Finite Group Databasebeta

← #13069964

Subgroups — #13069964

Order 1408.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#10623050C211yesmaximal, characteristic
2C11×#428C211yesmaximal, characteristic
3#10622590C211yesmaximal, characteristic
4#10622577C211yesmaximal, characteristic
5#10622193C211yesmaximal, characteristic
6#10622192C211yesmaximal, characteristic
7#10622170C211yesmaximal, characteristic
8C2×C11×M16C2211yescharacteristic
9C11×#117C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11#66979C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4×Dic11C2211yescharacteristic
14C2×#4318C2211yescharacteristic
15#66943—21no—
16#66941—21no—
17#66931—22no—
18#66923—21no—
19#66922—21no—
20C11×#107—21no—
21C11×#106—21no—
22C11⋊#95—22no—
23#66872—21no—
24#66871—21no—
25C22×C4×C11—21no—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11—21no—
28C22×Dic11D412yes—
29C2×Dic22—22no—
30C11×M16—21no—
31C11×M16Q812yescomplemented
32C2×C8×C11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4D411yescharacteristic
36C11×C4⋊C4D411yescharacteristic
37C11×C22⋊C4—21no—
38C42×C11—21no—
39C22⋊Dic11—21no—
40C4⋊Dic11—22no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11D411yescharacteristic
44C4⋊Dic11D411yescharacteristic
45Dic11⋊C4—22no—
46Dic11⋊C4—22no—
47C4×Dic11—21no—
48C4×Dic11—21no—
49C4×Dic11Q812yescomplemented
50#4318—21no—
51#4318Q812yescomplemented
52C2×C11⋊C8—21no—
53#2061—111nomaximal, Sylow
54C23×C11C2×D411yescharacteristic
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—42no—
58C2×C4×C11—41no—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11C2×Q811yescharacteristic
63C2×C4×C11C2×Q811yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×Dic11—21no—
66C2×Dic11—21no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11—42no—
72Dic22—82no—
73C8×C11—22no—
74C11⋊C8—22no—
75#544—111no—
76#428—111no—
77#428D1111yescharacteristic
78#382—111no—
79#343—111no—
80#339—111no—
81#339—111no—
82C22×C11—21no—
83C22×C11—21no—
84C22×C11#12011yescharacteristic
85C22×C11C22⋊Q811yescharacteristic
86C22×C11C4⋊Q811yescharacteristic
87C4×C11—41no—
88C4×C11—41no—
89C4×C11—81no—
90C4×C11C22⋊Q811yescharacteristic
91C4×C11C22⋊Q811yescharacteristic
92C4×C11C4⋊Q811yescharacteristic
93C4×C11C4⋊Q811yescharacteristic
94Dic11—42no—
95Dic11—41no—
96Dic11—41no—
97Dic11—42no—
98C2×M16—111no—
99C2×M16C2×D1111yescharacteristic
100C4⋊Q8—221no—
101C4⋊Q8—221no—
102#125—221no—
103#125—221no—
104C22⋊Q8—222no—
105#117—111no—
106#117C2×D1111yescharacteristic
107C2×C4⋊C4—111no—
108C2×C4⋊C4C2×D1111yescharacteristic
109C2×C42—111no—
110#107—21no—
111#107—221no—
112#106—21no—
113#106—221no—
114#95—222no—
115C2×C11—21no—
116C2×C11—21no—
117C2×C11#39511yescharacteristic
118C2×C11#45411yescharacteristic
119C2×C11#45511yescharacteristic
120C2×Q8—222no—
121C22×C4—21no—
122C22×C4—112no—
123C22×C4—221no—
124C22×C4C22×D1111yescharacteristic
125M16—21no—
126M16—112no—
127M16—221no—
128M16Dic2212yescomplemented
129C2×C8—21no—
130C2×C8—221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—111no—
134C4⋊C4—111no—
135C4⋊C4—222no—
136C4⋊C4—222no—
137C4⋊C4—222no—
138C4⋊C4—221no—
139C4⋊C4—221no—
140C4⋊C4C22⋊D1111yescharacteristic
141C4⋊C4C22⋊D1111yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—221no—
144C42—21no—
145C42—112no—
146C42—221no—
147C42—221no—
148C11#206111yescharacteristic, complemented, Sylow
149C23D4×D1111yescharacteristic
150Q8—882no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—222no—
156C2×C4—221no—
157C2×C4—221no—
158C2×C4—222no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4—442no—
162C2×C4C2×Dic2211yescharacteristic
163C2×C4#433911yescharacteristic
164C2×C4D4×D1111yescharacteristic
165C2×C4Q8×D1111yescharacteristic
166C2×C4Q8×D1111yescharacteristic
167C2×C4C2×C22⋊D1111yescharacteristic
168C8—22no—
169C8—222no—
170C22—21no—
171C22—21no—
172C22#6694111yescharacteristic
173C22#6694911yescharacteristic
174C22#6699011yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—442no—
179C4—441no—
180C4—442no—
181C4—441no—
182C4#6694111yescharacteristic
183C4#6694911yescharacteristic
184C4#6697711yescharacteristic
185C4#6699711yescharacteristic
186C2—21no—
187C2—21no—
188C2#1062259211yescharacteristic
189C2#1062281411yescharacteristic
190C2#1062281511yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#428C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#428D11
hypocenterC11#2061
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
31. C11×M16Q8semidirect
49. C4×Dic11Q8semidirect
51. #4318Q8semidirect
128. M16Dic22semidirect
148. C11#2061semidirect

Maximal subgroups

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

subgroupindex
#106230502
C11×#4282
#106225902
#106225772
#106221932
#106221922
#106221702
#206111