Finite Group Databasebeta

← #7277986

Subgroups — #7277986

Order 512.

1178 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#42902C211yesmaximal, characteristic
2#42744C211yesmaximal, characteristic, complemented
3#32868C211yesmaximal, characteristic
4#32528C211yesmaximal, characteristic, complemented
5#32507C211yesmaximal, characteristic, complemented
6#32455C211yesmaximal, characteristic
7#32090C211yesmaximal, characteristic
8#31976C211yesmaximal, characteristic
9#31920C211yesmaximal, characteristic, complemented
10#31881C211yesmaximal, characteristic, complemented
11#31813C211yesmaximal, characteristic, complemented
12#31583C211yesmaximal, characteristic
13#31169C211yesmaximal, characteristic
14#31154C211yesmaximal, characteristic
15#30977C211yesmaximal, characteristic, complemented
16#29527C211yesmaximal, characteristic
17#29509C211yesmaximal, characteristic, complemented
18#29035C211yesmaximal, characteristic
19#28899C211yesmaximal, characteristic
20#28291C211yesmaximal, characteristic, complemented
21#28039C211yesmaximal, characteristic, complemented
22#27368C211yesmaximal, characteristic, complemented
23#27087C211yesmaximal, characteristic
24#26714C211yesmaximal, characteristic, complemented
25#26489C211yesmaximal, characteristic, complemented
26#26470C211yesmaximal, characteristic
27#26369C211yesmaximal, characteristic, complemented
28#26123C211yesmaximal, characteristic, complemented
29#25466C211yesmaximal, characteristic
30#24637C211yesmaximal, characteristic
31#22306C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38#2839—21no—
39#2838—21no—
40#2798—21no—
41#2789—21no—
42#2787—21no—
43#2776—21no—
44#2775—21no—
45#2769—21no—
46#2762—21no—
47#2744—21no—
48#2667—21no—
49#2666—21no—
50#2650—21no—
51#2645—21no—
52#2645C2211yescharacteristic
53#2644C2211yescharacteristic
54#2577—21no—
55#2571C2211yescharacteristic
56#2563C2211yescharacteristic
57#2550C2211yescharacteristic
58#2545C2211yescharacteristic
59#2533—21no—
60#2514C2211yescharacteristic
61#2514C2211yescharacteristic
62#2514C2211yescharacteristic
63#2511C2211yescharacteristic
64#2509C2211yescharacteristic
65#2509C2211yescharacteristic
66#2508C2211yescharacteristic
67#2507C2211yescharacteristic
68#2453C2211yescharacteristic
69#2451C2211yescharacteristic
70#2451C2211yescharacteristic
71#2451C2211yescharacteristic
72#2448C2211yescharacteristic
73#2448C2211yescharacteristic
74#2447C2211yescharacteristic
75#2446C2211yescharacteristic
76#2402C2211yescharacteristic
77#2370C2211yescharacteristic
78#2367C2211yescharacteristic
79#2356C2211yescharacteristic
80#2351C2211yescharacteristic
81#2331C2211yescharacteristic
82#2327C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2096C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2074C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2056C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2043C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2026C2211yescharacteristic
126#2026C2211yescharacteristic
127#2024C2211yescharacteristic
128#2023C2211yescharacteristic
129#2016C2211yescharacteristic
130#2015C2211yescharacteristic
131#1988C2211yescharacteristic
132#1983C2211yescharacteristic
133#1981C2211yescharacteristic
134#1981C2211yescharacteristic
135#1973C2211yescharacteristic
136#1971C2211yescharacteristic
137#1971C2211yescharacteristic
138#1969C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1943C2211yescharacteristic
146#1942C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1939C2211yescharacteristic
152#1939C2211yescharacteristic
153#1939C2211yescharacteristic
154#1939C2211yescharacteristic
155#1936C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1934C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1928C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1927C2211yescharacteristic
168#1926C2211yescharacteristic
169#1925C2211yescharacteristic
170#1925C2211yescharacteristic
171#1921C2211yescharacteristic
172#1920C2211yescharacteristic
173#1919C2211yescharacteristic
174#1918C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1877C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1843C2211yescharacteristic
192#1836C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1805C2211yescharacteristic
196#1803C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1763C2211yescharacteristic
201#1762C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218#501—42no—
219#478—42no—
220#477—42no—
221#475—42no—
222#464—42no—
223C4×Q16—42no—
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×#106C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#401—21no—
280#401—21no—
281#401—21no—
282#401—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#400D411yescharacteristic
301#400D411yescharacteristic
302#400D411yescharacteristic
303#400D411yescharacteristic
304#399—21no—
305#399—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398D411yescharacteristic
316#398D411yescharacteristic
317#398D411yescharacteristic
318#398D411yescharacteristic
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—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#391—21no—
340#391—21no—
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#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389C2311yescharacteristic
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#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—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#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#385—21no—
416#385—21no—
417#384C2311yescharacteristic
418#383—21no—
419#383—21no—
420#383—21no—
421#383—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380—21no—
432#380—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448#376—21no—
449#376C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×SD16—41no—
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514#125—22no—
515#125—41no—
516#124—22no—
517#124—41no—
518#124—41no—
519#124—41no—
520C4×Q8—22no—
521C4×Q8—22no—
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×D4—41no—
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⋊C4C2×D411yescharacteristic
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⋊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×C4⋊C4C2411yescharacteristic
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×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×C42—21no—
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616#107—22no—
617#107—22no—
618#107—41no—
619#107—41no—
620#107—41no—
621#107—41no—
622#106—22no—
623#106—22no—
624#106—41no—
625#106—41no—
626#106—41no—
627#106—41no—
628#106—41no—
629C4⋊C8—41no—
630C4⋊C8—41no—
631C4⋊C8—41no—
632C4⋊C8—41no—
633C4⋊C8—41no—
634C4⋊C8—41no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638C4⋊C8—41no—
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#103—41no—
658#102—22no—
659#102—22no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665#97—22no—
666#97—41no—
667#97—41no—
668C4×C8—41no—
669C4×C8—41no—
670C4×C8—41no—
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#95—21no—
725#95—21no—
726#95—21no—
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
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—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—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q82−1+412yes—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—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—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—42no—
790C22×C4—81no—
791C22×C4—81no—
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×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C2511yescharacteristic
807Q16—44no—
808Q16—82no—
809SD16—82no—
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—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C82−1+412yes—
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—21no—
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—41no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
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—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4H(5,𝔽2)12yes—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—42no—
927C42—42no—
928C42—42no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23C23×D411yescharacteristic
945Q8—22no—
946Q8—22no—
947Q8—41no—
948Q8—41no—
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—162no—
958Q8—162no—
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—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
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—162no—
1051C2×C4C2×H(5,𝔽2)11yescharacteristic
1052C2×C4C2×2−1+411yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4#58511yescharacteristic
1055C2×C4#58511yescharacteristic
1056C2×C4#58511yescharacteristic
1057C8—22no—
1058C8—41no—
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22#348811yescharacteristic
1073C22#348911yescharacteristic
1074C22#349711yescharacteristic
1075C22#358411yescharacteristic
1076C22#358411yescharacteristic
1077C22#358611yescharacteristic
1078C22#358611yescharacteristic
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—41no—
1083C4—42no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
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#353811yescharacteristic
1109C4#355311yescharacteristic
1110C4#356211yescharacteristic
1111C4#356511yescharacteristic
1112C2—161no—
1113C2#4767711yescharacteristic
1114C2#6205911yescharacteristic
1115C2#6209111yescharacteristic
1116C2#6216111yescharacteristic
1117C2#6219811yescharacteristic
1118C2#6240911yescharacteristic
1119C2#6241211yescharacteristic
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. #42744C2semidirect
4. #32528C2semidirect
5. #32507C2semidirect
9. #31920C2semidirect
10. #31881C2semidirect
11. #31813C2semidirect
15. #30977C2semidirect
17. #29509C2semidirect
20. #28291C2semidirect
21. #28039C2semidirect
22. #27368C2semidirect
24. #26714C2semidirect
25. #26489C2semidirect
27. #26369C2semidirect
28. #26123C2semidirect
31. #22306C2semidirect

Maximal subgroups

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

subgroupindex
#429022
#427442
#328682
#325282
#325072
#324552
#320902
#319762
#319202
#318812
#318132
#315832
#311692
#311542
#309772
#295272
#295092
#290352
#288992
#282912
#280392
#273682
#270872
#267142
#264892
#264702
#263692
#261232
#254662
#246372
#223062