Finite Group Databasebeta

← #13070048

Subgroups — #13070048

Order 1408.

256 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 79 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×(C2×D11)⋊C8C211yesmaximal, characteristic
2#10622600C211yesmaximal, characteristic
3#10622600C211yesmaximal, characteristic
4C2×#66871C211yesmaximal, characteristic, complemented
5C11×#340C211yesmaximal, characteristic, complemented
6#10622189C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×C4×D11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×(C2×D11)⋊C4—21no—
13C2×(C2×D11)⋊C4—21no—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11⋊#95—21no—
18C11⋊#95—21no—
19(C2×D11)⋊C8—22no—
20#66871—22no—
21C23×D11D411yescharacteristic
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C22×Dic11—21no—
26C22×Dic11—21no—
27C22×Dic11D411yescharacteristic
28C2×C4×D11—21no—
29C2×C4×D11—21no—
30C2×C4×D11—21no—
31C2×C4×D11—21no—
32C2×C4×D11—21no—
33C2×C4×D11—21no—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41(C2×D11)⋊C4—42no—
42(C2×D11)⋊C4—42no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11—21no—
46C4⋊Dic11—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8D412yes—
50#2076—111nomaximal, Sylow
51C23×C11C2×D411yescharacteristic
52C22×D11—21no—
53C22×D11—21no—
54C22×D11—21no—
55C22×D11—21no—
56C22×D11—21no—
57C22×D11—21no—
58C22×D11Q1612yes—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×Dic11—21no—
72C2×Dic11—21no—
73C2×Dic11—21no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C4×D11—41no—
81C4×D11—41no—
82C4×D11—41no—
83C4×D11—41no—
84C8×C11—41no—
85C11⋊C8—22no—
86C2×#107—111no—
87C2×C22⋊C8—111no—
88#380—111no—
89#380—111no—
90#340—111no—
91#340—111no—
92#340D1111yescharacteristic, complemented
93C22×C11#12111yescharacteristic
94C22×C11#12311yescharacteristic
95C22×C11#12311yescharacteristic
96C22×C11C2×Q1611yescharacteristic
97C22×C11#13511yescharacteristic
98C22×C11AGL(1,ℤ/8)11yescharacteristic
99C22×C11AGL(1,ℤ/8)11yescharacteristic
100C2×D11—22no—
101C2×D11—22no—
102C2×D11—22no—
103C2×D11—41no—
104C2×D11—41no—
105C2×D11—41no—
106C2×D11—41no—
107C4×C11—81no—
108C4×C11—81no—
109C4×C11#12311yescharacteristic
110C4×C11#12411yescharacteristic
111C4×C11#12611yescharacteristic
112C4×C11#12611yescharacteristic
113Dic11—41no—
114Dic11—81no—
115Dic11—81no—
116C23×C4—111no—
117C22×C8—111no—
118C22×C8C2×D1111yescharacteristic
119C2×C4⋊C4—111no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C22⋊C4—221no—
124C2×C22⋊C4—221no—
125#107—222no—
126C22⋊C8—222no—
127#95—221no—
128#95—221no—
129C2×C11#39711yescharacteristic
130C2×C11#46711yescharacteristic
131C2×C11#46911yescharacteristic
132C2×C11#48211yescharacteristic
133C2×C11#48211yescharacteristic
134C2×C11#48411yescharacteristic
135C2×C11#48411yescharacteristic
136D11—42no—
137C24—111no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—111no—
141C22×C4—221no—
142C22×C4—221no—
143C22×C4—221no—
144C22×C4—221no—
145C22×C4—221no—
146C22×C4—221no—
147C22×C4—221no—
148C22×C4—221no—
149C22×C4C22×D1111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—112no—
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—442no—
165C22⋊C4—442no—
166C11#207611yescharacteristic, complemented, Sylow
167C23—112no—
168C23—221no—
169C23—221no—
170C23—221no—
171C23—221no—
172C23—221no—
173C23—221no—
174C23D4×D1111yescharacteristic
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—221no—
182C2×C4—221no—
183C2×C4—221no—
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#433911yescharacteristic
196C2×C4#433911yescharacteristic
197C2×C4D4×D1111yescharacteristic
198C2×C4#434111yescharacteristic
199C2×C4#434311yescharacteristic
200C8—41no—
201C8—222no—
202C22—222no—
203C22—222no—
204C22—222no—
205C22—441no—
206C22—441no—
207C22—441no—
208C22—441no—
209C22#6693611yescharacteristic
210C22#6693711yescharacteristic
211C22#6694711yescharacteristic
212C22#6696411yescharacteristic
213C22#6696711yescharacteristic
214C22#6696911yescharacteristic
215C22Q16×D1111yescharacteristic
216C4—81no—
217C4—81no—
218C4—441no—
219C4—881no—
220C4—881no—
221C4#6692911yescharacteristic
222C4#6693811yescharacteristic
223C4#6694711yescharacteristic
224C4#6695111yescharacteristic
225C2—442no—
226C2#1062228811yescharacteristic
227C2#1062239211yescharacteristic
228C2#1062239511yescharacteristic
229C2#1062242211yescharacteristic
230C2#1062242611yescharacteristic
231C2#1062247911yescharacteristic
232C2#1062249711yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC23×D11D4
hypercenter#340D11
hypocenterC11#2076
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C2×#66871C2semidirect
5. C11×#340C2semidirect
6. #10622189C2semidirect
7. #10622167C2semidirect
92. #340D11semidirect
166. C11#2076semidirect

Maximal subgroups

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

subgroupindex
C2×(C2×D11)⋊C82
#106226002
C2×#668712
C11×#3402
#106221892
#106221672
#207611