Finite Group Databasebeta

← #7162136

Subgroups — #7162136

Order 512.

1581 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44955C211yesmaximal, characteristic
2#42672C211yesmaximal, characteristic, complemented
3#32181C211yesmaximal, characteristic, complemented
4#32174C211yesmaximal, characteristic, complemented
5#31652C211yesmaximal, characteristic, complemented
6#31637C211yesmaximal, characteristic, complemented
7#31012C211yesmaximal, characteristic, complemented
8#31007C211yesmaximal, characteristic, complemented
9#30537C211yesmaximal, characteristic, complemented
10#30531C211yesmaximal, characteristic, complemented
11#28899C211yesmaximal, characteristic, complemented
12#28881C211yesmaximal, characteristic, complemented
13#28745C211yesmaximal, characteristic, complemented
14#28428C211yesmaximal, characteristic, complemented
15#28411C211yesmaximal, characteristic, complemented
16#27786C211yesmaximal, characteristic, complemented
17#27247C211yesmaximal, characteristic, complemented
18#27245C211yesmaximal, characteristic, complemented
19#26471C211yesmaximal, characteristic, complemented
20#26332C211yesmaximal, characteristic, complemented
21#25732C211yesmaximal, characteristic
22#25643C211yesmaximal, characteristic, complemented
23#25369C211yesmaximal, characteristic, complemented
24#24917C211yesmaximal, characteristic, complemented
25#24904C211yesmaximal, characteristic, complemented
26#24664C211yesmaximal, characteristic, complemented
27#23768C211yesmaximal, characteristic, complemented
28#23194C211yesmaximal, characteristic, complemented
29#23059C211yesmaximal, characteristic, complemented
30#22548C211yesmaximal, characteristic, complemented
31#21813C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#492C2211yescharacteristic
36C2×#489C2211yescharacteristic, complemented
37C2×#488C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#474C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic, complemented
42C2×#462C2211yescharacteristic, complemented
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#446C2211yescharacteristic, complemented
48C2×#440C2211yescharacteristic
49C2×C4×Q16C2211yescharacteristic, complemented
50C2×#433C2211yescharacteristic
51#2838—21no—
52#2773—21no—
53#2762—21no—
54#2759—21no—
55#2755—21no—
56#2691—21no—
57#2685—21no—
58#2685—21no—
59#2672—21no—
60#2666—21no—
61#2655—21no—
62#2621C2211yescharacteristic
63#2568C2211yescharacteristic, complemented
64#2567C2211yescharacteristic, complemented
65#2565C2211yescharacteristic, complemented
66#2559—21no—
67#2550C2211yescharacteristic, complemented
68#2548C2211yescharacteristic
69#2548C2211yescharacteristic
70#2545C2211yescharacteristic
71#2544C2211yescharacteristic
72#2525—21no—
73#2514C2211yescharacteristic, complemented
74#2514C2211yescharacteristic, complemented
75#2492C2211yescharacteristic
76#2489C2211yescharacteristic
77#2476—21no—
78#2472—21no—
79#2448C2211yescharacteristic
80#2445C2211yescharacteristic
81#2435C2211yescharacteristic
82#2432C2211yescharacteristic
83#2423C2211yescharacteristic
84#2421C2211yescharacteristic
85#2411—21no—
86#2396C2211yescharacteristic
87#2367C2211yescharacteristic
88#2365C2211yescharacteristic, complemented
89#2355C2211yescharacteristic, complemented
90#2341C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2323C2211yescharacteristic
93#2314C2211yescharacteristic
94#2099C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic, complemented
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2016C2211yescharacteristic, complemented
123#2016C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic, complemented
130#2014C2211yescharacteristic
131#2014C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic
134#1985C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1982C2211yescharacteristic
139#1982C2211yescharacteristic
140#1981C2211yescharacteristic, complemented
141#1981C2211yescharacteristic, complemented
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic, complemented
145#1973C2211yescharacteristic, complemented
146#1971C2211yescharacteristic, complemented
147#1971C2211yescharacteristic, complemented
148#1969C2211yescharacteristic, complemented
149#1968C2211yescharacteristic
150#1961C2211yescharacteristic
151#1961C2211yescharacteristic
152#1960C2211yescharacteristic, complemented
153#1959C2211yescharacteristic
154#1959C2211yescharacteristic
155#1958C2211yescharacteristic
156#1958C2211yescharacteristic
157#1957C2211yescharacteristic
158#1949C2211yescharacteristic, complemented
159#1939C2211yescharacteristic, complemented
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic, complemented
162#1934C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic, complemented
166#1926C2211yescharacteristic, complemented
167#1925C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic
170#1924C2211yescharacteristic
171#1923C2211yescharacteristic
172#1917C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1878C2211yescharacteristic, complemented
179#1878C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#107C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215#556—24no—
216#556—42no—
217#535—24no—
218#535—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117C2311yescharacteristic
252C22×C22⋊C4—21no—
253#497—24no—
254#492—42no—
255#489—42no—
256#488—42no—
257#479—42no—
258#474—42no—
259#464—42no—
260#464—42no—
261#462—42no—
262#452—42no—
263#452—42no—
264#450—42no—
265#450—42no—
266#446—42no—
267#440—42no—
268C4×Q16—42no—
269#433—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
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×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#401—21no—
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#400D411yescharacteristic
340#399—21no—
341#399—21no—
342#399D411yescharacteristic
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398D411yescharacteristic
350#398D411yescharacteristic
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#396—21no—
357#396—21no—
358#396D411yescharacteristic
359#396D411yescharacteristic
360#395—21no—
361#395—21no—
362#395—21no—
363#395D411yescharacteristic
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#393—21no—
377#393D411yescharacteristic
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#390—21no—
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
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#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#383—21no—
450#383—21no—
451#382—21no—
452#382—21no—
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#380—21no—
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
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—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575#127—22no—
576#127—22no—
577#127—22no—
578#127—41no—
579#126—44no—
580#126—44no—
581#125—41no—
582#125—41no—
583#124—22no—
584#124—22no—
585#124—22no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—82no—
593#124#4114yes—
594#123—82no—
595C22⋊Q8—44no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602#121—44no—
603#121—44no—
604#120—44no—
605#120—44no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×D4—22no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622#117—22no—
623#117—22no—
624#117—44no—
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⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
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—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—22no—
723#107—22no—
724#107—41no—
725#107—41no—
726#106—41no—
727#106—41no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—22no—
775#97—22no—
776#97—41no—
777#97—41no—
778#97—41no—
779C4×C8—22no—
780C4×C8—22no—
781C4×C8—41no—
782#95—21no—
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#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840#41—82no—
841#41—82no—
842#41—82no—
843#41—82no—
844C2×Q8—22no—
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—21no—
858C2×Q8—21no—
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—41no—
869C2×Q8—41no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8C2×#4112yes—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—81no—
913C2×D4C2×#4112yes—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
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—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
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×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956Q16—44no—
957Q16—82no—
958Q16—82no—
959Q16—82no—
960SD16—44no—
961SD16—82no—
962SD16—82no—
963SD16—82no—
964SD16—82no—
965SD16—82no—
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—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8H(5,𝔽2)12yes—
989C2×C8H(5,𝔽2)12yes—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
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—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
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—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
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—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42C2×#4112yes—
1100C42H(5,𝔽2)12yes—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
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—41no—
1128C23—41no—
1129C23—84no—
1130C23—84no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—82no—
1154Q8—162no—
1155D4—22no—
1156D4—22no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
1168D4—84no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
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—21no—
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—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
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—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—162no—
1256C2×C4#54612yes—
1257C2×C4#54612yes—
1258C2×C4C22×#4111yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4#58511yescharacteristic
1263C2×C4#58511yescharacteristic
1264C8—22no—
1265C8—22no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—168no—
1301C22C2×#54611yescharacteristic
1302C22#348711yescharacteristic
1303C22#349811yescharacteristic
1304C22#358411yescharacteristic
1305C22#358511yescharacteristic
1306C22#358611yescharacteristic
1307C22#358611yescharacteristic
1308C4—22no—
1309C4—22no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4#351311yescharacteristic
1335C4#351411yescharacteristic
1336C4#354611yescharacteristic
1337C4#355811yescharacteristic
1338C2—81no—
1339C2—82no—
1340C2—161no—
1341C2—161no—
1342C2#4501811yescharacteristic
1343C2#6118011yescharacteristic
1344C2#6120711yescharacteristic
1345C2#6192511yescharacteristic
1346C2#6193911yescharacteristic
1347C2#6244211yescharacteristic
1348C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42672C2semidirect
3. #32181C2semidirect
4. #32174C2semidirect
5. #31652C2semidirect
6. #31637C2semidirect
7. #31012C2semidirect
8. #31007C2semidirect
9. #30537C2semidirect
10. #30531C2semidirect
11. #28899C2semidirect
12. #28881C2semidirect
13. #28745C2semidirect
14. #28428C2semidirect
15. #28411C2semidirect
16. #27786C2semidirect
17. #27247C2semidirect
18. #27245C2semidirect
19. #26471C2semidirect
20. #26332C2semidirect
22. #25643C2semidirect
23. #25369C2semidirect
24. #24917C2semidirect
25. #24904C2semidirect
26. #24664C2semidirect
27. #23768C2semidirect
28. #23194C2semidirect
29. #23059C2semidirect
30. #22548C2semidirect
36. C2×#489C22semidirect
38. C2×#479C22semidirect
41. C2×#464C22semidirect
42. C2×#462C22semidirect
47. C2×#446C22semidirect
49. C2×C4×Q16C22semidirect
63. #2568C22semidirect
64. #2567C22semidirect
65. #2565C22semidirect
67. #2550C22semidirect
73. #2514C22semidirect
74. #2514C22semidirect
88. #2365C22semidirect
89. #2355C22semidirect
94. #2099C22semidirect
95. #2095C22semidirect
96. #2093C22semidirect
98. #2085C22semidirect
101. #2074C22semidirect
102. #2073C22semidirect
104. #2068C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
113. #2042C22semidirect
119. #2025C22semidirect
120. #2024C22semidirect
122. #2016C22semidirect
123. #2016C22semidirect
129. #2015C22semidirect
134. #1985C22semidirect
140. #1981C22semidirect
141. #1981C22semidirect
144. #1973C22semidirect
145. #1973C22semidirect
146. #1971C22semidirect
147. #1971C22semidirect
148. #1969C22semidirect
152. #1960C22semidirect
158. #1949C22semidirect
159. #1939C22semidirect
161. #1935C22semidirect
162. #1934C22semidirect
163. #1933C22semidirect
165. #1926C22semidirect
166. #1926C22semidirect
172. #1917C22semidirect
173. #1916C22semidirect
176. #1880C22semidirect
177. #1878C22semidirect
178. #1878C22semidirect
179. #1878C22semidirect
180. #1878C22semidirect
185. #1863C22semidirect
186. #1805C22semidirect
188. #1803C22semidirect
193. #1776C22semidirect
194. C4×#107C22semidirect
195. #1771C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
201. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#449552
#426722
#321812
#321742
#316522
#316372
#310122
#310072
#305372
#305312
#288992
#288812
#287452
#284282
#284112
#277862
#272472
#272452
#264712
#263322
#257322
#256432
#253692
#249172
#249042
#246642
#237682
#231942
#230592
#225482
#218132