Finite Group Databasebeta

← #13069331

Subgroups — #13069331

Order 1408.

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

normal subgroups only

This group has 260 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
1C2×C11×C4⋊C8C211yesmaximal, characteristic
2C2×Dic11⋊C8C211yesmaximal, characteristic
3C2×Dic11⋊C8C211yesmaximal, characteristic
4C2×C8×Dic11C211yesmaximal, characteristic
5C4×Dic11⋊C4C211yesmaximal, characteristic
6#10622188C211yesmaximal, characteristic
7#10622162C211yesmaximal, characteristic
8C22×C8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11C2×Dic11⋊C4C411yescharacteristic
12C2×Dic11⋊C4C411yescharacteristic
13C2×C4×Dic11C2211yescharacteristic
14C2×C4×Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11×C4⋊C8—22no—
18C11⋊#95C411yescharacteristic
19C11⋊#95C411yescharacteristic
20Dic11⋊C8—22no—
21Dic11⋊C8—22no—
22C8×Dic11—22no—
23C22×C4×C11C2×C411yescharacteristic
24C22×C4×C11C2×C411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C22×Dic11C2×C411yescharacteristic
27C22×Dic11C2×C411yescharacteristic
28C22×Dic11C2×C411yescharacteristic
29C22×Dic11C2×C411yescharacteristic
30C2×C8×C11—21no—
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11D412yes—
36C42×C11—21no—
37C42×C11—21no—
38Dic11⋊C4—22no—
39Dic11⋊C4C814yescomplemented
40C4×Dic11—21no—
41C4×Dic11—21no—
42C4×Dic11D412yes—
43C4×Dic11Q812yes—
44C2×C11⋊C8—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8Q812yes—
50#1939—111nomaximal, Sylow
51C23×C11C22×C411yescharacteristic
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11C2×C812yes—
58C2×C4×C11C2×D411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×Q811yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—21no—
69C2×Dic11—21no—
70C2×Dic11—21no—
71C2×Dic11C4⋊C412yes—
72C2×Dic11C4⋊C412yes—
73C2×Dic11C2×C812yes—
74C2×Dic11C2×C812yes—
75C2×Dic11M1612yes—
76C8×C11—22no—
77C8×C11—41no—
78C11⋊C8—22no—
79C11⋊C8—41no—
80C2×C4⋊C8—111no—
81C2×C4⋊C8—111no—
82C2×C4⋊C8D1111yescharacteristic
83C2×C4×C8—111no—
84C4×C4⋊C4—111no—
85#336—111no—
86#336—111no—
87C22×C11C2×C4⋊C411yescharacteristic
88C22×C11C4×D411yescharacteristic
89C22×C11C4×Q811yescharacteristic
90C22×C11C22×C811yescharacteristic
91C22×C11C2×M1611yescharacteristic
92C22×C11#13111yescharacteristic
93C22×C11#13111yescharacteristic
94C4×C11—22no—
95C4×C11—41no—
96C4×C11#12111yescharacteristic
97C4×C11C22⋊Q811yescharacteristic
98C4×C11#12511yescharacteristic
99C4×C11C4⋊Q811yescharacteristic
100Dic11—22no—
101Dic11—22no—
102Dic11—41no—
103Dic11C4⋊C814yescomplemented
104C22×C8—111no—
105C22×C8—111no—
106C22×C8C2×D1111yescharacteristic
107C22×C8C2×D1111yescharacteristic
108C2×C4⋊C4—111no—
109C2×C4⋊C4—111no—
110C2×C42—111no—
111C2×C42—111no—
112C2×C42C2×D1111yescharacteristic
113C4⋊C8—22no—
114C4⋊C8—222no—
115C4⋊C8—222no—
116C4×C8—222no—
117#95—111no—
118#95—111no—
119C2×C11#38911yescharacteristic
120C2×C11C2×C4⋊C811yescharacteristic
121C2×C11#42411yescharacteristic
122C2×C11C8×D411yescharacteristic
123C2×C11#43611yescharacteristic
124C2×C11C8×Q811yescharacteristic
125C2×C11#44611yescharacteristic
126C22×C4—111no—
127C22×C4—111no—
128C22×C4—111no—
129C22×C4—111no—
130C22×C4C4×D1111yescharacteristic
131C22×C4C4×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—112no—
139C2×C8—221no—
140C2×C8—221no—
141C2×C8—221no—
142C2×C8—221no—
143C2×C8—221no—
144C2×C8C22⋊D1112yes—
145C4⋊C4—114no—
146C4⋊C4—222no—
147C42—21no—
148C42—21no—
149C42—112no—
150C42—112no—
151C42—221no—
152C42—221no—
153C11#193911yescharacteristic, complemented, Sylow
154C23C2×C4×D1111yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—112no—
161C2×C4—112no—
162C2×C4—112no—
163C2×C4—112no—
164C2×C4—112no—
165C2×C4—221no—
166C2×C4—221no—
167C2×C4—221no—
168C2×C4—221no—
169C2×C4—221no—
170C2×C4—221no—
171C2×C4—221no—
172C2×C4C8×D1112yes—
173C2×C4#433911yescharacteristic
174C2×C4D4×D1111yescharacteristic
175C2×C4#434111yescharacteristic
176C2×C4Q8×D1111yescharacteristic
177C2×C4Q8×D1111yescharacteristic
178C2×C4C2×C22⋊D1111yescharacteristic
179C8—22no—
180C8—41no—
181C8—222no—
182C8—441no—
183C22#6694011yescharacteristic
184C22C4⋊C4×D1111yescharacteristic
185C22C2×C8×D1111yescharacteristic
186C22#6695411yescharacteristic
187C22M16×D1111yescharacteristic
188C22#6696011yescharacteristic
189C22C4×C22⋊D1111yescharacteristic
190C4—22no—
191C4—41no—
192C4—114no—
193C4—222no—
194C4—222no—
195C4—441no—
196C4#6694211yescharacteristic
197C4#6694911yescharacteristic
198C4#6699211yescharacteristic
199C4#6699711yescharacteristic
200C2#1062244111yescharacteristic
201C2#1062244311yescharacteristic
202C2D11×C4⋊C811yescharacteristic
203C2#1062245211yescharacteristic
204C2#1062258511yescharacteristic
205C2C8×C22⋊D1111yescharacteristic
206C2#1062274111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D11
commutatorC22×C11C22×C8
FittingC2×C11×C4⋊C8C2
socle, prime radicalC23×C11C22×C4
cosocleC22×C4×C11C23
hypercenterC2×C4⋊C8D11
hypocenterC11#1939
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
39. Dic11⋊C4C8semidirect
103. Dic11C4⋊C8semidirect
153. C11#1939semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊C82
C2×Dic11⋊C82
C2×C8×Dic112
C4×Dic11⋊C42
#106221882
#106221622
#193911