Finite Group Databasebeta

← #7011624

Subgroups — #7011624

Order 512.

1487 conjugacy classes of subgroups.

The subgroup lattice has 1301 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59402C211yesmaximal, characteristic, complemented
2#40169C211yesmaximal, characteristic
3#32349C211yesmaximal, characteristic, complemented
4#32223C211yesmaximal, characteristic, complemented
5#31992C211yesmaximal, characteristic, complemented
6#31631C211yesmaximal, characteristic, complemented
7#31407C211yesmaximal, characteristic, complemented
8#30996C211yesmaximal, characteristic, complemented
9#30858C211yesmaximal, characteristic, complemented
10#30420C211yesmaximal, characteristic
11#29067C211yesmaximal, characteristic, complemented
12#28920C211yesmaximal, characteristic, complemented
13#28918C211yesmaximal, characteristic, complemented
14#28582C211yesmaximal, characteristic, complemented
15#28232C211yesmaximal, characteristic, complemented
16#28010C211yesmaximal, characteristic, complemented
17#27559C211yesmaximal, characteristic, complemented
18#27338C211yesmaximal, characteristic, complemented
19#27073C211yesmaximal, characteristic, complemented
20#27042C211yesmaximal, characteristic, complemented
21#26591C211yesmaximal, characteristic, complemented
22#25331C211yesmaximal, characteristic, complemented
23#25156C211yesmaximal, characteristic, complemented
24#25136C211yesmaximal, characteristic
25#25105C211yesmaximal, characteristic, complemented
26#24655C211yesmaximal, characteristic, complemented
27#23700C211yesmaximal, characteristic, complemented
28#23000C211yesmaximal, characteristic, complemented
29#22906C211yesmaximal, characteristic, complemented
30#22580C211yesmaximal, characteristic, complemented
31#22191C211yesmaximal, characteristic, complemented
32C2×#491C2211yescharacteristic, complemented
33C2×#470C2211yescharacteristic
34C2×#470C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#464C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×C4×Q16C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#431C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47#2850C2211yescharacteristic
48#2779—21no—
49#2776—21no—
50#2772—21no—
51#2749—21no—
52#2735—21no—
53#2697—21no—
54#2636—21no—
55#2595—21no—
56#2594—21no—
57#2587—21no—
58#2566C2211yescharacteristic
59#2558—21no—
60#2538C2211yescharacteristic
61#2538C2211yescharacteristic
62#2518—21no—
63#2515—21no—
64#2512C2211yescharacteristic
65#2511C2211yescharacteristic, complemented
66#2506C2211yescharacteristic, complemented
67#2495C2211yescharacteristic
68#2494C2211yescharacteristic, complemented
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic
71#2480—21no—
72#2448C2211yescharacteristic
73#2435C2211yescharacteristic
74#2429C2211yescharacteristic
75#2429C2211yescharacteristic, complemented
76#2427C2211yescharacteristic
77#2421C2211yescharacteristic
78#2415C2211yescharacteristic
79#2408C2211yescharacteristic
80#2370—21no—
81#2367C2211yescharacteristic
82#2365C2211yescharacteristic, complemented
83#2362C2211yescharacteristic
84#2351C2211yescharacteristic, complemented
85#2347C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2321—21no—
88C4×C22⋊Q8C2211yescharacteristic, complemented
89C4×C22⋊Q8C2211yescharacteristic, complemented
90C4×#123C2211yescharacteristic
91C4×#121C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2093C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2016C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2013C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic, complemented
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1989C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1969C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1958C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1941C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic, complemented
166#1894C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1873C2211yescharacteristic
176#1870C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1854C2211yescharacteristic
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1825C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1786C2211yescharacteristic
194C4×#106C2211yescharacteristic, complemented
195C8×C4⋊C4C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123D411yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#120—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#491—42no—
242#470—42no—
243#470—42no—
244#468—24no—
245#468—42no—
246#464—24no—
247#464—42no—
248#461—42no—
249#450—42no—
250#450—42no—
251C4×Q16—42no—
252C4×SD16—42no—
253#436—42no—
254#431—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#418—24no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#401—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#399—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#392—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
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#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388D411yescharacteristic
397#388D411yescharacteristic
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387D411yescharacteristic
409#387D411yescharacteristic
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#383—21no—
426#383—21no—
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381D411yescharacteristic
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—41no—
552#126—82no—
553#125—41no—
554#125—41no—
555#125—44no—
556#124—22no—
557#124—41no—
558#124—41no—
559#124—41no—
560#123—42no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—41no—
577#120—44no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—82no—
595#117—22no—
596#117—41no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—82no—
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—41no—
704#107—41no—
705#107—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102#4114yes—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750#97—41no—
751C4×C8—22no—
752C4×C8—22no—
753C4×C8—41no—
754C4×C8—41no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—42no—
803C24—42no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24C22×D411yescharacteristic
810C24C22×D411yescharacteristic
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8H(5,𝔽2)12yes—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—42no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4C2×#4112yes—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—42no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C2511yescharacteristic
908Q16—44no—
909Q16—82no—
910SD16—44no—
911SD16—82no—
912SD16—82no—
913SD16—82no—
914M16—82no—
915M16—82no—
916M16—82no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8C2×#4112yes—
940C2×C8H(5,𝔽2)12yes—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4C2×#4112yes—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—84no—
1088C23—84no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23—162no—
1094C23C23×D411yescharacteristic
1095Q8—22no—
1096Q8—22no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107D4—22no—
1108D4—22no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—82no—
1116D4—84no—
1117D4—84no—
1118D4—162no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—44no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—82no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4#57512yes—
1208C2×C4#57712yes—
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C8—22no—
1216C8—22no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C22—41no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—42no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—168no—
1252C22D4×#4111yescharacteristic
1253C22#348811yescharacteristic
1254C22#349611yescharacteristic
1255C22C2×#57511yescharacteristic
1256C22C2×#57711yescharacteristic
1257C22#358411yescharacteristic
1258C22#358611yescharacteristic
1259C4—22no—
1260C4—22no—
1261C4—41no—
1262C4—42no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4#349311yescharacteristic
1286C4#351911yescharacteristic
1287C4#356011yescharacteristic
1288C4#356011yescharacteristic
1289C2—81no—
1290C2—81no—
1291C2—82no—
1292C2—161no—
1293C2#4303211yescharacteristic
1294C2#6144811yescharacteristic
1295C2#6155011yescharacteristic
1296C2#6200611yescharacteristic
1297C2#6204411yescharacteristic
1298C2#6226511yescharacteristic
1299C2#6230211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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. #59402C2semidirect
3. #32349C2semidirect
4. #32223C2semidirect
5. #31992C2semidirect
6. #31631C2semidirect
7. #31407C2semidirect
8. #30996C2semidirect
9. #30858C2semidirect
11. #29067C2semidirect
12. #28920C2semidirect
13. #28918C2semidirect
14. #28582C2semidirect
15. #28232C2semidirect
16. #28010C2semidirect
17. #27559C2semidirect
18. #27338C2semidirect
19. #27073C2semidirect
20. #27042C2semidirect
21. #26591C2semidirect
22. #25331C2semidirect
23. #25156C2semidirect
25. #25105C2semidirect
26. #24655C2semidirect
27. #23700C2semidirect
28. #23000C2semidirect
29. #22906C2semidirect
30. #22580C2semidirect
31. #22191C2semidirect
32. C2×#491C22semidirect
34. C2×#470C22semidirect
42. C2×C4×Q16C22semidirect
45. C2×#431C22semidirect
65. #2511C22semidirect
66. #2506C22semidirect
68. #2494C22semidirect
75. #2429C22semidirect
82. #2365C22semidirect
84. #2351C22semidirect
88. C4×C22⋊Q8C22semidirect
89. C4×C22⋊Q8C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2077C22semidirect
99. #2074C22semidirect
101. #2072C22semidirect
103. #2068C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
124. #2016C22semidirect
129. #2001C22semidirect
132. #1989C22semidirect
134. #1969C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1941C22semidirect
142. #1940C22semidirect
144. #1935C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
157. #1921C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
165. #1894C22semidirect
166. #1894C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
177. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
185. #1851C22semidirect
186. #1844C22semidirect
189. #1809C22semidirect
190. #1805C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
194. C4×#106C22semidirect
195. C8×C4⋊C4C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
201. #1753C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#594022
#401692
#323492
#322232
#319922
#316312
#314072
#309962
#308582
#304202
#290672
#289202
#289182
#285822
#282322
#280102
#275592
#273382
#270732
#270422
#265912
#253312
#251562
#251362
#251052
#246552
#237002
#230002
#229062
#225802
#221912