Finite Group Databasebeta

← #7544475

Subgroups — #7544475

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59136C211yesmaximal, characteristic, complemented
2#36420C211yesmaximal, characteristic, complemented
3#32254C211yesmaximal, characteristic, complemented
4#32240C211yesmaximal, characteristic, complemented
5#31822C211yesmaximal, characteristic, complemented
6#31815C211yesmaximal, characteristic, complemented
7#28651C211yesmaximal, characteristic, complemented
8#27740C211yesmaximal, characteristic, complemented
9#27724C211yesmaximal, characteristic, complemented
10#27710C211yesmaximal, characteristic, complemented
11#27443C211yesmaximal, characteristic, complemented
12#27435C211yesmaximal, characteristic, complemented
13#26519C211yesmaximal, characteristic, complemented
14#26439C211yesmaximal, characteristic, complemented
15#26433C211yesmaximal, characteristic, complemented
16#26295C211yesmaximal, characteristic, complemented
17#26033C211yesmaximal, characteristic, complemented
18#26031C211yesmaximal, characteristic, complemented
19#25940C211yesmaximal, characteristic, complemented
20#25908C211yesmaximal, characteristic, complemented
21#25335C211yesmaximal, characteristic, complemented
22#25230C211yesmaximal, characteristic, complemented
23#25218C211yesmaximal, characteristic
24#24756C211yesmaximal, characteristic
25#23230C211yesmaximal, characteristic, complemented
26#23141C211yesmaximal, characteristic, complemented
27#23140C211yesmaximal, characteristic
28#22955C211yesmaximal, characteristic, complemented
29#22526C211yesmaximal, characteristic, complemented
30#21582C211yesmaximal, characteristic, complemented
31#21313C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#446C2211yescharacteristic
41C2×#423C2211yescharacteristic
42#2865—21no—
43#2850C2211yescharacteristic
44#2729—21no—
45#2729—21no—
46#2595—21no—
47#2592C2211yescharacteristic
48#2578—21no—
49#2570C2211yescharacteristic
50#2567C2211yescharacteristic
51#2563C2211yescharacteristic
52#2550C2211yescharacteristic
53#2550C2211yescharacteristic
54#2532—21no—
55#2531—21no—
56#2530—21no—
57#2513C2211yescharacteristic
58#2511C2211yescharacteristic
59#2500C2211yescharacteristic
60#2499C2211yescharacteristic
61#2492—21no—
62#2477—21no—
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2442C2211yescharacteristic
66#2442C2211yescharacteristic
67#2440—21no—
68#2417—21no—
69#2409—21no—
70#2409—21no—
71#2369C2211yescharacteristic
72#2367C2211yescharacteristic
73#2363C2211yescharacteristic
74#2362C2211yescharacteristic
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2356C2211yescharacteristic
78#2355C2211yescharacteristic
79#2354C2211yescharacteristic
80D4×C4⋊C4—21no—
81C4×C22⋊Q8C2211yescharacteristic
82C4×#121C2211yescharacteristic
83#2298—21no—
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2074C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2065C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2024C2211yescharacteristic
114#2024C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic
118#1993C2211yescharacteristic
119#1992C2211yescharacteristic
120#1991C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1987C2211yescharacteristic
128#1987C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1985C2211yescharacteristic
132#1983C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1947C2211yescharacteristic
136#1940C2211yescharacteristic
137#1940C2211yescharacteristic
138#1939C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic
147#1927C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1880C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1836C2211yescharacteristic
180#1835C2211yescharacteristic
181#1825C2211yescharacteristic
182#1805C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1802C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1771C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1749C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C23×Q8—21no—
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208#554—24no—
209#554—42no—
210C2×C4⋊Q8—24no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8D411yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#489—24no—
248#489—42no—
249#482—24no—
250#469—24no—
251#468—24no—
252#463—42no—
253#446—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260#423—42no—
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391D411yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389D411yescharacteristic
348#389C2311yescharacteristic
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#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—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#387D411yescharacteristic
387#387D411yescharacteristic
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385D411yescharacteristic
402#385D411yescharacteristic
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380D411yescharacteristic
418#380C2311yescharacteristic
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×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
443C43—21no—
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#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×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—44no—
495C22×Q8—82no—
496C22×Q8—82no—
497C22×Q8C2×D411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8#4114yes—
542#125—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#124—22no—
547#124—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—42no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—82no—
555C22⋊Q8—82no—
556#121—22no—
557#121—22no—
558#121—22no—
559#121#4114yes—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573C4×D4—82no—
574C4×D4—82no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—41no—
579#117—44no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
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—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
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⋊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×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C42—22no—
664C2×C42—22no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—22no—
688#106—22no—
689#106—22no—
690#106—41no—
691C4⋊C8—22no—
692C4⋊C8—22no—
693C4⋊C8—41no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721#97—22no—
722#97—22no—
723#97—41no—
724#97—41no—
725C4×C8—41no—
726C4×C8—41no—
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#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C24—21no—
776C24C22×D411yescharacteristic
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—41no—
786C2×Q8—41no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—816no—
799C2×D4—24no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4C2×#4112yes—
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—22no—
826C22×C4—22no—
827C22×C4—22no—
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—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C2×#4112yes—
873C22×C42−1+412yes—
874C22×C4C2511yescharacteristic
875SD16—82no—
876D8—82no—
877M16—82no—
878M16—82no—
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—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
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—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
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—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
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—
960C4⋊C4C2×#4112yes—
961C4⋊C4C2×#4112yes—
962C4⋊C42−1+412yes—
963C22⋊C4—24no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C42—22no—
994C42—22no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42C2×#4112yes—
1018C42H(5,𝔽2)12yes—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—22no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23#54812yes—
1040C23C23×D411yescharacteristic
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—82no—
1046Q8—84no—
1047Q8—84no—
1048Q8—84no—
1049Q8—84no—
1050D4—22no—
1051D4—22no—
1052D4—48no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—162no—
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—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—44no—
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—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—84no—
1144C2×C4—84no—
1145C2×C4—84no—
1146C2×C4—84no—
1147C2×C4—162no—
1148C2×C4—162no—
1149C2×C4#54612yes—
1150C2×C4#54612yes—
1151C2×C4#54812yes—
1152C2×C4#57512yes—
1153C2×C4C22×#4111yescharacteristic
1154C2×C4C22×#4111yescharacteristic
1155C2×C4C2×H(5,𝔽2)11yescharacteristic
1156C2×C4C2×2−1+411yescharacteristic
1157C2×C4C2×2−1+411yescharacteristic
1158C2×C4#58511yescharacteristic
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C8—41no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22C2×#54611yescharacteristic
1189C22C2×#54811yescharacteristic
1190C22#348911yescharacteristic
1191C22C2×#57511yescharacteristic
1192C22#358511yescharacteristic
1193C22#358511yescharacteristic
1194C22#358611yescharacteristic
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—41no—
1200C4—41no—
1201C4—42no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—42no—
1211C4—42no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4#348211yescharacteristic
1223C4#351411yescharacteristic
1224C4#351611yescharacteristic
1225C4#355211yescharacteristic
1226C2—42no—
1227C2—82no—
1228C2—161no—
1229C2#5907511yescharacteristic
1230C2#6115811yescharacteristic
1231C2#6117511yescharacteristic
1232C2#6131811yescharacteristic
1233C2#6133611yescharacteristic
1234C2#6211511yescharacteristic
1235C2#6223011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59136C2semidirect
2. #36420C2semidirect
3. #32254C2semidirect
4. #32240C2semidirect
5. #31822C2semidirect
6. #31815C2semidirect
7. #28651C2semidirect
8. #27740C2semidirect
9. #27724C2semidirect
10. #27710C2semidirect
11. #27443C2semidirect
12. #27435C2semidirect
13. #26519C2semidirect
14. #26439C2semidirect
15. #26433C2semidirect
16. #26295C2semidirect
17. #26033C2semidirect
18. #26031C2semidirect
19. #25940C2semidirect
20. #25908C2semidirect
21. #25335C2semidirect
22. #25230C2semidirect
25. #23230C2semidirect
26. #23141C2semidirect
28. #22955C2semidirect
29. #22526C2semidirect
30. #21582C2semidirect
31. #21313C2semidirect

Maximal subgroups

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

subgroupindex
#591362
#364202
#322542
#322402
#318222
#318152
#286512
#277402
#277242
#277102
#274432
#274352
#265192
#264392
#264332
#262952
#260332
#260312
#259402
#259082
#253352
#252302
#252182
#247562
#232302
#231412
#231402
#229552
#225262
#215822
#213132