Finite Group Databasebeta

← #6720762

Subgroups — #6720762

Order 512.

1771 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39863C211yesmaximal, characteristic, complemented
2#36235C211yesmaximal, characteristic, complemented
3#32984C211yesmaximal, characteristic, complemented
4#32047C211yesmaximal, characteristic, complemented
5#32034C211yesmaximal, characteristic, complemented
6#31848C211yesmaximal, characteristic, complemented
7#31775C211yesmaximal, characteristic, complemented
8#31740C211yesmaximal, characteristic, complemented
9#31726C211yesmaximal, characteristic, complemented
10#30715C211yesmaximal, characteristic, complemented
11#30635C211yesmaximal, characteristic, complemented
12#29735C211yesmaximal, characteristic, complemented
13#29600C211yesmaximal, characteristic, complemented
14#27400C211yesmaximal, characteristic, complemented
15#27341C211yesmaximal, characteristic, complemented
16#27261C211yesmaximal, characteristic, complemented
17#26928C211yesmaximal, characteristic, complemented
18#26720C211yesmaximal, characteristic, complemented
19#26239C211yesmaximal, characteristic, complemented
20#26205C211yesmaximal, characteristic, complemented
21#25995C211yesmaximal, characteristic, complemented
22#25568C211yesmaximal, characteristic, complemented
23#25540C211yesmaximal, characteristic, complemented
24#25538C211yesmaximal, characteristic, complemented
25#25109C211yesmaximal, characteristic, complemented
26#25083C211yesmaximal, characteristic, complemented
27#24874C211yesmaximal, characteristic, complemented
28#22921C211yesmaximal, characteristic, complemented
29#22490C211yesmaximal, characteristic, complemented
30#22028C211yesmaximal, characteristic, complemented
31#20908C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#555C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#487C2211yescharacteristic, complemented
37C2×#484C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#482C2211yescharacteristic, complemented
40C2×#483C2211yescharacteristic
41C2×#466C2211yescharacteristic, complemented
42C2×#465C2211yescharacteristic
43C2×#461C2211yescharacteristic, complemented
44C2×#449C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49#2850—21no—
50#2848C2211yescharacteristic
51#2847C2211yescharacteristic
52#2718—21no—
53#2710—21no—
54#2685—21no—
55#2670—21no—
56#2636—21no—
57#2610—21no—
58#2609—21no—
59#2603—21no—
60#2580—21no—
61#2542C2211yescharacteristic
62#2540C2211yescharacteristic
63#2500C2211yescharacteristic
64#2492C2211yescharacteristic
65#2491C2211yescharacteristic
66#2485C2211yescharacteristic
67#2476—21no—
68#2474—21no—
69#2472—21no—
70#2440C2211yescharacteristic
71#2439C2211yescharacteristic
72#2432C2211yescharacteristic
73#2429C2211yescharacteristic
74#2426C2211yescharacteristic
75#2424—21no—
76#2416C2211yescharacteristic
77#2415C2211yescharacteristic
78#2414C2211yescharacteristic
79#2414C2211yescharacteristic
80#2407C2211yescharacteristic
81#2363C2211yescharacteristic
82#2361C2211yescharacteristic
83#2354C2211yescharacteristic
84#2352C2211yescharacteristic
85#2346C2211yescharacteristic
86#2346C2211yescharacteristic
87#2326—21no—
88C4×#120C2211yescharacteristic
89#2290—21no—
90#2101C2211yescharacteristic, complemented
91#2095C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2074C2211yescharacteristic, complemented
97#2071C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2065C2211yescharacteristic, complemented
100#2058C2211yescharacteristic, complemented
101#2057C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2054C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2042C2211yescharacteristic, complemented
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic, complemented
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic, complemented
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic, complemented
119#2023C2211yescharacteristic, complemented
120#2023C2211yescharacteristic, complemented
121#2012C2211yescharacteristic, complemented
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#2000C2211yescharacteristic, complemented
128#1999C2211yescharacteristic
129#1999C2211yescharacteristic
130#1990C2211yescharacteristic, complemented
131#1988C2211yescharacteristic, complemented
132#1987C2211yescharacteristic, complemented
133#1983C2211yescharacteristic, complemented
134#1968C2211yescharacteristic, complemented
135#1958C2211yescharacteristic, complemented
136#1954C2211yescharacteristic
137#1954C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1934C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1925C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1923C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic, complemented
159#1892C2211yescharacteristic, complemented
160#1880C2211yescharacteristic, complemented
161#1879C2211yescharacteristic, complemented
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic, complemented
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic, complemented
174#1873C2211yescharacteristic, complemented
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1824C2211yescharacteristic
191#1823C2211yescharacteristic
192#1808C2211yescharacteristic
193#1803C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1779C2211yescharacteristic
196C4×#106C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#556—24no—
212#556—42no—
213#555—42no—
214#555—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225#525—24no—
226#525—42no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#120—21no—
246C2×#120—21no—
247C2×#120D411yescharacteristic
248C2×C4×Q8—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117—21no—
259C2×#117—21no—
260C2×#117—42no—
261C2×#117—42no—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4—21no—
272C22×C42—21no—
273#487—42no—
274#484—42no—
275#483—42no—
276#482—24no—
277#482—42no—
278#466—42no—
279#465—42no—
280#461—42no—
281#449—42no—
282C8×D4—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295#416—42no—
296#416—42no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
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×C22⋊C8—42no—
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340#400—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—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#393—21no—
366#393—21no—
367#393—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#391—21no—
373#391—21no—
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386D411yescharacteristic
427#386D411yescharacteristic
428#386D411yescharacteristic
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385D411yescharacteristic
438#385D411yescharacteristic
439#385D411yescharacteristic
440#384—21no—
441#384C2311yescharacteristic
442#382—21no—
443#382—21no—
444#382C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379D411yescharacteristic
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
466#376—21no—
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25C2×D411yescharacteristic
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#126—44no—
573#126—44no—
574#124—44no—
575#124—41no—
576#124—41no—
577#124—44no—
578#124—44no—
579#124—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—82no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—44no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—82no—
612#120—24no—
613#120—44no—
614#120—82no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—44no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—44no—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—44no—
637#117—44no—
638#117—44no—
639#117—41no—
640#117—41no—
641#117—41no—
642#117—41no—
643#117—41no—
644#117—41no—
645#117#4114yes—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—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—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—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—44no—
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—44no—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756#107—22no—
757#107—22no—
758#107—41no—
759#107—41no—
760#107—41no—
761#106—22no—
762#106—22no—
763#106—41no—
764#106—41no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C4×C8—41no—
808C4×C8—41no—
809C4×C8—41no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—22no—
841C24—22no—
842C24—21no—
843C24—21no—
844C24—41no—
845C24—41no—
846C24—41no—
847C24—41no—
848C24—41no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852C24C22×D411yescharacteristic
853#41—44no—
854#41—44no—
855#41—82no—
856#41—82no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
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—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—22no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C2×#4112yes—
992C22×C4H(5,𝔽2)12yes—
993C22×C4C2511yescharacteristic
994SD16—82no—
995SD16—82no—
996D8—82no—
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—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—82no—
1022C2×C8—82no—
1023C2×C8—82no—
1024C4⋊C4—22no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4C2×#4112yes—
1070C4⋊C4C2×#4112yes—
1071C4⋊C4H(5,𝔽2)12yes—
1072C4⋊C4H(5,𝔽2)12yes—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4#13514yes—
1125C42—24no—
1126C42—24no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—81no—
1142C42—81no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—44no—
1170C23—44no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—82no—
1186C23—82no—
1187C23—82no—
1188C23—82no—
1189C23—82no—
1190C23#54612yes—
1191C23C2×#13512yes—
1192C23C23×D411yescharacteristic
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—84no—
1202Q8—162no—
1203D4—44no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—82no—
1213D4—82no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—44no—
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—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4#54612yes—
1315C2×C4C2×#13512yes—
1316C2×C4C2×#13512yes—
1317C2×C4C22×#4111yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4#58511yescharacteristic
1322C2×C4#58511yescharacteristic
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—88no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22C2×#54611yescharacteristic
1375C22#348411yescharacteristic
1376C22#348511yescharacteristic
1377C22C22×#13511yescharacteristic
1378C22#358411yescharacteristic
1379C22#358511yescharacteristic
1380C22#358611yescharacteristic
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—41no—
1385C4—41no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—42no—
1392C4—42no—
1393C4—41no—
1394C4—42no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4#346011yescharacteristic
1406C4#350611yescharacteristic
1407C4#354211yescharacteristic
1408C4#354211yescharacteristic
1409C2—42no—
1410C2—42no—
1411C2—81no—
1412C2—81no—
1413C2—161no—
1414C2—161no—
1415C2#3777711yescharacteristic
1416C2#6112411yescharacteristic
1417C2#6118211yescharacteristic
1418C2#6156811yescharacteristic
1419C2#6162511yescharacteristic
1420C2#6170011yescharacteristic
1421C2#6175011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39863C2semidirect
2. #36235C2semidirect
3. #32984C2semidirect
4. #32047C2semidirect
5. #32034C2semidirect
6. #31848C2semidirect
7. #31775C2semidirect
8. #31740C2semidirect
9. #31726C2semidirect
10. #30715C2semidirect
11. #30635C2semidirect
12. #29735C2semidirect
13. #29600C2semidirect
14. #27400C2semidirect
15. #27341C2semidirect
16. #27261C2semidirect
17. #26928C2semidirect
18. #26720C2semidirect
19. #26239C2semidirect
20. #26205C2semidirect
21. #25995C2semidirect
22. #25568C2semidirect
23. #25540C2semidirect
24. #25538C2semidirect
25. #25109C2semidirect
26. #25083C2semidirect
27. #24874C2semidirect
28. #22921C2semidirect
29. #22490C2semidirect
30. #22028C2semidirect
31. #20908C2semidirect
36. C2×#487C22semidirect
39. C2×#482C22semidirect
41. C2×#466C22semidirect
43. C2×#461C22semidirect
90. #2101C22semidirect
91. #2095C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
96. #2074C22semidirect
97. #2071C22semidirect
98. #2068C22semidirect
99. #2065C22semidirect
100. #2058C22semidirect
101. #2057C22semidirect
102. #2055C22semidirect
103. #2054C22semidirect
104. #2043C22semidirect
105. #2043C22semidirect
106. #2042C22semidirect
110. #2036C22semidirect
112. #2035C22semidirect
114. #2034C22semidirect
118. #2033C22semidirect
119. #2023C22semidirect
120. #2023C22semidirect
121. #2012C22semidirect
126. #2000C22semidirect
127. #2000C22semidirect
130. #1990C22semidirect
131. #1988C22semidirect
132. #1987C22semidirect
133. #1983C22semidirect
134. #1968C22semidirect
135. #1958C22semidirect
138. #1949C22semidirect
139. #1942C22semidirect
140. #1934C22semidirect
141. #1934C22semidirect
142. #1934C22semidirect
143. #1933C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
146. #1925C22semidirect
147. #1925C22semidirect
152. #1921C22semidirect
153. #1921C22semidirect
154. #1920C22semidirect
155. #1918C22semidirect
158. #1892C22semidirect
159. #1892C22semidirect
160. #1880C22semidirect
161. #1879C22semidirect
164. #1875C22semidirect
173. #1873C22semidirect
174. #1873C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
186. #1854C22semidirect
189. #1825C22semidirect
193. #1803C22semidirect
196. C4×#106C22semidirect
197. C4×#103C22semidirect
198. C4×#102C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#398632
#362352
#329842
#320472
#320342
#318482
#317752
#317402
#317262
#307152
#306352
#297352
#296002
#274002
#273412
#272612
#269282
#267202
#262392
#262052
#259952
#255682
#255402
#255382
#251092
#250832
#248742
#229212
#224902
#220282
#209082