Finite Group Databasebeta

← #13069874

Subgroups — #13069874

Order 1408.

276 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 71 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×C11×SD16C211yesmaximal, characteristic
2C2×#66900C211yesmaximal, characteristic, complemented
3#10622838C211yesmaximal, characteristic, complemented
4C2×#66897C211yesmaximal, characteristic
5#10622828C211yesmaximal, characteristic
6#10622715C211yesmaximal, characteristic, complemented
7#10622190C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C2×C11×SD16—22no—
11C2×C11×SD16—22no—
12C2×C11×SD16—22no—
13C22×C8×C11C2211yescharacteristic
14#66979C2211yescharacteristic
15C2×#4318C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18#66900—22no—
19#66899—22no—
20#66897—22no—
21#66896—22no—
22Dic11⋊C8—22no—
23C24×C11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11D412yes—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11D412yes—
36C22×C4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C11×SD16—28no—
39C2×C8×C11—21no—
40C2×C8×C11—21no—
41C2×C8×C11D412yes—
42C22⋊Dic11—21no—
43C4⋊Dic11D412yes—
44C4×Dic11—21no—
45#4318—21no—
46#4318—21no—
47#4318—21no—
48#4318—21no—
49#4318—21no—
50#4318—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—21no—
54#2046—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—41no—
57C23×C11—41no—
58C23×C11—82no—
59C23×C11#4111yescharacteristic
60Q8×C11—22no—
61Q8×C11—22no—
62Q8×C11—41no—
63Q8×C11—41no—
64D4×C11—22no—
65D4×C11—22no—
66D4×C11—41no—
67D4×C11—41no—
68C2×C4×C11—22no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C2×Dic11—22no—
78C8×C11—22no—
79C11⋊C8—41no—
80C11⋊C8—41no—
81C11⋊C8—41no—
82C22×SD16D1111yescharacteristic
83#424—111no—
84#419—111no—
85#418—111no—
86C2×#101—111no—
87C2×#100—111no—
88#341—111no—
89C22×C11—22no—
90C22×C11—42no—
91C22×C11—82no—
92C22×C11—82no—
93C22×C11—82no—
94C22×C11#12111yescharacteristic
95C22×C11#12311yescharacteristic
96C22×C11#12311yescharacteristic
97C4×C11—42no—
98C4×C11#12011yescharacteristic
99C4×C11#12111yescharacteristic
100C4×C11#12111yescharacteristic
101C4×C11#12411yescharacteristic
102Dic11—42no—
103C22×Q8C2×D1111yescharacteristic
104C22×D4C2×D1111yescharacteristic
105C2×SD16—22no—
106C2×SD16—22no—
107C2×SD16—22no—
108C2×M16—111no—
109C2×M16—111no—
110C2×M16—111no—
111C22×C8C2×D1111yescharacteristic
112#117—111no—
113C4⋊C8—222no—
114#103—222no—
115#102—222no—
116#101—222no—
117#100—222no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11—82no—
121C2×C11#39411yescharacteristic
122C2×C11#47112yes—
123C24—21no—
124C2×Q8—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8C22⋊D1112yes—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4C22⋊D1112yes—
136C22×C4—21no—
137C22×C4C22×D1111yescharacteristic
138SD16—28no—
139M16—221no—
140M16—221no—
141M16—221no—
142M16—221no—
143M16—221no—
144M16—221no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—221no—
148C2×C8—221no—
149C2×C8—221no—
150C2×C8C22⋊D1112yes—
151C4⋊C4—112no—
152C22⋊C4—221no—
153C42—221no—
154C11#204611yescharacteristic, complemented, Sylow
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#434111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—222no—
172C2×C4D4×D1111yescharacteristic
173C2×C4#434111yescharacteristic
174C2×C4#434111yescharacteristic
175C2×C4C2×C22⋊D1111yescharacteristic
176C2×C4C2×C22⋊D1111yescharacteristic
177C2×C4C2×C22⋊D1111yescharacteristic
178C8—22no—
179C8—441no—
180C8—441no—
181C8—441no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#6698811yescharacteristic
188C22#6698811yescharacteristic
189C22#6699111yescharacteristic
190C4—42no—
191C4—442no—
192C4#6698911yescharacteristic
193C4#6699211yescharacteristic
194C4#6699211yescharacteristic
195C4#6700611yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1062279012yes—
200C2#1062283511yescharacteristic
subgroupG/H
centerC22#66991
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC22×C11×SD16C2
socleC22×C11#121
prime radicalC22×D4×C11C22
hypercenterC22×SD16D11
hypocenterC11#2046
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#66900C2semidirect
3. #10622838C2semidirect
6. #10622715C2semidirect
7. #10622190C2semidirect
154. C11#2046semidirect

Maximal subgroups

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

subgroupindex
C22×C11×SD162
C2×#669002
#106228382
C2×#668972
#106228282
#106227152
#106221902
#204611