Finite Group Databasebeta

← #13069875

Subgroups — #13069875

Order 1408.

276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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
2C2×C11×#101C211yesmaximal, characteristic, complemented
3#10622838C211yesmaximal, characteristic, complemented
4#10622744C211yesmaximal, characteristic
5C2×#66887C211yesmaximal, characteristic
6#10622732C211yesmaximal, characteristic, complemented
7#10622196C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C2×#4325—22no—
13C2×#4325—22no—
14C2×#4325—22no—
15#66979C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#101—22no—
19#66899—22no—
20#66887—22no—
21#66885—22no—
22Dic11⋊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—
40C11×M16—21no—
41C11×M16—21no—
42C2×C8×C11—21no—
43C2×C8×C11—21no—
44C22⋊Dic11—21no—
45#4325—28no—
46C4⋊Dic11D412yes—
47C4×Dic11—21no—
48#4318—21no—
49#4318—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—41no—
66C2×C4×C11—41no—
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×Dic11—22no—
74D44—22no—
75D44—22no—
76D44—41no—
77D44—41no—
78C8×C11—41no—
79C8×C11—41no—
80C11⋊C8—22no—
81C11⋊C8—41no—
82C22×SD16—111no—
83#424—111no—
84#419—111no—
85#418—111no—
86C2×#101D1111yescharacteristic, complemented
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#12011yescharacteristic
99C4×C11#12111yescharacteristic
100C4×C11#12111yescharacteristic
101C4×C11#12411yescharacteristic
102Dic11—42no—
103C22×Q8C2×D1111yescharacteristic
104C22×D4—111no—
105C2×SD16—222no—
106C2×SD16—222no—
107C2×SD16—222no—
108C2×M16—111no—
109C2×M16C2×D1111yescharacteristic
110C2×M16C2×D1111yescharacteristic
111C22×C8—111no—
112#117—111no—
113C4⋊C8—222no—
114#103—222no—
115#102—222no—
116#101—22no—
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×Q8C22⋊D1112yes—
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—21no—
142M16—21no—
143M16—221no—
144M16—221no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—112no—
148C2×C8—221no—
149C2×C8—221no—
150C2×C8—221no—
151C4⋊C4—112no—
152C22⋊C4—221no—
153C42—221no—
154C11#204611yescharacteristic, complemented, Sylow
155C23—222no—
156C23—441no—
157C23—441no—
158C23—882no—
159C23#433911yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—222no—
165D4—222no—
166D4—441no—
167D4—441no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—222no—
172C2×C4#433911yescharacteristic
173C2×C4D4×D1111yescharacteristic
174C2×C4D4×D1111yescharacteristic
175C2×C4D4×D1111yescharacteristic
176C2×C4#434111yescharacteristic
177C2×C4C2×C22⋊D1111yescharacteristic
178C8—41no—
179C8—41no—
180C8—222no—
181C8—441no—
182C22—22no—
183C22—442no—
184C22—882no—
185C22—882no—
186C22—882no—
187C22#6693611yescharacteristic
188C22#6693711yescharacteristic
189C22#6698211yescharacteristic
190C4—42no—
191C4—442no—
192C4#6693711yescharacteristic
193C4#6693811yescharacteristic
194C4#6699011yescharacteristic
195C4#6699211yescharacteristic
196C2—21no—
197C2—21no—
198C2—882no—
199C2#1062236712yes—
200C2#1062257211yescharacteristic
subgroupG/H
centerC22#66937
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#101C2
socleC22×C11#121
prime radicalC22×D44C22
hypercenterC2×#101D11
hypocenterC11#2046
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×C11×#101C2semidirect
3. #10622838C2semidirect
6. #10622732C2semidirect
7. #10622196C2semidirect
86. C2×#101D11semidirect
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
C2×C11×#1012
#106228382
#106227442
C2×#668872
#106227322
#106221962
#204611