Finite Group Databasebeta

← #13079990

Subgroups — #13079990

Order 1408.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#10623010C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3C11×#423C211yesmaximal, characteristic, complemented
4#10622750C212yesmaximal, complemented
5#10622747C212yesmaximal
6#10622463C211yesmaximal, characteristic, complemented
7#10622462C211yesmaximal, characteristic, complemented
8#10622458C212yesmaximal, complemented
9#10622455C211yesmaximal, characteristic, complemented
10#10622454C211yesmaximal, characteristic, complemented
11#10622442C212yesmaximal, complemented
12C2×C11×M16C2212yes—
13C2×C42×C11C2211yescharacteristic
14#66983C2211yescharacteristic
15#66982—21no—
16C4×C22⋊D11—21no—
17#66979—21no—
18#66977—21no—
19#66977C2212yes—
20#66977C2211yescharacteristic
21C2×Dic44C2212yes—
22C2×#4314C2212yes—
23#66929—21no—
24#66928C2211yescharacteristic
25C4×D44C2211yescharacteristic
26#66925—21no—
27#66923—21no—
28#66923C2211yescharacteristic
29#66922C2211yescharacteristic
30#66922C2211yescharacteristic
31C4×Dic22—21no—
32C4×Dic22C2212yes—
33C4×Dic22C2211yescharacteristic
34C11×C4⋊C8C2212yes—
35C11×C4⋊C8C2211yescharacteristic
36C11×C4⋊C8C2211yescharacteristic
37#66885C2212yes—
38#66882C2212yes—
39#66881C2212yes—
40#66880C2212yes—
41#66880C2212yes—
42#66880C2212yes—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11D411yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C2×D44C2311yescharacteristic
48C2×C4×D11—21no—
49C2×Dic22—21no—
50C2×Dic22C2312yes—
51C2×Dic22C2311yescharacteristic
52C11×M16—42no—
53C2×C8×C11C2312yes—
54C2×C8×C11C2312yes—
55C42×C11D411yescharacteristic
56C42×C11D411yescharacteristic
57C42×C11C2311yescharacteristic
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60C22⋊Dic11—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2311yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2312yes—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77C4×Dic11—22no—
78C4×Dic11—21no—
79Dic44—42no—
80#4314—42no—
81#3252—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C22⋊D11—42no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100D44—21no—
101D44—21no—
102C4×D11—42no—
103Dic22—22no—
104Dic22—21no—
105Dic22—22no—
106Dic22—21no—
107Dic22—42no—
108C8×C11—22no—
109C8×C11—22no—
110#533—111no—
111#529—111no—
112#479—112no—
113#477—111no—
114#476—111no—
115#470—112no—
116#468—112no—
117#464—112no—
118#462—111no—
119#461—111no—
120#423D1111yescharacteristic, complemented
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11C22×D411yescharacteristic
125C2×D11—41no—
126C2×D11—41no—
127C2×D11—41no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11#13712yes—
133C4×C11H(5,𝔽2)11yescharacteristic
134C4×C112−1+411yescharacteristic
135Dic11—42no—
136Dic11—41no—
137Dic11—41no—
138Dic11—42no—
139Dic11—41no—
140C2×Q16—112no—
141C2×SD16—112no—
142C2×M16C2×D1112yes—
143C4⋊Q8—111no—
144C4⋊Q8—111no—
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—111no—
155C4×Q8—112no—
156C4×Q8—221no—
157C4×D4—111no—
158C4×D4—221no—
159#117—221no—
160#117—221no—
161C2×C42C2×D1111yescharacteristic
162#107—112no—
163#106—112no—
164C4⋊C8C2×D1111yescharacteristic
165C4⋊C8C2×D1111yescharacteristic
166C4⋊C8C2×D1112yes—
167#103—112no—
168#103—112no—
169#103—112no—
170#102—112no—
171C2×C11—41no—
172C2×C11#53711yescharacteristic
173C2×C11C2×#13711yescharacteristic
174C2×C11#57511yescharacteristic
175D11—81no—
176C2×Q8—111no—
177C2×Q8—112no—
178C2×Q8—221no—
179C2×D4—111no—
180C2×D4—221no—
181C22×C4—221no—
182C22×C4D4411yescharacteristic
183C22×C4D4411yescharacteristic
184C22×C4C22×D1111yescharacteristic
185Q16—442no—
186SD16—442no—
187M16—42no—
188C2×C8C22×D1112yes—
189C2×C8C22×D1112yes—
190C4⋊C4—112no—
191C4⋊C4—111no—
192C4⋊C4—111no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—222no—
199C4⋊C4—221no—
200C4⋊C4—222no—
201C4⋊C4—221no—
202C22⋊C4—222no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C22⋊C4—221no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C42—221no—
209C42—222no—
210C42D4411yescharacteristic
211C42D4411yescharacteristic
212C42C22×D1111yescharacteristic
213C42C22×D1111yescharacteristic
214C11#325211yescharacteristic, complemented, Sylow
215C23—221no—
216C23C2×D4411yescharacteristic
217Q8—222no—
218Q8—221no—
219Q8—221no—
220Q8—222no—
221Q8—442no—
222D4—221no—
223D4—221no—
224D4—442no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—442no—
235C2×C4C2×D4411yescharacteristic
236C2×C4C2×D4411yescharacteristic
237C2×C4C2×D4411yescharacteristic
238C2×C4C2×D4411yescharacteristic
239C2×C4C2×D4411yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—441no—
247C22—441no—
248C22—441no—
249C22C22×D4411yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—441no—
255C4—441no—
256C4—442no—
257C4—441no—
258C4—442no—
259C4#6696212yes—
260C4#6703711yescharacteristic
261C4#6704011yescharacteristic
262C2—41no—
263C2—881no—
264C2#1062304111yescharacteristic
265C2C2×#6696211yescharacteristic
266C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#423C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#423D11
hypocenterC11#3252
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
3. C11×#423C2semidirect
4. #10622750C2semidirect
6. #10622463C2semidirect
7. #10622462C2semidirect
8. #10622458C2semidirect
9. #10622455C2semidirect
10. #10622454C2semidirect
11. #10622442C2semidirect
120. #423D11semidirect
214. C11#3252semidirect

Maximal subgroups

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

subgroupindex
#106230102
#106230012
C11×#4232
#106227502
#106227472
#106224632
#106224622
#106224582
#106224552
#106224542
#106224422
#325211