Finite Group Databasebeta

← #6624994

Subgroups — #6624994

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39602C211yesmaximal, characteristic, complemented
2#34211C211yesmaximal, characteristic, complemented
3#33152C211yesmaximal, characteristic, complemented
4#32967C211yesmaximal, characteristic, complemented
5#32962C211yesmaximal, characteristic, complemented
6#29118C211yesmaximal, characteristic, complemented
7#29115C211yesmaximal, characteristic, complemented
8#28128C211yesmaximal, characteristic, complemented
9#28126C211yesmaximal, characteristic
10#26916C211yesmaximal, characteristic, complemented
11#26906C211yesmaximal, characteristic, complemented
12#26901C211yesmaximal, characteristic, complemented
13#26891C211yesmaximal, characteristic, complemented
14#26783C211yesmaximal, characteristic, complemented
15#26776C211yesmaximal, characteristic, complemented
16#26766C211yesmaximal, characteristic, complemented
17#26761C211yesmaximal, characteristic, complemented
18#26471C211yesmaximal, characteristic, complemented
19#26469C211yesmaximal, characteristic, complemented
20#25859C211yesmaximal, characteristic, complemented
21#25326C211yesmaximal, characteristic, complemented
22#25326C211yesmaximal, characteristic, complemented
23#24215C211yesmaximal, characteristic
24#23225C211yesmaximal, characteristic, complemented
25#23218C211yesmaximal, characteristic, complemented
26#23005C211yesmaximal, characteristic, complemented
27#22999C211yesmaximal, characteristic, complemented
28#22626C211yesmaximal, characteristic, complemented
29C4×#482C211yesmaximal, characteristic, complemented
30#21462C211yesmaximal, characteristic, complemented
31#21458C211yesmaximal, characteristic
32C22×#124C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#479C2211yescharacteristic, complemented
40C2×#476C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#448C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#442C2211yescharacteristic
47C2×#440C2211yescharacteristic, complemented
48C2×C4×SD16C2211yescharacteristic, complemented
49C2×C4×D8C2211yescharacteristic
50#2851C2211yescharacteristic
51#2790—21no—
52#2784—21no—
53#2780—21no—
54#2720—21no—
55#2629C2211yescharacteristic
56#2628C2211yescharacteristic
57#2574—21no—
58#2566C2211yescharacteristic, complemented
59#2550C2211yescharacteristic, complemented
60#2509C2211yescharacteristic, complemented
61#2506C2211yescharacteristic, complemented
62#2505—21no—
63#2454—21no—
64#2454C2211yescharacteristic, complemented
65#2452C2211yescharacteristic, complemented
66#2450—21no—
67#2370C2211yescharacteristic, complemented
68#2367C2211yescharacteristic
69#2367C2211yescharacteristic
70#2367C2211yescharacteristic
71#2367C2211yescharacteristic
72#2367C2211yescharacteristic
73#2367C2211yescharacteristic
74#2367C2211yescharacteristic
75#2367C2211yescharacteristic
76#2349C2211yescharacteristic, complemented
77#2342—21no—
78#2342—21no—
79#2342—21no—
80#2342—21no—
81#2326—21no—
82#2326—21no—
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic
85#2310C2211yescharacteristic
86#2309C2211yescharacteristic
87C4×#124—21no—
88C4×#124—21no—
89C4×#121C2211yescharacteristic
90#2285C2211yescharacteristic
91C4×#117C2211yescharacteristic
92#2074C2211yescharacteristic, complemented
93#2074C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic, complemented
99#2065C2211yescharacteristic
100#2055C2211yescharacteristic, complemented
101#2055C2211yescharacteristic, complemented
102#2054C2211yescharacteristic
103#2054C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2024C2211yescharacteristic, complemented
113#2024C2211yescharacteristic, complemented
114#2012C2211yescharacteristic
115#2012C2211yescharacteristic
116#1989C2211yescharacteristic, complemented
117#1989C2211yescharacteristic, complemented
118#1983C2211yescharacteristic
119#1983C2211yescharacteristic
120#1958C2211yescharacteristic
121#1958C2211yescharacteristic
122#1949C2211yescharacteristic, complemented
123#1949C2211yescharacteristic, complemented
124#1939C2211yescharacteristic, complemented
125#1939C2211yescharacteristic, complemented
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1935C2211yescharacteristic, complemented
129#1935C2211yescharacteristic, complemented
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1933C2211yescharacteristic, complemented
133#1933C2211yescharacteristic, complemented
134#1928C2211yescharacteristic, complemented
135#1927C2211yescharacteristic, complemented
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic, complemented
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1920C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1917C2211yescharacteristic, complemented
147#1917C2211yescharacteristic, complemented
148#1916C2211yescharacteristic, complemented
149#1916C2211yescharacteristic, complemented
150#1880C2211yescharacteristic, complemented
151#1880C2211yescharacteristic, complemented
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1877C2211yescharacteristic, complemented
157#1877C2211yescharacteristic, complemented
158#1875C2211yescharacteristic
159#1865C2211yescharacteristic, complemented
160#1865C2211yescharacteristic, complemented
161#1865C2211yescharacteristic, complemented
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1863C2211yescharacteristic, complemented
166#1863C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic, complemented
180#1803C2211yescharacteristic, complemented
181#1798C2211yescharacteristic
182#1798C2211yescharacteristic
183#1797C2211yescharacteristic
184#1787C2211yescharacteristic
185#1787C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124—24no—
214C2×#124—24no—
215C2×#124—21no—
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C22⋊Q8—21no—
222C2×#121C2311yescharacteristic
223#519—42no—
224#519—42no—
225#518—42no—
226#518—42no—
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#488—24no—
255#488—24no—
256#482—24no—
257#479—42no—
258#479—42no—
259#476—42no—
260#474—42no—
261#463—24no—
262#463—24no—
263#448—24no—
264#447—24no—
265#442—42no—
266#440—42no—
267C4×SD16—42no—
268C4×D8—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#395—21no—
343#393—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#390—21no—
353#390—21no—
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
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#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384D411yescharacteristic
422#384D411yescharacteristic
423#384C2311yescharacteristic
424#382D411yescharacteristic
425#382D411yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#380—21no—
431#380—21no—
432#380D411yescharacteristic
433#380D411yescharacteristic
434#380D411yescharacteristic
435#380D411yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464#376—21no—
465C2×#95—21no—
466C43—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#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#125—22no—
555#125—22no—
556#125—41no—
557#125—41no—
558#125—82no—
559#124—28no—
560#124—28no—
561#124—22no—
562#124—22no—
563#124—22no—
564#124—22no—
565#124—22no—
566#124—22no—
567#124#4114yes—
568#124#4114yes—
569C22⋊Q8—82no—
570#121—22no—
571#121#4114yes—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—82no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—41no—
604#117—41no—
605#117—41no—
606#117—41no—
607#117—44no—
608#117—44no—
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⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C22⋊C4—28no—
653C2×C22⋊C4—28no—
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—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—21no—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—22no—
721#107—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768#97—41no—
769#97—41no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—41no—
773C4×C8—41no—
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#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813C24—24no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24C22×D411yescharacteristic
824C2×Q8—24no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—44no—
836C2×Q8—44no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—42no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8C2×#4112yes—
845C2×Q8C2×#4112yes—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4C2×#4112yes—
872C2×D4C2×#4112yes—
873C2×D4C2×#4112yes—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—24no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C2×#4112yes—
935C22×C42−1+412yes—
936C22×C4C2511yescharacteristic
937SD16—44no—
938SD16—44no—
939D8—44no—
940D8—44no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4C2×#4112yes—
1017C4⋊C4H(5,𝔽2)12yes—
1018C4⋊C4H(5,𝔽2)12yes—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C42—24no—
1059C42—22no—
1060C42—22no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42C2×#4112yes—
1084C42C2×#4112yes—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—48no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—84no—
1114C23—84no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23#54812yes—
1120C23C23×D411yescharacteristic
1121Q8—22no—
1122Q8—22no—
1123Q8—22no—
1124Q8—22no—
1125Q8—48no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—162no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—48no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—84no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—48no—
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—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—82no—
1226C2×C4—82no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4#52512yes—
1235C2×C4#52512yes—
1236C2×C4#54812yes—
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22C2×#52511yescharacteristic
1281C22C2×#54811yescharacteristic
1282C22#348411yescharacteristic
1283C22#358411yescharacteristic
1284C22#358411yescharacteristic
1285C22#358411yescharacteristic
1286C22#358511yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—42no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4#348111yescharacteristic
1314C4#348111yescharacteristic
1315C4#352011yescharacteristic
1316C4#352011yescharacteristic
1317C2—42no—
1318C2—82no—
1319C2—82no—
1320C2—82no—
1321C2#3652811yescharacteristic
1322C2#6055711yescharacteristic
1323C2#6058711yescharacteristic
1324C2#6133111yescharacteristic
1325C2#6134311yescharacteristic
1326C2#6166311yescharacteristic
1327C2#6169011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39602C2semidirect
2. #34211C2semidirect
3. #33152C2semidirect
4. #32967C2semidirect
5. #32962C2semidirect
6. #29118C2semidirect
7. #29115C2semidirect
8. #28128C2semidirect
10. #26916C2semidirect
11. #26906C2semidirect
12. #26901C2semidirect
13. #26891C2semidirect
14. #26783C2semidirect
15. #26776C2semidirect
16. #26766C2semidirect
17. #26761C2semidirect
18. #26471C2semidirect
19. #26469C2semidirect
20. #25859C2semidirect
21. #25326C2semidirect
22. #25326C2semidirect
24. #23225C2semidirect
25. #23218C2semidirect
26. #23005C2semidirect
27. #22999C2semidirect
28. #22626C2semidirect
29. C4×#482C2semidirect
30. #21462C2semidirect
38. C2×#479C22semidirect
39. C2×#479C22semidirect
47. C2×#440C22semidirect
48. C2×C4×SD16C22semidirect
58. #2566C22semidirect
59. #2550C22semidirect
60. #2509C22semidirect
61. #2506C22semidirect
64. #2454C22semidirect
65. #2452C22semidirect
67. #2370C22semidirect
76. #2349C22semidirect
92. #2074C22semidirect
93. #2074C22semidirect
96. #2068C22semidirect
98. #2066C22semidirect
100. #2055C22semidirect
101. #2055C22semidirect
112. #2024C22semidirect
113. #2024C22semidirect
116. #1989C22semidirect
117. #1989C22semidirect
122. #1949C22semidirect
123. #1949C22semidirect
124. #1939C22semidirect
125. #1939C22semidirect
128. #1935C22semidirect
129. #1935C22semidirect
132. #1933C22semidirect
133. #1933C22semidirect
134. #1928C22semidirect
135. #1927C22semidirect
137. #1926C22semidirect
139. #1925C22semidirect
140. #1921C22semidirect
141. #1921C22semidirect
142. #1920C22semidirect
143. #1920C22semidirect
144. #1919C22semidirect
145. #1918C22semidirect
146. #1917C22semidirect
147. #1917C22semidirect
148. #1916C22semidirect
149. #1916C22semidirect
150. #1880C22semidirect
151. #1880C22semidirect
156. #1877C22semidirect
157. #1877C22semidirect
159. #1865C22semidirect
160. #1865C22semidirect
161. #1865C22semidirect
165. #1863C22semidirect
166. #1863C22semidirect
167. #1863C22semidirect
179. #1803C22semidirect
180. #1803C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1770C22semidirect
193. C8×C4⋊C4C22semidirect
194. #1763C22semidirect
196. C4×#103C22semidirect
198. C4×#102C22semidirect
199. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#396022
#342112
#331522
#329672
#329622
#291182
#291152
#281282
#281262
#269162
#269062
#269012
#268912
#267832
#267762
#267662
#267612
#264712
#264692
#258592
#253262
#242152
#232252
#232182
#230052
#229992
#226262
C4×#4822
#214622
#214582