Finite Group Databasebeta

← #6694574

Subgroups — #6694574

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42698C211yesmaximal, characteristic
2#35958C211yesmaximal, characteristic, complemented
3#33041C211yesmaximal, characteristic, complemented
4#32611C211yesmaximal, characteristic
5#32601C211yesmaximal, characteristic
6#32549C211yesmaximal, characteristic, complemented
7#32548C211yesmaximal, characteristic, complemented
8#32439C211yesmaximal, characteristic, complemented
9#32429C211yesmaximal, characteristic, complemented
10#31647C211yesmaximal, characteristic
11#31644C211yesmaximal, characteristic
12#30210C211yesmaximal, characteristic, complemented
13#29991C211yesmaximal, characteristic
14#27748C211yesmaximal, characteristic
15#27731C211yesmaximal, characteristic
16#27138C211yesmaximal, characteristic, complemented
17#27132C211yesmaximal, characteristic, complemented
18#26698C211yesmaximal, characteristic
19#26695C211yesmaximal, characteristic
20#26539C211yesmaximal, characteristic, complemented
21#26523C211yesmaximal, characteristic, complemented
22#26326C211yesmaximal, characteristic
23#26324C211yesmaximal, characteristic
24#25001C211yesmaximal, characteristic, complemented
25#24995C211yesmaximal, characteristic, complemented
26#24689C211yesmaximal, characteristic
27#24645C211yesmaximal, characteristic
28#23096C211yesmaximal, characteristic, complemented
29#23064C211yesmaximal, characteristic, complemented
30#22308C211yesmaximal, characteristic, complemented
31#21128C211yesmaximal, characteristic
32C2×#479C2211yescharacteristic
33C2×#462C2211yescharacteristic
34C2×#440C2211yescharacteristic
35#2838—21no—
36#2747—21no—
37#2745—21no—
38#2742—21no—
39#2738—21no—
40#2666—21no—
41#2660C2211yescharacteristic
42#2654—21no—
43#2650—21no—
44#2642C2211yescharacteristic
45#2612—21no—
46#2605—21no—
47#2592C2211yescharacteristic
48#2592C2211yescharacteristic
49#2586—21no—
50#2585—21no—
51#2582C2211yescharacteristic
52#2582C2211yescharacteristic
53#2581C2211yescharacteristic
54#2581C2211yescharacteristic
55#2571C2211yescharacteristic
56#2570C2211yescharacteristic
57#2568C2211yescharacteristic
58#2566C2211yescharacteristic
59#2565C2211yescharacteristic
60#2547C2211yescharacteristic
61#2525—21no—
62#2520—21no—
63#2520—21no—
64#2514C2211yescharacteristic
65#2511C2211yescharacteristic
66#2448C2211yescharacteristic
67#2448C2211yescharacteristic
68#2402—21no—
69#2399C2211yescharacteristic
70#2370C2211yescharacteristic
71#2370C2211yescharacteristic
72#2369C2211yescharacteristic
73#2365C2211yescharacteristic
74#2356C2211yescharacteristic
75#2355C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2319C2211yescharacteristic
79#2276C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2097C2211yescharacteristic
87#2096C2211yescharacteristic
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2074C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2072C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2057C2211yescharacteristic
106#2056C2211yescharacteristic
107#2056C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2026C2211yescharacteristic
113#2026C2211yescharacteristic
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2023C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1989C2211yescharacteristic
123#1984C2211yescharacteristic
124#1984C2211yescharacteristic
125#1984C2211yescharacteristic
126#1984C2211yescharacteristic
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1981C2211yescharacteristic
130#1969C2211yescharacteristic
131#1969C2211yescharacteristic
132#1960C2211yescharacteristic
133#1958C2211yescharacteristic
134#1958C2211yescharacteristic
135#1956C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1865C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1835C2211yescharacteristic
187#1834C2211yescharacteristic
188#1832C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220#479—24no—
221#462—24no—
222#440—24no—
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×C4⋊C8C2311yescharacteristic
233C2×C4⋊C8C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×#103C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270#401—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#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398D411yescharacteristic
297#398D411yescharacteristic
298#398D411yescharacteristic
299#398D411yescharacteristic
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395D411yescharacteristic
313#395D411yescharacteristic
314#395D411yescharacteristic
315#395D411yescharacteristic
316#393—21no—
317#393—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
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#388—21no—
358#388—21no—
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#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#387—21no—
390#387—21no—
391#387—21no—
392#385—21no—
393#385—21no—
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#382—21no—
401#382—21no—
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
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
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436#376—21no—
437#376—21no—
438#376C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
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
481C22×Q8—21no—
482C22×Q8C2×D411yescharacteristic
483C22×Q8C2×D411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—41no—
492C2×Q16—41no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×SD16—22no—
496C2×SD16—41no—
497C2×SD16—41no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510#125—22no—
511#125—22no—
512#125—41no—
513#125—41no—
514#124—41no—
515#124—41no—
516#124—41no—
517#124—41no—
518C4×Q8—22no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8#4114yes—
532C4×D4—22no—
533C4×D4—22no—
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⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
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×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623#107—22no—
624#107—22no—
625#107—41no—
626#107—41no—
627#107—41no—
628#107—41no—
629#106—22no—
630#106—41no—
631#106—41no—
632C4⋊C8—22no—
633C4⋊C8—22no—
634C4⋊C8—41no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—41no—
644#103—41no—
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#103—41no—
656#103—41no—
657#102—22no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#97—22no—
665C4×C8—22no—
666C4×C8—41no—
667C4×C8—41no—
668C4×C8—41no—
669C4×C8—41no—
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#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#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
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—
737C2×Q8—22no—
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—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—41no—
756C2×Q8—41no—
757C2×Q8—41no—
758C2×Q8—41no—
759C2×Q8—41no—
760C2×Q8—42no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8C2×#4112yes—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C22×C4—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—42no—
786C22×C4—81no—
787C22×C4—81no—
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×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C2511yescharacteristic
803Q16—82no—
804Q16—82no—
805SD16—44no—
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×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—22no—
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—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
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—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—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4C2×#4112yes—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—81no—
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—24no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—42no—
923C42—42no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42C2×#4112yes—
937C422−1+412yes—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23C23×D411yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—41no—
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—82no—
959Q8—82no—
960Q8—162no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
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—22no—
989C2×C4—22no—
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—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—162no—
1050C2×C4#54812yes—
1051C2×C4#54812yes—
1052C2×C4#57812yes—
1053C2×C4C22×#4111yescharacteristic
1054C2×C4C2×2−1+411yescharacteristic
1055C2×C4#58511yescharacteristic
1056C2×C4#58511yescharacteristic
1057C2×C4#58511yescharacteristic
1058C2×C4#58511yescharacteristic
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22C2×#54811yescharacteristic
1075C22#348511yescharacteristic
1076C22#348711yescharacteristic
1077C22C2×#57811yescharacteristic
1078C22#358411yescharacteristic
1079C22#358411yescharacteristic
1080C22#358411yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—42no—
1094C4—42no—
1095C4—41no—
1096C4—41no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4#345511yescharacteristic
1111C4#351011yescharacteristic
1112C4#356511yescharacteristic
1113C4#356511yescharacteristic
1114C2—161no—
1115C2#3771111yescharacteristic
1116C2#6132811yescharacteristic
1117C2#6133111yescharacteristic
1118C2#6176811yescharacteristic
1119C2#6177111yescharacteristic
1120C2#6192911yescharacteristic
1121C2#6193111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35958C2semidirect
3. #33041C2semidirect
6. #32549C2semidirect
7. #32548C2semidirect
8. #32439C2semidirect
9. #32429C2semidirect
12. #30210C2semidirect
16. #27138C2semidirect
17. #27132C2semidirect
20. #26539C2semidirect
21. #26523C2semidirect
24. #25001C2semidirect
25. #24995C2semidirect
28. #23096C2semidirect
29. #23064C2semidirect
30. #22308C2semidirect

Maximal subgroups

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

subgroupindex
#426982
#359582
#330412
#326112
#326012
#325492
#325482
#324392
#324292
#316472
#316442
#302102
#299912
#277482
#277312
#271382
#271322
#266982
#266952
#265392
#265232
#263262
#263242
#250012
#249952
#246892
#246452
#230962
#230642
#223082
#211282