Finite Group Databasebeta

← #13070137

Subgroups — #13070137

Order 1408.

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

normal subgroups only

This group has 274 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×#390C211yesmaximal, characteristic
2C2×#66896C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66872C211yesmaximal, characteristic, complemented
5C2×#66871C211yesmaximal, characteristic, complemented
6#10622549C211yesmaximal, characteristic, complemented
7#10622162C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C22⋊C4—22no—
11C2×C42×C11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C22×C11⋊C8C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16#66896—22no—
17#66896—22no—
18C11⋊#95—22no—
19#66872—22no—
20#66871—22no—
21C24×C11—21no—
22C2×D4×C11—21no—
23C2×D4×C11—21no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11Q812yes—
28C22×C4×C11—21no—
29C22×C4×C11D412yes—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C22×Dic11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C22⋊C4—44no—
36C42×C11—21no—
37C42×C11—21no—
38C4⋊Dic11—21no—
39C4⋊Dic11—21no—
40C4⋊Dic11—21no—
41C4⋊Dic11—21no—
42C2×C11⋊C8—21no—
43C2×C11⋊C8—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8D412yes—
47C2×C11⋊C8D412yes—
48#2092—111nomaximal, Sylow
49C23×C11—22no—
50C23×C11—41no—
51C23×C11—41no—
52C23×C11—42no—
53C23×C11—42no—
54C23×C11C2×D411yescharacteristic
55D4×C11—22no—
56D4×C11—22no—
57D4×C11—41no—
58D4×C11—41no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—41no—
63C2×C4×C11—42no—
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×Q811yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—42no—
73C2×Dic11—42no—
74C11⋊C8—22no—
75C11⋊C8—22no—
76C2×#107—111no—
77C2×#106—111no—
78C2×#102—111no—
79C2×#102—111no—
80#390D1111yescharacteristic
81#382—111no—
82#336—111no—
83C22×C11—42no—
84C22×C11—44no—
85C22×C11—82no—
86C22×C11—81no—
87C22×C11—81no—
88C22×C11C22⋊Q811yescharacteristic
89C22×C11#12311yescharacteristic
90C22×C11#12711yescharacteristic
91C22×C11#13512yes—
92C22×C11AGL(1,ℤ/8)12yes—
93C4×C11—42no—
94C4×C11—81no—
95C4×C11C22⋊Q811yescharacteristic
96C4×C11C22⋊Q811yescharacteristic
97C4×C11#12311yescharacteristic
98C4×C11#12311yescharacteristic
99Dic11—81no—
100Dic11—81no—
101C22×D4C2×D1111yescharacteristic
102C22×C8—111no—
103C22×C8—111no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C22⋊C4—22no—
108C2×C42C2×D1111yescharacteristic
109#107—222no—
110#106—222no—
111#102—222no—
112#102—222no—
113#95—222no—
114C2×C11—82no—
115C2×C11#39911yescharacteristic
116C2×C11#47812yes—
117C2×C11#48212yes—
118C2×C11#49511yescharacteristic
119C2×C11#49611yescharacteristic
120C24—21no—
121C2×D4—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4Dic2212yes—
127C22×C4—21no—
128C22×C4—221no—
129C22×C4—221no—
130C22×C4C22⋊D1112yes—
131C22×C4C22×D1111yescharacteristic
132C2×C8—112no—
133C2×C8—112no—
134C2×C8—221no—
135C2×C8—221no—
136C2×C8—221no—
137C2×C8—221no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—221no—
141C4⋊C4—221no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C22⋊C4—44no—
145C42—21no—
146C42—21no—
147C11#209211yescharacteristic, complemented, Sylow
148C23—22no—
149C23—42no—
150C23—41no—
151C23—41no—
152C23—42no—
153C23C2×C22⋊D1111yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—442no—
164C2×C4—441no—
165C2×C4—441no—
166C2×C4—442no—
167C2×C4C2×Dic2211yescharacteristic
168C2×C4#433911yescharacteristic
169C2×C4D4×D1111yescharacteristic
170C2×C4D4×D1111yescharacteristic
171C2×C4#434111yescharacteristic
172C2×C4#434111yescharacteristic
173C8—222no—
174C8—222no—
175C22—42no—
176C22—44no—
177C22—82no—
178C22—81no—
179C22—81no—
180C22#6697711yescharacteristic
181C22#6698512yes—
182C22#6698811yescharacteristic
183C22#6699311yescharacteristic
184C22#6700312yes—
185C4—42no—
186C4—81no—
187C4—881no—
188C4—881no—
189C4#6693111yescharacteristic
190C4#6693111yescharacteristic
191C4#6693611yescharacteristic
192C4#6693611yescharacteristic
193C2—82no—
194C2#1062256211yescharacteristic
195C2#1062262212yes—
196C2#1062264812yes—
197C2#1062267211yescharacteristic
198C2#1062268711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2092
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
4. C2×#66872C2semidirect
5. C2×#66871C2semidirect
6. #10622549C2semidirect
7. #10622162C2semidirect
147. C11#2092semidirect

Maximal subgroups

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

subgroupindex
C11×#3902
C2×#668962
C2×#668722
C2×#668712
#106225492
#106221622
#209211