Finite Group Databasebeta

← #6909851

Subgroups — #6909851

Order 512.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1245 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38098C211yesmaximal, characteristic, complemented
2#37704C211yesmaximal, characteristic
3#32830C211yesmaximal, characteristic, complemented
4#32794C211yesmaximal, characteristic, complemented
5#31743C211yesmaximal, characteristic, complemented
6#31741C211yesmaximal, characteristic, complemented
7#31459C211yesmaximal, characteristic, complemented
8#31457C211yesmaximal, characteristic, complemented
9#30954C211yesmaximal, characteristic, complemented
10#30949C211yesmaximal, characteristic, complemented
11#30777C211yesmaximal, characteristic, complemented
12#30775C211yesmaximal, characteristic, complemented
13#30188C211yesmaximal, characteristic, complemented
14#30102C211yesmaximal, characteristic, complemented
15#30074C211yesmaximal, characteristic, complemented
16#29977C211yesmaximal, characteristic, complemented
17#29697C211yesmaximal, characteristic, complemented
18#29330C211yesmaximal, characteristic, complemented
19#29284C211yesmaximal, characteristic, complemented
20#26422C211yesmaximal, characteristic, complemented
21#26416C211yesmaximal, characteristic, complemented
22#26340C211yesmaximal, characteristic, complemented
23#26338C211yesmaximal, characteristic, complemented
24#26212C211yesmaximal, characteristic
25#26206C211yesmaximal, characteristic, complemented
26#26130C211yesmaximal, characteristic
27#26128C211yesmaximal, characteristic, complemented
28#25811C211yesmaximal, characteristic, complemented
29#24074C211yesmaximal, characteristic, complemented
30C2×#2058C211yesmaximal, characteristic, complemented
31#21997C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C22×#106C2211yescharacteristic
41C22×#106C2211yescharacteristic
42#2857C2211yescharacteristic
43#2850C2211yescharacteristic
44#2807—21no—
45#2792—21no—
46#2774—21no—
47#2731—21no—
48#2729—21no—
49#2729—21no—
50#2716—21no—
51#2674—21no—
52#2647C2211yescharacteristic
53#2640C2211yescharacteristic
54#2628C2211yescharacteristic
55#2628C2211yescharacteristic
56#2570C2211yescharacteristic
57#2564—21no—
58#2551C2211yescharacteristic
59#2505—21no—
60#2492C2211yescharacteristic
61#2491C2211yescharacteristic
62#2481—21no—
63#2452C2211yescharacteristic
64#2451C2211yescharacteristic
65#2449—21no—
66#2443—21no—
67#2442C2211yescharacteristic
68#2441C2211yescharacteristic
69#2440—21no—
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2436—21no—
73#2417C2211yescharacteristic
74#2416C2211yescharacteristic
75#2409—21no—
76#2361C2211yescharacteristic
77#2360C2211yescharacteristic
78#2352C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2331C2211yescharacteristic
81#2330C2211yescharacteristic
82#2317C2211yescharacteristic
83C2×#389C2211yescharacteristic
84#2290C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2101C2211yescharacteristic
92#2101C2211yescharacteristic
93#2096C2211yescharacteristic
94#2096C2211yescharacteristic
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2074C2211yescharacteristic
108#2073C2211yescharacteristic
109#2072C2211yescharacteristic
110#2071C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2058C2211yescharacteristic
125#2058C2211yescharacteristic
126#2058C2211yescharacteristic
127#2058C2211yescharacteristic
128#2058C2211yescharacteristic
129#2042C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2035C2211yescharacteristic
134#2035C2211yescharacteristic
135#2034C2211yescharacteristic
136#2034C2211yescharacteristic
137#2026C2211yescharacteristic
138#2025C2211yescharacteristic
139#2024C2211yescharacteristic
140#2023C2211yescharacteristic
141#1990C2211yescharacteristic
142#1990C2211yescharacteristic
143#1989C2211yescharacteristic
144#1989C2211yescharacteristic
145#1948C2211yescharacteristic
146#1948C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1875C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1873C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1840C2211yescharacteristic
192#1832C2211yescharacteristic
193#1825C2211yescharacteristic
194#1825C2211yescharacteristic
195#1818C2211yescharacteristic
196#1805C2211yescharacteristic
197#1804C2211yescharacteristic
198#1798C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8—21no—
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#542—42no—
207#542—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—42no—
212C2×C4⋊Q8—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#498—42no—
251#498—42no—
252#483—42no—
253#481—42no—
254#476—42no—
255#475—42no—
256C2×#106—42no—
257C2×#106—42no—
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#399—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#393—21no—
336#393—21no—
337#393—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386D411yescharacteristic
403#386D411yescharacteristic
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#385D411yescharacteristic
415#385D411yescharacteristic
416#384—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376C2311yescharacteristic
443C2×#95—21no—
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—44no—
497C22×Q8—82no—
498C22×Q8—82no—
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—82no—
543#126—44no—
544#125—22no—
545#125—41no—
546#124—41no—
547#124—41no—
548#124—44no—
549#124—82no—
550#123—44no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—41no—
555C22⋊Q8—44no—
556C22⋊Q8—82no—
557C22⋊Q8—82no—
558C22⋊Q8—82no—
559C22⋊Q8—82no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—41no—
564#121—82no—
565C4×Q8—22no—
566C4×Q8—41no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—82no—
572C4×D4—82no—
573#117—22no—
574#117—41no—
575#117—41no—
576#117—41no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
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⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—82no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—41no—
679C2×C42—41no—
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#103—22no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#102—22no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C4×C8—41no—
730C4×C8—41no—
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#95—21no—
766#95—21no—
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777C24—21no—
778C24C22×D411yescharacteristic
779C24C22×D411yescharacteristic
780C2×Q8—24no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8—816no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—81no—
819C2×D4—81no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C42−1+412yes—
882C22×C42−1+412yes—
883C22×C4C2511yescharacteristic
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—44no—
909C2×C8—44no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4H(5,𝔽2)12yes—
977C4⋊C4H(5,𝔽2)12yes—
978C4⋊C42−1+412yes—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—41no—
1018C42—41no—
1019C42—42no—
1020C42—42no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23#53612yes—
1044C23#57712yes—
1045C23#57712yes—
1046C23C23×D411yescharacteristic
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—84no—
1052Q8—84no—
1053Q8—84no—
1054Q8—84no—
1055Q8—162no—
1056Q8—162no—
1057D4—44no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—84no—
1063D4—162no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—44no—
1105C2×C4—44no—
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—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—84no—
1153C2×C4—84no—
1154C2×C4—84no—
1155C2×C4—162no—
1156C2×C4—162no—
1157C2×C4—162no—
1158C2×C4#53612yes—
1159C2×C4#57712yes—
1160C2×C4#57712yes—
1161C2×C4C2×H(5,𝔽2)11yescharacteristic
1162C2×C4C2×H(5,𝔽2)11yescharacteristic
1163C2×C4C2×2−1+411yescharacteristic
1164C2×C4C2×2−1+411yescharacteristic
1165C2×C4C2×2−1+411yescharacteristic
1166C2×C4#58511yescharacteristic
1167C8—41no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22#324414yes—
1196C22C2×#53611yescharacteristic
1197C22#348411yescharacteristic
1198C22#348911yescharacteristic
1199C22C2×#57711yescharacteristic
1200C22C2×#57711yescharacteristic
1201C22C2×#57711yescharacteristic
1202C22C2×#57711yescharacteristic
1203C4—22no—
1204C4—22no—
1205C4—22no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—42no—
1211C4—42no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—42no—
1217C4—41no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4#354111yescharacteristic
1231C4#354111yescharacteristic
1232C4#355211yescharacteristic
1233C4#355211yescharacteristic
1234C2—24no—
1235C2—81no—
1236C2—161no—
1237C2#4058911yescharacteristic
1238C2C2×#324411yescharacteristic
1239C2#6088111yescharacteristic
1240C2#6163111yescharacteristic
1241C2#6163311yescharacteristic
1242C2#6220211yescharacteristic
1243C2#6220511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2416C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38098C2semidirect
3. #32830C2semidirect
4. #32794C2semidirect
5. #31743C2semidirect
6. #31741C2semidirect
7. #31459C2semidirect
8. #31457C2semidirect
9. #30954C2semidirect
10. #30949C2semidirect
11. #30777C2semidirect
12. #30775C2semidirect
13. #30188C2semidirect
14. #30102C2semidirect
15. #30074C2semidirect
16. #29977C2semidirect
17. #29697C2semidirect
18. #29330C2semidirect
19. #29284C2semidirect
20. #26422C2semidirect
21. #26416C2semidirect
22. #26340C2semidirect
23. #26338C2semidirect
25. #26206C2semidirect
27. #26128C2semidirect
28. #25811C2semidirect
29. #24074C2semidirect
30. C2×#2058C2semidirect
31. #21997C2semidirect

Maximal subgroups

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

subgroupindex
#380982
#377042
#328302
#327942
#317432
#317412
#314592
#314572
#309542
#309492
#307772
#307752
#301882
#301022
#300742
#299772
#296972
#293302
#292842
#264222
#264162
#263402
#263382
#262122
#262062
#261302
#261282
#258112
#240742
C2×#20582
#219972