Finite Group Databasebeta

← #13075639

Subgroups — #13075639

Order 1408.

592 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66938C212yesmaximal, complemented
2C11×#394C211yesmaximal, characteristic, complemented
3#10622836C212yesmaximal, complemented
4#10622604C211yesmaximal, characteristic, complemented
5#10622587C211yesmaximal, characteristic, complemented
6#10622573C212yesmaximal, complemented
7#10622570C212yesmaximal, complemented
8#10622558C212yesmaximal, complemented
9#10622282C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C22×D44C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27#66938—28no—
28C11×#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C24×C11C2312yes—
33C23×D11C2312yes—
34C2×D4×C11—42no—
35C2×D4×C11—41no—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—24no—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—42no—
43C2×C22⋊D11—42no—
44C2×C22⋊D11—42no—
45C2×C22⋊D11—42no—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C2×D44—42no—
50C2×D44—41no—
51C2×Dic22—41no—
52C2×Dic22—41no—
53C2×Dic22D414yescomplemented
54C11×C4⋊C4—41no—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—42no—
57C22⋊Dic11—24no—
58C22⋊Dic11—24no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—42no—
63Dic11⋊C4—42no—
64C4×Dic11—24no—
65C4×Dic11—41no—
66#2733—111nomaximal, Sylow
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11C2411yescharacteristic
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82D4×C11—44no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11C2×D412yes—
93C22⋊D11—48no—
94C22⋊D11—48no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D414yes—
103C2×Dic11#4114yes—
104D44—44no—
105Dic22—44no—
106C2×#124—112no—
107#394—111no—
108#394D1111yescharacteristic, complemented
109#392—112no—
110#392—112no—
111#391—111no—
112#390—112no—
113#388—112no—
114#388—112no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11C22×D411yescharacteristic
123C22×C11C2×#4112yes—
124C22×C11H(5,𝔽2)11yescharacteristic
125C22×C11H(5,𝔽2)12yes—
126C22×C11H(5,𝔽2)11yescharacteristic
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C4×C11—22no—
135C4×C11—42no—
136C4×C11—41no—
137C4×C11—41no—
138Dic11—24no—
139Dic11—24no—
140Dic11—42no—
141C22×Q8—111no—
142C22×D4—112no—
143C22×D4—112no—
144C22×D4—111no—
145C22×D4C2×D1111yescharacteristic
146#124—228no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C22⋊C4—112no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—112no—
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4C2×D1112yes—
156C2×C22⋊C4C2×D1112yes—
157C2×C42—112no—
158C2×C42—111no—
159#95—111no—
160#95—112no—
161#95—112no—
162#95C2×D1111yescharacteristic
163C2×C11—82no—
164C2×C11#53411yescharacteristic
165C2×C11#53812yes—
166C2×C11#55012yes—
167C2×C11#55511yescharacteristic
168C2×C11H(3,𝔽4)11yescharacteristic
169D11—82no—
170C24—112no—
171C24C22×D1112yes—
172C2×Q8—114no—
173C2×Q8—441no—
174C2×Q8—441no—
175C2×D4—42no—
176C2×D4—41no—
177C2×D4—224no—
178C2×D4—224no—
179C2×D4—442no—
180C2×D4—441no—
181C2×D4—442no—
182C2×D4—442no—
183C2×D4—442no—
184C2×D4—442no—
185C22×C4—112no—
186C22×C4—112no—
187C22×C4—112no—
188C22×C4C22×D1111yescharacteristic
189C22×C4C22×D1111yescharacteristic
190C22×C4C22×D1112yes—
191C22×C4C22×D1111yescharacteristic
192C4⋊C4—41no—
193C4⋊C4—442no—
194C22⋊C4—24no—
195C22⋊C4—42no—
196C22⋊C4—224no—
197C22⋊C4—224no—
198C22⋊C4—224no—
199C22⋊C4—224no—
200C22⋊C4—224no—
201C22⋊C4—442no—
202C42—224no—
203C42—441no—
204C11#273311yescharacteristic, complemented, Sylow
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—222no—
213C23—222no—
214C23—222no—
215C23—222no—
216C23—222no—
217C23—222no—
218C23—222no—
219C23C23×D1111yescharacteristic
220Q8—444no—
221D4—44no—
222D4—444no—
223D4—448no—
224D4—448no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—114no—
235C2×C4—114no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4D4×D1112yes—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—442no—
252C22—442no—
253C22—442no—
254C22—442no—
255C22—442no—
256C22—442no—
257C22—442no—
258C22C2×D4×D1111yescharacteristic
259C22#6703712yes—
260C22#6703711yescharacteristic
261C22#41×D1112yes—
262C22#6704211yescharacteristic
263C4—22no—
264C4—41no—
265C4—41no—
266C4—42no—
267C4—224no—
268C4—224no—
269C4—442no—
270C2—82no—
271C2—882no—
272C2#1062312511yescharacteristic
273C2#1062313012yes—
274C2#1062313611yescharacteristic
275C2#1062318812yes—
276C2#1062320111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2733
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66938C2semidirect
2. C11×#394C2semidirect
3. #10622836C2semidirect
4. #10622604C2semidirect
5. #10622587C2semidirect
6. #10622573C2semidirect
7. #10622570C2semidirect
8. #10622558C2semidirect
9. #10622282C2semidirect
53. C2×Dic22D4semidirect
108. #394D11semidirect
204. C11#2733semidirect

Maximal subgroups

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

subgroupindex
C2×#669382
C11×#3942
#106228362
#106226042
#106225872
#106225732
#106225702
#106225582
#106222822
#273311