Finite Group Databasebeta

← #7028379

Subgroups — #7028379

Order 512.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59401C211yesmaximal, characteristic, complemented
2#59094C211yesmaximal, characteristic, complemented
3#32176C211yesmaximal, characteristic, complemented
4#31815C211yesmaximal, characteristic, complemented
5#31408C211yesmaximal, characteristic, complemented
6#31298C211yesmaximal, characteristic, complemented
7#31189C211yesmaximal, characteristic, complemented
8#30934C211yesmaximal, characteristic, complemented
9#30471C211yesmaximal, characteristic, complemented
10#30468C211yesmaximal, characteristic, complemented
11#29037C211yesmaximal, characteristic, complemented
12#28117C211yesmaximal, characteristic, complemented
13#27343C211yesmaximal, characteristic, complemented
14#27116C211yesmaximal, characteristic, complemented
15#26982C211yesmaximal, characteristic, complemented
16#26944C211yesmaximal, characteristic, complemented
17#26781C211yesmaximal, characteristic, complemented
18#26629C211yesmaximal, characteristic, complemented
19#26602C211yesmaximal, characteristic, complemented
20#26380C211yesmaximal, characteristic, complemented
21#24912C211yesmaximal, characteristic, complemented
22#24737C211yesmaximal, characteristic, complemented
23#24491C211yesmaximal, characteristic, complemented
24#24444C211yesmaximal, characteristic, complemented
25#24245C211yesmaximal, characteristic, complemented
26#24151C211yesmaximal, characteristic, complemented
27#23574C211yesmaximal, characteristic, complemented
28#23195C211yesmaximal, characteristic, complemented
29#22883C211yesmaximal, characteristic, complemented
30#22359C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#483C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#469C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#461C2211yescharacteristic, complemented
42C2×#449C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#440C2211yescharacteristic, complemented
47C2×#440C2211yescharacteristic, complemented
48C2×C4×SD16C2211yescharacteristic, complemented
49C2×C4×D8C2211yescharacteristic
50C2×#417C2211yescharacteristic
51#2786—21no—
52#2778—21no—
53#2711—21no—
54#2707—21no—
55#2600—21no—
56#2576—21no—
57#2545C2211yescharacteristic
58#2535—21no—
59#2535C2211yescharacteristic
60#2513C2211yescharacteristic, complemented
61#2508C2211yescharacteristic, complemented
62#2494C2211yescharacteristic
63#2491C2211yescharacteristic
64#2472—21no—
65#2464—21no—
66#2458—21no—
67#2452C2211yescharacteristic
68#2448C2211yescharacteristic
69#2444—21no—
70#2437—21no—
71#2435C2211yescharacteristic
72#2432C2211yescharacteristic
73#2428C2211yescharacteristic
74#2428C2211yescharacteristic, complemented
75#2426—21no—
76#2426C2211yescharacteristic
77#2420C2211yescharacteristic, complemented
78#2417C2211yescharacteristic
79#2416C2211yescharacteristic
80#2411—21no—
81#2367C2211yescharacteristic
82#2366C2211yescharacteristic, complemented
83#2364—21no—
84#2361C2211yescharacteristic, complemented
85#2360C2211yescharacteristic
86#2349C2211yescharacteristic, complemented
87#2345C2211yescharacteristic, complemented
88#2342—21no—
89#2341C2211yescharacteristic
90C4×#123C2211yescharacteristic
91C4×#121C2211yescharacteristic
92C4×#121C2211yescharacteristic
93C2×#390C2211yescharacteristic
94#2101C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic, complemented
123#2013C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2011C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic, complemented
132#2000C2211yescharacteristic, complemented
133#1999C2211yescharacteristic
134#1987C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1982C2211yescharacteristic, complemented
137#1981C2211yescharacteristic, complemented
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic
143#1954C2211yescharacteristic
144#1941C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1924C2211yescharacteristic, complemented
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1895C2211yescharacteristic, complemented
167#1894C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1870C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic, complemented
189#1851C2211yescharacteristic, complemented
190#1824C2211yescharacteristic
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1797C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#546—42no—
215#546—42no—
216#533—42no—
217#533—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#125—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42C2311yescharacteristic
264#496—24no—
265#483—42no—
266#481—42no—
267#476—42no—
268#469—42no—
269#463—42no—
270#463—42no—
271#461—42no—
272#449—24no—
273#449—42no—
274#447—24no—
275#447—42no—
276#440—42no—
277#440—42no—
278C4×SD16—42no—
279C4×D8—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293#417—42no—
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×#102C2311yescharacteristic
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×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#401—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—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#394—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388D411yescharacteristic
412#388D411yescharacteristic
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386D411yescharacteristic
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385D411yescharacteristic
442#382—21no—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381—21no—
446#381D411yescharacteristic
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C2×#95—21no—
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—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
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×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8#4114yes—
565C2×M16—41no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#127—22no—
581#127—41no—
582#125—44no—
583#124—22no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—82no—
590#123—42no—
591#123—44no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—44no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—82no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—44no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—44no—
610#121—41no—
611#121—41no—
612#121—82no—
613#121—82no—
614#120—44no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—44no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—82no—
635C4×D4—82no—
636C4×D4—82no—
637C4×D4—82no—
638#117—44no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—22no—
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—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—41no—
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⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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×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—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—44no—
721C2×C22⋊C4—44no—
722C2×C22⋊C4—82no—
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—41no—
739C2×C42—41no—
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#107—22no—
748#107—41no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106—41no—
753#106—41no—
754#106—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799#97—22no—
800#97—41no—
801#97—41no—
802C4×C8—41no—
803C4×C8—41no—
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#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851#41—44no—
852#41—82no—
853#41—82no—
854#41—82no—
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—42no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8H(5,𝔽2)12yes—
870C2×D4—22no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
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—21no—
892C2×D4—21no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4C2×#4112yes—
927C2×D4C2×#4112yes—
928C22×C4—22no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—22no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
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—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—81no—
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×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C2511yescharacteristic
995SD16—44no—
996SD16—44no—
997SD16—44no—
998SD16—82no—
999D8—44no—
1000D8—82no—
1001D8—82no—
1002D8—82no—
1003M16—82no—
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—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8C2×#4112yes—
1028C4⋊C4—24no—
1029C4⋊C4—22no—
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—42no—
1059C4⋊C4—42no—
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⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4H(5,𝔽2)12yes—
1071C4⋊C4H(5,𝔽2)12yes—
1072C22⋊C4—24no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
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—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
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—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—41no—
1134C42—41no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—81no—
1139C42—81no—
1140C42—81no—
1141C42—81no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—22no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—84no—
1184C23—84no—
1185C23—84no—
1186C23—84no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23#57712yes—
1191C23C23×D411yescharacteristic
1192Q8—22no—
1193Q8—22no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—84no—
1201D4—22no—
1202D4—22no—
1203D4—22no—
1204D4—22no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—82no—
1218D4—84no—
1219D4—84no—
1220D4—84no—
1221D4—84no—
1222D4—84no—
1223D4—84no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
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—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—44no—
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—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—82no—
1308C2×C4—84no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4—162no—
1316C2×C4#57512yes—
1317C2×C4C22×#4111yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4#58511yescharacteristic
1322C2×C4#58511yescharacteristic
1323C8—22no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—42no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—42no—
1348C22—42no—
1349C22—41no—
1350C22—41no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—168no—
1374C22D4×#4111yescharacteristic
1375C22#348411yescharacteristic
1376C22#348811yescharacteristic
1377C22C2×#57511yescharacteristic
1378C22C2×#57711yescharacteristic
1379C22#358511yescharacteristic
1380C22#358511yescharacteristic
1381C4—22no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—42no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—42no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—42no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4#350511yescharacteristic
1406C4#351911yescharacteristic
1407C4#353311yescharacteristic
1408C4#354611yescharacteristic
1409C2—42no—
1410C2—81no—
1411C2—82no—
1412C2—82no—
1413C2—161no—
1414C2—161no—
1415C2#4311111yescharacteristic
1416C2#6146411yescharacteristic
1417C2#6152211yescharacteristic
1418C2#6159411yescharacteristic
1419C2#6165311yescharacteristic
1420C2#6197011yescharacteristic
1421C2#6201611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #59401C2semidirect
2. #59094C2semidirect
3. #32176C2semidirect
4. #31815C2semidirect
5. #31408C2semidirect
6. #31298C2semidirect
7. #31189C2semidirect
8. #30934C2semidirect
9. #30471C2semidirect
10. #30468C2semidirect
11. #29037C2semidirect
12. #28117C2semidirect
13. #27343C2semidirect
14. #27116C2semidirect
15. #26982C2semidirect
16. #26944C2semidirect
17. #26781C2semidirect
18. #26629C2semidirect
19. #26602C2semidirect
20. #26380C2semidirect
21. #24912C2semidirect
22. #24737C2semidirect
23. #24491C2semidirect
24. #24444C2semidirect
25. #24245C2semidirect
26. #24151C2semidirect
27. #23574C2semidirect
28. #23195C2semidirect
29. #22883C2semidirect
30. #22359C2semidirect
31. #22046C2semidirect
36. C2×#483C22semidirect
37. C2×#476C22semidirect
41. C2×#461C22semidirect
46. C2×#440C22semidirect
47. C2×#440C22semidirect
48. C2×C4×SD16C22semidirect
60. #2513C22semidirect
61. #2508C22semidirect
74. #2428C22semidirect
77. #2420C22semidirect
82. #2366C22semidirect
84. #2361C22semidirect
86. #2349C22semidirect
87. #2345C22semidirect
94. #2101C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2075C22semidirect
99. #2074C22semidirect
100. #2066C22semidirect
101. #2066C22semidirect
105. #2065C22semidirect
106. #2057C22semidirect
110. #2043C22semidirect
119. #2034C22semidirect
121. #2023C22semidirect
122. #2014C22semidirect
123. #2013C22semidirect
131. #2000C22semidirect
132. #2000C22semidirect
134. #1987C22semidirect
136. #1982C22semidirect
137. #1981C22semidirect
140. #1968C22semidirect
144. #1941C22semidirect
145. #1939C22semidirect
149. #1935C22semidirect
151. #1934C22semidirect
152. #1927C22semidirect
159. #1924C22semidirect
160. #1924C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
166. #1895C22semidirect
167. #1894C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
177. #1877C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
183. #1865C22semidirect
185. #1864C22semidirect
186. #1862C22semidirect
188. #1853C22semidirect
189. #1851C22semidirect
191. #1805C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#594012
#590942
#321762
#318152
#314082
#312982
#311892
#309342
#304712
#304682
#290372
#281172
#273432
#271162
#269822
#269442
#267812
#266292
#266022
#263802
#249122
#247372
#244912
#244442
#242452
#241512
#235742
#231952
#228832
#223592
#220462