Finite Group Databasebeta

← #13069876

Subgroups — #13069876

Order 1408.

276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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×#4325C211yesmaximal, characteristic
2C11×#419C211yesmaximal, characteristic, complemented
3C2×#66900C211yesmaximal, characteristic, complemented
4C2×#66887C211yesmaximal, characteristic
5#10622614C211yesmaximal, characteristic
6#10622612C211yesmaximal, characteristic, complemented
7#10622196C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×#117C2211yescharacteristic
12C2×#4325—22no—
13C2×#4325—22no—
14C2×#4325—22no—
15C2×#4318C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#103—22no—
19#66900—22no—
20#66887—22no—
21#66873—22no—
22C4⋊(C11⋊C8)—22no—
23C23×D11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11D412yes—
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C2×D44—21no—
33C2×D44—21no—
34C2×D44—21no—
35C2×D44—21no—
36C2×D44—21no—
37C2×D44D412yes—
38C11×M16—21no—
39C11×M16—21no—
40C2×C8×C11—21no—
41C11×C4⋊C4D412yes—
42C11×C22⋊C4—21no—
43C42×C11—21no—
44#4325—28no—
45#4318—21no—
46#4318—21no—
47#4318—21no—
48#4318—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8D412yes—
54#2046—111nomaximal, Sylow
55C23×C11#4111yescharacteristic
56C22×D11—22no—
57C22×D11—41no—
58C22×D11—41no—
59C22×D11—82no—
60Q8×C11—22no—
61Q8×C11—22no—
62Q8×C11—41no—
63Q8×C11—41no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×C4×C11#4111yescharacteristic
74D44—22no—
75D44—22no—
76D44—41no—
77D44—41no—
78C8×C11—41no—
79C11⋊C8—22no—
80C11⋊C8—41no—
81C11⋊C8—41no—
82C22×SD16—111no—
83#424—111no—
84#419D1111yescharacteristic, complemented
85#418—111no—
86C2×#101—111no—
87C2×#100—111no—
88#341—111no—
89C22×C11—22no—
90C22×C11#12111yescharacteristic
91C22×C11#12311yescharacteristic
92C22×C11#12311yescharacteristic
93C2×D11—42no—
94C2×D11—82no—
95C2×D11—82no—
96C2×D11—82no—
97C4×C11—42no—
98C4×C11—42no—
99C4×C11#12011yescharacteristic
100C4×C11#12111yescharacteristic
101C4×C11#12111yescharacteristic
102C4×C11#12411yescharacteristic
103C22×Q8C2×D1111yescharacteristic
104C22×D4—111no—
105C2×SD16—222no—
106C2×SD16—222no—
107C2×SD16—222no—
108C2×M16—111no—
109C2×M16—111no—
110C2×M16C2×D1111yescharacteristic
111C22×C8—111no—
112#117C2×D1111yescharacteristic
113C4⋊C8—222no—
114#103—22no—
115#102—222no—
116#101—222no—
117#100—222no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11#39411yescharacteristic
121C2×C11#47112yes—
122D11—82no—
123C24—221no—
124C2×Q8—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8D4412yes—
130C2×D4—112no—
131C2×D4—221no—
132C2×D4—221no—
133C2×D4—221no—
134C2×D4—221no—
135C2×D4—221no—
136C22×C4—21no—
137C22×C4C22×D1111yescharacteristic
138SD16—228no—
139M16—21no—
140M16—21no—
141M16—221no—
142M16—221no—
143M16—221no—
144M16—221no—
145C2×C8—21no—
146C2×C8—112no—
147C2×C8—221no—
148C2×C8—221no—
149C2×C8—221no—
150C2×C8—221no—
151C4⋊C4C22⋊D1112yes—
152C22⋊C4—21no—
153C42—21no—
154C11#204611yescharacteristic, complemented, Sylow
155C23—222no—
156C23—441no—
157C23—441no—
158C23—882no—
159C23#434111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—222no—
165D4—222no—
166D4—441no—
167D4—441no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4C2×D4411yescharacteristic
173C2×C4#433911yescharacteristic
174C2×C4D4×D1111yescharacteristic
175C2×C4D4×D1111yescharacteristic
176C2×C4#434111yescharacteristic
177C2×C4C2×C22⋊D1111yescharacteristic
178C8—41no—
179C8—222no—
180C8—441no—
181C8—441no—
182C22—22no—
183C22—442no—
184C22—882no—
185C22—882no—
186C22—882no—
187C22#6693611yescharacteristic
188C22#6693911yescharacteristic
189C22#6699211yescharacteristic
190C4—42no—
191C4—42no—
192C4#6693511yescharacteristic
193C4#6693811yescharacteristic
194C4#6698311yescharacteristic
195C4#6699111yescharacteristic
196C2—21no—
197C2—21no—
198C2—882no—
199C2#1062257411yescharacteristic
200C2#1062281612yes—
subgroupG/H
centerC22#66992
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#419C2
socleC22×C11#121
prime radicalC22×D44C22
hypercenter#419D11
hypocenterC11#2046
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C11×#419C2semidirect
3. C2×#66900C2semidirect
6. #10622612C2semidirect
7. #10622196C2semidirect
84. #419D11semidirect
154. C11#2046semidirect

Maximal subgroups

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

subgroupindex
C22×#43252
C11×#4192
C2×#669002
C2×#668872
#106226142
#106226122
#106221962
#204611