Finite Group Databasebeta

← #7533518

Subgroups — #7533518

Order 512.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44964C211yesmaximal, characteristic
2#35958C211yesmaximal, characteristic, complemented
3#31662C211yesmaximal, characteristic
4#31649C211yesmaximal, characteristic, complemented
5#31647C211yesmaximal, characteristic, complemented
6#31635C211yesmaximal, characteristic, complemented
7#29151C211yesmaximal, characteristic, complemented
8#29151C211yesmaximal, characteristic, complemented
9#28198C211yesmaximal, characteristic, complemented
10#28186C211yesmaximal, characteristic, complemented
11#27759C211yesmaximal, characteristic
12#27752C211yesmaximal, characteristic, complemented
13#26711C211yesmaximal, characteristic, complemented
14#26702C211yesmaximal, characteristic, complemented
15#26696C211yesmaximal, characteristic, complemented
16#26692C211yesmaximal, characteristic
17#26118C211yesmaximal, characteristic, complemented
18#26113C211yesmaximal, characteristic, complemented
19#25006C211yesmaximal, characteristic, complemented
20#24997C211yesmaximal, characteristic, complemented
21#24641C211yesmaximal, characteristic, complemented
22#24635C211yesmaximal, characteristic
23#24207C211yesmaximal, characteristic, complemented
24#24194C211yesmaximal, characteristic
25#23154C211yesmaximal, characteristic, complemented
26#22779C211yesmaximal, characteristic, complemented
27#22770C211yesmaximal, characteristic, complemented
28#22549C211yesmaximal, characteristic
29#22541C211yesmaximal, characteristic, complemented
30#21511C211yesmaximal, characteristic, complemented
31#21511C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38C2×#441C2211yescharacteristic
39C2×#441C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42#2718—21no—
43#2715—21no—
44#2695—21no—
45#2680—21no—
46#2666—21no—
47#2660C2211yescharacteristic
48#2612—21no—
49#2605—21no—
50#2586—21no—
51#2585—21no—
52#2582C2211yescharacteristic
53#2582C2211yescharacteristic
54#2581C2211yescharacteristic
55#2571C2211yescharacteristic
56#2570C2211yescharacteristic
57#2568C2211yescharacteristic
58#2565C2211yescharacteristic
59#2545C2211yescharacteristic
60#2544C2211yescharacteristic
61#2538C2211yescharacteristic
62#2520—21no—
63#2520—21no—
64#2474—21no—
65#2468—21no—
66#2449—21no—
67#2448C2211yescharacteristic
68#2447C2211yescharacteristic
69#2446C2211yescharacteristic
70#2445C2211yescharacteristic
71#2413—21no—
72#2402—21no—
73#2399C2211yescharacteristic
74#2370C2211yescharacteristic
75#2369C2211yescharacteristic
76#2356C2211yescharacteristic
77#2355C2211yescharacteristic
78#2355C2211yescharacteristic
79#2355C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82#2326C2211yescharacteristic
83#2326C2211yescharacteristic
84#2276C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2073C2211yescharacteristic
96#2071C2211yescharacteristic
97#2056C2211yescharacteristic
98#2056C2211yescharacteristic
99#2055C2211yescharacteristic
100#2055C2211yescharacteristic
101#2043C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2041C2211yescharacteristic
105#2026C2211yescharacteristic
106#2026C2211yescharacteristic
107#2025C2211yescharacteristic
108#2025C2211yescharacteristic
109#2024C2211yescharacteristic
110#2024C2211yescharacteristic
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#2016C2211yescharacteristic
114#2015C2211yescharacteristic
115#2015C2211yescharacteristic
116#2014C2211yescharacteristic
117#1985C2211yescharacteristic
118#1984C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1982C2211yescharacteristic
124#1981C2211yescharacteristic
125#1961C2211yescharacteristic
126#1959C2211yescharacteristic
127#1959C2211yescharacteristic
128#1958C2211yescharacteristic
129#1958C2211yescharacteristic
130#1958C2211yescharacteristic
131#1958C2211yescharacteristic
132#1956C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1940C2211yescharacteristic
136#1939C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1917C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1834C2211yescharacteristic
176#1834C2211yescharacteristic
177#1805C2211yescharacteristic
178#1805C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1771C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#559—24no—
208#559—42no—
209#556—24no—
210#556—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C22×C4⋊C4—21no—
243#464—24no—
244#464—24no—
245#446—42no—
246C8×Q8—42no—
247#441—24no—
248#441—42no—
249C4×SD16—24no—
250C4×SD16—42no—
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398D411yescharacteristic
322#398D411yescharacteristic
323#398D411yescharacteristic
324#398D411yescharacteristic
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395D411yescharacteristic
336#395D411yescharacteristic
337#395D411yescharacteristic
338#395D411yescharacteristic
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—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#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#384—21no—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#380—21no—
430#380—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451#376—21no—
452#376—21no—
453#376C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2×D411yescharacteristic
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16—41no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528#127—22no—
529#127—41no—
530#126—44no—
531#126—44no—
532#125—41no—
533#125—41no—
534#124—22no—
535#124—22no—
536#124—22no—
537#124—22no—
538#124—22no—
539#124—41no—
540#124—41no—
541#124—44no—
542#124#4114yes—
543#123—44no—
544#123—44no—
545#123—82no—
546C22⋊Q8—44no—
547C22⋊Q8—82no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8#4114yes—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—44no—
575#117—44no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—82no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#106—22no—
674#106—22no—
675#106—41no—
676#106—41no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#97—22no—
718#97—22no—
719#97—41no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—41no—
723C4×C8—41no—
724C4×C8—41no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778C24—21no—
779C24—21no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—41no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—42no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8C2×#4112yes—
806C2×Q8C2×#4112yes—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4C2×#4112yes—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C2511yescharacteristic
866Q16—44no—
867Q16—44no—
868SD16—44no—
869SD16—44no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4C2×#4112yes—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C42—24no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42C2×#4112yes—
1005C42C2×#4112yes—
1006C42H(5,𝔽2)12yes—
1007C422−1+412yes—
1008C23—22no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C23×D411yescharacteristic
1023Q8—22no—
1024Q8—22no—
1025Q8—22no—
1026Q8—22no—
1027Q8—44no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—82no—
1037Q8—162no—
1038D4—22no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—84no—
1047D4—162no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—84no—
1128C2×C4—84no—
1129C2×C4—162no—
1130C2×C4—162no—
1131C2×C4#54612yes—
1132C2×C4#54612yes—
1133C2×C4#54812yes—
1134C2×C4#54812yes—
1135C2×C4#57712yes—
1136C2×C4C22×#4111yescharacteristic
1137C2×C4C22×#4111yescharacteristic
1138C2×C4C2×H(5,𝔽2)11yescharacteristic
1139C2×C4C2×2−1+411yescharacteristic
1140C2×C4#58511yescharacteristic
1141C2×C4#58511yescharacteristic
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22C2×#54611yescharacteristic
1165C22C2×#54811yescharacteristic
1166C22#348711yescharacteristic
1167C22C2×#57711yescharacteristic
1168C22#358411yescharacteristic
1169C22#358411yescharacteristic
1170C22#358611yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4#347511yescharacteristic
1200C4#350611yescharacteristic
1201C4#351511yescharacteristic
1202C4#354711yescharacteristic
1203C2—82no—
1204C2—161no—
1205C2#5903411yescharacteristic
1206C2#6117211yescharacteristic
1207C2#6119711yescharacteristic
1208C2#6132711yescharacteristic
1209C2#6135011yescharacteristic
1210C2#6191611yescharacteristic
1211C2#6193011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
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
4. #31649C2semidirect
5. #31647C2semidirect
6. #31635C2semidirect
7. #29151C2semidirect
8. #29151C2semidirect
9. #28198C2semidirect
10. #28186C2semidirect
12. #27752C2semidirect
13. #26711C2semidirect
14. #26702C2semidirect
15. #26696C2semidirect
17. #26118C2semidirect
18. #26113C2semidirect
19. #25006C2semidirect
20. #24997C2semidirect
21. #24641C2semidirect
23. #24207C2semidirect
25. #23154C2semidirect
26. #22779C2semidirect
27. #22770C2semidirect
29. #22541C2semidirect
30. #21511C2semidirect
31. #21511C2semidirect

Maximal subgroups

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

subgroupindex
#449642
#359582
#316622
#316492
#316472
#316352
#291512
#281982
#281862
#277592
#277522
#267112
#267022
#266962
#266922
#261182
#261132
#250062
#249972
#246412
#246352
#242072
#241942
#231542
#227792
#227702
#225492
#225412
#215112