Finite Group Databasebeta

← #13079991

Subgroups — #13079991

Order 1408.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623259C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic
3C11×#476C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622632C211yesmaximal, characteristic, complemented
6#10622481C212yesmaximal, complemented
7#10622470C212yesmaximal, complemented
8#10622462C211yesmaximal, characteristic, complemented
9#10622450C211yesmaximal, characteristic, complemented
10#10622393C212yesmaximal
11#10622380C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×D4×C11C2211yescharacteristic
14#66999—21no—
15Q8×Dic11—21no—
16#66991C2211yescharacteristic
17#66989C2211yescharacteristic
18C2×#4324C2212yes—
19C4×C22⋊D11—21no—
20#66979—21no—
21C2×Dic44C2212yes—
22C2×#4313C2212yes—
23#66950C2211yescharacteristic
24#66950C2212yes—
25#66945—21no—
26#66943—21no—
27#66943C2211yescharacteristic
28#66940C2212yes—
29#66936—21no—
30#66932—21no—
31C42×D11C2211yescharacteristic
32#66922C2211yescharacteristic
33C4×Dic22C2211yescharacteristic
34C11×#106C2212yes—
35C11×C4⋊C8C2211yescharacteristic
36C11×#102C2212yes—
37#66880C2212yes—
38Dic11⋊C8C2212yes—
39#66874C2212yes—
40#66874C2212yes—
41#66871C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C2×C22⋊D11—21no—
47C2×C4×D11D411yescharacteristic
48C2×C4×D11D411yescharacteristic
49C2×C4×D11C2311yescharacteristic
50C2×Dic22C2311yescharacteristic
51C2×Dic22C2312yes—
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C4⋊C4C2311yescharacteristic
56C11×C22⋊C4—21no—
57C42×C11C2311yescharacteristic
58C22⋊Dic11—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11—21no—
61#4324—42no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11—21no—
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—21no—
71Dic11⋊C4—22no—
72Dic11⋊C4—21no—
73C4×Dic11—22no—
74C4×Dic11—21no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79Dic44—42no—
80#4313—42no—
81#3252—111nomaximal, Sylow
82C23×C11—21no—
83C22×D11C2×D411yescharacteristic
84Q8×C11—42no—
85D4×C11—21no—
86D4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2411yescharacteristic
93C22⋊D11—42no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—21no—
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99C2×Dic11C2×D411yescharacteristic
100C4×D11—22no—
101C4×D11—21no—
102C4×D11—21no—
103C4×D11—41no—
104Dic22—21no—
105Dic22—22no—
106Dic22—21no—
107Dic22—22no—
108C8×C11—22no—
109C11⋊C8—22no—
110#533—111no—
111#529—111no—
112#479—112no—
113#477—111no—
114#476D1111yescharacteristic, complemented
115#470—112no—
116#468—112no—
117#464—112no—
118#462—111no—
119#461—111no—
120#423—111no—
121C22×C11—41no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11C22×D411yescharacteristic
125C2×D11—21no—
126C2×D11—21no—
127C2×D11—21no—
128C4×C11—21no—
129C4×C11—41no—
130C4×C11—42no—
131C4×C11#13712yes—
132C4×C11H(5,𝔽2)11yescharacteristic
133C4×C112−1+411yescharacteristic
134Dic11—21no—
135Dic11—21no—
136Dic11—21no—
137Dic11—41no—
138Dic11—42no—
139Dic11—41no—
140C2×Q16—112no—
141C2×SD16—112no—
142C2×M16—112no—
143C4⋊Q8—111no—
144C4⋊Q8C2×D1111yescharacteristic
145#126—221no—
146#125—111no—
147#125—221no—
148#124—111no—
149#123—221no—
150C22⋊Q8—111no—
151C22⋊Q8—112no—
152C22⋊Q8—221no—
153#121—111no—
154C4×Q8—112no—
155C4×Q8—111no—
156C4×Q8—221no—
157C4×D4—221no—
158C4×D4C2×D1111yescharacteristic
159#117—221no—
160#117—221no—
161C2×C42—111no—
162#107—112no—
163#106C2×D1112yes—
164C4⋊C8—112no—
165C4⋊C8—111no—
166C4⋊C8C2×D1111yescharacteristic
167#103—112no—
168#103—112no—
169#103—112no—
170#102C2×D1112yes—
171C2×C11—81no—
172C2×C11#53711yescharacteristic
173C2×C11C2×#13711yescharacteristic
174C2×C11#57511yescharacteristic
175D11—41no—
176C2×Q8—21no—
177C2×Q8—111no—
178C2×Q8—112no—
179C2×D4—221no—
180C2×D4C22×D1111yescharacteristic
181C22×C4—21no—
182C22×C4—111no—
183C22×C4—111no—
184C22×C4—111no—
185Q16—442no—
186SD16—442no—
187M16—442no—
188C2×C8—112no—
189C2×C8C22×D1112yes—
190C4⋊C4—21no—
191C4⋊C4—111no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—222no—
196C4⋊C4—222no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4C22×D1112yes—
201C4⋊C4C22×D1111yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—222no—
204C22⋊C4—221no—
205C22⋊C4—221no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C42—111no—
209C42—111no—
210C42—111no—
211C42—222no—
212C42—221no—
213C42C22×D1111yescharacteristic
214C11#325211yescharacteristic, complemented, Sylow
215C23—21no—
216C23—111no—
217Q8—42no—
218Q8—221no—
219Q8—222no—
220Q8—222no—
221Q8—221no—
222D4—21no—
223D4—21no—
224D4—442no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—111no—
229C2×C4—111no—
230C2×C4—111no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—222no—
237C2×C4—441no—
238C2×C4D4×D1111yescharacteristic
239C2×C4D4×D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—22no—
242C8—222no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—221no—
247C22—221no—
248C22—221no—
249C22C2×D4×D1111yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—221no—
254C4—221no—
255C4—221no—
256C4—441no—
257C4—441no—
258C4—442no—
259C4#6696812yes—
260C4#6704011yescharacteristic
261C4#6704211yescharacteristic
262C2—81no—
263C2—441no—
264C2#1062316011yescharacteristic
265C2C2×#6696811yescharacteristic
266C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#476D11
hypocenterC11#3252
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#476C2semidirect
4. #10622704C2semidirect
5. #10622632C2semidirect
6. #10622481C2semidirect
7. #10622470C2semidirect
8. #10622462C2semidirect
9. #10622450C2semidirect
11. #10622380C2semidirect
114. #476D11semidirect
214. C11#3252semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106230882
C11×#4762
#106227042
#106226322
#106224812
#106224702
#106224622
#106224502
#106223932
#106223802
#325211