Finite Group Databasebeta

← #13073093

Subgroups — #13073093

Order 1408.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#66999C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#391C211yesmaximal, characteristic, complemented
4#10622843C211yesmaximal, characteristic, complemented
5#10622589C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622548C211yesmaximal, characteristic, complemented
8#10622281C214yesmaximal
9#10622270C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×C4×D11C2211yescharacteristic
12C22×C4×D11C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#66999—24no—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2214yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2214yes—
24C2×C4×Dic11C2211yescharacteristic
25C4⋊C4×D11—24no—
26C11×#95C2214yes—
27C11⋊#95C2212yes—
28C11⋊#95C2214yes—
29C23×D11C2311yescharacteristic
30C2×Q8×C11—22no—
31C2×Q8×C11—22no—
32C2×Q8×C11—22no—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2311yescharacteristic
40C22×Dic11C2312yes—
41C2×C4×D11—24no—
42C2×C4×D11—22no—
43C2×C4×D11—22no—
44C2×C4×D11—44no—
45C2×C4×D11D414yes—
46C11×C4⋊C4—22no—
47C42×C11—22no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4Q818yescomplemented
50C4⋊Dic11—22no—
51C4⋊Dic11—22no—
52C4⋊Dic11—44no—
53Dic11⋊C4—24no—
54Dic11⋊C4—24no—
55Dic11⋊C4—44no—
56C4×Dic11—22no—
57#2502—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59C22×D11—21no—
60C22×D11—21no—
61C22×D11—22no—
62C22×D11C2×D412yes—
63C22×D11C2×Q814yes—
64Q8×C11—44no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—24no—
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×Q814yes—
74C2×C4×C11#4112yes—
75C2×C4×C11#4112yes—
76C2×Dic11—22no—
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—24no—
83C2×Dic11—24no—
84C2×Dic11C2×D412yes—
85C2×Dic11C2×Q814yes—
86C4×D11—28no—
87C4×D11—48no—
88C2×C22⋊Q8—111no—
89C22×C4⋊C4—111no—
90#398—114no—
91#391—111no—
92#391D1111yescharacteristic, complemented
93#385—114no—
94#384—111no—
95#384—111no—
96C4×C22⋊C4—111no—
97C22×C11C22×D411yescharacteristic
98C22×C11C22×Q812yes—
99C22×C11C2×#4111yescharacteristic
100C22×C11C2×#4111yescharacteristic
101C22×C11H(5,𝔽2)12yes—
102C2×D11—22no—
103C2×D11—22no—
104C2×D11—24no—
105C2×D11—24no—
106C2×D11C4⋊Q814yes—
107C4×C11—24no—
108C4×C11—42no—
109C4×C11—42no—
110C4×C11#12314yes—
111Dic11—22no—
112Dic11—24no—
113Dic11—42no—
114Dic11—42no—
115C22×Q8C2×D1111yescharacteristic
116C23×C4—111no—
117C23×C4—112no—
118C22⋊Q8—224no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—114no—
124C2×C4⋊C4—114no—
125C2×C4⋊C4—224no—
126C2×C4⋊C4C2×D1111yescharacteristic
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C42—111no—
130C2×C42C2×D1111yescharacteristic
131#95—112no—
132#95—114no—
133#95C2×D1114yes—
134C2×C11C2×#12311yescharacteristic
135C2×C11C2×C4⋊Q811yescharacteristic
136C2×C11#53511yescharacteristic
137C2×C11#55412yes—
138C2×C11#55412yes—
139D11—24no—
140C24—111no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×Q8—22no—
144C22×C4—112no—
145C22×C4—111no—
146C22×C4—114no—
147C22×C4—112no—
148C22×C4—112no—
149C22×C4—224no—
150C22×C4—222no—
151C22×C4—222no—
152C22×C4—444no—
153C22×C4C22×D1112yes—
154C22×C4C22×D1112yes—
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—224no—
159C4⋊C4—224no—
160C4⋊C4—222no—
161C4⋊C4—222no—
162C4⋊C4—444no—
163C4⋊C4—444no—
164C22⋊C4—118no—
165C22⋊C4—224no—
166C42—22no—
167C42—222no—
168C11#250211yescharacteristic, complemented, Sylow
169C23—112no—
170C23—114no—
171C23—221no—
172C23—221no—
173C23—222no—
174C23C23×D1111yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—112no—
184C2×C4—114no—
185C2×C4—222no—
186C2×C4—221no—
187C2×C4—221no—
188C2×C4—222no—
189C2×C4—228no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—224no—
193C2×C4—224no—
194C2×C4—448no—
195C2×C4#433912yes—
196C2×C4D4×D1112yes—
197C2×C4#434112yes—
198C2×C4Q8×D1114yes—
199C22—114no—
200C22—222no—
201C22—224no—
202C22—224no—
203C22—222no—
204C22C2×#433911yescharacteristic
205C22C2×D4×D1111yescharacteristic
206C22C2×#434111yescharacteristic
207C22C2×Q8×D1112yes—
208C22#6704212yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—222no—
213C4—224no—
214C4—442no—
215C4—442no—
216C4#6693614yes—
217C2—224no—
218C2C2×#6693611yescharacteristic
219C2#1062311012yes—
220C2#1062316612yes—
221C2#1062320511yescharacteristic
222C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC23×D11C23
hypercenter#391D11
hypocenterC11#2502
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. C11×#391C2semidirect
4. #10622843C2semidirect
5. #10622589C2semidirect
7. #10622548C2semidirect
9. #10622270C2semidirect
49. (C2×D11)⋊C4Q8semidirect
92. #391D11semidirect
168. C11#2502semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4⋊C4×D112
C11×#3912
#106228432
#106225892
C4×(C2×D11)⋊C42
#106225482
#106222812
#106222702
#250211