Finite Group Databasebeta

← #6537608

Subgroups — #6537608

Order 512.

1805 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37704C211yesmaximal, characteristic, complemented
2#34476C211yesmaximal, characteristic, complemented
3#30177C211yesmaximal, characteristic, complemented
4#30055C211yesmaximal, characteristic, complemented
5#29718C211yesmaximal, characteristic, complemented
6#29566C211yesmaximal, characteristic, complemented
7#29401C211yesmaximal, characteristic, complemented
8#29120C211yesmaximal, characteristic, complemented
9#28576C211yesmaximal, characteristic, complemented
10#27443C211yesmaximal, characteristic, complemented
11#27424C211yesmaximal, characteristic, complemented
12#27252C211yesmaximal, characteristic, complemented
13#27231C211yesmaximal, characteristic, complemented
14#26915C211yesmaximal, characteristic, complemented
15#26890C211yesmaximal, characteristic, complemented
16#26737C211yesmaximal, characteristic, complemented
17#26722C211yesmaximal, characteristic, complemented
18#26204C211yesmaximal, characteristic, complemented
19#26198C211yesmaximal, characteristic, complemented
20#24434C211yesmaximal, characteristic
21#24426C211yesmaximal, characteristic, complemented
22#24302C211yesmaximal, characteristic, complemented
23#23947C211yesmaximal, characteristic, complemented
24#23827C211yesmaximal, characteristic, complemented
25#23579C211yesmaximal, characteristic, complemented
26C2×#2023C211yesmaximal, characteristic, complemented
27#23134C211yesmaximal, characteristic, complemented
28#23128C211yesmaximal, characteristic, complemented
29#22870C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#22791C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic, complemented
34C22×C4⋊Q8C2211yescharacteristic
35C2×#477C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#467C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2850C2211yescharacteristic
48#2731—21no—
49#2729—21no—
50#2716—21no—
51#2674—21no—
52#2640C2211yescharacteristic, complemented
53#2628C2211yescharacteristic, complemented
54#2492C2211yescharacteristic, complemented
55#2491C2211yescharacteristic, complemented
56#2481—21no—
57#2452C2211yescharacteristic, complemented
58#2451C2211yescharacteristic, complemented
59#2443—21no—
60#2436—21no—
61#2417C2211yescharacteristic
62#2416C2211yescharacteristic
63#2409—21no—
64#2377—21no—
65#2376—21no—
66#2367C2211yescharacteristic
67#2361C2211yescharacteristic
68#2361C2211yescharacteristic
69#2360C2211yescharacteristic
70#2360C2211yescharacteristic
71#2358—21no—
72#2354C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74#2342—21no—
75#2341C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77#2335—21no—
78#2331C2211yescharacteristic, complemented
79#2326C2211yescharacteristic
80#2324—21no—
81#2324C2211yescharacteristic
82#2321—21no—
83#2319C2211yescharacteristic
84#2315—21no—
85#2311C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2290C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2075C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic, complemented
99#2057C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2054C2211yescharacteristic
104#2054C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic, complemented
108#2036C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic, complemented
112#2024C2211yescharacteristic, complemented
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#1999C2211yescharacteristic
129#1987C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1970C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1924C2211yescharacteristic, complemented
146#1923C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic, complemented
159#1880C2211yescharacteristic, complemented
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic, complemented
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic, complemented
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1840C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1818C2211yescharacteristic, complemented
187#1797C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1763C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196#1752C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1750C2211yescharacteristic, complemented
199#1746C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8—21no—
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—24no—
215#546—24no—
216#542—42no—
217#542—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—42no—
221C2×C4⋊Q8—42no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#126—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#477—42no—
268#477—42no—
269#467—24no—
270#465—24no—
271#452—42no—
272#450—24no—
273#449—42no—
274#447—24no—
275#440—42no—
276C4×D8—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102—42no—
297C2×#102—42no—
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#386D411yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385D411yescharacteristic
428#385D411yescharacteristic
429#384C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—44no—
508C22×Q8—82no—
509C22×Q8—82no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4#4114yes—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×Q16—22no—
541C2×Q16—41no—
542C2×Q16—41no—
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×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582#126—44no—
583#124—22no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—44no—
588#124—82no—
589#123—28no—
590#123—44no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—41no—
596C22⋊Q8—44no—
597C22⋊Q8—82no—
598C22⋊Q8#4114yes—
599#121—28no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—41no—
606#121—82no—
607#120—28no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—82no—
625C4×D4—82no—
626C4×D4—82no—
627#117—41no—
628#117—41no—
629#117—82no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—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—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—28no—
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—82no—
715C2×C22⋊C4—82no—
716C2×C22⋊C4—82no—
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#107—22no—
743#107—22no—
744#107—22no—
745#107—41no—
746#107—41no—
747#106—22no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—41no—
785#97—41no—
786C4×C8—41no—
787C4×C8—41no—
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#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—24no—
828C24—21no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837#41—82no—
838#41—82no—
839#41—82no—
840#41—82no—
841C2×Q8—24no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—816no—
865C2×Q8C2×#4112yes—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—24no—
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—44no—
889C2×D4—44no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4C2×#4112yes—
905C2×D4C2×#4112yes—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—22no—
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—21no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C2×#4112yes—
975C22×C4C2×#4112yes—
976C22×C4C2511yescharacteristic
977Q16—82no—
978SD16—44no—
979SD16—82no—
980SD16—82no—
981D8—44no—
982D8—82no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—82no—
1008C2×C8—82no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4C2×#4112yes—
1056C4⋊C4H(5,𝔽2)12yes—
1057C4⋊C4H(5,𝔽2)12yes—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—24no—
1062C22⋊C4—22no—
1063C22⋊C4—24no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—41no—
1113C42—41no—
1114C42—42no—
1115C42—42no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—22no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—48no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—84no—
1156C23—84no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23#52512yes—
1162C23#57612yes—
1163C23#57812yes—
1164C23C23×D411yescharacteristic
1165Q8—22no—
1166Q8—22no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—84no—
1174Q8—84no—
1175Q8—84no—
1176Q8—84no—
1177D4—22no—
1178D4—22no—
1179D4—22no—
1180D4—22no—
1181D4—44no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—162no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—44no—
1238C2×C4—44no—
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—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4#52512yes—
1288C2×C4#57712yes—
1289C2×C4C22×#4111yescharacteristic
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4#58511yescharacteristic
1294C2×C4#58511yescharacteristic
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—42no—
1313C22—41no—
1314C22—42no—
1315C22—42no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—168no—
1338C22#312414yes—
1339C22C2×#52511yescharacteristic
1340C22#348411yescharacteristic
1341C22#350011yescharacteristic
1342C22C2×#57611yescharacteristic
1343C22C2×#57711yescharacteristic
1344C22C2×#57811yescharacteristic
1345C22#358511yescharacteristic
1346C4—22no—
1347C4—22no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—42no—
1357C4—42no—
1358C4—41no—
1359C4—42no—
1360C4—41no—
1361C4—41no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4#350511yescharacteristic
1372C4#350511yescharacteristic
1373C4#351411yescharacteristic
1374C4#351411yescharacteristic
1375C2—24no—
1376C2—81no—
1377C2—82no—
1378C2—82no—
1379C2—161no—
1380C2#3570311yescharacteristic
1381C2C2×#312411yescharacteristic
1382C2#6059711yescharacteristic
1383C2#6160911yescharacteristic
1384C2#6163211yescharacteristic
1385C2#6255211yescharacteristic
1386C2#6260411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24434C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37704C2semidirect
2. #34476C2semidirect
3. #30177C2semidirect
4. #30055C2semidirect
5. #29718C2semidirect
6. #29566C2semidirect
7. #29401C2semidirect
8. #29120C2semidirect
9. #28576C2semidirect
10. #27443C2semidirect
11. #27424C2semidirect
12. #27252C2semidirect
13. #27231C2semidirect
14. #26915C2semidirect
15. #26890C2semidirect
16. #26737C2semidirect
17. #26722C2semidirect
18. #26204C2semidirect
19. #26198C2semidirect
21. #24426C2semidirect
22. #24302C2semidirect
23. #23947C2semidirect
24. #23827C2semidirect
25. #23579C2semidirect
26. C2×#2023C2semidirect
27. #23134C2semidirect
28. #23128C2semidirect
29. #22870C2semidirect
30. #22854C2semidirect
31. #22791C2semidirect
33. C2×#542C22semidirect
35. C2×#477C22semidirect
36. C2×#477C22semidirect
52. #2640C22semidirect
53. #2628C22semidirect
54. #2492C22semidirect
55. #2491C22semidirect
57. #2452C22semidirect
58. #2451C22semidirect
78. #2331C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2085C22semidirect
92. #2076C22semidirect
93. #2075C22semidirect
94. #2074C22semidirect
97. #2072C22semidirect
98. #2071C22semidirect
99. #2057C22semidirect
100. #2057C22semidirect
107. #2042C22semidirect
108. #2036C22semidirect
111. #2033C22semidirect
112. #2024C22semidirect
113. #2024C22semidirect
123. #2015C22semidirect
129. #1987C22semidirect
130. #1987C22semidirect
134. #1936C22semidirect
135. #1935C22semidirect
137. #1933C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
140. #1927C22semidirect
143. #1925C22semidirect
144. #1925C22semidirect
145. #1924C22semidirect
146. #1923C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
152. #1918C22semidirect
153. #1917C22semidirect
154. #1916C22semidirect
158. #1880C22semidirect
159. #1880C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
165. #1878C22semidirect
168. #1877C22semidirect
170. #1874C22semidirect
174. #1872C22semidirect
183. #1840C22semidirect
184. #1824C22semidirect
185. #1823C22semidirect
186. #1818C22semidirect
190. #1763C22semidirect
192. #1762C22semidirect
193. C4×#103C22semidirect
194. C4×#103C22semidirect
198. #1750C22semidirect
199. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#377042
#344762
#301772
#300552
#297182
#295662
#294012
#291202
#285762
#274432
#274242
#272522
#272312
#269152
#268902
#267372
#267222
#262042
#261982
#244342
#244262
#243022
#239472
#238272
#235792
C2×#20232
#231342
#231282
#228702
#228542
#227912