Finite Group Databasebeta

← #14738959

Subgroups — #14738959

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622700C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic
5#13068066C214yesmaximal, complemented
6#13067980C214yesmaximal, complemented
7#13067392C211yesmaximal, characteristic, complemented
8#13067271C211yesmaximal, characteristic, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622841—22no—
16#10622744—21no—
17#10622734—21no—
18#10622705C2212yescomplemented
19#10622703—22no—
20#10622700—22no—
21#10622700C2214yes—
22#10622694C2212yescomplemented
23C2×#66873—21no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622460—22no—
28#10622459C2212yes—
29#10622455C2212yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2214yescomplemented
34#10622120C2212yescomplemented
35#10622119C2212yescomplemented
36#10622117C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C2×C11×M16—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—24no—
49C2×(C2×D11)⋊C4—21no—
50#66979—21no—
51C2×C4⋊Dic11D411yescharacteristic
52#66977—21no—
53#66977—21no—
54C22×C11⋊C8—21no—
55C2×C8×D11—24no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44D412yes—
59C4×D44C2312yes—
60#66923—21no—
61#66922C2311yescharacteristic
62#66922C2311yescharacteristic
63C4×Dic22—21no—
64C4×Dic22—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C4⋊C8C2312yes—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66899—24no—
71C22⋊(C11⋊C8)D412yes—
72#66885—22no—
73#66885—22no—
74(C2×D11)⋊C8—24no—
75#66882—22no—
76#66881—22no—
77#66873—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8C2312yes—
83#19387—111nomaximal, Sylow
84C23×D11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—82no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C2×D44—21no—
94C2×D44—22no—
95C2×D44Q1614yescomplemented
96C2×D44C2×D412yes—
97C2×C4×D11—22no—
98C2×C4×D11—22no—
99C2×C4×D11—82no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11C2411yescharacteristic
113C22⋊Dic11—41no—
114#4326—84no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11C2×D412yes—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8C2×D414yes—
129C8×D11—84no—
130#3209—111no—
131#3077—111no—
132C2×#474—111no—
133#2972—111no—
134#1683—114no—
135#1669—114no—
136#1571—111no—
137#1549D1111yescharacteristic, complemented
138#1542—111no—
139C23×C11#12111yescharacteristic
140C22×D11—22no—
141C22×D11—24no—
142C22×D11—81no—
143C22×D11—81no—
144Q8×C11—44no—
145Q8×C11—82no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×Q1612yes—
154C2×C4×C11#13512yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162D44—22no—
163D44—24no—
164D44C2×Q1614yes—
165C4×D11—44no—
166C4×D11—82no—
167Dic22—42no—
168Dic22—81no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—42no—
173#533—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×C4×D4—111no—
176#494—112no—
177#487—112no—
178#478—222no—
179#476—112no—
180#474—114no—
181#474—112no—
182#474—222no—
183#462—222no—
184#451—222no—
185C8×D4—114no—
186C8×D4—222no—
187#431—111no—
188#431C2×D1111yescharacteristic
189#428—221no—
190C2×#107—221no—
191#423C2×D1111yescharacteristic
192C2×C4⋊C8—111no—
193#418—221no—
194C2×#102—221no—
195C2×C22⋊C8—222no—
196#335—114no—
197#333—112no—
198#332—112no—
199#332C2×D1114yescomplemented
200C22×C11—21no—
201C22×C11—21no—
202C22×C11#46712yes—
203C22×C11C2×#12111yescharacteristic
204C2×D11—24no—
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—84no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—82no—
212C4×C11#46712yes—
213C4×C11C22×Q1611yescharacteristic
214C4×C11C2×#13511yescharacteristic
215C4×C11#57612yes—
216Dic11—42no—
217Dic11—81no—
218Dic11—81no—
219C22×Q8—21no—
220C22×D4—111no—
221C23×C4—221no—
222C2×Q16—224no—
223C2×M16—21no—
224C22×C8—224no—
225C22×C8—221no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—111no—
230C4⋊Q8—111no—
231C4⋊Q8C22×D1112yes—
232#125—221no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235C4×Q8—221no—
236C4×Q8—221no—
237C4×D4—112no—
238C4×D4—112no—
239C4×D4—221no—
240C4×D4—221no—
241#117—221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—111no—
245C2×C22⋊C4—221no—
246C2×C42C22×D1111yescharacteristic
247#107—224no—
248#107—222no—
249#106—222no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8C22×D1112yes—
255C4⋊C8C22×D1112yes—
256#103—224no—
257#102—224no—
258#102—222no—
259#102—222no—
260C22⋊C8—21no—
261C22⋊C8—112no—
262C22⋊C8—224no—
263C4×C8—21no—
264C4×C8—112no—
265C2×C11—22no—
266C2×C11#304111yescharacteristic
267C2×C11C2×#46711yescharacteristic
268C2×C11#306911yescharacteristic
269D11—44no—
270C24—221no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×D4—114no—
277C2×D4—112no—
278C2×D4—221no—
279C2×D4—222no—
280C22×C4—41no—
281C22×C4—221no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—882no—
285C22×C4#433911yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288Q16—884no—
289M16—42no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—114no—
293C2×C8—222no—
294C2×C8—442no—
295C2×C8—884no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—112no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—222no—
309C22⋊C4—222no—
310C22⋊C4—441no—
311C42—441no—
312C42#433911yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C23×D1111yescharacteristic
316C11#1938711yescharacteristic, complemented, Sylow
317C23—222no—
318C23—224no—
319C23—881no—
320C23—881no—
321C23#6693711yescharacteristic
322Q8—44no—
323Q8—82no—
324Q8—442no—
325Q8—881no—
326D4—114no—
327D4—222no—
328D4—224no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—222no—
334C2×C4—444no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4#6693711yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6696912yes—
343C2×C4Q16×D1112yes—
344C2×C4C2×#433911yescharacteristic
345C2×C4C2×D4×D1111yescharacteristic
346C2×C4C2×D4×D1111yescharacteristic
347C8—42no—
348C8—42no—
349C8—224no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—224no—
354C22—442no—
355C22—442no—
356C22—884no—
357C22#1062242612yes—
358C22C2×#6693711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—442no—
364C4—881no—
365C4—881no—
366C4#1062242612yes—
367C4C2×#6696911yescharacteristic
368C4C2×Q16×D1111yescharacteristic
369C4#1062330512yes—
370C2—22no—
371C2—444no—
372C2#1307811811yescharacteristic
373C2C2×#1062242611yescharacteristic
374C2#1307835211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1549D11
hypocenterC11#19387
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
5. #13068066C2semidirect
6. #13067980C2semidirect
7. #13067392C2semidirect
8. #13067271C2semidirect
9. C11×#1549C2semidirect
18. #10622705C22semidirect
22. #10622694C22semidirect
33. C11×#332C22semidirect
34. #10622120C22semidirect
35. #10622119C22semidirect
36. #10622117C22semidirect
95. C2×D44Q16semidirect
137. #1549D11semidirect
199. #332C2×D11semidirect
316. C11#19387semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130784152
C2×#106227002
#130776392
#130680662
#130679802
#130673922
#130672712
C11×#15492
#1938711