Finite Group Databasebeta

← #13070052

Subgroups — #13070052

Order 1408.

256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C11×#380C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic
4C2×#66872C211yesmaximal, characteristic, complemented
5#10622167C211yesmaximal, characteristic, complemented
6#10622167C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C23×C4×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4—21no—
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11×#95—21no—
18C11⋊#95—21no—
19C22⋊(C11⋊C8)—22no—
20#66872—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×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11D411yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C22×Dic11—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C22⋊C4—42no—
39C22⋊Dic11—42no—
40C4⋊Dic11—21no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8D412yes—
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×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C2×C4×C11#4111yescharacteristic
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84C11⋊C8—22no—
85C11⋊C8—41no—
86C2×#106—111no—
87C2×C22⋊C8—111no—
88#380—111no—
89#380D1111yescharacteristic
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—81no—
109C4×C11—81no—
110C4×C11#12311yescharacteristic
111C4×C11#12411yescharacteristic
112C4×C11#12611yescharacteristic
113C4×C11#12611yescharacteristic
114Dic11—81no—
115Dic11—81no—
116C23×C4C2×D1111yescharacteristic
117C22×C8—111no—
118C22×C8—111no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4—221no—
125#106—222no—
126C22⋊C8—222no—
127#95—21no—
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
137C24C22⋊D1111yescharacteristic
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—221no—
147C22×C4—221no—
148C22×C4C22⋊D1111yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C2×C8—112no—
151C2×C8—221no—
152C2×C8—221no—
153C2×C8—221no—
154C2×C8—221no—
155C2×C8—221no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—221no—
161C4⋊C4—221no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C22⋊C4—42no—
165C22⋊C4—442no—
166C11#207711yescharacteristic, complemented, Sylow
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#432412yes—
174C23C2×C22⋊D1111yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—441no—
189C2×C4—441no—
190C2×C4—441no—
191C2×C4—441no—
192C2×C4—441no—
193C2×C4—441no—
194C2×C4#433911yescharacteristic
195C2×C4#433911yescharacteristic
196C2×C4D4×D1111yescharacteristic
197C2×C4#434111yescharacteristic
198C2×C4#434111yescharacteristic
199C2×C4#434111yescharacteristic
200C8—222no—
201C8—441no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#6698211yescharacteristic
210C22C2×#432411yescharacteristic
211C22#6698811yescharacteristic
212C22#6699211yescharacteristic
213C22#6699511yescharacteristic
214C22#6700211yescharacteristic
215C22#6700311yescharacteristic
216C4—41no—
217C4—81no—
218C4—81no—
219C4—881no—
220C4—881no—
221C4#6693211yescharacteristic
222C4#6693211yescharacteristic
223C4#6693611yescharacteristic
224C4#6693811yescharacteristic
225C2—42no—
226C2#1062256511yescharacteristic
227C2#1062258411yescharacteristic
228C2#1062261611yescharacteristic
229C2#1062264711yescharacteristic
230C2#1062265411yescharacteristic
231C2#1062265811yescharacteristic
232C2#1062266211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#380C2
socleC23×C11C2×D4
prime radicalC24×C11D4
hypercenter#380D11
hypocenterC11#2077
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
4. C2×#66872C2semidirect
5. #10622167C2semidirect
6. #10622167C2semidirect
7. #10622167C2semidirect
166. C11#2077semidirect

Maximal subgroups

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

subgroupindex
C11×#3802
#106228252
C2×C22⋊(C11⋊C8)2
C2×#668722
#106221672
#207711