Finite Group Databasebeta

← #7607443

Subgroups — #7607443

Order 512.

1411 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45343C211yesmaximal, characteristic, complemented
2#45197C211yesmaximal, characteristic
3#32118C211yesmaximal, characteristic
4#32113C211yesmaximal, characteristic
5#31497C211yesmaximal, characteristic, complemented
6#31488C211yesmaximal, characteristic, complemented
7#29102C211yesmaximal, characteristic, complemented
8#29101C211yesmaximal, characteristic, complemented
9#28918C211yesmaximal, characteristic
10#28918C211yesmaximal, characteristic
11#28093C211yesmaximal, characteristic, complemented
12#28087C211yesmaximal, characteristic, complemented
13#27777C211yesmaximal, characteristic, complemented
14#27638C211yesmaximal, characteristic, complemented
15#27069C211yesmaximal, characteristic, complemented
16#27066C211yesmaximal, characteristic, complemented
17#27012C211yesmaximal, characteristic, complemented
18#27009C211yesmaximal, characteristic, complemented
19#26457C211yesmaximal, characteristic, complemented
20#26335C211yesmaximal, characteristic, complemented
21#25293C211yesmaximal, characteristic, complemented
22#24646C211yesmaximal, characteristic, complemented
23#24346C211yesmaximal, characteristic, complemented
24#24163C211yesmaximal, characteristic
25#23233C211yesmaximal, characteristic, complemented
26#23227C211yesmaximal, characteristic, complemented
27#23071C211yesmaximal, characteristic, complemented
28#22521C211yesmaximal, characteristic, complemented
29#21602C211yesmaximal, characteristic, complemented
30#21543C211yesmaximal, characteristic
31#21413C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×C8×Q8C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2800—21no—
43#2793—21no—
44#2740—21no—
45#2725—21no—
46#2719—21no—
47#2719—21no—
48#2716—21no—
49#2689—21no—
50#2577—21no—
51#2568C2211yescharacteristic
52#2560—21no—
53#2552C2211yescharacteristic
54#2550—21no—
55#2546C2211yescharacteristic
56#2538C2211yescharacteristic
57#2525—21no—
58#2519—21no—
59#2513C2211yescharacteristic
60#2512—21no—
61#2512C2211yescharacteristic
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic
64#2492C2211yescharacteristic
65#2490C2211yescharacteristic
66#2490C2211yescharacteristic
67#2489C2211yescharacteristic
68#2469—21no—
69#2453—21no—
70#2453C2211yescharacteristic
71#2451C2211yescharacteristic
72#2429C2211yescharacteristic
73#2429C2211yescharacteristic
74#2396C2211yescharacteristic
75#2370C2211yescharacteristic
76#2370C2211yescharacteristic
77#2370C2211yescharacteristic
78#2365C2211yescharacteristic
79#2365C2211yescharacteristic
80#2357C2211yescharacteristic
81#2355C2211yescharacteristic
82#2324C2211yescharacteristic
83#2323C2211yescharacteristic
84#2314C2211yescharacteristic
85#2097C2211yescharacteristic
86#2096C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2077C2211yescharacteristic
90#2076C2211yescharacteristic
91#2074C2211yescharacteristic
92#2072C2211yescharacteristic
93#2066C2211yescharacteristic
94#2066C2211yescharacteristic
95#2059C2211yescharacteristic
96#2059C2211yescharacteristic
97#2059C2211yescharacteristic
98#2057C2211yescharacteristic
99#2055C2211yescharacteristic
100#2055C2211yescharacteristic
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2043C2211yescharacteristic
104#2043C2211yescharacteristic
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2025C2211yescharacteristic
112#2023C2211yescharacteristic
113#2013C2211yescharacteristic
114#2013C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#1992C2211yescharacteristic
118#1991C2211yescharacteristic
119#1991C2211yescharacteristic
120#1990C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1988C2211yescharacteristic
126#1985C2211yescharacteristic
127#1981C2211yescharacteristic
128#1981C2211yescharacteristic
129#1981C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1960C2211yescharacteristic
134#1956C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1942C2211yescharacteristic
138#1940C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1894C2211yescharacteristic
166#1894C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1809C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1798C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#557—24no—
209#557—42no—
210#541—24no—
211#541—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2311yescharacteristic
243#491—24no—
244#491—24no—
245#478—24no—
246#468—24no—
247#461—42no—
248C8×Q8—42no—
249#440—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293#405—42no—
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400D411yescharacteristic
310#399D411yescharacteristic
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#398D411yescharacteristic
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396D411yescharacteristic
335#396D411yescharacteristic
336#395—21no—
337#395D411yescharacteristic
338#394—21no—
339#394—21no—
340#393—21no—
341#393D411yescharacteristic
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
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#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—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#387—21no—
416#386—21no—
417#385—21no—
418#384—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#383—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
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⋊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×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
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×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4C2411yescharacteristic
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—44no—
531#126—44no—
532#126—44no—
533#126—82no—
534#126—82no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—22no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—44no—
543#125—44no—
544#125—44no—
545#125—44no—
546#125#4114yes—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—82no—
554#121—22no—
555#121—41no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—44no—
569C4×D4—22no—
570C4×D4—22no—
571#117—22no—
572#117—22no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
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—21no—
607C2×C4⋊C4—21no—
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⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677#107—22no—
678#107—22no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—22no—
683#106—41no—
684#106—41no—
685#106—41no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103#4114yes—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720#97—22no—
721#97—22no—
722#97—22no—
723#97—41no—
724C4×C8—22no—
725C4×C8—41no—
726C4×C8—41no—
727C4×C8—41no—
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#95—21no—
767#95—21no—
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—
779C24C22×D411yescharacteristic
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—21no—
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—42no—
801C2×Q8—42no—
802C2×Q8—81no—
803C2×Q8C2×#4112yes—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—42no—
811C2×D4—81no—
812C2×D4—81no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
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—42no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C2511yescharacteristic
851SD16—44no—
852SD16—82no—
853SD16—82no—
854M16—44no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—44no—
878C2×C8C2×#4112yes—
879C2×C82−1+412yes—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
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—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4C2×#4112yes—
948C4⋊C4C2×#4112yes—
949C4⋊C4C2×#4112yes—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42C2×#4112yes—
1001C42H(5,𝔽2)12yes—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23C23×D411yescharacteristic
1017Q8—22no—
1018Q8—22no—
1019Q8—44no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—84no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—162no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
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—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
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—162no—
1122C2×C4#54612yes—
1123C2×C4#54612yes—
1124C2×C4#57712yes—
1125C2×C4C22×#4111yescharacteristic
1126C2×C4C22×#4111yescharacteristic
1127C2×C4C2×H(5,𝔽2)11yescharacteristic
1128C2×C4C2×2−1+411yescharacteristic
1129C2×C4#58511yescharacteristic
1130C2×C4#58511yescharacteristic
1131C8—22no—
1132C8—22no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22C2×#54611yescharacteristic
1154C22D4×#4111yescharacteristic
1155C22#349711yescharacteristic
1156C22C2×#57711yescharacteristic
1157C22#358411yescharacteristic
1158C22#358611yescharacteristic
1159C22#358611yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—42no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—42no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4#348011yescharacteristic
1189C4#351811yescharacteristic
1190C4#352011yescharacteristic
1191C4#354011yescharacteristic
1192C2—81no—
1193C2—161no—
1194C2#5975511yescharacteristic
1195C2#6117411yescharacteristic
1196C2#6122411yescharacteristic
1197C2#6155011yescharacteristic
1198C2#6155611yescharacteristic
1199C2#6240211yescharacteristic
1200C2#6240911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45343C2semidirect
5. #31497C2semidirect
6. #31488C2semidirect
7. #29102C2semidirect
8. #29101C2semidirect
11. #28093C2semidirect
12. #28087C2semidirect
13. #27777C2semidirect
14. #27638C2semidirect
15. #27069C2semidirect
16. #27066C2semidirect
17. #27012C2semidirect
18. #27009C2semidirect
19. #26457C2semidirect
20. #26335C2semidirect
21. #25293C2semidirect
22. #24646C2semidirect
23. #24346C2semidirect
25. #23233C2semidirect
26. #23227C2semidirect
27. #23071C2semidirect
28. #22521C2semidirect
29. #21602C2semidirect
31. #21413C2semidirect

Maximal subgroups

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

subgroupindex
#453432
#451972
#321182
#321132
#314972
#314882
#291022
#291012
#289182
#280932
#280872
#277772
#276382
#270692
#270662
#270122
#270092
#264572
#263352
#252932
#246462
#243462
#241632
#232332
#232272
#230712
#225212
#216022
#215432
#214132