Finite Group Databasebeta

← #13069871

Subgroups — #13069871

Order 1408.

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

normal subgroups only

This group has 296 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×#4323C211yesmaximal, characteristic
2C11×#418C211yesmaximal, characteristic, complemented
3C2×#66897C211yesmaximal, characteristic, complemented
4C2×#66887C211yesmaximal, characteristic, complemented
5#10622614C211yesmaximal, characteristic, complemented
6#10622612C211yesmaximal, characteristic, complemented
7#10622196C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×#117C2211yescharacteristic
12C2×#4323—22no—
13C2×#4323—22no—
14C2×#4323—22no—
15C2×#4318C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#102—22no—
19#66897—22no—
20#66887—22no—
21#66873—22no—
22C4⋊(C11⋊C8)—22no—
23C24×C11—21no—
24C23×D11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11D412yes—
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#4323—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#2045—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—41no—
57C23×C11—41no—
58C23×C11—82no—
59C23×C11#4111yescharacteristic
60C22×D11—22no—
61C22×D11—41no—
62C22×D11—41no—
63C22×D11—82no—
64D4×C11—22no—
65D4×C11—22no—
66D4×C11—41no—
67D4×C11—41no—
68C2×C4×C11—22no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75D44—22no—
76D44—22no—
77D44—41no—
78D44—41no—
79C8×C11—41no—
80C11⋊C8—22no—
81C11⋊C8—41no—
82C11⋊C8—41no—
83C22×D8—111no—
84#424—111no—
85#418—111no—
86#418D1111yescharacteristic, complemented
87C2×#100—111no—
88C2×#100—111no—
89#341—111no—
90C22×C11—22no—
91C22×C11—42no—
92C22×C11—82no—
93C22×C11—82no—
94C22×C11—82no—
95C22×C11#12111yescharacteristic
96C22×C11#12311yescharacteristic
97C22×C11#12311yescharacteristic
98C2×D11—42no—
99C2×D11—82no—
100C2×D11—82no—
101C2×D11—82no—
102C4×C11—42no—
103C4×C11#12011yescharacteristic
104C4×C11#12111yescharacteristic
105C4×C11#12111yescharacteristic
106C4×C11#12411yescharacteristic
107C22×D4—111no—
108C22×D4C2×D1111yescharacteristic
109C2×D8—222no—
110C2×D8—222no—
111C2×D8—222no—
112C2×M16—111no—
113C2×M16—111no—
114C2×M16C2×D1111yescharacteristic
115C22×C8—111no—
116#117C2×D1111yescharacteristic
117C4⋊C8—222no—
118#102—22no—
119#102—222no—
120#100—222no—
121#100—222no—
122C2×C11—21no—
123C2×C11—21no—
124C2×C11—82no—
125C2×C11#39411yescharacteristic
126C2×C11#47212yes—
127D11—82no—
128C24—21no—
129C24—221no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—112no—
136C2×D4—221no—
137C2×D4—221no—
138C2×D4—221no—
139C2×D4—221no—
140C2×D4—221no—
141C2×D4D4412yes—
142C22×C4C22×D1111yescharacteristic
143D8—228no—
144M16—21no—
145M16—21no—
146M16—221no—
147M16—221no—
148M16—221no—
149M16—221no—
150C2×C8—21no—
151C2×C8—112no—
152C2×C8—221no—
153C2×C8—221no—
154C2×C8—221no—
155C2×C8—221no—
156C4⋊C4C22⋊D1112yes—
157C22⋊C4—21no—
158C42—21no—
159C11#204511yescharacteristic, complemented, Sylow
160C23—22no—
161C23—41no—
162C23—41no—
163C23—82no—
164C23—222no—
165C23—441no—
166C23—441no—
167C23—882no—
168C23#434111yescharacteristic
169D4—22no—
170D4—22no—
171D4—41no—
172D4—41no—
173D4—222no—
174D4—222no—
175D4—441no—
176D4—441no—
177C2×C4—22no—
178C2×C4C2×D4411yescharacteristic
179C2×C4#433911yescharacteristic
180C2×C4D4×D1111yescharacteristic
181C2×C4D4×D1111yescharacteristic
182C2×C4#434111yescharacteristic
183C2×C4C2×C22⋊D1111yescharacteristic
184C8—41no—
185C8—222no—
186C8—441no—
187C8—441no—
188C22—22no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—442no—
194C22—882no—
195C22—882no—
196C22—882no—
197C22#6693611yescharacteristic
198C22#6693911yescharacteristic
199C22#6699211yescharacteristic
200C4—42no—
201C4#6693511yescharacteristic
202C4#6693811yescharacteristic
203C4#6698311yescharacteristic
204C4#6699111yescharacteristic
205C2—21no—
206C2—21no—
207C2—82no—
208C2—882no—
209C2#1062257411yescharacteristic
210C2#1062281212yes—
subgroupG/H
centerC22#66992
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#418C2
socleC22×C11#121
prime radicalC22×#4323C2
hypercenter#418D11
hypocenterC11#2045
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C11×#418C2semidirect
3. C2×#66897C2semidirect
4. C2×#66887C2semidirect
5. #10622614C2semidirect
6. #10622612C2semidirect
7. #10622196C2semidirect
86. #418D11semidirect
159. C11#2045semidirect

Maximal subgroups

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

subgroupindex
C22×#43232
C11×#4182
C2×#668972
C2×#668872
#106226142
#106226122
#106221962
#204511