Finite Group Databasebeta

← #13070097

Subgroups — #13070097

Order 1408.

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

normal subgroups only

This group has 214 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
1C11×#389C211yesmaximal, characteristic
2C2×#66872C211yesmaximal, characteristic
3C2×#66871C211yesmaximal, characteristic
4#10622549C211yesmaximal, characteristic
5#10622167C211yesmaximal, characteristic
6#10622167C211yesmaximal, characteristic
7#10622162C211yesmaximal, characteristic
8C2×C11×C4⋊C4—21no—
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C22×C11⋊C8C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C11×#95—21no—
17C11⋊#95—21no—
18C11⋊#95—21no—
19#66872—22no—
20#66871—22no—
21C22×C4×C11—21no—
22C22×C4×C11—21no—
23C22×C4×C11D411yescharacteristic
24C22×C4×C11D411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C22×Dic11—21no—
27C22×Dic11—21no—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—21no—
30C11×C4⋊C4—21no—
31C11×C4⋊C4—42no—
32C11×C4⋊C4D412yes—
33C42×C11—21no—
34C42×C11—21no—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4⋊Dic11—21no—
38C4⋊Dic11—21no—
39C2×C11⋊C8—21no—
40C2×C11⋊C8—21no—
41C2×C11⋊C8—21no—
42C2×C11⋊C8—21no—
43C2×C11⋊C8Q812yes—
44C2×C11⋊C8Q812yes—
45#2085—111nomaximal, Sylow
46C23×C11C2×D411yescharacteristic
47C2×C4×C11—22no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×Q811yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×Dic11—41no—
66C2×Dic11—41no—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C11⋊C8—22no—
72C11⋊C8—22no—
73C2×#107—111no—
74C2×#106—111no—
75#389D1111yescharacteristic
76#382—111no—
77#340—111no—
78#340—111no—
79#336—111no—
80C22×C11#12111yescharacteristic
81C22×C11#12311yescharacteristic
82C22×C11C4⋊Q811yescharacteristic
83C22×C11#13511yescharacteristic
84C22×C11#13511yescharacteristic
85C22×C11AGL(1,ℤ/8)11yescharacteristic
86C22×C11#13711yescharacteristic
87C4×C11—42no—
88C4×C11—41no—
89C4×C11—41no—
90C4×C11—81no—
91C4×C11C22⋊Q811yescharacteristic
92C4×C11C22⋊Q811yescharacteristic
93C4×C11#12511yescharacteristic
94C4×C11#12511yescharacteristic
95Dic11—81no—
96Dic11—81no—
97C22×C8—111no—
98C22×C8—111no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—111no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4C2×D1111yescharacteristic
103C2×C4⋊C4C2×D1111yescharacteristic
104C2×C42C2×D1111yescharacteristic
105#107—222no—
106#106—222no—
107#95—21no—
108#95—221no—
109#95—221no—
110C2×C11#39811yescharacteristic
111C2×C11#46311yescharacteristic
112C2×C11#46411yescharacteristic
113C2×C11#48211yescharacteristic
114C2×C11#48511yescharacteristic
115C2×C11#49911yescharacteristic
116C2×C11#50111yescharacteristic
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—221no—
120C22×C4—221no—
121C22×C4C22⋊D1111yescharacteristic
122C22×C4C22⋊D1111yescharacteristic
123C22×C4C22×D1111yescharacteristic
124C2×C8—112no—
125C2×C8—112no—
126C2×C8—221no—
127C2×C8—221no—
128C2×C8—221no—
129C2×C8—221no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—42no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C4⋊C4—221no—
137C4⋊C4—221no—
138C4⋊C4D4412yes—
139C42—21no—
140C42—21no—
141C11#208511yescharacteristic, complemented, Sylow
142C23C2×C22⋊D1111yescharacteristic
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—441no—
156C2×C4—441no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4C2×D4411yescharacteristic
162C2×C4#433911yescharacteristic
163C2×C4#434111yescharacteristic
164C2×C4#434111yescharacteristic
165C2×C4Q8×D1111yescharacteristic
166C2×C4Q8×D1111yescharacteristic
167C8—222no—
168C8—222no—
169C22#6698311yescharacteristic
170C22#6698511yescharacteristic
171C22#6698811yescharacteristic
172C22#6699511yescharacteristic
173C22#6699711yescharacteristic
174C22#6700311yescharacteristic
175C22#6700311yescharacteristic
176C4—42no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—881no—
181C4—881no—
182C4#6694211yescharacteristic
183C4#6694211yescharacteristic
184C4#6695011yescharacteristic
185C4#6695011yescharacteristic
186C2#1062259611yescharacteristic
187C2#1062262911yescharacteristic
188C2#1062264111yescharacteristic
189C2#1062264811yescharacteristic
190C2#1062265811yescharacteristic
191C2#1062267711yescharacteristic
192C2#1062269311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#389C2
socle, prime radicalC23×C11C2×D4
hypercenter#389D11
hypocenterC11#2085
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
141. C11#2085semidirect

Maximal subgroups

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

subgroupindex
C11×#3892
C2×#668722
C2×#668712
#106225492
#106221672
#106221622
#208511