Finite Group Databasebeta

← #14775134

Subgroups — #14775134

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic
3#13069351C211yesmaximal, characteristic, complemented
4#13069309C211yesmaximal, characteristic, complemented
5#13069247C211yesmaximal, characteristic, complemented
6#13069187C211yesmaximal, characteristic, complemented
7#13069184C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic
9#13068884C211yesmaximal, characteristic, complemented
10#13068809C211yesmaximal, characteristic
11#13068514C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic
14C2×#10622167C211yesmaximal, characteristic
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#389—21no—
23C11×#389C2211yescharacteristic
24C11×#387—21no—
25C11×#385—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622657C418yescomplemented
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622555—21no—
41C22⋊C4×Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48#10622267—21no—
49#10622267—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8C2×C414yes—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C414yes—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—41no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—41no—
111#66899C2×C414yescomplemented
112#66899C2×C414yescomplemented
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)C2×C414yes—
119#66872—22no—
120#66872—41no—
121#66871C2×C414yescomplemented
122#66871C2×C414yescomplemented
123#66867—22no—
124#66867—41no—
125#22932—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—81no—
158C22×Dic11—81no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4#4112yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C42×C11—81no—
178C22⋊Dic11—42no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11C22×C412yes—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—44no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×C11⋊C8#4112yes—
205C2×#484—111no—
206#2360D1111yescharacteristic
207#2345—111no—
208#1943—111no—
209#1935—111no—
210#1927—111no—
211#1918—111no—
212#1918—111no—
213#1892—111no—
214#1865—111no—
215#1853—111no—
216#1776—111no—
217#1763—111no—
218#1752—111no—
219C2×#340—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4×D412yes—
225C23×C11#13712yes—
226C23×C11#13712yes—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—84no—
263C2×C4×C11C4×D412yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—84no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C23×C8—111no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×C4×Q8C2×D1111yescharacteristic
290C22×C4⋊C4—111no—
291C22×C4⋊C4C2×D1111yescharacteristic
292#484—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×C22⋊C8—111no—
302C2×#97—111no—
303C2×#97—111no—
304#391C2×D1111yescharacteristic
305#389—21no—
306#389—111no—
307#389—111no—
308#389C2×D1111yescharacteristic
309#387—21no—
310#387—221no—
311#387—221no—
312#385—21no—
313#380—111no—
314#380—221no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4—221no—
320C4×C22⋊C4C2×D1111yescharacteristic
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11#44114yes—
338C22×C11C2×C4×D411yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11C4×#4111yescharacteristic
355C4×C11#52011yescharacteristic
356C4×C11#55111yescharacteristic
357C4×C11#55211yescharacteristic
358Dic11—42no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—222no—
371C22×C8—222no—
372C22×C8—441no—
373C22⋊Q8—22no—
374C22⋊Q8C4×D1114yes—
375C4×Q8—22no—
376C4×Q8—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4C22⋊D1111yescharacteristic
398C2×C22⋊C4C22⋊D1111yescharacteristic
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#107—114no—
407#106—222no—
408#106—441no—
409#103—114no—
410#103—114no—
411#103—222no—
412#103—441no—
413C22⋊C8—114no—
414#97—222no—
415#97—441no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95C22⋊D1111yescharacteristic
426#95C22⋊D1111yescharacteristic
427C2×C11—24no—
428C2×C11#235911yescharacteristic
429C2×C11C2×#44111yescharacteristic
430C2×C11#294611yescharacteristic
431C2×C11#331411yescharacteristic
432C2×C11#332011yescharacteristic
433C2×C11#334411yescharacteristic
434C2×C11#334611yescharacteristic
435C24C2×C22⋊D1111yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4C2×C4×D1112yes—
461C22×C4#433912yes—
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—112no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—444no—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—112no—
490C4⋊C4—112no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4C2×C4×D1112yes—
501C4⋊C4#434112yes—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—442no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—81no—
512C42—881no—
513C42—881no—
514C11#2293211yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C4×C22⋊D1112yes—
520C23#6699512yes—
521C23#6700412yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—884no—
571C2×C4C4×C22⋊D1112yes—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—222no—
579C8—222no—
580C8—222no—
581C8—441no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1062264314yes—
589C22C2×C4×C22⋊D1111yescharacteristic
590C22#1062333711yescharacteristic
591C22C2×#6699511yescharacteristic
592C22C2×#6700411yescharacteristic
593C22#1062335511yescharacteristic
594C22#1062336611yescharacteristic
595C22#1062336811yescharacteristic
596C4—22no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—42no—
604C4—81no—
605C4—442no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4C4×#434111yescharacteristic
610C4#1062307211yescharacteristic
611C4#1062307711yescharacteristic
612C4#1062308711yescharacteristic
613C2—24no—
614C2#1307160211yescharacteristic
615C2C2×#1062264311yescharacteristic
616C2#1307744411yescharacteristic
617C2#1308069711yescharacteristic
618C2#1308078711yescharacteristic
619C2#1308107111yescharacteristic
620C2#1308109511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2360D11
hypocenterC11#22932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069309C2semidirect
5. #13069247C2semidirect
6. #13069187C2semidirect
7. #13069184C2semidirect
9. #13068884C2semidirect
11. #13068514C2semidirect
12. #13068446C2semidirect
35. #10622657C4semidirect
111. #66899C2×C4semidirect
112. #66899C2×C4semidirect
121. #66871C2×C4semidirect
122. #66871C2×C4semidirect
514. C11#22932semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130714912
#130693512
#130693092
#130692472
#130691872
#130691842
#130690402
#130688842
#130688092
#130685142
#130684462
#130683942
C2×#106221672
C11×#23602
#2293211