Finite Group Databasebeta

← #7000639

Subgroups — #7000639

Order 512.

1785 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59057C211yesmaximal, characteristic, complemented
2#39030C211yesmaximal, characteristic, complemented
3#32193C211yesmaximal, characteristic, complemented
4#32035C211yesmaximal, characteristic, complemented
5#31382C211yesmaximal, characteristic, complemented
6#31332C211yesmaximal, characteristic, complemented
7#30887C211yesmaximal, characteristic, complemented
8#30704C211yesmaximal, characteristic, complemented
9#30509C211yesmaximal, characteristic, complemented
10#30501C211yesmaximal, characteristic, complemented
11#29483C211yesmaximal, characteristic, complemented
12#29052C211yesmaximal, characteristic, complemented
13#28924C211yesmaximal, characteristic, complemented
14#28602C211yesmaximal, characteristic, complemented
15#27130C211yesmaximal, characteristic, complemented
16#27049C211yesmaximal, characteristic, complemented
17#27018C211yesmaximal, characteristic, complemented
18#26738C211yesmaximal, characteristic, complemented
19#26635C211yesmaximal, characteristic, complemented
20#25496C211yesmaximal, characteristic, complemented
21#25401C211yesmaximal, characteristic, complemented
22#25172C211yesmaximal, characteristic, complemented
23#25108C211yesmaximal, characteristic, complemented
24#24790C211yesmaximal, characteristic, complemented
25#24109C211yesmaximal, characteristic, complemented
26#23969C211yesmaximal, characteristic, complemented
27#23573C211yesmaximal, characteristic, complemented
28#23117C211yesmaximal, characteristic, complemented
29#23039C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#22180C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#532C2211yescharacteristic, complemented
34C2×#488C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic, complemented
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×#442C2211yescharacteristic
47C2×#435C2211yescharacteristic, complemented
48C2×C8×D4C2211yescharacteristic
49C2×#428C2211yescharacteristic, complemented
50C22×#102C2211yescharacteristic
51#2854C2211yescharacteristic
52#2779—21no—
53#2730—21no—
54#2730—21no—
55#2703—21no—
56#2697—21no—
57#2685—21no—
58#2648—21no—
59#2562C2211yescharacteristic
60#2548C2211yescharacteristic, complemented
61#2541C2211yescharacteristic
62#2540C2211yescharacteristic
63#2540C2211yescharacteristic, complemented
64#2537C2211yescharacteristic
65#2512C2211yescharacteristic
66#2497C2211yescharacteristic
67#2490—21no—
68#2490C2211yescharacteristic
69#2485C2211yescharacteristic
70#2467—21no—
71#2454—21no—
72#2454C2211yescharacteristic
73#2428—21no—
74#2427C2211yescharacteristic
75#2427C2211yescharacteristic, complemented
76#2424—21no—
77#2416C2211yescharacteristic
78#2416C2211yescharacteristic, complemented
79#2414C2211yescharacteristic
80#2408C2211yescharacteristic
81#2408C2211yescharacteristic
82#2407—21no—
83#2407—21no—
84#2369C2211yescharacteristic, complemented
85#2366—21no—
86#2363C2211yescharacteristic
87#2361C2211yescharacteristic
88#2361C2211yescharacteristic, complemented
89D4×C22⋊C4C2211yescharacteristic
90#2312—21no—
91C4×C22⋊Q8C2211yescharacteristic, complemented
92C4×#121C2211yescharacteristic
93C4×#121C2211yescharacteristic
94#2099C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2071C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2057C2211yescharacteristic, complemented
103#2054C2211yescharacteristic
104#2042C2211yescharacteristic, complemented
105#2041C2211yescharacteristic, complemented
106#2041C2211yescharacteristic, complemented
107#2036C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic, complemented
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic, complemented
114#2034C2211yescharacteristic, complemented
115#2034C2211yescharacteristic, complemented
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic, complemented
119#2025C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1999C2211yescharacteristic
133#1999C2211yescharacteristic
134#1989C2211yescharacteristic, complemented
135#1983C2211yescharacteristic, complemented
136#1973C2211yescharacteristic
137#1972C2211yescharacteristic
138#1970C2211yescharacteristic
139#1959C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1894C2211yescharacteristic, complemented
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic, complemented
167#1893C2211yescharacteristic, complemented
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic, complemented
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic
176#1875C2211yescharacteristic, complemented
177#1875C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1870C2211yescharacteristic
181#1869C2211yescharacteristic
182#1869C2211yescharacteristic
183#1869C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic, complemented
189#1862C2211yescharacteristic, complemented
190#1853C2211yescharacteristic
191#1852C2211yescharacteristic
192#1824C2211yescharacteristic
193#1823C2211yescharacteristic, complemented
194#1807C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#554—42no—
216#554—42no—
217#532—42no—
218#532—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127—21no—
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121D411yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268C22×C42C2311yescharacteristic
269#488—42no—
270#485—42no—
271#469—24no—
272#469—42no—
273#466—42no—
274#466—42no—
275#465—24no—
276#463—42no—
277#450—42no—
278#447—24no—
279#447—42no—
280#442—42no—
281#442—42no—
282#435—42no—
283C8×D4—42no—
284#428—42no—
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102—42no—
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×#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×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#400—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#391—21no—
375#391—21no—
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390D411yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389D411yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388D411yescharacteristic
419#388D411yescharacteristic
420#387—21no—
421#387—21no—
422#387—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#386—21no—
433#386—21no—
434#386D411yescharacteristic
435#386D411yescharacteristic
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#384C2311yescharacteristic
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380D411yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
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—44no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
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×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
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
541C23×C4C2411yescharacteristic
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582#127—41no—
583#127—41no—
584#127—44no—
585#126—82no—
586#125—41no—
587#125—41no—
588#125—44no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—44no—
594#123—82no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—42no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—44no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—82no—
626#121—82no—
627#121—82no—
628#120—82no—
629#120—82no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—44no—
647C4×D4—44no—
648C4×D4—82no—
649C4×D4—82no—
650C4×D4—82no—
651#117—41no—
652#117—41no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—44no—
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—41no—
755C2×C42—41no—
756C2×C42C2×D411yescharacteristic
757C2×C42C2×D411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—41no—
765#107—41no—
766#106—22no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—41no—
771#106—41no—
772C4⋊C8—22no—
773C4⋊C8—41no—
774#103—22no—
775#103—22no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102#4114yescomplemented
802C22⋊C8—22no—
803C22⋊C8—22no—
804C22⋊C8—22no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C22⋊C8—41no—
808C22⋊C8—41no—
809C22⋊C8—41no—
810#97—41no—
811#97—41no—
812#97—41no—
813C4×C8—22no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—42no—
846C24—42no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24C22×D411yescharacteristic
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855#41—816no—
856C2×Q8—24no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—21no—
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—41no—
896C2×D4—41no—
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—44no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—82no—
922C2×D4—82no—
923C2×D4—82no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4C2×#4112yes—
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—22no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C2511yescharacteristic
1007SD16—82no—
1008SD16—82no—
1009D8—44no—
1010D8—44no—
1011D8—82no—
1012D8—82no—
1013M16—44no—
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×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—82no—
1037C2×C8—82no—
1038C2×C8—82no—
1039C2×C8C2×#4112yes—
1040C2×C8H(5,𝔽2)12yes—
1041C4⋊C4—24no—
1042C4⋊C4—22no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4C2×#4112yes—
1084C4⋊C4H(5,𝔽2)12yes—
1085C4⋊C4H(5,𝔽2)12yes—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
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—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—41no—
1150C42—41no—
1151C42—42no—
1152C42—42no—
1153C42—81no—
1154C42—81no—
1155C42—81no—
1156C42—81no—
1157C42—81no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—84no—
1206C23—84no—
1207C23—162no—
1208C23—162no—
1209C23—162no—
1210C23—162no—
1211C23—162no—
1212C23#57512yes—
1213C23#57612yes—
1214C23C23×D411yescharacteristic
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—84no—
1220D4—22no—
1221D4—22no—
1222D4—44no—
1223D4—44no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—84no—
1239D4—82no—
1240D4—84no—
1241D4—84no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—84no—
1246D4—84no—
1247D4—162no—
1248D4—162no—
1249D4—162no—
1250D4—162no—
1251D4—162no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—44no—
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—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—82no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—162no—
1337C2×C4—162no—
1338C2×C4—162no—
1339C2×C4—162no—
1340C2×C4#57712yes—
1341C2×C4C22×#4111yescharacteristic
1342C2×C4C2×H(5,𝔽2)11yescharacteristic
1343C2×C4C2×H(5,𝔽2)11yescharacteristic
1344C2×C4C2×H(5,𝔽2)11yescharacteristic
1345C2×C4#58511yescharacteristic
1346C2×C4#58511yescharacteristic
1347C8—22no—
1348C8—22no—
1349C8—41no—
1350C8—41no—
1351C8—41no—
1352C8—41no—
1353C8—41no—
1354C8—41no—
1355C22—22no—
1356C22—22no—
1357C22—22no—
1358C22—22no—
1359C22—22no—
1360C22—22no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—42no—
1371C22—41no—
1372C22—42no—
1373C22—41no—
1374C22—42no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—81no—
1401C22—81no—
1402C22—81no—
1403C22—81no—
1404C22—168no—
1405C22D4×#4111yescharacteristic
1406C22#348411yescharacteristic
1407C22#349611yescharacteristic
1408C22C2×#57511yescharacteristic
1409C22C2×#57611yescharacteristic
1410C22C2×#57711yescharacteristic
1411C22#358511yescharacteristic
1412C4—22no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—42no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—41no—
1424C4—42no—
1425C4—42no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4—81no—
1433C4—81no—
1434C4—81no—
1435C4#350611yescharacteristic
1436C4#351911yescharacteristic
1437C4#354611yescharacteristic
1438C4#356211yescharacteristic
1439C2—42no—
1440C2—42no—
1441C2—81no—
1442C2—82no—
1443C2—161no—
1444C2—161no—
1445C2—161no—
1446C2#4301211yescharacteristic
1447C2#6145411yescharacteristic
1448C2#6149811yescharacteristic
1449C2#6159411yescharacteristic
1450C2#6160911yescharacteristic
1451C2#6225711yescharacteristic
1452C2#6235511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59057C2semidirect
2. #39030C2semidirect
3. #32193C2semidirect
4. #32035C2semidirect
5. #31382C2semidirect
6. #31332C2semidirect
7. #30887C2semidirect
8. #30704C2semidirect
9. #30509C2semidirect
10. #30501C2semidirect
11. #29483C2semidirect
12. #29052C2semidirect
13. #28924C2semidirect
14. #28602C2semidirect
15. #27130C2semidirect
16. #27049C2semidirect
17. #27018C2semidirect
18. #26738C2semidirect
19. #26635C2semidirect
20. #25496C2semidirect
21. #25401C2semidirect
22. #25172C2semidirect
23. #25108C2semidirect
24. #24790C2semidirect
25. #24109C2semidirect
26. #23969C2semidirect
27. #23573C2semidirect
28. #23117C2semidirect
29. #23039C2semidirect
30. #22858C2semidirect
31. #22180C2semidirect
33. C2×#532C22semidirect
34. C2×#488C22semidirect
35. C2×#485C22semidirect
47. C2×#435C22semidirect
49. C2×#428C22semidirect
60. #2548C22semidirect
63. #2540C22semidirect
75. #2427C22semidirect
78. #2416C22semidirect
84. #2369C22semidirect
88. #2361C22semidirect
91. C4×C22⋊Q8C22semidirect
94. #2099C22semidirect
95. #2075C22semidirect
96. #2071C22semidirect
98. #2067C22semidirect
100. #2059C22semidirect
101. #2058C22semidirect
102. #2057C22semidirect
104. #2042C22semidirect
105. #2041C22semidirect
106. #2041C22semidirect
109. #2035C22semidirect
113. #2034C22semidirect
114. #2034C22semidirect
115. #2034C22semidirect
118. #2033C22semidirect
119. #2025C22semidirect
134. #1989C22semidirect
135. #1983C22semidirect
139. #1959C22semidirect
140. #1948C22semidirect
141. #1944C22semidirect
142. #1943C22semidirect
144. #1935C22semidirect
146. #1927C22semidirect
151. #1926C22semidirect
154. #1924C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
162. #1894C22semidirect
166. #1893C22semidirect
167. #1893C22semidirect
169. #1892C22semidirect
176. #1875C22semidirect
177. #1875C22semidirect
183. #1869C22semidirect
184. #1865C22semidirect
186. #1863C22semidirect
188. #1862C22semidirect
189. #1862C22semidirect
193. #1823C22semidirect
194. #1807C22semidirect
195. C4×#106C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
199. #1753C22semidirect
201. #1749C22semidirect
202. C2×#336C22semidirect
801. #102#41semidirect

Maximal subgroups

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

subgroupindex
#590572
#390302
#321932
#320352
#313822
#313322
#308872
#307042
#305092
#305012
#294832
#290522
#289242
#286022
#271302
#270492
#270182
#267382
#266352
#254962
#254012
#251722
#251082
#247902
#241092
#239692
#235732
#231172
#230392
#228582
#221802