Finite Group Databasebeta

← #13076787

Subgroups — #13076787

Order 1408.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#394C211yesmaximal, characteristic
2#10622835C212yesmaximal
3#10622592C211yesmaximal, characteristic, complemented
4#10622587C211yesmaximal, characteristic, complemented
5#10622566C212yesmaximal, complemented
6#10622564C212yesmaximal, complemented
7#10622560C212yesmaximal, complemented
8#10622560C212yesmaximal, complemented
9#10622273C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C11×#95C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2312yes—
32C2×D4×C11—42no—
33C2×D4×C11—41no—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C2×Dic22—22no—
43C2×Dic22—41no—
44C2×Dic22—41no—
45C2×Dic22—42no—
46C2×Dic22—41no—
47C11×C4⋊C4—41no—
48C11×C22⋊C4—24no—
49C11×C22⋊C4—42no—
50C22⋊Dic11—42no—
51C22⋊Dic11—42no—
52C22⋊Dic11—42no—
53C22⋊Dic11—42no—
54C4⋊Dic11—42no—
55Dic11⋊C4—42no—
56C4×Dic11—41no—
57#2832—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11C2411yescharacteristic
66D4×C11—44no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11#4112yes—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89Dic22—44no—
90Dic22—44no—
91#400—112no—
92#397—112no—
93#395—111no—
94#394—112no—
95#394D1111yescharacteristic
96#393—112no—
97#393—112no—
98#391—111no—
99#388—112no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11C2×#4111yescharacteristic
108C22×C11H(5,𝔽2)11yescharacteristic
109C22×C11H(5,𝔽2)12yes—
110C22×C11H(5,𝔽2)11yescharacteristic
111C22×C112−1+412yes—
112C4×C11—22no—
113C4×C11—42no—
114C4×C11—41no—
115C4×C11—41no—
116Dic11—42no—
117Dic11—42no—
118Dic11—42no—
119Dic11—42no—
120C22×Q8—111no—
121C22×Q8—111no—
122C22×D4C2×D1111yescharacteristic
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C22⋊C4C2×D1112yes—
131C2×C22⋊C4C2×D1112yes—
132C2×C42—111no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—112no—
138#95—112no—
139#95—111no—
140#95C2×D1111yescharacteristic
141C2×C11—82no—
142C2×C11#53811yescharacteristic
143C2×C11#54212yes—
144C2×C11H(3,𝔽4)11yescharacteristic
145C2×C11#56212yes—
146C2×C11#56311yescharacteristic
147C24C22×D1112yes—
148C2×Q8—222no—
149C2×Q8—441no—
150C2×Q8—441no—
151C2×Q8—442no—
152C2×Q8—441no—
153C2×D4—41no—
154C2×D4—42no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—442no—
165C4⋊C4—442no—
166C22⋊C4—24no—
167C22⋊C4—42no—
168C22⋊C4—442no—
169C22⋊C4—442no—
170C22⋊C4—442no—
171C22⋊C4—442no—
172C42—441no—
173C11#283211yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C23×D1111yescharacteristic
182Q8—444no—
183Q8—444no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4#434112yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#434111yescharacteristic
215C22#6703712yes—
216C22#6703711yescharacteristic
217C22#6704211yescharacteristic
218C22#6704312yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—442no—
224C4—442no—
225C4—442no—
226C4—442no—
227C2—82no—
228C2#1062312511yescharacteristic
229C2#1062313412yes—
230C2#1062314811yescharacteristic
231C2#1062319812yes—
232C2#1062320311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2832
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
3. #10622592C2semidirect
4. #10622587C2semidirect
5. #10622566C2semidirect
6. #10622564C2semidirect
7. #10622560C2semidirect
8. #10622560C2semidirect
9. #10622273C2semidirect
173. C11#2832semidirect

Maximal subgroups

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

subgroupindex
C11×#3942
#106228352
#106225922
#106225872
#106225662
#106225642
#106225602
#106222732
#283211