Finite Group Databasebeta

← #6569180

Subgroups — #6569180

Order 512.

1237 conjugacy classes of subgroups.

The subgroup lattice has 1121 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39757C211yesmaximal, characteristic, complemented
2#38981C211yesmaximal, characteristic
3#30355C211yesmaximal, characteristic
4#30351C211yesmaximal, characteristic, complemented
5#30207C211yesmaximal, characteristic
6#29568C211yesmaximal, characteristic
7#29565C211yesmaximal, characteristic, complemented
8#29531C211yesmaximal, characteristic, complemented
9#29529C211yesmaximal, characteristic
10#29214C211yesmaximal, characteristic, complemented
11#29092C211yesmaximal, characteristic
12#29090C211yesmaximal, characteristic, complemented
13#29084C211yesmaximal, characteristic
14#29082C211yesmaximal, characteristic, complemented
15#28380C211yesmaximal, characteristic
16#28028C211yesmaximal, characteristic, complemented
17#28027C211yesmaximal, characteristic
18#28018C211yesmaximal, characteristic
19#28016C211yesmaximal, characteristic, complemented
20#25476C211yesmaximal, characteristic, complemented
21#25474C211yesmaximal, characteristic, complemented
22#25299C211yesmaximal, characteristic
23#25297C211yesmaximal, characteristic
24#23820C211yesmaximal, characteristic, complemented
25#23792C211yesmaximal, characteristic, complemented
26#23790C211yesmaximal, characteristic
27#23103C211yesmaximal, characteristic
28#23097C211yesmaximal, characteristic
29#23070C211yesmaximal, characteristic, complemented
30#23064C211yesmaximal, characteristic, complemented
31#20574C211yesmaximal, characteristic, complemented
32C2×#479C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38#2861C2211yescharacteristic
39#2859C2211yescharacteristic
40#2810—21no—
41#2810—21no—
42#2805—21no—
43#2805—21no—
44#2787—21no—
45#2777—21no—
46#2775—21no—
47#2745—21no—
48#2645C2211yescharacteristic
49#2644C2211yescharacteristic
50#2642C2211yescharacteristic
51#2642C2211yescharacteristic
52#2596—21no—
53#2592C2211yescharacteristic
54#2584C2211yescharacteristic
55#2581C2211yescharacteristic
56#2581C2211yescharacteristic
57#2573—21no—
58#2533—21no—
59#2533—21no—
60#2533—21no—
61#2533—21no—
62#2525—21no—
63#2514C2211yescharacteristic
64#2513C2211yescharacteristic
65#2511C2211yescharacteristic
66#2511C2211yescharacteristic
67#2511C2211yescharacteristic
68#2511C2211yescharacteristic
69#2494—21no—
70#2454C2211yescharacteristic
71#2453C2211yescharacteristic
72#2370C2211yescharacteristic
73#2367C2211yescharacteristic
74#2356C2211yescharacteristic
75#2356C2211yescharacteristic
76#2330C2211yescharacteristic
77#2330C2211yescharacteristic
78#2320C2211yescharacteristic
79#2319C2211yescharacteristic
80C4×C4⋊Q8C2211yescharacteristic
81C4×#125C2211yescharacteristic
82#2295C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2095C2211yescharacteristic
86#2094C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2074C2211yescharacteristic
92#2074C2211yescharacteristic
93#2072C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2026C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2016C2211yescharacteristic
122#2013C2211yescharacteristic
123#1992C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1991C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1971C2211yescharacteristic
132#1971C2211yescharacteristic
133#1971C2211yescharacteristic
134#1971C2211yescharacteristic
135#1969C2211yescharacteristic
136#1969C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1944C2211yescharacteristic
146#1943C2211yescharacteristic
147#1942C2211yescharacteristic
148#1941C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1920C2211yescharacteristic
171#1919C2211yescharacteristic
172#1918C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181C4×#107C2211yescharacteristic
182C4×#106C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1770C2211yescharacteristic
186#1770C2211yescharacteristic
187#1770C2211yescharacteristic
188C8×C4⋊C4C2211yescharacteristic
189#1768C2211yescharacteristic
190#1768C2211yescharacteristic
191#1767C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1746C2211yescharacteristic
201#1746C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218#479—24no—
219#479—24no—
220#464—24no—
221#464—24no—
222#446—24no—
223C8×Q8—24no—
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#401—21no—
279#401—21no—
280#400—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#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#393—21no—
318#391D411yescharacteristic
319#391D411yescharacteristic
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#391C2311yescharacteristic
334#391C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
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#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389D411yescharacteristic
355#389D411yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
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#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#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387D411yescharacteristic
409#387D411yescharacteristic
410#387D411yescharacteristic
411#387D411yescharacteristic
412#385—21no—
413#385—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#383—21no—
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445#376—21no—
446#376—21no—
447#376C2311yescharacteristic
448#376C2311yescharacteristic
449C43C2311yescharacteristic
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16—41no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512#125—22no—
513#125—22no—
514#125—22no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519#125—41no—
520#124—22no—
521#124—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×D4—22no—
531C4×D4—41no—
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⋊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⋊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×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619#107—22no—
620#107—22no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#106—22no—
626#106—22no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631C4⋊C8—22no—
632C4⋊C8—22no—
633C4⋊C8—22no—
634C4⋊C8—22no—
635C4⋊C8#4114yes—
636C4⋊C8#4114yes—
637#103—22no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102—41no—
659#102—41no—
660#102—41no—
661#97—22no—
662#97—22no—
663#97—41no—
664#97—41no—
665#97—41no—
666#97—41no—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—22no—
670C4×C8—22no—
671C4×C8—41no—
672C4×C8—41no—
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#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#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743C24—21no—
744C2×Q8—22no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—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—41no—
764C2×Q8—41no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—42no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C2511yescharacteristic
804Q16—82no—
805Q16—82no—
806SD16—82no—
807SD16—82no—
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×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8C2×#4112yes—
829C2×C8C2×#4112yes—
830C2×C8C2×#4112yes—
831C2×C8C2×#4112yes—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
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—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
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—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C42−1+412yes—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—41no—
922C42—41no—
923C42—41no—
924C42—41no—
925C42—42no—
926C42—42no—
927C42—42no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42C2×#4112yes—
937C42C2×#4112yes—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23C23×D411yescharacteristic
946Q8—44no—
947Q8—41no—
948Q8—41no—
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
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—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—22no—
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—162no—
1049C2×C4#53212yes—
1050C2×C4#53212yes—
1051C2×C4C22×#4111yescharacteristic
1052C2×C4C22×#4111yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4#58511yescharacteristic
1055C2×C4#58511yescharacteristic
1056C2×C4#58511yescharacteristic
1057C8—22no—
1058C8—22no—
1059C8—22no—
1060C8—22no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22C2×#53211yescharacteristic
1073C22#348711yescharacteristic
1074C22#348911yescharacteristic
1075C22#358411yescharacteristic
1076C22#358411yescharacteristic
1077C22#358611yescharacteristic
1078C22#358611yescharacteristic
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—42no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4#351811yescharacteristic
1109C4#351811yescharacteristic
1110C4#352111yescharacteristic
1111C4#352111yescharacteristic
1112C2—161no—
1113C2#3604811yescharacteristic
1114C2#6068511yescharacteristic
1115C2#6072611yescharacteristic
1116C2#6191811yescharacteristic
1117C2#6191811yescharacteristic
1118C2#6219611yescharacteristic
1119C2#6219811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39757C2semidirect
4. #30351C2semidirect
7. #29565C2semidirect
8. #29531C2semidirect
10. #29214C2semidirect
12. #29090C2semidirect
14. #29082C2semidirect
16. #28028C2semidirect
19. #28016C2semidirect
20. #25476C2semidirect
21. #25474C2semidirect
24. #23820C2semidirect
25. #23792C2semidirect
29. #23070C2semidirect
30. #23064C2semidirect
31. #20574C2semidirect

Maximal subgroups

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

subgroupindex
#397572
#389812
#303552
#303512
#302072
#295682
#295652
#295312
#295292
#292142
#290922
#290902
#290842
#290822
#283802
#280282
#280272
#280182
#280162
#254762
#254742
#252992
#252972
#238202
#237922
#237902
#231032
#230972
#230702
#230642
#205742