Finite Group Databasebeta

← #6832137

Subgroups — #6832137

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42696C211yesmaximal, characteristic, complemented
2#42490C211yesmaximal, characteristic, complemented
3#33046C211yesmaximal, characteristic, complemented
4#32605C211yesmaximal, characteristic, complemented
5#32598C211yesmaximal, characteristic, complemented
6#32440C211yesmaximal, characteristic, complemented
7#32438C211yesmaximal, characteristic, complemented
8#31157C211yesmaximal, characteristic, complemented
9#31153C211yesmaximal, characteristic, complemented
10#30879C211yesmaximal, characteristic, complemented
11#30878C211yesmaximal, characteristic, complemented
12#29961C211yesmaximal, characteristic, complemented
13#29723C211yesmaximal, characteristic, complemented
14#29087C211yesmaximal, characteristic, complemented
15#29083C211yesmaximal, characteristic, complemented
16#28433C211yesmaximal, characteristic, complemented
17#28410C211yesmaximal, characteristic, complemented
18#27267C211yesmaximal, characteristic, complemented
19#27255C211yesmaximal, characteristic, complemented
20#26837C211yesmaximal, characteristic, complemented
21#26829C211yesmaximal, characteristic, complemented
22#26362C211yesmaximal, characteristic, complemented
23#26360C211yesmaximal, characteristic, complemented
24#25309C211yesmaximal, characteristic, complemented
25#25301C211yesmaximal, characteristic, complemented
26#24367C211yesmaximal, characteristic
27#24367C211yesmaximal, characteristic
28#22874C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#21605C211yesmaximal, characteristic, complemented
31#21235C211yesmaximal, characteristic
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#491C2211yescharacteristic, complemented
34C2×#488C2211yescharacteristic, complemented
35C2×#487C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#461C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#446C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2842—21no—
52#2827—21no—
53#2788—21no—
54#2787—21no—
55#2784—21no—
56#2780—21no—
57#2780—21no—
58#2770—21no—
59#2768—21no—
60#2683—21no—
61#2653—21no—
62#2649—21no—
63#2628C2211yescharacteristic
64#2626—21no—
65#2626—21no—
66#2621C2211yescharacteristic
67#2592C2211yescharacteristic, complemented
68#2568C2211yescharacteristic, complemented
69#2566C2211yescharacteristic
70#2566C2211yescharacteristic
71#2546C2211yescharacteristic, complemented
72#2545C2211yescharacteristic, complemented
73#2538C2211yescharacteristic
74#2538C2211yescharacteristic
75#2518—21no—
76#2514C2211yescharacteristic, complemented
77#2513C2211yescharacteristic, complemented
78#2454C2211yescharacteristic
79#2454C2211yescharacteristic
80#2452C2211yescharacteristic
81#2452C2211yescharacteristic
82#2448C2211yescharacteristic, complemented
83#2446C2211yescharacteristic, complemented
84#2441C2211yescharacteristic
85#2441C2211yescharacteristic
86#2437—21no—
87#2432C2211yescharacteristic
88#2432C2211yescharacteristic
89#2396C2211yescharacteristic
90#2360C2211yescharacteristic
91#2360C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93D4×C22⋊C4C2211yescharacteristic
94#2311C2211yescharacteristic
95#2309C2211yescharacteristic
96#2097C2211yescharacteristic, complemented
97#2096C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2092C2211yescharacteristic, complemented
100#2088C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2043C2211yescharacteristic, complemented
123#2043C2211yescharacteristic, complemented
124#2042C2211yescharacteristic, complemented
125#2042C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic, complemented
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic, complemented
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#2013C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic
136#1993C2211yescharacteristic, complemented
137#1984C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1960C2211yescharacteristic, complemented
149#1959C2211yescharacteristic, complemented
150#1956C2211yescharacteristic, complemented
151#1948C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1933C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1919C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1873C2211yescharacteristic
183#1873C2211yescharacteristic
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic
188#1853C2211yescharacteristic
189#1852C2211yescharacteristic
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1835C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244#491—42no—
245#488—42no—
246#487—42no—
247#479—42no—
248#479—42no—
249#463—42no—
250#463—42no—
251#461—42no—
252#461—42no—
253#450—24no—
254#450—24no—
255#446—42no—
256#440—42no—
257C4×SD16—42no—
258#428—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#416—42no—
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×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102—42no—
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309#405—42no—
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#401—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400D411yescharacteristic
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399D411yescharacteristic
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#398D411yescharacteristic
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396D411yescharacteristic
362#396D411yescharacteristic
363#395—21no—
364#395D411yescharacteristic
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#393—21no—
370#393—21no—
371#393—21no—
372#393—21no—
373#393D411yescharacteristic
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#383—21no—
449#382—21no—
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4#4114yes—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529AGL(1,ℤ/8)—416no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576#125—41no—
577#125—41no—
578#125—41no—
579#125—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—82no—
589C22⋊Q8—82no—
590C22⋊Q8—82no—
591C22⋊Q8—82no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—22no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765#97—22no—
766#97—22no—
767#97—41no—
768#97—41no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—41no—
772C4×C8—41no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—24no—
818C24—21no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826#41—44no—
827#41—44no—
828#41—82no—
829#41—82no—
830C2×Q8—22no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×D4—24no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—42no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C2×D4C2×#4112yes—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
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—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2×#4112yes—
931C22×C42−1+412yes—
932C22×C4C2511yescharacteristic
933SD16—44no—
934SD16—44no—
935SD16—44no—
936SD16—44no—
937SD16—82no—
938SD16—82no—
939D8—44no—
940D8—44no—
941M16—28no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—44no—
964C2×C8H(5,𝔽2)12yes—
965C2×C8H(5,𝔽2)12yes—
966C2×C8H(5,𝔽2)12yes—
967C4⋊C4—22no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C22⋊C4—22no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—22no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—84no—
1114C23—84no—
1115C23—84no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23#54812yes—
1121C23C23×D411yescharacteristic
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—82no—
1135Q8—162no—
1136D4—22no—
1137D4—22no—
1138D4—22no—
1139D4—22no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—84no—
1149D4—84no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—84no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4#54812yes—
1237C2×C4#57712yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—22no—
1245C8—22no—
1246C8—22no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22C2×#54811yescharacteristic
1282C22#349611yescharacteristic
1283C22#349811yescharacteristic
1284C22C2×#57711yescharacteristic
1285C22#358411yescharacteristic
1286C22#358511yescharacteristic
1287C22#358611yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4#345911yescharacteristic
1315C4#349011yescharacteristic
1316C4#353611yescharacteristic
1317C4#356111yescharacteristic
1318C2—42no—
1319C2—82no—
1320C2—82no—
1321C2—161no—
1322C2#3942011yescharacteristic
1323C2#6132611yescharacteristic
1324C2#6133311yescharacteristic
1325C2#6230811yescharacteristic
1326C2#6235211yescharacteristic
1327C2#6246111yescharacteristic
1328C2#6246611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
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. #42696C2semidirect
2. #42490C2semidirect
3. #33046C2semidirect
4. #32605C2semidirect
5. #32598C2semidirect
6. #32440C2semidirect
7. #32438C2semidirect
8. #31157C2semidirect
9. #31153C2semidirect
10. #30879C2semidirect
11. #30878C2semidirect
12. #29961C2semidirect
13. #29723C2semidirect
14. #29087C2semidirect
15. #29083C2semidirect
16. #28433C2semidirect
17. #28410C2semidirect
18. #27267C2semidirect
19. #27255C2semidirect
20. #26837C2semidirect
21. #26829C2semidirect
22. #26362C2semidirect
23. #26360C2semidirect
24. #25309C2semidirect
25. #25301C2semidirect
28. #22874C2semidirect
29. #22854C2semidirect
30. #21605C2semidirect
33. C2×#491C22semidirect
34. C2×#488C22semidirect
35. C2×#487C22semidirect
36. C2×#479C22semidirect
37. C2×#479C22semidirect
44. C2×#446C22semidirect
67. #2592C22semidirect
68. #2568C22semidirect
71. #2546C22semidirect
72. #2545C22semidirect
76. #2514C22semidirect
77. #2513C22semidirect
82. #2448C22semidirect
83. #2446C22semidirect
96. #2097C22semidirect
97. #2096C22semidirect
98. #2095C22semidirect
99. #2092C22semidirect
100. #2088C22semidirect
101. #2086C22semidirect
104. #2072C22semidirect
105. #2071C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
122. #2043C22semidirect
123. #2043C22semidirect
124. #2042C22semidirect
125. #2042C22semidirect
126. #2026C22semidirect
127. #2025C22semidirect
128. #2024C22semidirect
129. #2023C22semidirect
136. #1993C22semidirect
137. #1984C22semidirect
148. #1960C22semidirect
149. #1959C22semidirect
150. #1956C22semidirect
151. #1948C22semidirect
152. #1947C22semidirect
153. #1939C22semidirect
155. #1936C22semidirect
156. #1935C22semidirect
157. #1935C22semidirect
158. #1935C22semidirect
160. #1934C22semidirect
161. #1933C22semidirect
162. #1933C22semidirect
163. #1933C22semidirect
166. #1921C22semidirect
167. #1919C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
184. #1865C22semidirect
186. #1863C22semidirect
192. #1835C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1770C22semidirect

Maximal subgroups

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

subgroupindex
#426962
#424902
#330462
#326052
#325982
#324402
#324382
#311572
#311532
#308792
#308782
#299612
#297232
#290872
#290832
#284332
#284102
#272672
#272552
#268372
#268292
#263622
#263602
#253092
#253012
#243672
#228742
#228542
#216052
#212352