Finite Group Databasebeta

← #7574535

Subgroups — #7574535

Order 512.

1267 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45189C211yesmaximal, characteristic
2#35870C211yesmaximal, characteristic, complemented
3#32350C211yesmaximal, characteristic, complemented
4#32182C211yesmaximal, characteristic
5#31655C211yesmaximal, characteristic
6#30896C211yesmaximal, characteristic, complemented
7#29568C211yesmaximal, characteristic
8#29565C211yesmaximal, characteristic, complemented
9#29026C211yesmaximal, characteristic, complemented
10#28895C211yesmaximal, characteristic
11#28024C211yesmaximal, characteristic
12#27562C211yesmaximal, characteristic, complemented
13#27430C211yesmaximal, characteristic
14#27380C211yesmaximal, characteristic, complemented
15#27205C211yesmaximal, characteristic, complemented
16#27153C211yesmaximal, characteristic
17#27152C211yesmaximal, characteristic, complemented
18#27069C211yesmaximal, characteristic
19#27029C211yesmaximal, characteristic, complemented
20#26845C211yesmaximal, characteristic
21#26772C211yesmaximal, characteristic, complemented
22#26610C211yesmaximal, characteristic
23#26606C211yesmaximal, characteristic
24#26591C211yesmaximal, characteristic
25#23268C211yesmaximal, characteristic, complemented
26#23233C211yesmaximal, characteristic, complemented
27#23111C211yesmaximal, characteristic
28#23014C211yesmaximal, characteristic, complemented
29#22815C211yesmaximal, characteristic, complemented
30#21128C211yesmaximal, characteristic
31#21127C211yesmaximal, characteristic, complemented
32C2×#491C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#462C2211yescharacteristic
35C2×#441C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38#2773—21no—
39#2773—21no—
40#2770—21no—
41#2738—21no—
42#2655—21no—
43#2642C2211yescharacteristic
44#2590—21no—
45#2585—21no—
46#2575—21no—
47#2565C2211yescharacteristic
48#2546C2211yescharacteristic
49#2533—21no—
50#2533—21no—
51#2529—21no—
52#2529—21no—
53#2528—21no—
54#2524—21no—
55#2514C2211yescharacteristic
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2511C2211yescharacteristic
59#2509C2211yescharacteristic
60#2508C2211yescharacteristic
61#2495—21no—
62#2454C2211yescharacteristic
63#2453C2211yescharacteristic
64#2448C2211yescharacteristic
65#2448C2211yescharacteristic
66#2446C2211yescharacteristic
67#2446C2211yescharacteristic
68#2402—21no—
69#2402C2211yescharacteristic
70#2370C2211yescharacteristic
71#2370C2211yescharacteristic
72#2367C2211yescharacteristic
73#2365C2211yescharacteristic
74#2365C2211yescharacteristic
75#2365C2211yescharacteristic
76#2356C2211yescharacteristic
77#2356C2211yescharacteristic
78#2355C2211yescharacteristic
79#2351C2211yescharacteristic
80#2320C2211yescharacteristic
81#2319C2211yescharacteristic
82#2276C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2097C2211yescharacteristic
87#2084C2211yescharacteristic
88#2074C2211yescharacteristic
89#2074C2211yescharacteristic
90#2073C2211yescharacteristic
91#2068C2211yescharacteristic
92#2068C2211yescharacteristic
93#2066C2211yescharacteristic
94#2066C2211yescharacteristic
95#2066C2211yescharacteristic
96#2065C2211yescharacteristic
97#2059C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2055C2211yescharacteristic
101#2055C2211yescharacteristic
102#2043C2211yescharacteristic
103#2043C2211yescharacteristic
104#2043C2211yescharacteristic
105#2026C2211yescharacteristic
106#2026C2211yescharacteristic
107#2025C2211yescharacteristic
108#2016C2211yescharacteristic
109#2016C2211yescharacteristic
110#2015C2211yescharacteristic
111#2015C2211yescharacteristic
112#2013C2211yescharacteristic
113#2013C2211yescharacteristic
114#2013C2211yescharacteristic
115#1989C2211yescharacteristic
116#1981C2211yescharacteristic
117#1973C2211yescharacteristic
118#1973C2211yescharacteristic
119#1971C2211yescharacteristic
120#1971C2211yescharacteristic
121#1969C2211yescharacteristic
122#1968C2211yescharacteristic
123#1968C2211yescharacteristic
124#1960C2211yescharacteristic
125#1959C2211yescharacteristic
126#1949C2211yescharacteristic
127#1947C2211yescharacteristic
128#1943C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1846C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1770C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
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×D4C2311yescharacteristic
224#491—24no—
225#464—24no—
226#462—24no—
227#441—24no—
228#440—24no—
229C4×Q16—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#401—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400D411yescharacteristic
295#400D411yescharacteristic
296#400D411yescharacteristic
297#400D411yescharacteristic
298#399—21no—
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#398D411yescharacteristic
310#398D411yescharacteristic
311#398D411yescharacteristic
312#398D411yescharacteristic
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389—21no—
339#389—21no—
340#389—21no—
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#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
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#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#385—21no—
402#385—21no—
403#384C2311yescharacteristic
404#383—21no—
405#383—21no—
406#383—21no—
407#383—21no—
408#382—21no—
409#382—21no—
410#382—21no—
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#380—21no—
417#380—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⋊C4C2311yescharacteristic
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—
444#376—21no—
445#376—21no—
446#376—21no—
447#376C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C2×Q16—41no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522#125—22no—
523#125—41no—
524#125—41no—
525#125—41no—
526#124—22no—
527#124—41no—
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—41no—
544C4×D4—22no—
545C4×D4—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636#107—22no—
637#107—22no—
638#107—41no—
639#107—41no—
640#107—41no—
641#106—22no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646C4⋊C8—22no—
647C4⋊C8—22no—
648C4⋊C8—41no—
649C4⋊C8—41no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103#4114yes—
672#103#4114yes—
673#102—22no—
674#102—22no—
675#102—41no—
676#102—41no—
677#102—41no—
678#97—22no—
679#97—22no—
680#97—22no—
681#97—41no—
682#97—41no—
683C4×C8—22no—
684C4×C8—41no—
685C4×C8—41no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
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#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
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
753C24—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—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×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8C2×#4112yes—
777C2×Q8C2×#4112yes—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
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—42no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
817Q16—44no—
818Q16—44no—
819Q16—82no—
820SD16—44no—
821SD16—82no—
822SD16—82no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
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×C8C2×#4112yes—
846C2×C8C2×#4112yes—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
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—41no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
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—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4C2×#4112yes—
910C4⋊C4C2×#4112yes—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—42no—
939C42—42no—
940C42—42no—
941C42—42no—
942C42—42no—
943C42—42no—
944C42—42no—
945C42—42no—
946C42—42no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23C23×D411yescharacteristic
963Q8—22no—
964Q8—22no—
965Q8—22no—
966Q8—22no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971Q8—41no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978Q8—41no—
979D4—41no—
980D4—41no—
981D4—41no—
982D4—41no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
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—162no—
1071C2×C4C22×#4111yescharacteristic
1072C2×C4C22×#4111yescharacteristic
1073C2×C4#58511yescharacteristic
1074C2×C4#58511yescharacteristic
1075C2×C4#58511yescharacteristic
1076C2×C4#58511yescharacteristic
1077C8—22no—
1078C8—22no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C8—41no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22D4×#4111yescharacteristic
1093C22D4×#4111yescharacteristic
1094C22#348711yescharacteristic
1095C22#358411yescharacteristic
1096C22#358611yescharacteristic
1097C22#358611yescharacteristic
1098C22#358611yescharacteristic
1099C4—42no—
1100C4—42no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—42no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—42no—
1115C4—41no—
1116C4—41no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4#347511yescharacteristic
1129C4#349311yescharacteristic
1130C4#352111yescharacteristic
1131C4#356611yescharacteristic
1132C2—161no—
1133C2#5915711yescharacteristic
1134C2#6151211yescharacteristic
1135C2#6151211yescharacteristic
1136C2#6153011yescharacteristic
1137C2#6155011yescharacteristic
1138C2#6191811yescharacteristic
1139C2#6194611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
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. #35870C2semidirect
3. #32350C2semidirect
6. #30896C2semidirect
8. #29565C2semidirect
9. #29026C2semidirect
12. #27562C2semidirect
14. #27380C2semidirect
15. #27205C2semidirect
17. #27152C2semidirect
19. #27029C2semidirect
21. #26772C2semidirect
25. #23268C2semidirect
26. #23233C2semidirect
28. #23014C2semidirect
29. #22815C2semidirect
31. #21127C2semidirect

Maximal subgroups

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

subgroupindex
#451892
#358702
#323502
#321822
#316552
#308962
#295682
#295652
#290262
#288952
#280242
#275622
#274302
#273802
#272052
#271532
#271522
#270692
#270292
#268452
#267722
#266102
#266062
#265912
#232682
#232332
#231112
#230142
#228152
#211282
#211272