Finite Group Databasebeta

← #13081360

Subgroups — #13081360

Order 1408.

338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623263C211yesmaximal, characteristic
2Q8×Dic22C211yesmaximal, characteristic, complemented
3C11×#462C211yesmaximal, characteristic, complemented
4#10622798C212yesmaximal
5#10622797C212yesmaximal, complemented
6#10622694C211yesmaximal, characteristic, complemented
7C4×#4325C211yesmaximal, characteristic
8#10622455C211yesmaximal, characteristic
9#10622444C211yesmaximal, characteristic, complemented
10#10622408C212yesmaximal
11#10622404C212yesmaximal, complemented
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#67000C2212yes—
16Q8×Dic11C2212yes—
17Q8×Dic11C2212yes—
18C2×#4325C2211yescharacteristic
19#66951—22no—
20#66950—21no—
21#66945—21no—
22#66941—22no—
23#66941C2212yes—
24C4×D44C2211yescharacteristic
25#66922—21no—
26#66922C2211yescharacteristic
27C4×Dic22—21no—
28C4×Dic22C2211yescharacteristic
29C11×C4⋊C8C2211yescharacteristic
30C11×#103C2212yes—
31#66899C2211yescharacteristic
32#66899C2212yes—
33#66899C2212yes—
34#66885C2212yes—
35#66881C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2211yescharacteristic
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2312yes—
42C2×Q8×C11C2311yescharacteristic
43C2×D44C2311yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22—22no—
46C2×Dic22—21no—
47C2×Dic22D411yescharacteristic
48C11×Q16—24no—
49C2×C8×C11C2312yes—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4C2311yescharacteristic
54C42×C11—21no—
55C42×C11C2311yescharacteristic
56#4325—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—21no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11C2311yescharacteristic
65C4⋊Dic11C2312yes—
66Dic11⋊C4—22no—
67Dic11⋊C4D412yes—
68C4×Dic11—22no—
69C4×Dic11—22no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#3369—111nomaximal, Sylow
74C22×D11—21no—
75Q8×C11—21no—
76Q8×C11—22no—
77Q8×C11—22no—
78Q8×C11#4112yes—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89D44—21no—
90D44—21no—
91C4×D11—42no—
92Dic22—22no—
93Dic22—82no—
94Dic22—81no—
95C8×C11—22no—
96C11⋊C8—21no—
97C11⋊C8—21no—
98Q82—111no—
99#556—111no—
100#489—112no—
101#487—111no—
102#476—111no—
103#475—112no—
104#464—112no—
105#462D1111yescharacteristic, complemented
106#446—111no—
107#441—112no—
108C4×SD16—111no—
109C22×C11C22×D411yescharacteristic
110C2×D11—41no—
111C2×D11—41no—
112C2×D11—41no—
113C4×C11—22no—
114C4×C11—21no—
115C4×C11—42no—
116C4×C11—41no—
117C4×C11#13712yes—
118C4×C11C2×#4111yescharacteristic
119C4×C112−1+411yescharacteristic
120Dic11—22no—
121Dic11—22no—
122Dic11—41no—
123Dic11—42no—
124C2×Q16C2×D1112yes—
125C2×SD16—111no—
126C4⋊Q8—112no—
127C4⋊Q8—111no—
128C4⋊Q8—221no—
129C4⋊Q8—222no—
130C4⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#124—112no—
133C22⋊Q8—221no—
134C4×Q8—111no—
135C4×Q8—112no—
136C4×Q8—112no—
137C4×Q8—221no—
138C4×Q8C2×D1111yescharacteristic
139C4×D4—111no—
140#117—221no—
141#106—112no—
142#106—111no—
143C4⋊C8—112no—
144C4⋊C8C2×D1111yescharacteristic
145#103—111no—
146#103—112no—
147#103—112no—
148#103C2×D1112yes—
149#102—112no—
150#102—111no—
151#97—112no—
152C4×C8—111no—
153C2×C11#54811yescharacteristic
154C2×C11C2×#13711yescharacteristic
155C2×C11#57711yescharacteristic
156D11—81no—
157C2×Q8—111no—
158C2×Q8—222no—
159C2×Q8—221no—
160C2×Q8C22×D1112yes—
161C2×Q8C22×D1111yescharacteristic
162C2×D4—111no—
163C22×C4—221no—
164Q16—24no—
165SD16—222no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8C22×D1112yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—111no—
173C4⋊C4—112no—
174C4⋊C4—112no—
175C4⋊C4—111no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—221no—
180C4⋊C4C22×D1111yescharacteristic
181C22⋊C4—222no—
182C22⋊C4—222no—
183C22⋊C4—221no—
184C42—21no—
185C42—112no—
186C42—222no—
187C42—222no—
188C42C22×D1111yescharacteristic
189C11#336911yescharacteristic, complemented, Sylow
190C23—221no—
191Q8—21no—
192Q8—22no—
193Q8—22no—
194Q8—222no—
195Q8—881no—
196Q8—882no—
197Q8#434112yes—
198D4—221no—
199D4—221no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—112no—
204C2×C4—112no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—442no—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—221no—
213C8—221no—
214C22—441no—
215C22—441no—
216C22—441no—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—22no—
220C4—41no—
221C4—42no—
222C4—222no—
223C4—222no—
224C4—441no—
225C4—442no—
226C4#6697112yes—
227C4C2×#434111yescharacteristic
228C4#6704311yescharacteristic
229C2—881no—
230C2#1062312911yescharacteristic
231C2C2×#6697111yescharacteristic
232C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#462D11
hypocenterC11#3369
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
2. Q8×Dic22C2semidirect
3. C11×#462C2semidirect
5. #10622797C2semidirect
6. #10622694C2semidirect
9. #10622444C2semidirect
11. #10622404C2semidirect
105. #462D11semidirect
189. C11#3369semidirect

Maximal subgroups

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

subgroupindex
#106232632
Q8×Dic222
C11×#4622
#106227982
#106227972
#106226942
C4×#43252
#106224552
#106224442
#106224082
#106224042
#336911