Finite Group Databasebeta

← #7203087

Subgroups — #7203087

Order 512.

1697 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45611C211yesmaximal, characteristic, complemented
2D4×C22⋊Q8C211yesmaximal, characteristic
3#33009C211yesmaximal, characteristic
4#32953C211yesmaximal, characteristic
5#32790C211yesmaximal, characteristic, complemented
6#32741C211yesmaximal, characteristic, complemented
7#32589C211yesmaximal, characteristic, complemented
8#32551C211yesmaximal, characteristic, complemented
9#32448C211yesmaximal, characteristic, complemented
10#32342C211yesmaximal, characteristic, complemented
11#31806C211yesmaximal, characteristic, complemented
12#31708C211yesmaximal, characteristic, complemented
13#31478C211yesmaximal, characteristic, complemented
14#31452C211yesmaximal, characteristic, complemented
15#31252C211yesmaximal, characteristic, complemented
16#31081C211yesmaximal, characteristic, complemented
17#30946C211yesmaximal, characteristic, complemented
18#30779C211yesmaximal, characteristic, complemented
19#27555C211yesmaximal, characteristic, complemented
20#27552C211yesmaximal, characteristic, complemented
21#27525C211yesmaximal, characteristic
22#27523C211yesmaximal, characteristic
23#27315C211yesmaximal, characteristic, complemented
24#27245C211yesmaximal, characteristic
25#26384C211yesmaximal, characteristic, complemented
26#26119C211yesmaximal, characteristic, complemented
27#26040C211yesmaximal, characteristic, complemented
28#25838C211yesmaximal, characteristic, complemented
29#24921C211yesmaximal, characteristic
30#24342C211yesmaximal, characteristic, complemented
31#23339C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C22×C22⋊Q8—21no—
34C22×C4×D4C2211yescharacteristic
35C2×#500C2211yescharacteristic, complemented
36C2×#484C2211yescharacteristic
37C2×#477C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2855C2211yescharacteristic
46#2848—21no—
47#2833—21no—
48#2776—21no—
49#2745—21no—
50#2738—21no—
51#2713—21no—
52#2690—21no—
53#2677—21no—
54#2581C2211yescharacteristic, complemented
55#2570C2211yescharacteristic, complemented
56#2551C2211yescharacteristic, complemented
57#2546C2211yescharacteristic, complemented
58#2542C2211yescharacteristic
59#2538C2211yescharacteristic
60#2514C2211yescharacteristic, complemented
61#2511C2211yescharacteristic, complemented
62#2506C2211yescharacteristic, complemented
63#2495C2211yescharacteristic
64#2494C2211yescharacteristic
65#2492C2211yescharacteristic
66#2452C2211yescharacteristic
67#2452C2211yescharacteristic
68#2451C2211yescharacteristic, complemented
69#2449—21no—
70#2449—21no—
71#2440C2211yescharacteristic
72#2440C2211yescharacteristic
73#2437—21no—
74#2437—21no—
75#2423C2211yescharacteristic
76#2417—21no—
77#2409—21no—
78#2381—21no—
79D4×C4⋊C4C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2072C2211yescharacteristic, complemented
111#2072C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2066C2211yescharacteristic, complemented
115#2066C2211yescharacteristic, complemented
116#2065C2211yescharacteristic
117#2057C2211yescharacteristic, complemented
118#2057C2211yescharacteristic, complemented
119#2057C2211yescharacteristic, complemented
120#2057C2211yescharacteristic, complemented
121#2057C2211yescharacteristic, complemented
122#2057C2211yescharacteristic, complemented
123#2057C2211yescharacteristic, complemented
124#2057C2211yescharacteristic, complemented
125#2057C2211yescharacteristic, complemented
126#2055C2211yescharacteristic
127#2055C2211yescharacteristic
128#2036C2211yescharacteristic
129#2036C2211yescharacteristic
130#2024C2211yescharacteristic, complemented
131#2024C2211yescharacteristic, complemented
132#2023C2211yescharacteristic
133#1993C2211yescharacteristic, complemented
134#1988C2211yescharacteristic, complemented
135#1985C2211yescharacteristic, complemented
136#1984C2211yescharacteristic, complemented
137#1973C2211yescharacteristic
138#1947C2211yescharacteristic, complemented
139#1947C2211yescharacteristic, complemented
140#1944C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic, complemented
148#1933C2211yescharacteristic, complemented
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1880C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic, complemented
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1845C2211yescharacteristic, complemented
188#1836C2211yescharacteristic, complemented
189#1824C2211yescharacteristic
190#1817C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208D4×Q8—42no—
209D4×Q8—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#125—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—48no—
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—42no—
238C2×C4×D4—42no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4—21no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#500—42no—
256#484—42no—
257#477—42no—
258#474—42no—
259#474—42no—
260#474—42no—
261#450—42no—
262#440—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#401—21no—
312#401—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391D411yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389—21no—
363#389—21no—
364#389—21no—
365#389D411yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—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#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385D411yescharacteristic
416#385D411yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#383—21no—
423#383—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380D411yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—44no—
498C22×Q8—44no—
499C22×Q8—82no—
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—44no—
521C23×C4—44no—
522C23×C4—82no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—44no—
551C4⋊Q8—82no—
552#125—82no—
553C22⋊Q8—24no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C22⋊Q8—44no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—82no—
567C22⋊Q8—82no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—44no—
589C4×D4—44no—
590C2×C4⋊C4—22no—
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⋊C4—21no—
609C2×C4⋊C4—21no—
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—41no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
660C2×C22⋊C4—21no—
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—44no—
673C2×C22⋊C4—44no—
674C2×C22⋊C4—44no—
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—22no—
695#107—22no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—41no—
706#106—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—41no—
738#97—41no—
739C4×C8—41no—
740C4×C8—41no—
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#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—24no—
790C24—21no—
791C24—42no—
792C24—42no—
793C24—42no—
794C24—42no—
795C24—81no—
796C24—81no—
797C24C22×D411yescharacteristic
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—41no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—816no—
823C2×D4—24no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4H(5,𝔽2)12yes—
839C2×D42−1+412yes—
840C2×D42−1+412yes—
841C2×D42−1+412yes—
842C22×C4—24no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—816no—
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C2511yescharacteristic
910SD16—44no—
911SD16—82no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4AGL(1,ℤ/8)14yes—
1003C4⋊C4H(5,𝔽2)12yes—
1004C22⋊C4—24no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—41no—
1043C42—41no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—22no—
1053C23—22no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—48no—
1059C23—48no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—84no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—84no—
1075C23#57812yes—
1076C23C23×D411yescharacteristic
1077Q8—44no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—84no—
1083Q8—84no—
1084Q8—84no—
1085Q8—162no—
1086Q8—162no—
1087D4—22no—
1088D4—22no—
1089D4—22no—
1090D4—22no—
1091D4—22no—
1092D4—48no—
1093D4—41no—
1094D4—41no—
1095D4#56314yes—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—44no—
1133C2×C4—48no—
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—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—82no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—84no—
1188C2×C4C2×AGL(1,ℤ/8)12yes—
1189C2×C4C2×AGL(1,ℤ/8)12yes—
1190C2×C4C2×AGL(1,ℤ/8)12yes—
1191C2×C4#57612yes—
1192C2×C4C2×H(5,𝔽2)11yescharacteristic
1193C2×C4C2×H(5,𝔽2)11yescharacteristic
1194C2×C4C2×2−1+411yescharacteristic
1195C2×C4C2×2−1+411yescharacteristic
1196C2×C4C2×2−1+411yescharacteristic
1197C2×C4#58511yescharacteristic
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C22—24no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—42no—
1212C22—42no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—42no—
1217C22—41no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—816no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22#348411yescharacteristic
1229C22#348611yescharacteristic
1230C22#348911yescharacteristic
1231C22C22×AGL(1,ℤ/8)11yescharacteristic
1232C22C2×#57611yescharacteristic
1233C22C2×#57811yescharacteristic
1234C22#358611yescharacteristic
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—41no—
1241C4—42no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4C2×#56311yescharacteristic
1263C4#353511yescharacteristic
1264C4#353811yescharacteristic
1265C4#354111yescharacteristic
1266C2—42no—
1267C2—44no—
1268C2—82no—
1269C2#4544611yescharacteristic
1270C2#6159111yescharacteristic
1271C2#6162211yescharacteristic
1272C2#6183711yescharacteristic
1273C2#6184911yescharacteristic
1274C2#6210911yescharacteristic
1275C2#6220111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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. #45611C2semidirect
5. #32790C2semidirect
6. #32741C2semidirect
7. #32589C2semidirect
8. #32551C2semidirect
9. #32448C2semidirect
10. #32342C2semidirect
11. #31806C2semidirect
12. #31708C2semidirect
13. #31478C2semidirect
14. #31452C2semidirect
15. #31252C2semidirect
16. #31081C2semidirect
17. #30946C2semidirect
18. #30779C2semidirect
19. #27555C2semidirect
20. #27552C2semidirect
23. #27315C2semidirect
25. #26384C2semidirect
26. #26119C2semidirect
27. #26040C2semidirect
28. #25838C2semidirect
30. #24342C2semidirect
31. #23339C2semidirect
35. C2×#500C22semidirect
37. C2×#477C22semidirect
54. #2581C22semidirect
55. #2570C22semidirect
56. #2551C22semidirect
57. #2546C22semidirect
60. #2514C22semidirect
61. #2511C22semidirect
62. #2506C22semidirect
68. #2451C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
91. #2099C22semidirect
92. #2095C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
97. #2086C22semidirect
98. #2086C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
101. #2083C22semidirect
110. #2072C22semidirect
111. #2072C22semidirect
112. #2068C22semidirect
114. #2066C22semidirect
115. #2066C22semidirect
117. #2057C22semidirect
118. #2057C22semidirect
119. #2057C22semidirect
120. #2057C22semidirect
121. #2057C22semidirect
122. #2057C22semidirect
123. #2057C22semidirect
124. #2057C22semidirect
125. #2057C22semidirect
130. #2024C22semidirect
131. #2024C22semidirect
133. #1993C22semidirect
134. #1988C22semidirect
135. #1985C22semidirect
136. #1984C22semidirect
138. #1947C22semidirect
139. #1947C22semidirect
140. #1944C22semidirect
141. #1943C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
147. #1933C22semidirect
148. #1933C22semidirect
156. #1921C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
162. #1916C22semidirect
173. #1863C22semidirect
187. #1845C22semidirect
188. #1836C22semidirect

Maximal subgroups

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

subgroupindex
#456112
D4×C22⋊Q82
#330092
#329532
#327902
#327412
#325892
#325512
#324482
#323422
#318062
#317082
#314782
#314522
#312522
#310812
#309462
#307792
#275552
#275522
#275252
#275232
#273152
#272452
#263842
#261192
#260402
#258382
#249212
#243422
#233392