C2×#428C2211yescharacteristic, complemented
47C2×#428C2211yescharacteristic, complemented
48C2×#417C2211yescharacteristic
49C2×#417C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2855C2211yescharacteristic, complemented
52#2792—21no—
53#2791—21no—
54#2790—21no—
55#2720—21no—
56#2708—21no—
57#2697—21no—
58#2627—21no—
59#2567C2211yescharacteristic, complemented
60#2553—21no—
61#2552C2211yescharacteristic, complemented
62#2547C2211yescharacteristic
63#2511C2211yescharacteristic, complemented
64#2507C2211yescharacteristic, complemented
65#2502C2211yescharacteristic
66#2497C2211yescharacteristic
67#2489C2211yescharacteristic
68#2480—21no—
69#2473—21no—
70#2470—21no—
71#2454C2211yescharacteristic
72#2449—21no—
73#2447C2211yescharacteristic
74#2440C2211yescharacteristic
75#2440C2211yescharacteristic, complemented
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2429C2211yescharacteristic
79#2423C2211yescharacteristic
80#2420—21no—
81#2418—21no—
82#2417C2211yescharacteristic
83#2415C2211yescharacteristic
84#2367C2211yescharacteristic
85#2363C2211yescharacteristic
86#2360C2211yescharacteristic, complemented
87D4×C4⋊C4C2211yescharacteristic
88#2342—21no—
89D4×C22⋊C4C2211yescharacteristic
90#2322—21no—
91C4×#123C2211yescharacteristic
92#2297C2211yescharacteristic
93C2×#384C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2096C2211yescharacteristic, complemented
97#2095C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2094C2211yescharacteristic
100#2094C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic
103#2093C2211yescharacteristic
104#2087C2211yescharacteristic, complemented
105#2083C2211yescharacteristic, complemented
106#2077C2211yescharacteristic
107#2072C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2059C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2056C2211yescharacteristic, complemented
117#2056C2211yescharacteristic, complemented
118#2055C2211yescharacteristic
119#2043C2211yescharacteristic, complemented
120#2043C2211yescharacteristic, complemented
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2035C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2023C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2001C2211yescharacteristic
134#1992C2211yescharacteristic, complemented
135#1992C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1971C2211yescharacteristic, complemented
141#1971C2211yescharacteristic, complemented
142#1959C2211yescharacteristic
143#1959C2211yescharacteristic
144#1959C2211yescharacteristic
145#1959C2211yescharacteristic
146#1948C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1873C2211yescharacteristic, complemented
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic, complemented
185#1853C2211yescharacteristic
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1807C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216#529—24no—
217#529—42no—
218C2×#126—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×#123D411yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#487—42no—
256#484—42no—
257#476—42no—
258#470—42no—
259#468—24no—
260#467—42no—
261#462—42no—
262#452—42no—
263#450—42no—
264C4×SD16—42no—
265#435—42no—
266#432—42no—
267#428—42no—
268#428—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#417—42no—
287#417—42no—
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×#102—42no—
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×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#395—21no—
359#395—21no—
360#395—21no—
361#395—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388D411yescharacteristic
405#388D411yescharacteristic
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387D411yescharacteristic
415#387D411yescharacteristic
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386D411yescharacteristic
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385D411yescharacteristic
437#384—21no—
438#384—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#382—21no—
446#381—21no—
447#381—21no—
448#381D411yescharacteristic
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458#379—21no—
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8—22no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#126—44no—
567#125—22no—
568#125—41no—
569#125—82no—
570#124—22no—
571#124—22no—
572#124—22no—
573#124—41no—
574#124—41no—
575#124—41no—
576#123—24no—
577#123—44no—
578#123—44no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—82no—
590C22⋊Q8—82no—
591#121—22no—
592#121—44no—
593#121#4114yes—
594#120—44no—
595C4×Q8—22no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—44no—
608C4×D4—82no—
609#117—44no—
610#117—41no—
611#117—41no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—82no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
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—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—22no—
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—22no—
732#106—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—22no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779#97—41no—
780#97—41no—
781#97—41no—
782C4×C8—22no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
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#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—44no—
836#41—44no—
837#41—82no—
838#41—82no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—41no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4C2×#4112yes—
887C2×D42−1+412yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4H(5,𝔽2)12yes—
953C22×C4C2511yescharacteristic
954Q16—82no—
955Q16—82no—
956SD16—44no—
957SD16—82no—
958M16—44no—
959M16—44no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—82no—
983C2×C8H(5,𝔽2)12yes—
984C2×C8H(5,𝔽2)12yes—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
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⋊C4C2×#4112yes—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
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#13714yes—
1083C42—22no—
1084C42—22no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—22no—
1114C23—22no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—162no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23#54612yes—
1135C23C2×#13712yes—
1136C23C23×D411yescharacteristic
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—162no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—22no—
1154D4—44no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
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—44no—
1201C2×C4—44no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
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—84no—
1248C2×C4—84no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4#54612yes—
1255C2×C4C2×#13712yes—
1256C2×C4C2×#13712yes—
1257C2×C4C22×#4111yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4C2×2−1+411yescharacteristic
1262C2×C4#58511yescharacteristic
1263C8—22no—
1264C8—22no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—168no—
1300C22C2×#54611yescharacteristic
1301C22#348911yescharacteristic
1302C22#349811yescharacteristic
1303C22C22×#13711yescharacteristic
1304C22#358511yescharacteristic
1305C22#358511yescharacteristic
1306C22#358611yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4#351311yescharacteristic
1334C4#352011yescharacteristic
1335C4#353411yescharacteristic
1336C4#353611yescharacteristic
1337C2—42no—
1338C2—42no—
1339C2—82no—
1340C2—82no—
1341C2#4402211yescharacteristic
1342C2#6116211yescharacteristic
1343C2#6117711yescharacteristic
1344C2#6210811yescharacteristic
1345C2#6222811yescharacteristic
1346C2#6244111yescharacteristic
1347C2#6244811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39604C2semidirect
3. #32105C2semidirect
4. #32074C2semidirect
5. #31922C2semidirect
6. #31586C2semidirect
7. #31534C2semidirect
8. #31302C2semidirect
9. #30635C2semidirect
10. #30600C2semidirect
11. #28957C2semidirect
12. #28419C2semidirect
13. #28342C2semidirect
14. #28078C2semidirect
15. #27274C2semidirect
16. #27088C2semidirect
17. #26544C2semidirect
18. #26359C2semidirect
19. #26148C2semidirect
20. #25958C2semidirect
21. #25505C2semidirect
22. #25098C2semidirect
23. #24901C2semidirect
24. #24791C2semidirect
25. #24511C2semidirect
27. #23734C2semidirect
28. #23035C2semidirect
29. #22912C2semidirect
31. #21867C2semidirect
34. C2×#487C22semidirect
37. C2×#470C22semidirect
40. C2×#462C22semidirect
45. C2×#432C22semidirect
46. C2×#428C22semidirect
47. C2×#428C22semidirect
51. #2855C22semidirect
59. #2567C22semidirect
61. #2552C22semidirect
63. #2511C22semidirect
64. #2507C22semidirect
75. #2440C22semidirect
86. #2360C22semidirect
93. C2×#384C22semidirect
94. #2096C22semidirect
95. #2096C22semidirect
96. #2096C22semidirect
97. #2095C22semidirect
98. #2095C22semidirect
104. #2087C22semidirect
105. #2083C22semidirect
107. #2072C22semidirect
108. #2068C22semidirect
109. #2068C22semidirect
111. #2066C22semidirect
114. #2059C22semidirect
115. #2057C22semidirect
116. #2056C22semidirect
117. #2056C22semidirect
119. #2043C22semidirect
120. #2043C22semidirect
128. #2026C22semidirect
134. #1992C22semidirect
135. #1992C22semidirect
140. #1971C22semidirect
141. #1971C22semidirect
146. #1948C22semidirect
147. #1943C22semidirect
148. #1942C22semidirect
149. #1940C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
165. #1894C22semidirect
168. #1878C22semidirect
173. #1873C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
184. #1854C22semidirect
186. #1851C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
197. #1776C22semidirect
198. #1770C22semidirect
200. #1753C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#591032
#396042
#321052
#320742
#319222
#315862
#315342
#313022
#306352
#306002
#289572
#284192
#283422
#280782
#272742
#270882
#265442
#263592
#261482
#259582
#255052
#250982
#249012
#247912
#245112
#244522
#237342
#230352
#229122
#224192
#218672