Finite Group Databasebeta

← #6436438

Subgroups — #6436438

Order 512.

1268 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35345C211yesmaximal, characteristic, complemented
2#35269C211yesmaximal, characteristic
3#30387C211yesmaximal, characteristic, complemented
4#30386C211yesmaximal, characteristic, complemented
5#30381C211yesmaximal, characteristic, complemented
6#30380C211yesmaximal, characteristic, complemented
7#30375C211yesmaximal, characteristic, complemented
8#30373C211yesmaximal, characteristic
9#30371C211yesmaximal, characteristic, complemented
10#30369C211yesmaximal, characteristic
11#30307C211yesmaximal, characteristic, complemented
12#30282C211yesmaximal, characteristic, complemented
13#30235C211yesmaximal, characteristic, complemented
14#30217C211yesmaximal, characteristic, complemented
15#29882C211yesmaximal, characteristic, complemented
16#29882C211yesmaximal, characteristic, complemented
17#29850C211yesmaximal, characteristic
18#29849C211yesmaximal, characteristic
19#23793C211yesmaximal, characteristic, complemented
20#23792C211yesmaximal, characteristic, complemented
21#23791C211yesmaximal, characteristic, complemented
22#23790C211yesmaximal, characteristic, complemented
23#23765C211yesmaximal, characteristic, complemented
24#23764C211yesmaximal, characteristic
25#23759C211yesmaximal, characteristic, complemented
26#23758C211yesmaximal, characteristic
27#21723C211yesmaximal, characteristic, complemented
28#21722C211yesmaximal, characteristic, complemented
29#21643C211yesmaximal, characteristic, complemented
30#21643C211yesmaximal, characteristic, complemented
31#20468C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#433C2211yescharacteristic
37C2×#433C2211yescharacteristic
38#2864C2211yescharacteristic
39#2864C2211yescharacteristic
40#2863C2211yescharacteristic
41#2861C2211yescharacteristic
42#2860C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2629C2211yescharacteristic
47#2629C2211yescharacteristic
48#2629C2211yescharacteristic
49#2629C2211yescharacteristic
50#2629C2211yescharacteristic
51#2625C2211yescharacteristic
52#2624C2211yescharacteristic
53#2620C2211yescharacteristic
54#2608—21no—
55#2608—21no—
56#2608—21no—
57#2608—21no—
58#2606—21no—
59#2606—21no—
60#2606—21no—
61#2606—21no—
62#2525—21no—
63#2522—21no—
64#2519—21no—
65#2518—21no—
66#2518—21no—
67#2515—21no—
68#2466—21no—
69#2460—21no—
70#2330C2211yescharacteristic
71#2330C2211yescharacteristic
72#2330C2211yescharacteristic
73#2330C2211yescharacteristic
74#2330C2211yescharacteristic
75#2326C2211yescharacteristic
76#2320C2211yescharacteristic
77#2319C2211yescharacteristic
78C4×C22⋊Q8C2211yescharacteristic
79C4×#121C2211yescharacteristic
80#2283C2211yescharacteristic
81#2283C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2096C2211yescharacteristic
94#2095C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2088C2211yescharacteristic
102#2088C2211yescharacteristic
103#2087C2211yescharacteristic
104#2087C2211yescharacteristic
105#2086C2211yescharacteristic
106#2086C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2077C2211yescharacteristic
112#2077C2211yescharacteristic
113#2077C2211yescharacteristic
114#2077C2211yescharacteristic
115#2076C2211yescharacteristic
116#2076C2211yescharacteristic
117#2075C2211yescharacteristic
118#2075C2211yescharacteristic
119#2074C2211yescharacteristic
120#2074C2211yescharacteristic
121#2073C2211yescharacteristic
122#2073C2211yescharacteristic
123#2068C2211yescharacteristic
124#2068C2211yescharacteristic
125#2067C2211yescharacteristic
126#2067C2211yescharacteristic
127#2066C2211yescharacteristic
128#2066C2211yescharacteristic
129#2065C2211yescharacteristic
130#2065C2211yescharacteristic
131#2059C2211yescharacteristic
132#2059C2211yescharacteristic
133#2059C2211yescharacteristic
134#2059C2211yescharacteristic
135#2036C2211yescharacteristic
136#2036C2211yescharacteristic
137#2035C2211yescharacteristic
138#2035C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2033C2211yescharacteristic
143#2026C2211yescharacteristic
144#2026C2211yescharacteristic
145#2025C2211yescharacteristic
146#2025C2211yescharacteristic
147#1992C2211yescharacteristic
148#1992C2211yescharacteristic
149#1992C2211yescharacteristic
150#1992C2211yescharacteristic
151#1992C2211yescharacteristic
152#1992C2211yescharacteristic
153#1959C2211yescharacteristic
154#1959C2211yescharacteristic
155#1944C2211yescharacteristic
156#1944C2211yescharacteristic
157#1943C2211yescharacteristic
158#1943C2211yescharacteristic
159#1942C2211yescharacteristic
160#1942C2211yescharacteristic
161#1941C2211yescharacteristic
162#1941C2211yescharacteristic
163#1936C2211yescharacteristic
164#1936C2211yescharacteristic
165#1935C2211yescharacteristic
166#1935C2211yescharacteristic
167#1934C2211yescharacteristic
168#1934C2211yescharacteristic
169#1933C2211yescharacteristic
170#1933C2211yescharacteristic
171#1845C2211yescharacteristic
172#1844C2211yescharacteristic
173#1834C2211yescharacteristic
174#1834C2211yescharacteristic
175#1776C2211yescharacteristic
176#1776C2211yescharacteristic
177#1776C2211yescharacteristic
178#1776C2211yescharacteristic
179C4×#107C2211yescharacteristic
180C4×#107C2211yescharacteristic
181C4×#106C2211yescharacteristic
182C4×#106C2211yescharacteristic
183#1768C2211yescharacteristic
184#1768C2211yescharacteristic
185#1767C2211yescharacteristic
186C4×C4⋊C8C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191C4×#103C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199#1745C2211yescharacteristic
200#1744C2211yescharacteristic
201#1726C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×#126—21no—
204C2×#125—21no—
205C2×#125C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×#121C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#499—24no—
220#499—24no—
221#488—24no—
222#488—24no—
223#433—24no—
224#433—24no—
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277#400—21no—
278#399—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#396—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#396—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—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#386—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#383—21no—
400#383—21no—
401#383—21no—
402#383—21no—
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381—21no—
411#381—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4D411yescharacteristic
421C4×C4⋊C4D411yescharacteristic
422C4×C4⋊C4D411yescharacteristic
423C4×C4⋊C4D411yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4D411yescharacteristic
435C4×C22⋊C4D411yescharacteristic
436C4×C22⋊C4D411yescharacteristic
437C4×C22⋊C4D411yescharacteristic
438#376—21no—
439#376—21no—
440#376C2311yescharacteristic
441#376C2311yescharacteristic
442C43C2311yescharacteristic
443C43C2311yescharacteristic
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
484C22×Q8C2411yescharacteristic
485C22×D4—21no—
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4C2×D411yescharacteristic
489C23×C4C2×D411yescharacteristic
490C23×C4C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499#126—82no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125—22no—
504#125—22no—
505#125—22no—
506#125—41no—
507#125—41no—
508#125—41no—
509#125—41no—
510#125—82no—
511#124—22no—
512#124—22no—
513C22⋊Q8—41no—
514C22⋊Q8—41no—
515#121—41no—
516#121—41no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—82no—
522#117—22no—
523#117—22no—
524#117—41no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4C2×D411yescharacteristic
604C2×C22⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632#107—22no—
633#107—22no—
634#107—22no—
635#107—22no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#106—22no—
641#106—22no—
642#106—22no—
643#106—22no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648C4⋊C8—22no—
649C4⋊C8—22no—
650C4⋊C8—22no—
651C4⋊C8—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#102—22no—
661#102—22no—
662#102—22no—
663#102—22no—
664#102—41no—
665#102—41no—
666#102—41no—
667#102—41no—
668C22⋊C8—22no—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—22no—
672#97—22no—
673#97—22no—
674#97—22no—
675#97—22no—
676#97—41no—
677#97—41no—
678C4×C8—22no—
679C4×C8—22no—
680C4×C8—41no—
681C4×C8—41no—
682C4×C8#4114yes—
683C4×C8#4114yes—
684#95—21no—
685#95—21no—
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#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736C24—21no—
737C24C22×D411yescharacteristic
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—42no—
751C2×D4—81no—
752C2×D4—81no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—42no—
781C22×C4—81no—
782C22×C4—81no—
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C2511yescharacteristic
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8C2×#4112yes—
818C2×C8C2×#4112yes—
819C2×C8C2×#4112yes—
820C2×C8C2×#4112yes—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—41no—
896C22⋊C4—41no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—81no—
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—
916C42—22no—
917C42—22no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—41no—
934C42—42no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42C2×#4112yes—
942C42C2×#4112yes—
943C422−1+412yes—
944C422−1+412yes—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23C23×D411yescharacteristic
960Q8—41no—
961Q8—41no—
962Q8—41no—
963Q8—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—84no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
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—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
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—82no—
1054C2×C4—82no—
1055C2×C4—162no—
1056C2×C4#53212yes—
1057C2×C4#53212yes—
1058C2×C4#53612yes—
1059C2×C4#53612yes—
1060C2×C4C22×#4111yescharacteristic
1061C2×C4C22×#4111yescharacteristic
1062C2×C4C2×2−1+411yescharacteristic
1063C2×C4C2×2−1+411yescharacteristic
1064C2×C4#58511yescharacteristic
1065C2×C4#58511yescharacteristic
1066C8—22no—
1067C8—22no—
1068C8—22no—
1069C8—22no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22C2×#53211yescharacteristic
1089C22C2×#53611yescharacteristic
1090C22#344911yescharacteristic
1091C22#358411yescharacteristic
1092C22#358411yescharacteristic
1093C22#358511yescharacteristic
1094C22#358611yescharacteristic
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4#346111yescharacteristic
1124C4#346111yescharacteristic
1125C4#346111yescharacteristic
1126C4#346111yescharacteristic
1127C2—81no—
1128C2—161no—
1129C2#3463111yescharacteristic
1130C2#6071711yescharacteristic
1131C2#6072111yescharacteristic
1132C2#6087511yescharacteristic
1133C2#6087611yescharacteristic
1134C2#6099711yescharacteristic
1135C2#6099911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35345C2semidirect
3. #30387C2semidirect
4. #30386C2semidirect
5. #30381C2semidirect
6. #30380C2semidirect
7. #30375C2semidirect
9. #30371C2semidirect
11. #30307C2semidirect
12. #30282C2semidirect
13. #30235C2semidirect
14. #30217C2semidirect
15. #29882C2semidirect
16. #29882C2semidirect
19. #23793C2semidirect
20. #23792C2semidirect
21. #23791C2semidirect
22. #23790C2semidirect
23. #23765C2semidirect
25. #23759C2semidirect
27. #21723C2semidirect
28. #21722C2semidirect
29. #21643C2semidirect
30. #21643C2semidirect
31. #20468C2semidirect

Maximal subgroups

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

subgroupindex
#353452
#352692
#303872
#303862
#303812
#303802
#303752
#303732
#303712
#303692
#303072
#302822
#302352
#302172
#298822
#298502
#298492
#237932
#237922
#237912
#237902
#237652
#237642
#237592
#237582
#217232
#217222
#216432
#204682