Finite Group Databasebeta

← #6474173

Subgroups — #6474173

Order 512.

1371 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37326C211yesmaximal, characteristic
2#37323C211yesmaximal, characteristic, complemented
3#33212C211yesmaximal, characteristic, complemented
4#33186C211yesmaximal, characteristic
5#33142C211yesmaximal, characteristic
6#33141C211yesmaximal, characteristic, complemented
7#30188C211yesmaximal, characteristic
8#30187C211yesmaximal, characteristic, complemented
9#29787C211yesmaximal, characteristic
10#29786C211yesmaximal, characteristic, complemented
11#29101C211yesmaximal, characteristic, complemented
12#29097C211yesmaximal, characteristic, complemented
13#29075C211yesmaximal, characteristic, complemented
14#29073C211yesmaximal, characteristic, complemented
15#29030C211yesmaximal, characteristic, complemented
16#29027C211yesmaximal, characteristic, complemented
17#29022C211yesmaximal, characteristic, complemented
18#29021C211yesmaximal, characteristic, complemented
19#28020C211yesmaximal, characteristic, complemented
20#28010C211yesmaximal, characteristic, complemented
21#28008C211yesmaximal, characteristic, complemented
22#27996C211yesmaximal, characteristic, complemented
23#26495C211yesmaximal, characteristic, complemented
24#26485C211yesmaximal, characteristic, complemented
25#26266C211yesmaximal, characteristic, complemented
26#26259C211yesmaximal, characteristic, complemented
27#22203C211yesmaximal, characteristic, complemented
28#22200C211yesmaximal, characteristic
29#21543C211yesmaximal, characteristic
30#21537C211yesmaximal, characteristic, complemented
31#20439C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#497C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×#424C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C2×#405C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2850C2211yescharacteristic
48#2810—21no—
49#2809—21no—
50#2807—21no—
51#2805—21no—
52#2798—21no—
53#2786—21no—
54#2783—21no—
55#2750—21no—
56#2747—21no—
57#2747—21no—
58#2728—21no—
59#2726—21no—
60#2723—21no—
61#2690—21no—
62#2690—21no—
63#2689—21no—
64#2625C2211yescharacteristic
65#2625C2211yescharacteristic
66#2625C2211yescharacteristic
67#2624C2211yescharacteristic
68#2512C2211yescharacteristic
69#2511C2211yescharacteristic
70#2511C2211yescharacteristic
71#2511C2211yescharacteristic
72#2509C2211yescharacteristic
73#2508C2211yescharacteristic
74#2506C2211yescharacteristic
75#2506C2211yescharacteristic
76#2452C2211yescharacteristic
77#2451C2211yescharacteristic
78#2451C2211yescharacteristic
79#2451C2211yescharacteristic
80#2448C2211yescharacteristic
81#2447C2211yescharacteristic
82#2446C2211yescharacteristic
83#2446C2211yescharacteristic
84#2324C2211yescharacteristic
85#2323C2211yescharacteristic
86#2323C2211yescharacteristic
87#2323C2211yescharacteristic
88#2296C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2100C2211yescharacteristic
92#2100C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2023C2211yescharacteristic
121#1990C2211yescharacteristic
122#1990C2211yescharacteristic
123#1973C2211yescharacteristic
124#1971C2211yescharacteristic
125#1971C2211yescharacteristic
126#1969C2211yescharacteristic
127#1969C2211yescharacteristic
128#1969C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1960C2211yescharacteristic
134#1959C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1944C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1926C2211yescharacteristic
161#1921C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1862C2211yescharacteristic
181#1847C2211yescharacteristic
182#1844C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#106C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1770C2211yescharacteristic
194#1770C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1729C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#124C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#500—42no—
233#497—42no—
234#470—24no—
235#470—24no—
236#468—24no—
237#468—24no—
238#440—42no—
239C4×Q16—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252#424—24no—
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281#405—24no—
282#405—42no—
283C4×M16—42no—
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#399—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389D411yescharacteristic
375#389D411yescharacteristic
376#389D411yescharacteristic
377#389D411yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
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#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385D411yescharacteristic
433#385D411yescharacteristic
434#385D411yescharacteristic
435#385D411yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382—21no—
440#382C2311yescharacteristic
441#381—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
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
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C2×M16#4114yes—
518C2×M16#4114yes—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539#126—82no—
540#125—82no—
541#125—82no—
542#124—41no—
543#124—41no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—82no—
551C22⋊Q8—82no—
552C22⋊Q8—82no—
553#121—22no—
554#121—22no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×D4—41no—
562C4×D4—41no—
563#117—22no—
564#117—22no—
565#117—41no—
566#117—41no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—41no—
654C2×C42—41no—
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663#107—22no—
664#107—22no—
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—41no—
674#106—41no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#97—22no—
704#97—22no—
705#97—22no—
706#97—22no—
707#97—41no—
708#97—41no—
709C4×C8—22no—
710C4×C8—22no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—41no—
714C4×C8—41no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
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#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24C22×D411yescharacteristic
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C2×#4112yes—
850C22×C4C2×#4112yes—
851C22×C4C2511yescharacteristic
852Q16—44no—
853Q16—82no—
854SD16—44no—
855SD16—82no—
856M16—28no—
857M16—44no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—44no—
877C2×C8—44no—
878C2×C8C2×#4112yes—
879C2×C8C2×#4112yes—
880C2×C8C2×#4112yes—
881C2×C8C2×#4112yes—
882C2×C8H(5,𝔽2)12yes—
883C2×C82−1+412yes—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—41no—
988C42—41no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23#53212yes—
1010C23C23×D411yescharacteristic
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—162no—
1024Q8—162no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—162no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4—162no—
1118C2×C4#53212yes—
1119C2×C4#57712yes—
1120C2×C4#57812yes—
1121C2×C4C22×#4111yescharacteristic
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C2×H(5,𝔽2)11yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C2×C4#58511yescharacteristic
1126C2×C4#58511yescharacteristic
1127C8—22no—
1128C8—22no—
1129C8—22no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8#53914yes—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22C2×#53211yescharacteristic
1150C22#349611yescharacteristic
1151C22#349711yescharacteristic
1152C22C2×#57711yescharacteristic
1153C22C2×#57811yescharacteristic
1154C22#358511yescharacteristic
1155C22#358611yescharacteristic
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4C2×#53911yescharacteristic
1185C4#345511yescharacteristic
1186C4#350511yescharacteristic
1187C4#350711yescharacteristic
1188C2—42no—
1189C2—161no—
1190C2#3500611yescharacteristic
1191C2#6072311yescharacteristic
1192C2#6072711yescharacteristic
1193C2#6231711yescharacteristic
1194C2#6231911yescharacteristic
1195C2#6240211yescharacteristic
1196C2#6240411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37323C2semidirect
3. #33212C2semidirect
6. #33141C2semidirect
8. #30187C2semidirect
10. #29786C2semidirect
11. #29101C2semidirect
12. #29097C2semidirect
13. #29075C2semidirect
14. #29073C2semidirect
15. #29030C2semidirect
16. #29027C2semidirect
17. #29022C2semidirect
18. #29021C2semidirect
19. #28020C2semidirect
20. #28010C2semidirect
21. #28008C2semidirect
22. #27996C2semidirect
23. #26495C2semidirect
24. #26485C2semidirect
25. #26266C2semidirect
26. #26259C2semidirect
27. #22203C2semidirect
30. #21537C2semidirect
31. #20439C2semidirect

Maximal subgroups

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

subgroupindex
#373262
#373232
#332122
#331862
#331422
#331412
#301882
#301872
#297872
#297862
#291012
#290972
#290752
#290732
#290302
#290272
#290222
#290212
#280202
#280102
#280082
#279962
#264952
#264852
#262662
#262592
#222032
#222002
#215432
#215372
#204392