Finite Group Databasebeta

← #6580152

Subgroups — #6580152

Order 512.

1884 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#36255C211yesmaximal, characteristic, complemented
2D4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33149C211yesmaximal, characteristic, complemented
4#33051C211yesmaximal, characteristic, complemented
5#32908C211yesmaximal, characteristic
6#29095C211yesmaximal, characteristic, complemented
7#29083C211yesmaximal, characteristic, complemented
8#27744C211yesmaximal, characteristic, complemented
9#27711C211yesmaximal, characteristic, complemented
10#27697C211yesmaximal, characteristic, complemented
11#27571C211yesmaximal, characteristic, complemented
12#27566C211yesmaximal, characteristic, complemented
13#27446C211yesmaximal, characteristic, complemented
14#27443C211yesmaximal, characteristic, complemented
15#26414C211yesmaximal, characteristic, complemented
16#26408C211yesmaximal, characteristic, complemented
17#26119C211yesmaximal, characteristic, complemented
18#25939C211yesmaximal, characteristic, complemented
19#25334C211yesmaximal, characteristic, complemented
20#25305C211yesmaximal, characteristic, complemented
21#25007C211yesmaximal, characteristic, complemented
22#24531C211yesmaximal, characteristic
23#24530C211yesmaximal, characteristic, complemented
24#23011C211yesmaximal, characteristic, complemented
25#22870C211yesmaximal, characteristic
26#22854C211yesmaximal, characteristic, complemented
27#22778C211yesmaximal, characteristic, complemented
28#22758C211yesmaximal, characteristic, complemented
29#22523C211yesmaximal, characteristic, complemented
30#21599C211yesmaximal, characteristic, complemented
31C2×#1762C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C22×C22⋊Q8—21no—
34C22×C4×D4C2211yescharacteristic
35C2×#489C2211yescharacteristic, complemented
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#446C2211yescharacteristic, complemented
41C2×#440C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#97C2211yescharacteristic
46#2857C2211yescharacteristic
47#2852—21no—
48#2850C2211yescharacteristic
49#2848—21no—
50#2594—21no—
51#2592C2211yescharacteristic, complemented
52#2577—21no—
53#2570C2211yescharacteristic, complemented
54#2542C2211yescharacteristic
55#2538C2211yescharacteristic
56#2532—21no—
57#2514C2211yescharacteristic, complemented
58#2512C2211yescharacteristic, complemented
59#2510—21no—
60#2504C2211yescharacteristic
61#2502C2211yescharacteristic
62#2478—21no—
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2450—21no—
66#2449—21no—
67#2449—21no—
68#2440C2211yescharacteristic
69#2440C2211yescharacteristic
70#2437—21no—
71#2437—21no—
72#2417—21no—
73#2409—21no—
74#2367C2211yescharacteristic, complemented
75#2361C2211yescharacteristic
76#2360C2211yescharacteristic
77#2356C2211yescharacteristic, complemented
78#2355C2211yescharacteristic, complemented
79#2354C2211yescharacteristic, complemented
80D4×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86#2290—21no—
87C2×C4×C4⋊C4C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2024C2211yescharacteristic, complemented
109#2024C2211yescharacteristic, complemented
110#2023C2211yescharacteristic, complemented
111#2023C2211yescharacteristic, complemented
112#1993C2211yescharacteristic, complemented
113#1993C2211yescharacteristic, complemented
114#1990C2211yescharacteristic, complemented
115#1988C2211yescharacteristic, complemented
116#1987C2211yescharacteristic, complemented
117#1987C2211yescharacteristic, complemented
118#1987C2211yescharacteristic, complemented
119#1985C2211yescharacteristic, complemented
120#1973C2211yescharacteristic
121#1970C2211yescharacteristic
122#1959C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1940C2211yescharacteristic, complemented
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic, complemented
128#1936C2211yescharacteristic, complemented
129#1936C2211yescharacteristic, complemented
130#1936C2211yescharacteristic, complemented
131#1935C2211yescharacteristic, complemented
132#1935C2211yescharacteristic, complemented
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic, complemented
135#1933C2211yescharacteristic, complemented
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1921C2211yescharacteristic, complemented
139#1921C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1918C2211yescharacteristic, complemented
144#1917C2211yescharacteristic, complemented
145#1917C2211yescharacteristic, complemented
146#1893C2211yescharacteristic
147#1893C2211yescharacteristic
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic
150#1880C2211yescharacteristic
151#1879C2211yescharacteristic
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1874C2211yescharacteristic
163#1872C2211yescharacteristic
164#1863C2211yescharacteristic, complemented
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic, complemented
168#1852C2211yescharacteristic
169#1852C2211yescharacteristic
170#1850C2211yescharacteristic
171#1850C2211yescharacteristic
172#1836C2211yescharacteristic, complemented
173#1836C2211yescharacteristic, complemented
174#1834C2211yescharacteristic, complemented
175#1824C2211yescharacteristic
176#1824C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1803C2211yescharacteristic, complemented
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic, complemented
185#1797C2211yescharacteristic
186#1771C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212D4×Q8—24no—
213D4×Q8—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#124C2311yescharacteristic
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×#121C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—24no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—42no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C22×C4⋊C4—21no—
252C22×C4⋊C4—21no—
253C22×C4⋊C4—21no—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C42—21no—
261C22×C42C2311yescharacteristic
262#489—42no—
263#463—24no—
264#463—42no—
265#450—24no—
266#447—24no—
267#446—42no—
268#440—24no—
269C4×D8—24no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102—24no—
287C2×#102—24no—
288C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97—42no—
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#401—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#391—21no—
342#391—21no—
343#391D411yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389D411yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
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#388—21no—
376#388—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#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#383—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376—21no—
451C2×#95—21no—
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—44no—
499C22×Q8—44no—
500C22×Q8—82no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4#4114yes—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—44no—
527C23×C4—44no—
528C23×C4—82no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#126—82no—
565#124—22no—
566#124—22no—
567C22⋊Q8—24no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—82no—
581#121—22no—
582#121—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—41no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—44no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—44no—
606C4×D4—44no—
607C4×D4#4114yes—
608#117—82no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
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—21no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—44no—
642C2×C4⋊C4—44no—
643C2×C4⋊C4—44no—
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⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
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—44no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—82no—
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—22no—
723#107—41no—
724#107—41no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102#4114yes—
755C22⋊C8—22no—
756C22⋊C8—22no—
757#97—22no—
758#97—22no—
759#97—22no—
760#97—41no—
761#97—41no—
762#97—41no—
763C4×C8—22no—
764C4×C8—41no—
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#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#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—24no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—41no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—816no—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4C2×#4112yes—
860C2×D4C2×#4112yes—
861C2×D4C2×#4112yes—
862C2×D4C2×#4112yes—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—24no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—816no—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2×#4112yes—
937C22×C42−1+412yes—
938C22×C4C2511yescharacteristic
939SD16—44no—
940SD16—82no—
941D8—44no—
942D8—82no—
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—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—44no—
967C2×C8—44no—
968C2×C8C2×#4112yes—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—22no—
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—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4C2×#4112yes—
1027C4⋊C4C2×#4112yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—24no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
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⋊C4AGL(1,ℤ/8)14yes—
1063C42—22no—
1064C42—22no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42C2×#4112yes—
1083C42H(5,𝔽2)12yes—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—48no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—48no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—84no—
1116C23#54812yes—
1117C23C2×AGL(1,ℤ/8)12yes—
1118C23#57812yes—
1119C23C23×D411yescharacteristic
1120Q8—44no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—84no—
1126Q8—84no—
1127Q8—84no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—48no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4#52914yes—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
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—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
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—44no—
1183C2×C4—44no—
1184C2×C4—48no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
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—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4#54612yes—
1234C2×C4#54612yes—
1235C2×C4#54812yes—
1236C2×C4C2×AGL(1,ℤ/8)12yes—
1237C2×C4C2×AGL(1,ℤ/8)12yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—22no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—816no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22#336714yes—
1281C22C2×#54611yescharacteristic
1282C22C2×#54811yescharacteristic
1283C22D4×#4111yescharacteristic
1284C22C22×AGL(1,ℤ/8)11yescharacteristic
1285C22C2×#57811yescharacteristic
1286C22#358511yescharacteristic
1287C22#358511yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4C2×#52911yescharacteristic
1315C4#349511yescharacteristic
1316C4#350511yescharacteristic
1317C4#352011yescharacteristic
1318C2—24no—
1319C2—44no—
1320C2—82no—
1321C2—161no—
1322C2#3610811yescharacteristic
1323C2#6115511yescharacteristic
1324C2#6119411yescharacteristic
1325C2C2×#336711yescharacteristic
1326C2#6133211yescharacteristic
1327C2#6145111yescharacteristic
1328C2#6152411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
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. #36255C2semidirect
2. D4×C22⋊Q8C2semidirect
3. #33149C2semidirect
4. #33051C2semidirect
6. #29095C2semidirect
7. #29083C2semidirect
8. #27744C2semidirect
9. #27711C2semidirect
10. #27697C2semidirect
11. #27571C2semidirect
12. #27566C2semidirect
13. #27446C2semidirect
14. #27443C2semidirect
15. #26414C2semidirect
16. #26408C2semidirect
17. #26119C2semidirect
18. #25939C2semidirect
19. #25334C2semidirect
20. #25305C2semidirect
21. #25007C2semidirect
23. #24530C2semidirect
24. #23011C2semidirect
26. #22854C2semidirect
27. #22778C2semidirect
28. #22758C2semidirect
29. #22523C2semidirect
30. #21599C2semidirect
31. C2×#1762C2semidirect
35. C2×#489C22semidirect
40. C2×#446C22semidirect
51. #2592C22semidirect
53. #2570C22semidirect
57. #2514C22semidirect
58. #2512C22semidirect
74. #2367C22semidirect
77. #2356C22semidirect
78. #2355C22semidirect
79. #2354C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2100C22semidirect
91. #2100C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2087C22semidirect
95. #2086C22semidirect
98. #2072C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
103. #2067C22semidirect
108. #2024C22semidirect
109. #2024C22semidirect
110. #2023C22semidirect
111. #2023C22semidirect
112. #1993C22semidirect
113. #1993C22semidirect
114. #1990C22semidirect
115. #1988C22semidirect
116. #1987C22semidirect
117. #1987C22semidirect
118. #1987C22semidirect
119. #1985C22semidirect
122. #1959C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1940C22semidirect
127. #1936C22semidirect
128. #1936C22semidirect
129. #1936C22semidirect
130. #1936C22semidirect
131. #1935C22semidirect
132. #1935C22semidirect
134. #1933C22semidirect
135. #1933C22semidirect
138. #1921C22semidirect
139. #1921C22semidirect
140. #1921C22semidirect
141. #1921C22semidirect
142. #1921C22semidirect
143. #1918C22semidirect
144. #1917C22semidirect
145. #1917C22semidirect
164. #1863C22semidirect
167. #1862C22semidirect
172. #1836C22semidirect
173. #1836C22semidirect
174. #1834C22semidirect
181. #1803C22semidirect
184. #1802C22semidirect
186. #1771C22semidirect
187. #1771C22semidirect
188. #1770C22semidirect

Maximal subgroups

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

subgroupindex
#362552
D4×C22⋊Q82
#331492
#330512
#329082
#290952
#290832
#277442
#277112
#276972
#275712
#275662
#274462
#274432
#264142
#264082
#261192
#259392
#253342
#253052
#250072
#245312
#245302
#230112
#228702
#228542
#227782
#227582
#225232
#215992
C2×#17622