Finite Group Databasebeta

← #13069310

Subgroups — #13069310

Order 1408.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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×#102C211yesmaximal, characteristic
2#10622834C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66879C211yesmaximal, characteristic, complemented
5#10622586C211yesmaximal, characteristic, complemented
6#10622189C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C22⋊Dic11—21no—
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4—21no—
16C2×C4×Dic11C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#102—22no—
19#66896C414yescomplemented
20C11⋊#95—21no—
21#66879—22no—
22C24×C11—21no—
23C2×D4×C11—21no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11C2×C412yes—
29C22×C4×C11—21no—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C22×Dic11—21no—
33C22×Dic11D411yescharacteristic
34C22×Dic11D411yescharacteristic
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C2×C8×C11D412yes—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C22⋊Dic11—42no—
41C22⋊Dic11—42no—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11C2×C412yes—
46Dic11⋊C4—42no—
47C4×Dic11—21no—
48C4×Dic11—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8C2×C412yes—
52#1936—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—41no—
55C23×C11—41no—
56C23×C11—41no—
57C23×C11—41no—
58C23×C11—41no—
59C23×C11—41no—
60C23×C11C2×D411yescharacteristic
61D4×C11—22no—
62D4×C11—22no—
63D4×C11—41no—
64D4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11C22×C411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×Dic11—22no—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84C2×Dic11—41no—
85C2×Dic11—41no—
86C8×C11—22no—
87C11⋊C8—22no—
88C2×#102—111no—
89C2×#102D1111yescharacteristic
90C2×#97—111no—
91#390—111no—
92#389—111no—
93#340—111no—
94#340—111no—
95C22×C11—42no—
96C22×C11—42no—
97C22×C11—42no—
98C22×C11—81no—
99C22×C11—81no—
100C22×C11—81no—
101C22×C11—81no—
102C22×C11C4×D411yescharacteristic
103C22×C11#12111yescharacteristic
104C22×C11#12411yescharacteristic
105C22×C11AGL(1,ℤ/8)11yescharacteristic
106C22×C11AGL(1,ℤ/8)11yescharacteristic
107C22×C11AGL(1,ℤ/8)11yescharacteristic
108C22×C11#13711yescharacteristic
109C4×C11—81no—
110C4×C11#11711yescharacteristic
111C4×C11C4×D411yescharacteristic
112C4×C11#12311yescharacteristic
113C4×C11#12611yescharacteristic
114Dic11—42no—
115Dic11—41no—
116Dic11—41no—
117Dic11—81no—
118C22×D4C2×D1111yescharacteristic
119C22×C8—111no—
120C22×C8C2×D1111yescharacteristic
121C2×C4⋊C4—111no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—221no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C22⋊C4—221no—
126C2×C22⋊C4—221no—
127C2×C42—111no—
128#102—22no—
129#102—114no—
130#97—222no—
131#95—221no—
132C2×C11—82no—
133C2×C11#38811yescharacteristic
134C2×C11#44011yescharacteristic
135C2×C11#44211yescharacteristic
136C2×C11#46811yescharacteristic
137C2×C11#46911yescharacteristic
138C2×C11#48911yescharacteristic
139C2×C11#49011yescharacteristic
140C24—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C4×D1112yes—
147C22×C4—21no—
148C22×C4—111no—
149C22×C4—111no—
150C22×C4—221no—
151C22×C4—221no—
152C22×C4C22×D1111yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—112no—
156C2×C8—221no—
157C2×C8—221no—
158C2×C8C22⋊D1112yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—112no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C4⋊C4—221no—
165C4⋊C4—442no—
166C22⋊C4—442no—
167C22⋊C4—442no—
168C42—221no—
169C42—221no—
170C11#193611yescharacteristic, complemented, Sylow
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23D4×D1111yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—222no—
187C2×C4—221no—
188C2×C4—221no—
189C2×C4—221no—
190C2×C4—221no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—441no—
194C2×C4—441no—
195C2×C4—441no—
196C2×C4—441no—
197C2×C4—441no—
198C2×C4C2×C4×D1111yescharacteristic
199C2×C4#433911yescharacteristic
200C2×C4#434111yescharacteristic
201C2×C4#434111yescharacteristic
202C2×C4#434111yescharacteristic
203C2×C4C2×C22⋊D1111yescharacteristic
204C8—22no—
205C8—222no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22(C22⋊D11)⋊C411yescharacteristic
214C22#6693811yescharacteristic
215C22#6696411yescharacteristic
216C22#6696411yescharacteristic
217C22#6696711yescharacteristic
218C22#6696811yescharacteristic
219C22#6699111yescharacteristic
220C4—81no—
221C4—441no—
222C4—441no—
223C4—442no—
224C4—881no—
225C4#6693011yescharacteristic
226C4#6693211yescharacteristic
227C4C4×C22⋊D1111yescharacteristic
228C4#6698811yescharacteristic
229C2—82no—
230C2#1062237011yescharacteristic
231C2#1062237711yescharacteristic
232C2#1062237811yescharacteristic
233C2#1062239811yescharacteristic
234C2#1062255711yescharacteristic
235C2#1062277211yescharacteristic
236C2#1062278711yescharacteristic
subgroupG/H
centerC23D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
cosocleC22×C4×C11C23
hypercenterC2×#102D11
hypocenterC11#1936
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
4. C2×#66879C2semidirect
5. #10622586C2semidirect
6. #10622189C2semidirect
7. #10622167C2semidirect
19. #66896C4semidirect
170. C11#1936semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1022
#106228342
C2×#668962
C2×#668792
#106225862
#106221892
#106221672
#193611