Finite Group Databasebeta

← #7232003

Subgroups — #7232003

Order 512.

1124 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53155C211yesmaximal, characteristic
2#53034C211yesmaximal, characteristic, complemented
3#33285C211yesmaximal, characteristic, complemented
4#33283C211yesmaximal, characteristic
5#32855C211yesmaximal, characteristic, complemented
6#32813C211yesmaximal, characteristic
7#32249C211yesmaximal, characteristic, complemented
8#32249C211yesmaximal, characteristic, complemented
9#32239C211yesmaximal, characteristic, complemented
10#32236C211yesmaximal, characteristic
11#31813C211yesmaximal, characteristic, complemented
12#31810C211yesmaximal, characteristic
13#31809C211yesmaximal, characteristic, complemented
14#31805C211yesmaximal, characteristic
15#31655C211yesmaximal, characteristic
16#31650C211yesmaximal, characteristic
17#31639C211yesmaximal, characteristic
18#31635C211yesmaximal, characteristic, complemented
19#29100C211yesmaximal, characteristic
20#29098C211yesmaximal, characteristic, complemented
21#29093C211yesmaximal, characteristic
22#29090C211yesmaximal, characteristic, complemented
23#28901C211yesmaximal, characteristic
24#28892C211yesmaximal, characteristic, complemented
25#28883C211yesmaximal, characteristic
26#28880C211yesmaximal, characteristic
27#27832C211yesmaximal, characteristic, complemented
28#27829C211yesmaximal, characteristic
29#27820C211yesmaximal, characteristic, complemented
30#27818C211yesmaximal, characteristic, complemented
31#21678C211yesmaximal, characteristic, complemented
32#2843—21no—
33#2839—21no—
34#2838—21no—
35#2836—21no—
36#2834—21no—
37#2833—21no—
38#2833—21no—
39#2831—21no—
40#2791—21no—
41#2777—21no—
42#2776—21no—
43#2776—21no—
44#2770—21no—
45#2764—21no—
46#2758—21no—
47#2745—21no—
48#2647C2211yescharacteristic
49#2647C2211yescharacteristic
50#2642C2211yescharacteristic
51#2640C2211yescharacteristic
52#2567C2211yescharacteristic
53#2566C2211yescharacteristic
54#2565C2211yescharacteristic
55#2565C2211yescharacteristic
56#2552C2211yescharacteristic
57#2550C2211yescharacteristic
58#2550C2211yescharacteristic
59#2550C2211yescharacteristic
60#2514C2211yescharacteristic
61#2514C2211yescharacteristic
62#2514C2211yescharacteristic
63#2514C2211yescharacteristic
64#2514C2211yescharacteristic
65#2513C2211yescharacteristic
66#2513C2211yescharacteristic
67#2511C2211yescharacteristic
68#2454C2211yescharacteristic
69#2453C2211yescharacteristic
70#2453C2211yescharacteristic
71#2451C2211yescharacteristic
72#2448C2211yescharacteristic
73#2447C2211yescharacteristic
74#2446C2211yescharacteristic
75#2446C2211yescharacteristic
76#2402C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2100C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2065C2211yescharacteristic
101#2056C2211yescharacteristic
102#2056C2211yescharacteristic
103#2056C2211yescharacteristic
104#2056C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2026C2211yescharacteristic
112#2026C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2023C2211yescharacteristic
121#2016C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2013C2211yescharacteristic
125#1993C2211yescharacteristic
126#1993C2211yescharacteristic
127#1992C2211yescharacteristic
128#1992C2211yescharacteristic
129#1991C2211yescharacteristic
130#1991C2211yescharacteristic
131#1991C2211yescharacteristic
132#1990C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1989C2211yescharacteristic
136#1988C2211yescharacteristic
137#1973C2211yescharacteristic
138#1971C2211yescharacteristic
139#1969C2211yescharacteristic
140#1968C2211yescharacteristic
141#1960C2211yescharacteristic
142#1959C2211yescharacteristic
143#1958C2211yescharacteristic
144#1956C2211yescharacteristic
145#1939C2211yescharacteristic
146#1939C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1935C2211yescharacteristic
156#1935C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1933C2211yescharacteristic
166#1933C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1925C2211yescharacteristic
171#1921C2211yescharacteristic
172#1921C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1880C2211yescharacteristic
180#1880C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1878C2211yescharacteristic
185#1877C2211yescharacteristic
186#1877C2211yescharacteristic
187#1832C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1802C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#106C2311yescharacteristic
222C2×#106C2311yescharacteristic
223C2×C4⋊C8C2311yescharacteristic
224C2×C4⋊C8C2311yescharacteristic
225C2×C4⋊C8C2311yescharacteristic
226C2×C4⋊C8C2311yescharacteristic
227C2×C4⋊C8C2311yescharacteristic
228C2×C4⋊C8C2311yescharacteristic
229C2×#103C2311yescharacteristic
230C2×#103C2311yescharacteristic
231C2×#103C2311yescharacteristic
232C2×#103C2311yescharacteristic
233C2×#103C2311yescharacteristic
234C2×#103C2311yescharacteristic
235C2×#103C2311yescharacteristic
236C2×#103C2311yescharacteristic
237C2×#103C2311yescharacteristic
238C2×#103C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263#401—21no—
264#401—21no—
265#401—21no—
266#401—21no—
267#401—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400D411yescharacteristic
288#400D411yescharacteristic
289#400D411yescharacteristic
290#400D411yescharacteristic
291#399—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—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#398D411yescharacteristic
312#398D411yescharacteristic
313#398D411yescharacteristic
314#398D411yescharacteristic
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—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#387—21no—
402#387—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#383—21no—
414#383—21no—
415#383—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#380—21no—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433#376C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8C2411yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×Q8C2411yescharacteristic
483C22×D4C2411yescharacteristic
484C23×C4—21no—
485C2×Q16—41no—
486C2×Q16—41no—
487C2×Q16—41no—
488C2×Q16—41no—
489C2×Q16—41no—
490C2×Q16—41no—
491C2×SD16—41no—
492C2×SD16—41no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511#125—41no—
512#125—41no—
513#125—41no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519#124—41no—
520#124—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×D4—41no—
528C4×D4—41no—
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⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
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×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613#107—41no—
614#107—41no—
615#106—41no—
616#106—41no—
617C4⋊C8—41no—
618C4⋊C8—41no—
619C4⋊C8—41no—
620C4⋊C8—41no—
621C4⋊C8—41no—
622C4⋊C8—41no—
623#103—22no—
624#103—22no—
625#103—22no—
626#103—41no—
627#103—41no—
628#103—41no—
629#103—41no—
630#103—41no—
631#103—41no—
632#103—41no—
633#103—41no—
634#103—41no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103—41no—
639#103—41no—
640#103—41no—
641#102—22no—
642#102—41no—
643#102—41no—
644#102—41no—
645#102—41no—
646#102—41no—
647#97—22no—
648#97—41no—
649#97—41no—
650#97—41no—
651#97—41no—
652C4×C8—41no—
653C4×C8—41no—
654C4×C8—41no—
655C4×C8—41no—
656C4×C8—41no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
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#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C24—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C22×C4—21no—
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—81no—
776C22×C4—81no—
777C22×C4—81no—
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
793Q16—82no—
794Q16—82no—
795SD16—82no—
796SD16—82no—
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×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C82−1+412yes—
821C4⋊C4—21no—
822C4⋊C4—21no—
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—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—42no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
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—
890C22⋊C4—81no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C22⋊C4—81no—
895C22⋊C4—81no—
896C22⋊C4—81no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—42no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C23×D411yescharacteristic
932Q8—41no—
933Q8—41no—
934Q8—41no—
935Q8—41no—
936Q8—41no—
937Q8—41no—
938Q8—41no—
939Q8—41no—
940Q8—41no—
941Q8—41no—
942Q8—41no—
943Q8—41no—
944Q8—162no—
945Q8—162no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
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—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
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—162no—
1038C2×C4C2×2−1+411yescharacteristic
1039C2×C4#58511yescharacteristic
1040C2×C4#58511yescharacteristic
1041C2×C4#58511yescharacteristic
1042C2×C4#58511yescharacteristic
1043C2×C4#58511yescharacteristic
1044C8—22no—
1045C8—41no—
1046C8—41no—
1047C8—41no—
1048C8—41no—
1049C8—41no—
1050C8—41no—
1051C8—41no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22#349711yescharacteristic
1060C22#350011yescharacteristic
1061C22#350011yescharacteristic
1062C22#358411yescharacteristic
1063C22#358411yescharacteristic
1064C22#358611yescharacteristic
1065C22#358611yescharacteristic
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4#353111yescharacteristic
1096C4#355311yescharacteristic
1097C4#356811yescharacteristic
1098C4#356811yescharacteristic
1099C2—161no—
1100C2#4623911yescharacteristic
1101C2#6240911yescharacteristic
1102C2#6241211yescharacteristic
1103C2#6255511yescharacteristic
1104C2#6256511yescharacteristic
1105C2#6260011yescharacteristic
1106C2#6261211yescharacteristic
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. #53034C2semidirect
3. #33285C2semidirect
5. #32855C2semidirect
7. #32249C2semidirect
8. #32249C2semidirect
9. #32239C2semidirect
11. #31813C2semidirect
13. #31809C2semidirect
18. #31635C2semidirect
20. #29098C2semidirect
22. #29090C2semidirect
24. #28892C2semidirect
27. #27832C2semidirect
29. #27820C2semidirect
30. #27818C2semidirect
31. #21678C2semidirect

Maximal subgroups

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

subgroupindex
#531552
#530342
#332852
#332832
#328552
#328132
#322492
#322392
#322362
#318132
#318102
#318092
#318052
#316552
#316502
#316392
#316352
#291002
#290982
#290932
#290902
#289012
#288922
#288832
#288802
#278322
#278292
#278202
#278182
#216782