Finite Group Databasebeta

← #13079951

Subgroups — #13079951

Order 1408.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623111C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic, complemented
4#10622801C212yesmaximal, complemented
5#10622798C212yesmaximal, complemented
6#10622696C211yesmaximal, characteristic, complemented
7#10622633C211yesmaximal, characteristic, complemented
8#10622459C211yesmaximal, characteristic, complemented
9D11×C4⋊C8C211yesmaximal, characteristic, complemented
10#10622420C212yesmaximal
11#10622409C212yesmaximal, complemented
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#67000C2211yescharacteristic
16#66999C2212yes—
17#66999C2211yescharacteristic
18Q8×Dic11C2212yes—
19C2×#4325C2212yes—
20C2×C8×D11C2212yes—
21#66951—21no—
22#66950—21no—
23#66948C2211yescharacteristic
24#66947—21no—
25#66945—21no—
26#66943—21no—
27#66943C2211yescharacteristic
28#66940—21no—
29C4×D44—21no—
30C4×D44C2211yescharacteristic
31#66925—21no—
32C42×D11C2211yescharacteristic
33#66922C2211yescharacteristic
34C11×C4⋊C8C2211yescharacteristic
35C11×#103C2212yes—
36#66899C2212yes—
37#66899C2212yes—
38#66885C2212yes—
39#66882C2212yes—
40Dic11⋊C8C2212yes—
41#66872C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11C2311yescharacteristic
44C2×Q8×C11C2312yes—
45C2×D44—21no—
46C2×D44C2311yescharacteristic
47C2×C4×D11—21no—
48C2×C4×D11D411yescharacteristic
49C2×C4×D11D411yescharacteristic
50C2×C4×D11C2311yescharacteristic
51C2×Dic22—21no—
52C11×Q16—42no—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2311yescharacteristic
58C42×C11—21no—
59C42×C11C2311yescharacteristic
60#4325—42no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11C2312yes—
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—22no—
75C4×Dic11—22no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C2×C11⋊C8C2312yes—
80C8×D11—42no—
81#3248—111nomaximal, Sylow
82C22×D11—21no—
83C22×D11C2×D411yescharacteristic
84Q8×C11—22no—
85Q8×C11—21no—
86Q8×C11—21no—
87Q8×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99D44—21no—
100D44—21no—
101D44—42no—
102C4×D11—22no—
103C4×D11—22no—
104C4×D11—21no—
105C4×D11—21no—
106C4×D11—42no—
107Dic22—42no—
108C8×C11—22no—
109C11⋊C8—22no—
110#533—111no—
111#529—111no—
112#479—112no—
113#475—111no—
114#474—111no—
115#467—112no—
116#465—112no—
117#464—112no—
118#462D1111yescharacteristic, complemented
119#461—111no—
120C2×C4⋊C8—111no—
121C22×C11C22×D411yescharacteristic
122C2×D11—21no—
123C2×D11—21no—
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C2×D11#13712yes—
128C4×C11—21no—
129C4×C11—42no—
130C4×C11—41no—
131C4×C11—41no—
132C4×C11#13512yes—
133C4×C11H(5,𝔽2)11yescharacteristic
134C4×C112−1+411yescharacteristic
135Dic11—21no—
136Dic11—21no—
137Dic11—21no—
138Dic11—42no—
139Dic11—41no—
140C2×Q16C2×D1112yes—
141C2×SD16—112no—
142C22×C8—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—221no—
156C4×Q8C2×D1111yescharacteristic
157C4×D4—111no—
158C4×D4—221no—
159#117—221no—
160#117—221no—
161C2×C42—111no—
162#107—112no—
163#106—112no—
164C4⋊C8—112no—
165C4⋊C8—111no—
166C4⋊C8C2×D1111yescharacteristic
167#103—112no—
168#103—112no—
169#103C2×D1112yes—
170#102—112no—
171C2×C11#53711yescharacteristic
172C2×C11C2×#13511yescharacteristic
173C2×C11C2×#13711yescharacteristic
174D11—22no—
175D11—81no—
176C2×Q8—221no—
177C2×Q8C22×D1111yescharacteristic
178C2×Q8C22×D1112yes—
179C2×D4—111no—
180C2×D4—221no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—111no—
184C22×C4—221no—
185Q16—42no—
186SD16—442no—
187C2×C8—112no—
188C2×C8—442no—
189C2×C8C22×D1112yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—112no—
194C4⋊C4—111no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—221no—
201C4⋊C4C22×D1111yescharacteristic
202C22⋊C4—221no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C22⋊C4—222no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C42—21no—
209C42—111no—
210C42—111no—
211C42—111no—
212C42—222no—
213C42C22×D1111yescharacteristic
214C11#324811yescharacteristic, complemented, Sylow
215C23—111no—
216C23—221no—
217Q8—22no—
218Q8—21no—
219Q8—21no—
220Q8—22no—
221Q8—442no—
222D4—221no—
223D4—221no—
224D4—442no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—111no—
229C2×C4—111no—
230C2×C4—111no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—221no—
237C2×C4—442no—
238C2×C4D4×D1111yescharacteristic
239C2×C4D4×D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—22no—
242C8—222no—
243C22—112no—
244C22—221no—
245C22—221no—
246C22—441no—
247C22—441no—
248C22—441no—
249C22C2×D4×D1111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—221no—
255C4—221no—
256C4—221no—
257C4—441no—
258C4—442no—
259C4#6697212yes—
260C4#6703711yescharacteristic
261C4#6704311yescharacteristic
262C2—222no—
263C2—881no—
264C2#1062313911yescharacteristic
265C2C2×#6697211yescharacteristic
266C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#462D11
hypocenterC11#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#462C2semidirect
4. #10622801C2semidirect
5. #10622798C2semidirect
6. #10622696C2semidirect
7. #10622633C2semidirect
8. #10622459C2semidirect
9. D11×C4⋊C8C2semidirect
11. #10622409C2semidirect
118. #462D11semidirect
214. C11#3248semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106231112
C11×#4622
#106228012
#106227982
#106226962
#106226332
#106224592
D11×C4⋊C82
#106224202
#106224092
#324811