Finite Group Databasebeta

← #13076559

Subgroups — #13076559

Order 1408.

480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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×#386C211yesmaximal, characteristic
2#10622834C211yesmaximal, characteristic
3#10622833C211yesmaximal, characteristic
4#10622823C212yesmaximal, complemented
5#10622560C212yesmaximal, complemented
6#10622560C212yesmaximal, complemented
7#10622559C212yesmaximal, complemented
8#10622273C212yesmaximal, complemented
9#10622259C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C22×Dic22C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C11×#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C24×C11C2311yescharacteristic
33C2×D4×C11—41no—
34C2×D4×C11—41no—
35C2×D4×C11Q814yescomplemented
36C22×C4×C11—41no—
37C22×C4×C11—42no—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×Dic11—42no—
42C22×Dic11—41no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×Dic22—24no—
48C2×Dic22—42no—
49C2×Dic22—42no—
50C11×C22⋊C4—41no—
51C11×C22⋊C4—42no—
52C22⋊Dic11—24no—
53C22⋊Dic11—24no—
54C22⋊Dic11—42no—
55C22⋊Dic11—41no—
56C4⋊Dic11—41no—
57Dic11⋊C4—42no—
58Dic11⋊C4—42no—
59C4×Dic11—41no—
60#2804—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—21no—
65C23×C11—22no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11C2×Q812yes—
70C23×C11C2×Q812yes—
71C23×C11C2411yescharacteristic
72D4×C11—44no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—44no—
82C2×C4×C11C2×Q812yes—
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—
93C2×Dic11—22no—
94C2×Dic11—44no—
95C2×Dic11#4114yes—
96Dic22—48no—
97#400—112no—
98#393—112no—
99#393—112no—
100#391—112no—
101#390—111no—
102#386—111no—
103#386D1111yescharacteristic
104#385—112no—
105#385—112no—
106C22×C11—22no—
107C22×C11—22no—
108C22×C11—24no—
109C22×C11—24no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11C22×Q811yescharacteristic
117C22×C11C2×#4112yes—
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C11H(5,𝔽2)12yes—
120C22×C11H(5,𝔽2)11yescharacteristic
121C4×C11—22no—
122C4×C11—42no—
123C4×C11—42no—
124Dic11—24no—
125Dic11—42no—
126Dic11—42no—
127Dic11—42no—
128C22×Q8—112no—
129C22×D4C2×D1111yescharacteristic
130C23×C4—111no—
131C23×C4C2×D1111yescharacteristic
132C2×C4⋊C4—112no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—111no—
135C2×C22⋊C4—112no—
136C2×C22⋊C4—112no—
137C2×C22⋊C4—112no—
138C2×C22⋊C4—111no—
139C2×C22⋊C4C2×D1112yes—
140C2×C22⋊C4C2×D1111yescharacteristic
141C2×C42—111no—
142#95—112no—
143#95—112no—
144#95—112no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95C2×D1112yes—
149C2×C11—42no—
150C2×C11—42no—
151C2×C11#53812yes—
152C2×C11#54311yescharacteristic
153C2×C11#55412yes—
154C2×C11#55911yescharacteristic
155C2×C11H(3,𝔽4)11yescharacteristic
156C24C22×D1111yescharacteristic
157C24C22×D1111yescharacteristic
158C2×Q8—224no—
159C2×Q8—442no—
160C2×Q8—442no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4Dic2214yescomplemented
164C22×C4—42no—
165C22×C4—41no—
166C22×C4—112no—
167C22×C4—112no—
168C22×C4—112no—
169C22×C4—112no—
170C22×C4—442no—
171C22×C4—441no—
172C22×C4C22×D1112yes—
173C22×C4C22×D1112yes—
174C22×C4C22×D1111yescharacteristic
175C4⋊C4—442no—
176C4⋊C4—442no—
177C4⋊C4—441no—
178C22⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—224no—
181C22⋊C4—224no—
182C22⋊C4—442no—
183C22⋊C4—441no—
184C42—441no—
185C11#280411yescharacteristic, complemented, Sylow
186C23—22no—
187C23—21no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23C2×Dic2212yes—
195C23C2×Dic2212yes—
196C23C23×D1111yescharacteristic
197Q8—448no—
198D4—44no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—114no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—444no—
221C2×C4C2×Dic2212yes—
222C22—22no—
223C22—22no—
224C22—24no—
225C22—24no—
226C22—41no—
227C22—41no—
228C22—42no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22C22×Dic2211yescharacteristic
233C22#6703711yescharacteristic
234C22#6703711yescharacteristic
235C22#6703712yes—
236C22#41×D1112yes—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—224no—
241C4—442no—
242C4—442no—
243C4—442no—
244C2—42no—
245C2—42no—
246C2#1062301411yescharacteristic
247C2#1062307012yes—
248C2#1062312511yescharacteristic
249C2#1062314412yes—
250C2#1062319511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2804
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #10622823C2semidirect
5. #10622560C2semidirect
6. #10622560C2semidirect
7. #10622559C2semidirect
8. #10622273C2semidirect
9. #10622259C2semidirect
35. C2×D4×C11Q8semidirect
163. C2×D4Dic22semidirect
185. C11#2804semidirect

Maximal subgroups

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

subgroupindex
C11×#3862
#106228342
#106228332
#106228232
#106225602
#106225592
#106222732
#106222592
#280411