Finite Group Databasebeta

← #13078472

Subgroups — #13078472

Order 1408.

376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#10623035C211yesmaximal, characteristic
2#10623031C211yesmaximal, characteristic, complemented
3C2×C11×#107C211yesmaximal, characteristic, complemented
4#10622726C211yesmaximal, characteristic
5#10622715C211yesmaximal, characteristic, complemented
6#10622579C211yesmaximal, characteristic
7#10622577C211yesmaximal, characteristic, complemented
8#10622504C212yesmaximal, complemented
9#10622503C212yesmaximal, complemented
10#10622490C212yesmaximal, complemented
11#10622488C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C4×C22⋊D11—22no—
17#66979C2211yescharacteristic
18#66979C2211yescharacteristic
19#66977—22no—
20C2×#4318C2211yescharacteristic
21#66946C2212yes—
22#66945—21no—
23C4⋊C4×D11—21no—
24#66943—21no—
25#66943C2212yes—
26#66941—21no—
27#66941C2212yes—
28#66940C2212yes—
29C11×#107C2212yes—
30C11×#107C2212yes—
31#66885C2211yescharacteristic
32#66885C2211yescharacteristic
33#66880C2211yescharacteristic
34#66880C2211yescharacteristic
35Dic11⋊C8C2212yes—
36Dic11⋊C8C2212yes—
37#66874C2212yes—
38#66873C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—21no—
45#4339—22no—
46#4339Q814yescomplemented
47C2×D44C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—21no—
50C2×Dic22—22no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11—22no—
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2312yes—
58C11×C4⋊C4C2312yes—
59C22⋊Dic11—21no—
60C22⋊Dic11D412yes—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C4×Dic11—21no—
72C4×Dic11C2312yes—
73#4318—22no—
74C2×C11⋊C8C2312yes—
75#3083—111nomaximal, Sylow
76C23×C11C2×D411yescharacteristic
77C22×D11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—81no—
81C2×C4×C11—81no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×Q812yes—
84C2×C4×C11#4112yes—
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—24no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92D44—21no—
93D44C2×Q812yes—
94C4×D11—24no—
95C4×D11—82no—
96Dic22—21no—
97Dic22—82no—
98Dic22C2×Q812yes—
99C8×C11—21no—
100C8×C11—21no—
101C11⋊C8—22no—
102#544—111no—
103#520—111no—
104#479—112no—
105#478—112no—
106#477—112no—
107#474—112no—
108#428—111no—
109C2×#107D1111yescharacteristic, complemented
110#424—111no—
111#417—111no—
112#416—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11C22⋊Q812yes—
116C22×C11C22×D411yescharacteristic
117C2×D11—22no—
118C2×D11—41no—
119C2×D11—41no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11C22⋊Q812yes—
123C4×C11C22×Q811yescharacteristic
124C4×C11C2×#4111yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—22no—
128Dic11—41no—
129Dic11—41no—
130C2×#41—111no—
131C2×M16—111no—
132C22×C8C2×D1111yescharacteristic
133C4⋊Q8—112no—
134C4⋊Q8—221no—
135#125—112no—
136#125—221no—
137C22⋊Q8—222no—
138C4×Q8—112no—
139C4×D4—112no—
140C4×D4—222no—
141#117—111no—
142#117—111no—
143#117—221no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4C2×D1111yescharacteristic
146C2×C4⋊C4C2×D1111yescharacteristic
147#107—112no—
148#107C2×D1112yes—
149#107C2×D1112yes—
150#106—112no—
151C4⋊C8—112no—
152C4⋊C8—112no—
153#103—111no—
154#103—111no—
155#103—112no—
156#102—111no—
157#102—111no—
158#102—112no—
159C2×C11—22no—
160C2×C11C2×C22⋊Q811yescharacteristic
161C2×C11#57611yescharacteristic
162C2×C11#57811yescharacteristic
163D11—42no—
164#41—114no—
165#41—222no—
166C2×Q8—111no—
167C2×Q8—222no—
168C2×D4—111no—
169C2×D4—221no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—222no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175M16—222no—
176C2×C8—22no—
177C2×C8—112no—
178C2×C8C22×D1111yescharacteristic
179C2×C8C22×D1111yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—111no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—111no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4C22×D1112yes—
191C4⋊C4C22×D1112yes—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—221no—
195C42—112no—
196C42—222no—
197C42—221no—
198C11#308311yescharacteristic, complemented, Sylow
199C23—221no—
200C23D4×D1111yescharacteristic
201Q8—112no—
202Q8—221no—
203Q8—882no—
204D4—112no—
205D4—224no—
206D4—221no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—112no—
212C2×C4—112no—
213C2×C4—221no—
214C2×C4—224no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—882no—
218C2×C4#433912yes—
219C2×C4D4×D1111yescharacteristic
220C2×C4Q8×D1112yes—
221C2×C4C23×D1111yescharacteristic
222C8—21no—
223C8—21no—
224C8—222no—
225C22—21no—
226C22—21no—
227C22—222no—
228C22—441no—
229C22—441no—
230C22#6694912yes—
231C22C2×D4×D1111yescharacteristic
232C4—42no—
233C4—42no—
234C4—222no—
235C4—222no—
236C4—222no—
237C4—441no—
238C4—441no—
239C4#6694912yes—
240C4C2×#433911yescharacteristic
241C4C2×Q8×D1111yescharacteristic
242C2—22no—
243C2—442no—
244C2C2×#6694911yescharacteristic
245C2#1062328811yescharacteristic
246C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#107C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenterC2×#107D11
hypocenterC11#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #10623031C2semidirect
3. C2×C11×#107C2semidirect
5. #10622715C2semidirect
7. #10622577C2semidirect
8. #10622504C2semidirect
9. #10622503C2semidirect
10. #10622490C2semidirect
11. #10622488C2semidirect
46. #4339Q8semidirect
109. C2×#107D11semidirect
198. C11#3083semidirect

Maximal subgroups

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

subgroupindex
#106230352
#106230312
C2×C11×#1072
#106227262
#106227152
#106225792
#106225772
#106225042
#106225032
#106224902
#106224882
#308311