Finite Group Databasebeta

← #13076596

Subgroups — #13076596

Order 1408.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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×#390C211yesmaximal, characteristic
2#10622835C212yesmaximal
3#10622591C212yesmaximal, complemented
4#10622566C212yesmaximal, complemented
5#10622564C212yesmaximal, complemented
6#10622564C212yesmaximal, complemented
7#10622560C212yesmaximal, complemented
8#10622542C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2312yes—
32C2×D4×C11—22no—
33C2×D4×C11—41no—
34C2×D4×C11—41no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×Dic22—22no—
44C2×Dic22—41no—
45C2×Dic22—41no—
46C11×C4⋊C4—41no—
47C11×C22⋊C4—24no—
48C11×C22⋊C4—24no—
49C42×C11—41no—
50C22⋊Dic11—42no—
51C22⋊Dic11—42no—
52C22⋊Dic11—42no—
53C22⋊Dic11—42no—
54C4⋊Dic11—22no—
55C4⋊Dic11—41no—
56C4⋊Dic11—41no—
57Dic11⋊C4—24no—
58C4×Dic11—42no—
59#2808—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11C2411yescharacteristic
68D4×C11—44no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11#4112yes—
79C2×C4×C11#4112yes—
80C2×C4×C11#4112yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93Dic22—44no—
94#397—112no—
95#394—112no—
96#393—112no—
97#391—111no—
98#390D1111yescharacteristic
99#389—111no—
100#388—112no—
101#388—112no—
102#387—112no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11C2×#4111yescharacteristic
111C22×C11C2×#4111yescharacteristic
112C22×C11C2×#4111yescharacteristic
113C22×C11H(5,𝔽2)11yescharacteristic
114C22×C11H(5,𝔽2)11yescharacteristic
115C22×C11H(5,𝔽2)11yescharacteristic
116C22×C112−1+411yescharacteristic
117C4×C11—22no—
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—42no—
121Dic11—42no—
122Dic11—42no—
123Dic11—42no—
124Dic11—42no—
125C22×Q8—111no—
126C22×D4C2×D1111yescharacteristic
127C2×C4⋊C4—112no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C22⋊C4—112no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4—112no—
136C2×C22⋊C4C2×D1112yes—
137C2×C22⋊C4C2×D1112yes—
138C2×C42—112no—
139C2×C42C2×D1111yescharacteristic
140#95—112no—
141#95—112no—
142#95—112no—
143#95—112no—
144#95—112no—
145#95—112no—
146C2×C11—82no—
147C2×C11#53811yescharacteristic
148C2×C11#53811yescharacteristic
149C2×C11#53911yescharacteristic
150C2×C11#55511yescharacteristic
151C2×C11#55611yescharacteristic
152C2×C11#55911yescharacteristic
153C2×C11#56211yescharacteristic
154C24C22×D1112yes—
155C2×Q8—222no—
156C2×Q8—441no—
157C2×Q8—441no—
158C2×D4—22no—
159C2×D4—41no—
160C2×D4—41no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—112no—
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—224no—
171C4⋊C4—222no—
172C4⋊C4—441no—
173C4⋊C4—441no—
174C22⋊C4—24no—
175C22⋊C4—24no—
176C22⋊C4—442no—
177C22⋊C4—442no—
178C22⋊C4—442no—
179C22⋊C4—442no—
180C42—41no—
181C42—442no—
182C11#280811yescharacteristic, complemented, Sylow
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23C23×D1111yescharacteristic
191Q8—444no—
192D4—44no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4#433912yes—
215C2×C4#434112yes—
216C2×C4#434112yes—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×#433911yescharacteristic
225C22C2×#434111yescharacteristic
226C22C2×#434111yescharacteristic
227C22#6703711yescharacteristic
228C22#6703711yescharacteristic
229C22#6704211yescharacteristic
230C22#6704311yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—442no—
236C4—442no—
237C4—442no—
238C4—442no—
239C2—82no—
240C2#1062302511yescharacteristic
241C2#1062307311yescharacteristic
242C2#1062309411yescharacteristic
243C2#1062313311yescharacteristic
244C2#1062314811yescharacteristic
245C2#1062321511yescharacteristic
246C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2808
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
3. #10622591C2semidirect
4. #10622566C2semidirect
5. #10622564C2semidirect
6. #10622564C2semidirect
7. #10622560C2semidirect
8. #10622542C2semidirect
9. #10622541C2semidirect
182. C11#2808semidirect

Maximal subgroups

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

subgroupindex
C11×#3902
#106228352
#106225912
#106225662
#106225642
#106225602
#106225422
#106225412
#280811