Finite Group Databasebeta

← #14645893

Subgroups — #14645893

Order 2816.

804 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623253C211yesmaximal, characteristic
2#13068618C212yesmaximal
3C2×#10622184C211yesmaximal, characteristic
4C2×#10622094C212yesmaximal
5C11×#1956C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×#66997—22no—
8#10623253—22no—
9#10623253—24no—
10#10623253C414yescomplemented
11C2×#66941—22no—
12C2×#66940—22no—
13C2×C4×Dic22C2212yes—
14C2×C11×#103—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C2×#66874—22no—
18C2×C4⋊(C11⋊C8)C2212yes—
19#10622184—22no—
20#10622167—22no—
21#10622094—24no—
22C22×Q8×C11D412yes—
23C22×Dic22—22no—
24C22×Dic22D412yes—
25C22×C8×C11—21no—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8C2×C412yes—
28C11×C4⋊Q8D412yes—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33#66997—28no—
34#66997—28no—
35C2×C4⋊Dic11D412yes—
36C2×Dic11⋊C4—24no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—22no—
39C2×C4×Dic11—22no—
40C22×C11⋊C8—22no—
41#66941—28no—
42#66941—28no—
43#66940—28no—
44#66940—28no—
45C4×Dic22—22no—
46C4×Dic22—22no—
47C4×Dic22C2×C414yes—
48C4×Dic22D414yes—
49C11×#103—44no—
50C4×C8×C11—22no—
51#66874—44no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#8451—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11—42no—
57C2×Q8×C11—42no—
58C2×Q8×C11C22⋊C414yes—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D412yes—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C2×Dic22—28no—
66C2×Dic22—22no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×Dic22—82no—
70C2×Dic22—82no—
71C2×Dic22C22⋊C414yes—
72C2×Dic22SD1614yes—
73C2×Dic22Q1614yes—
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—24no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D412yes—
85C4⋊Dic11—22no—
86C4⋊Dic11C22⋊C414yes—
87Dic11⋊C4—216no—
88Dic11⋊C4—24no—
89Dic11⋊C4—24no—
90C4×Dic11—28no—
91C4×Dic11—24no—
92C4×Dic11—24no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96C2×Q82—111no—
97#1956D1111yescharacteristic
98#1803—112no—
99C2×#333—111no—
100C2×Q8⋊C8—112no—
101C23×C11#12011yescharacteristic
102Q8×C11—44no—
103Q8×C11—82no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—24no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—82no—
110C2×C4×C11—81no—
111C2×C4×C11C2×C22⋊C412yes—
112C2×C4×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11#12012yes—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11C2×SD1612yes—
116C2×C4×C11C2×Q1612yes—
117C2×C4×C11#13712yes—
118C2×C4×C11#13712yes—
119C2×Dic11—24no—
120C2×Dic11—24no—
121C2×Dic11—24no—
122C2×Dic11—24no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125Dic22—24no—
126Dic22—24no—
127Dic22—24no—
128Dic22—88no—
129Dic22#10318yescomplemented
130C8×C11—42no—
131C11⋊C8—82no—
132Q82—114no—
133Q82—224no—
134Q82—222no—
135C2×C4⋊Q8—222no—
136C2×C4⋊Q8—222no—
137C2×C4⋊Q8C2×D1111yescharacteristic
138C2×C4×Q8—112no—
139C2×C4×Q8—222no—
140C2×C4⋊C8—112no—
141C2×#103—22no—
142C2×#103—222no—
143C2×C4×C8C2×D1111yescharacteristic
144#384C2×D1111yescharacteristic
145#340—222no—
146#333—222no—
147Q8⋊C8—224no—
148C22×C11#37911yescharacteristic
149C22×C11#44812yes—
150C22×C11#45112yes—
151C22×C11#45311yescharacteristic
152C22×C11#45511yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—44no—
156C4×C11—161no—
157C4×C11C2×#10312yes—
158C4×C11#41912yes—
159C4×C11#44812yes—
160C4×C11#45112yes—
161Dic11—28no—
162Dic11—44no—
163C22×Q8—112no—
164C22×Q8—222no—
165C22×Q8C22⋊D1112yes—
166C22×C8—21no—
167C22×C8—222no—
168C4⋊Q8—22no—
169C4⋊Q8—228no—
170C4⋊Q8—228no—
171C4⋊Q8—228no—
172C4⋊Q8—228no—
173C4⋊Q8C4×D1112yes—
174C4⋊Q8D4412yes—
175C4×Q8—114no—
176C4×Q8—114no—
177C4×Q8—228no—
178C4×Q8—228no—
179C4×Q8—222no—
180C4×Q8—222no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—224no—
186C2×C4⋊C4—222no—
187C2×C42—222no—
188C2×C42—222no—
189C2×C42C22×D1111yescharacteristic
190C4⋊C8—222no—
191C4⋊C8—222no—
192#103—44no—
193#103—444no—
194C4×C8—22no—
195C2×C11#162311yescharacteristic
196C2×C11#163311yescharacteristic
197C2×C11#164512yes—
198C2×C11#178712yes—
199C2×C11#179211yescharacteristic
200C2×Q8—22no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—114no—
204C2×Q8—114no—
205C2×Q8—114no—
206C2×Q8—228no—
207C2×Q8—222no—
208C2×Q8—222no—
209C2×Q8—222no—
210C2×Q8—882no—
211C2×Q8—882no—
212C2×Q8(C2×D11)⋊C414yes—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4D4×D1112yes—
218C22×C4C2×C22⋊D1111yescharacteristic
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—442no—
223C2×C8—442no—
224C2×C8—442no—
225C4⋊C4—24no—
226C4⋊C4—24no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—114no—
231C4⋊C4—2216no—
232C4⋊C4—222no—
233C4⋊C4—224no—
234C4⋊C4—224no—
235C42—228no—
236C42—224no—
237C42—224no—
238C42C2×C4×D1111yescharacteristic
239C42C2×D4411yescharacteristic
240C42D4×D1112yes—
241C11#845111yescharacteristic, complemented, Sylow
242C23#6699011yescharacteristic
243Q8—44no—
244Q8—82no—
245Q8—118no—
246Q8—224no—
247Q8—224no—
248Q8—224no—
249Q8—888no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—24no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—82no—
256C2×C4—81no—
257C2×C4—224no—
258C2×C4—224no—
259C2×C4—224no—
260C2×C4—224no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4C22⋊C4×D1112yes—
264C2×C4#6693512yes—
265C2×C4SD16×D1112yes—
266C2×C4#6696812yes—
267C2×C4Q16×D1112yes—
268C2×C4#6697112yes—
269C2×C4C2×(C2×D11)⋊C411yescharacteristic
270C2×C4#6699011yescharacteristic
271C8—42no—
272C8—882no—
273C22#1062256811yescharacteristic
274C22#1062267411yescharacteristic
275C22#1062269011yescharacteristic
276C22#1062278312yes—
277C22#1062279912yes—
278C4—21no—
279C4—21no—
280C4—44no—
281C4—161no—
282C4—228no—
283C4—444no—
284C4D11×#10312yes—
285C4#1062241512yes—
286C4#1062241912yes—
287C4#1062242112yes—
288C2#1306769211yescharacteristic
289C2#1306775411yescharacteristic
290C2#1306783412yes—
291C2#1306854912yes—
292C2#1306856911yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1956C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1956D11
hypocenterC11#8451
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
10. #10623253C4semidirect
129. Dic22#103semidirect
241. C11#8451semidirect

Maximal subgroups

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

subgroupindex
C2×#106232532
#130686182
C2×#106221842
C2×#106220942
C11×#19562
#845111