Finite Group Databasebeta

← #13069484

Subgroups — #13069484

Order 1408.

304 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#4326C211yesmaximal, characteristic
2C2×C11×#103C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic
4C2×#66880C211yesmaximal, characteristic
5C2×#66879C211yesmaximal, characteristic
6#10622587C211yesmaximal, characteristic
7C2×#66872C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×#4326—22no—
13C2×#4326—22no—
14C2×#4326C414yescomplemented
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4×Dic11C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#103—22no—
19C11⋊#95—22no—
20C11⋊#95—22no—
21#66880—22no—
22#66879—22no—
23#66872—22no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11C2×C412yes—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11C2311yescharacteristic
33C22×Dic11—21no—
34C22×Dic11—21no—
35C22×Dic11D412yes—
36C2×Dic22—21no—
37C2×Dic22—21no—
38C2×Dic22—21no—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22C2×C412yes—
42C2×C8×C11—21no—
43C2×C8×C11—21no—
44C2×C8×C11D412yes—
45C11×C4⋊C4—21no—
46C11×C4⋊C4—21no—
47#4326—28no—
48C4⋊Dic11—21no—
49C4⋊Dic11—21no—
50C4×Dic11—21no—
51C4×Dic11—21no—
52C2×C11⋊C8C2×C412yes—
53C2×C11⋊C8D412yes—
54C2×C11⋊C8D412yes—
55#1971—111nomaximal, Sylow
56C23×C11C2×D411yescharacteristic
57Q8×C11—22no—
58Q8×C11—22no—
59Q8×C11—41no—
60Q8×C11—41no—
61C2×C4×C11—22no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11—42no—
66C2×C4×C11C22×C411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—42no—
80Dic22—22no—
81Dic22—22no—
82Dic22—41no—
83Dic22—41no—
84C8×C11—22no—
85C11⋊C8C22⋊C414yes—
86C22×Q16—111no—
87C2×#106—111no—
88C2×#103—111no—
89C2×#103D1111yescharacteristic
90C2×#97—111no—
91#391—111no—
92#391—111no—
93C22×C11C4×D411yescharacteristic
94C22×C11#12111yescharacteristic
95C22×C11#12711yescharacteristic
96C22×C11#13712yes—
97C22×C11#13712yes—
98C4×C11—42no—
99C4×C11—81no—
100C4×C11C2×C22⋊C411yescharacteristic
101C4×C11C4×D411yescharacteristic
102C4×C11#12111yescharacteristic
103C4×C11#12411yescharacteristic
104Dic11—42no—
105Dic11—42no—
106Dic11—81no—
107C22×Q8—111no—
108C22×Q8C2×D1111yescharacteristic
109C2×Q16—114no—
110C2×Q16—222no—
111C2×Q16—222no—
112C22×C8—111no—
113C22×C8C2×D1111yescharacteristic
114C2×C4⋊C4—111no—
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C42—111no—
117#106—222no—
118#103—22no—
119#103—222no—
120#97—222no—
121#95—222no—
122#95—222no—
123C2×C11#39011yescharacteristic
124C2×C11#44112yes—
125C2×C11#47012yes—
126C2×C11#49711yescharacteristic
127C2×C11#49711yescharacteristic
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—112no—
134C2×Q8—221no—
135C2×Q8—221no—
136C2×Q8—221no—
137C2×Q8—221no—
138C2×Q8—221no—
139C2×Q8C4×D1112yes—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—112no—
143C22×C4—221no—
144C22×C4—221no—
145C22×C4C22×D1111yescharacteristic
146Q16—228no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—112no—
150C2×C8—112no—
151C2×C8—112no—
152C2×C8C22⋊D1112yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—221no—
156C4⋊C4—221no—
157C42—221no—
158C42—221no—
159C11#197111yescharacteristic, complemented, Sylow
160C23D4×D1111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—222no—
166Q8—222no—
167Q8—441no—
168Q8—441no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—41no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—441no—
179C2×C4—441no—
180C2×C4—442no—
181C2×C4—441no—
182C2×C4C2×C4×D1111yescharacteristic
183C2×C4#433911yescharacteristic
184C2×C4D4×D1111yescharacteristic
185C2×C4D4×D1111yescharacteristic
186C2×C4#434111yescharacteristic
187C2×C4C2×C22⋊D1111yescharacteristic
188C8—22no—
189C8—114no—
190C22(C22⋊D11)⋊C411yescharacteristic
191C22#6693711yescharacteristic
192C22#6696812yes—
193C22#6697112yes—
194C22#6699311yescharacteristic
195C4—42no—
196C4—81no—
197C4—442no—
198C4—442no—
199C4—881no—
200C4C22⋊C4×D1111yescharacteristic
201C4#6693811yescharacteristic
202C4C4×C22⋊D1111yescharacteristic
203C4#6699211yescharacteristic
204C2#1062240212yes—
205C2#1062242912yes—
206C2#1062257011yescharacteristic
207C2#1062278011yescharacteristic
208C2#1062280311yescharacteristic
subgroupG/H
centerC23D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socle, prime radicalC23×C11C2×D4
cosocleC22×C4×C11C23
hypercenterC2×#103D11
hypocenterC11#1971
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
14. C2×#4326C4semidirect
159. C11#1971semidirect

Maximal subgroups

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

subgroupindex
C22×#43262
C2×C11×#1032
#106228432
C2×#668802
C2×#668792
#106225872
C2×#668722
#197111