Finite Group Databasebeta

← #13070113

Subgroups — #13070113

Order 1408.

224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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×Dic11⋊C8C211yesmaximal, characteristic
2#10622598C211yesmaximal, characteristic
3#10622586C211yesmaximal, characteristic
4C2×#66871C211yesmaximal, characteristic
5C11×#340C211yesmaximal, characteristic
6#10622189C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C22×C8×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11—21no—
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11⋊#95—21no—
18C11⋊#95—21no—
19Dic11⋊C8—22no—
20#66871—22no—
21C22×C4×C11—21no—
22C22×C4×C11—21no—
23C22×C4×C11C2311yescharacteristic
24C22×Dic11—21no—
25C22×Dic11—21no—
26C22×Dic11D411yescharacteristic
27C22×Dic11D411yescharacteristic
28C2×C8×C11—21no—
29C2×C8×C11—21no—
30C2×C8×C11—21no—
31C11×C4⋊C4—21no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4Q812yes—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4⋊Dic11—21no—
38C4⋊Dic11—42no—
39C4⋊Dic11Q812yes—
40Dic11⋊C4—42no—
41C4×Dic11—21no—
42C4×Dic11—21no—
43C2×C11⋊C8—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8D412yes—
46#2087—111nomaximal, Sylow
47C23×C11C2×D411yescharacteristic
48C2×C4×C11—22no—
49C2×C4×C11—41no—
50C2×C4×C11—41no—
51C2×C4×C11—41no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×Q811yescharacteristic
56C2×C4×C11C2×Q811yescharacteristic
57C2×C4×C11#4111yescharacteristic
58C2×C4×C11#4111yescharacteristic
59C2×C4×C11#4111yescharacteristic
60C2×Dic11—21no—
61C2×Dic11—21no—
62C2×Dic11—21no—
63C2×Dic11—22no—
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—41no—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11Q1612yes—
72C8×C11—41no—
73C11⋊C8—22no—
74C2×#107—111no—
75C2×C4⋊C8—111no—
76#389—111no—
77#389—111no—
78#340—111no—
79#340—111no—
80#340D1111yescharacteristic
81C22×C11#12111yescharacteristic
82C22×C11C22⋊Q811yescharacteristic
83C22×C11C22⋊Q811yescharacteristic
84C22×C11C2×Q1611yescharacteristic
85C22×C11#13511yescharacteristic
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C22×C11AGL(1,ℤ/8)11yescharacteristic
88C4×C11—42no—
89C4×C11—81no—
90C4×C11#12311yescharacteristic
91C4×C11#12511yescharacteristic
92C4×C11#12511yescharacteristic
93C4×C11C4⋊Q811yescharacteristic
94Dic11—22no—
95Dic11—41no—
96Dic11—42no—
97Dic11—81no—
98C22×C8—111no—
99C22×C8C2×D1111yescharacteristic
100C2×C4⋊C4—111no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4—221no—
103C2×C4⋊C4—221no—
104C2×C4⋊C4C2×D1111yescharacteristic
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C42—111no—
107#107—222no—
108C4⋊C8—222no—
109#95—221no—
110#95—221no—
111C2×C11#39811yescharacteristic
112C2×C11#46711yescharacteristic
113C2×C11#46911yescharacteristic
114C2×C11#47711yescharacteristic
115C2×C11#47711yescharacteristic
116C2×C11#47811yescharacteristic
117C2×C11#47811yescharacteristic
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—111no—
121C22×C4—111no—
122C22×C4—221no—
123C22×C4—221no—
124C22×C4C22×D1111yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—112no—
129C2×C8—221no—
130C2×C8—221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—112no—
135C4⋊C4—221no—
136C4⋊C4—221no—
137C4⋊C4—221no—
138C4⋊C4—442no—
139C4⋊C4—442no—
140C4⋊C4Dic2212yes—
141C42—221no—
142C42—221no—
143C11#208711yescharacteristic, complemented, Sylow
144C23D4×D1111yescharacteristic
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—112no—
152C2×C4—221no—
153C2×C4—221no—
154C2×C4—221no—
155C2×C4—222no—
156C2×C4—221no—
157C2×C4—221no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4—441no—
162C2×C4—441no—
163C2×C4C2×Dic2211yescharacteristic
164C2×C4#433911yescharacteristic
165C2×C4#433911yescharacteristic
166C2×C4D4×D1111yescharacteristic
167C2×C4#434111yescharacteristic
168C2×C4Q8×D1111yescharacteristic
169C8—41no—
170C8—222no—
171C22#6693111yescharacteristic
172C22#6693711yescharacteristic
173C22#6694911yescharacteristic
174C22#6696411yescharacteristic
175C22#6696711yescharacteristic
176C22#6696911yescharacteristic
177C22Q16×D1111yescharacteristic
178C4—42no—
179C4—81no—
180C4—222no—
181C4—442no—
182C4—441no—
183C4—881no—
184C4#6692311yescharacteristic
185C4#6693611yescharacteristic
186C4#6694111yescharacteristic
187C4#6694211yescharacteristic
188C2#1062227011yescharacteristic
189C2#1062237611yescharacteristic
190C2#1062239511yescharacteristic
191C2#1062240711yescharacteristic
192C2#1062242611yescharacteristic
193C2#1062248411yescharacteristic
194C2#1062248811yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socle, prime radicalC23×C11C2×D4
hypercenter#340D11
hypocenterC11#2087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
143. C11#2087semidirect

Maximal subgroups

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

subgroupindex
C2×Dic11⋊C82
#106225982
#106225862
C2×#668712
C11×#3402
#106221892
#106221672
#208711