Finite Group Databasebeta

← #13070049

Subgroups — #13070049

Order 1408.

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

normal subgroups only

This group has 256 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
1C2×C11×C22⋊C8C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic
4C2×#66881C211yesmaximal, characteristic, complemented
5#10622189C211yesmaximal, characteristic, complemented
6#10622189C211yesmaximal, characteristic, complemented
7#10622189C211yesmaximal, characteristic, complemented
8C23×C4×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C22⋊Dic11—21no—
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C11×C22⋊C8—22no—
18C11⋊#95—21no—
19C11⋊#95—21no—
20#66881—22no—
21C24×C11D411yescharacteristic
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11D411yescharacteristic
29C22×C4×C11C2311yescharacteristic
30C22×Dic11—21no—
31C22×Dic11—21no—
32C22×Dic11—21no—
33C22×Dic11—21no—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C2×C8×C11—21no—
39C2×C8×C11D412yes—
40C22⋊Dic11—42no—
41C22⋊Dic11—42no—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11—21no—
46C4⋊Dic11—21no—
47C4⋊Dic11—21no—
48C4⋊Dic11—21no—
49C4⋊Dic11—21no—
50#2077—111nomaximal, Sylow
51C23×C11—21no—
52C23×C11—21no—
53C23×C11—21no—
54C23×C11—21no—
55C23×C11—21no—
56C23×C11—21no—
57C23×C11SD1612yes—
58C23×C11C2×D411yescharacteristic
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C2×Dic11—41no—
73C2×Dic11—41no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84C8×C11—22no—
85C8×C11—41no—
86C2×#106—111no—
87C2×C22⋊C8D1111yescharacteristic
88#380—111no—
89#380—111no—
90#340—111no—
91#340—111no—
92#340—111no—
93C22×C11—22no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—41no—
97C22×C11—41no—
98C22×C11—41no—
99C22×C11—41no—
100C22×C11#12111yescharacteristic
101C22×C11#12311yescharacteristic
102C22×C11#12311yescharacteristic
103C22×C11C2×SD1611yescharacteristic
104C22×C11#13511yescharacteristic
105C22×C11AGL(1,ℤ/8)11yescharacteristic
106C22×C11#13711yescharacteristic
107C4×C11—41no—
108C4×C11#12311yescharacteristic
109C4×C11#12411yescharacteristic
110C4×C11#12611yescharacteristic
111C4×C11#12611yescharacteristic
112Dic11—81no—
113Dic11—81no—
114Dic11—81no—
115Dic11—81no—
116C23×C4C2×D1111yescharacteristic
117C22×C8C2×D1111yescharacteristic
118C22×C8C2×D1111yescharacteristic
119C2×C4⋊C4—111no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—111no—
123C2×C22⋊C4—221no—
124C2×C22⋊C4—221no—
125#106—222no—
126C22⋊C8—22no—
127#95—221no—
128#95—221no—
129C2×C11—42no—
130C2×C11#39711yescharacteristic
131C2×C11#46511yescharacteristic
132C2×C11#46811yescharacteristic
133C2×C11#48111yescharacteristic
134C2×C11#48211yescharacteristic
135C2×C11#48311yescharacteristic
136C2×C11#48511yescharacteristic
137C24D4411yescharacteristic
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—221no—
145C22×C4—221no—
146C22×C4—221no—
147C22×C4—221no—
148C22×C4D4411yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8C22⋊D1112yes—
156C4⋊C4—221no—
157C4⋊C4—221no—
158C4⋊C4—221no—
159C4⋊C4—221no—
160C4⋊C4—221no—
161C4⋊C4—221no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C22⋊C4—442no—
165C22⋊C4—442no—
166C11#207711yescharacteristic, complemented, Sylow
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#431412yes—
174C23C2×D4411yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—441no—
183C2×C4—441no—
184C2×C4—441no—
185C2×C4—441no—
186C2×C4—441no—
187C2×C4—441no—
188C2×C4—441no—
189C2×C4—441no—
190C2×C4—441no—
191C2×C4—441no—
192C2×C4—441no—
193C2×C4—441no—
194C2×C4#433911yescharacteristic
195C2×C4#434111yescharacteristic
196C2×C4#434111yescharacteristic
197C2×C4#434111yescharacteristic
198C2×C4#434111yescharacteristic
199C2×C4C2×C22⋊D1111yescharacteristic
200C8—22no—
201C8—41no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#6693911yescharacteristic
210C22#6693911yescharacteristic
211C22C2×#431411yescharacteristic
212C22#6695711yescharacteristic
213C22#6696111yescharacteristic
214C22#6696211yescharacteristic
215C22#6698311yescharacteristic
216C4—41no—
217C4—881no—
218C4—881no—
219C4—881no—
220C4—881no—
221C4#6693211yescharacteristic
222C4#6693211yescharacteristic
223C4#6698811yescharacteristic
224C4#6698911yescharacteristic
225C2—42no—
226C2#1062233411yescharacteristic
227C2#1062233611yescharacteristic
228C2#1062234811yescharacteristic
229C2#1062235011yescharacteristic
230C2#1062256611yescharacteristic
231C2#1062272711yescharacteristic
232C2#1062274711yescharacteristic
subgroupG/H
centerC23C2×D44
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×C22⋊C8C2
socleC23×C11C2×D4
prime radicalC24×C11D4
hypercenterC2×C22⋊C8D11
hypocenterC11#2077
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#66881C2semidirect
5. #10622189C2semidirect
6. #10622189C2semidirect
7. #10622189C2semidirect
166. C11#2077semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊C82
#106228252
C2×#668812
#106221892
#207711