Finite Group Databasebeta

← #6581564

Subgroups — #6581564

Order 512.

1379 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35968C211yesmaximal, characteristic
2#35868C211yesmaximal, characteristic, complemented
3#33284C211yesmaximal, characteristic
4#33075C211yesmaximal, characteristic, complemented
5#33039C211yesmaximal, characteristic
6#29022C211yesmaximal, characteristic, complemented
7#29018C211yesmaximal, characteristic, complemented
8#28052C211yesmaximal, characteristic, complemented
9#28049C211yesmaximal, characteristic, complemented
10#27758C211yesmaximal, characteristic
11#27732C211yesmaximal, characteristic, complemented
12#27554C211yesmaximal, characteristic, complemented
13#27553C211yesmaximal, characteristic, complemented
14#27367C211yesmaximal, characteristic, complemented
15#27360C211yesmaximal, characteristic, complemented
16#26766C211yesmaximal, characteristic, complemented
17#26765C211yesmaximal, characteristic, complemented
18#26541C211yesmaximal, characteristic
19#26522C211yesmaximal, characteristic, complemented
20#26173C211yesmaximal, characteristic, complemented
21#26169C211yesmaximal, characteristic, complemented
22#24826C211yesmaximal, characteristic, complemented
23#24747C211yesmaximal, characteristic
24#23013C211yesmaximal, characteristic, complemented
25#23013C211yesmaximal, characteristic, complemented
26#22997C211yesmaximal, characteristic
27#22973C211yesmaximal, characteristic, complemented
28#22765C211yesmaximal, characteristic, complemented
29#22759C211yesmaximal, characteristic, complemented
30#21679C211yesmaximal, characteristic, complemented
31#20505C211yesmaximal, characteristic, complemented
32C2×#479C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×#441C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41#2651—21no—
42#2647—21no—
43#2647C2211yescharacteristic
44#2641C2211yescharacteristic
45#2597—21no—
46#2593—21no—
47#2570—21no—
48#2570C2211yescharacteristic
49#2565C2211yescharacteristic
50#2552—21no—
51#2552C2211yescharacteristic
52#2548C2211yescharacteristic
53#2531—21no—
54#2526—21no—
55#2513C2211yescharacteristic
56#2512C2211yescharacteristic
57#2509—21no—
58#2509C2211yescharacteristic
59#2507—21no—
60#2507C2211yescharacteristic
61#2506—21no—
62#2506—21no—
63#2506C2211yescharacteristic
64#2506C2211yescharacteristic
65#2479—21no—
66#2468—21no—
67#2448C2211yescharacteristic
68#2448C2211yescharacteristic
69#2402—21no—
70#2402C2211yescharacteristic
71#2395—21no—
72#2370C2211yescharacteristic
73#2367C2211yescharacteristic
74#2367C2211yescharacteristic
75#2366C2211yescharacteristic
76#2357C2211yescharacteristic
77#2354C2211yescharacteristic
78#2351C2211yescharacteristic
79#2351C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81Q8×C4⋊C4C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84#2276C2211yescharacteristic
85#2276C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2074C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#1992C2211yescharacteristic
111#1991C2211yescharacteristic
112#1989C2211yescharacteristic
113#1982C2211yescharacteristic
114#1961C2211yescharacteristic
115#1959C2211yescharacteristic
116#1959C2211yescharacteristic
117#1957C2211yescharacteristic
118#1949C2211yescharacteristic
119#1948C2211yescharacteristic
120#1948C2211yescharacteristic
121#1948C2211yescharacteristic
122#1944C2211yescharacteristic
123#1943C2211yescharacteristic
124#1940C2211yescharacteristic
125#1940C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1916C2211yescharacteristic
153#1916C2211yescharacteristic
154#1916C2211yescharacteristic
155#1916C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1835C2211yescharacteristic
177#1834C2211yescharacteristic
178#1832C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1803C2211yescharacteristic
183#1803C2211yescharacteristic
184#1802C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#106C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191#1770C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#126—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228#479—24no—
229#464—24no—
230#464—24no—
231#460—24no—
232#441—24no—
233#441—24no—
234C4×Q16—24no—
235C4×SD16—24no—
236C4×SD16—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400D411yescharacteristic
296#400D411yescharacteristic
297#400D411yescharacteristic
298#400D411yescharacteristic
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398D411yescharacteristic
313#398D411yescharacteristic
314#398D411yescharacteristic
315#398D411yescharacteristic
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390—21no—
331#390—21no—
332#390—21no—
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
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#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#385—21no—
399#385—21no—
400#384—21no—
401#384—21no—
402#384—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#382—21no—
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446#376—21no—
447#376—21no—
448#376C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16#4114yes—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512#127—22no—
513#127—22no—
514#126—82no—
515#125—22no—
516#125—22no—
517#125—82no—
518#125—82no—
519#125—82no—
520#124—22no—
521#124—22no—
522#124—41no—
523#124—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8#4114yes—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—82no—
549#117—82no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
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×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—22no—
659#107—41no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—41no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—41no—
682#103—41no—
683#103#4114yes—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#97—22no—
699#97—22no—
700#97—41no—
701#97—41no—
702#97—41no—
703C4×C8—22no—
704C4×C8—22no—
705C4×C8—22no—
706C4×C8—22no—
707C4×C8—41no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C24—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8C2×#4112yes—
767C2×Q8C2×#4112yes—
768C2×Q8C2×#4112yes—
769C2×Q8C2×#4112yes—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—81no—
785C2×D4—81no—
786C2×D4—81no—
787C2×D4—81no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C2511yescharacteristic
823Q16—28no—
824SD16—44no—
825SD16—44no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×#4112yes—
849C2×C8C2×#4112yes—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4C2×#4112yes—
921C4⋊C4C2×#4112yes—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C42—24no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42C2×#4112yes—
975C422−1+412yes—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23C23×D411yescharacteristic
991Q8—22no—
992Q8—22no—
993Q8—22no—
994Q8—22no—
995Q8—22no—
996Q8—41no—
997Q8—41no—
998Q8#52914yes—
999D4—41no—
1000D4—41no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—41no—
1007D4—84no—
1008D4—162no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
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—84no—
1091C2×C4—162no—
1092C2×C4#54812yes—
1093C2×C4#54812yes—
1094C2×C4#57712yes—
1095C2×C4C22×#4111yescharacteristic
1096C2×C4C22×#4111yescharacteristic
1097C2×C4C22×#4111yescharacteristic
1098C2×C4C2×2−1+411yescharacteristic
1099C2×C4#58511yescharacteristic
1100C2×C4#58511yescharacteristic
1101C8—22no—
1102C8—22no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22C2×#54811yescharacteristic
1124C22D4×#4111yescharacteristic
1125C22D4×#4111yescharacteristic
1126C22C2×#57711yescharacteristic
1127C22#358411yescharacteristic
1128C22#358511yescharacteristic
1129C22#358611yescharacteristic
1130C4—24no—
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—42no—
1135C4—41no—
1136C4—41no—
1137C4—42no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4C2×#52911yescharacteristic
1159C4#351211yescharacteristic
1160C4#351511yescharacteristic
1161C4#351511yescharacteristic
1162C2—161no—
1163C2—161no—
1164C2#3611211yescharacteristic
1165C2#6132711yescharacteristic
1166C2#6133611yescharacteristic
1167C2#6152011yescharacteristic
1168C2#6153411yescharacteristic
1169C2#6153711yescharacteristic
1170C2#6154611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35868C2semidirect
4. #33075C2semidirect
6. #29022C2semidirect
7. #29018C2semidirect
8. #28052C2semidirect
9. #28049C2semidirect
11. #27732C2semidirect
12. #27554C2semidirect
13. #27553C2semidirect
14. #27367C2semidirect
15. #27360C2semidirect
16. #26766C2semidirect
17. #26765C2semidirect
19. #26522C2semidirect
20. #26173C2semidirect
21. #26169C2semidirect
22. #24826C2semidirect
24. #23013C2semidirect
25. #23013C2semidirect
27. #22973C2semidirect
28. #22765C2semidirect
29. #22759C2semidirect
30. #21679C2semidirect
31. #20505C2semidirect

Maximal subgroups

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

subgroupindex
#359682
#358682
#332842
#330752
#330392
#290222
#290182
#280522
#280492
#277582
#277322
#275542
#275532
#273672
#273602
#267662
#267652
#265412
#265222
#261732
#261692
#248262
#247472
#230132
#229972
#229732
#227652
#227592
#216792
#205052