Finite Group Databasebeta

← #13081646

Subgroups — #13081646

Order 1408.

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

normal subgroups only

This group has 350 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#10623263C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#462C211yesmaximal, characteristic, complemented
4#10622803C212yesmaximal
5#10622795C212yesmaximal, complemented
6#10622705C211yesmaximal, characteristic, complemented
7C4×#4325C211yesmaximal, characteristic
8#10622454C211yesmaximal, characteristic
9#10622444C211yesmaximal, characteristic, complemented
10#10622411C212yesmaximal
11#10622402C212yesmaximal, complemented
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#67000C2212yes—
16Q8×Dic11C2212yes—
17#66997C2212yes—
18C2×#4326C2212yes—
19C2×#4326C2212yes—
20C2×#4325C2211yescharacteristic
21C2×#4314C2212yes—
22#66951—22no—
23#66950—21no—
24#66945—21no—
25#66942—22no—
26#66940C2212yes—
27C4×D44C2211yescharacteristic
28#66923—21no—
29#66922C2211yescharacteristic
30C4×Dic22—21no—
31C4×Dic22C2211yescharacteristic
32C11×C4⋊C8C2211yescharacteristic
33C11×#103C2212yes—
34#66899C2211yescharacteristic
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2211yescharacteristic
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×Q8×C11C2312yes—
43C2×D44C2311yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22D411yescharacteristic
46C2×Dic22C2312yes—
47C11×Q16—42no—
48C2×C8×C11C2312yes—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4C2311yescharacteristic
53C42×C11—21no—
54C42×C11C2311yescharacteristic
55#4326—24no—
56#4326—42no—
57#4325—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—21no—
61C4⋊Dic11—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2311yescharacteristic
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4D412yes—
70C4×Dic11—22no—
71C4×Dic11—22no—
72C4×Dic11C2312yes—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#4314—42no—
76#3398—111nomaximal, Sylow
77C22×D11—21no—
78Q8×C11—21no—
79Q8×C11—22no—
80Q8×C11—22no—
81Q8×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92D44—21no—
93D44—21no—
94C4×D11—42no—
95Dic22—22no—
96Dic22—22no—
97Dic22—22no—
98C8×C11—22no—
99C11⋊C8—21no—
100C11⋊C8#4112yes—
101#557—111no—
102#556—111no—
103#497—112no—
104#494—111no—
105#464—112no—
106#462—112no—
107#462D1111yescharacteristic, complemented
108#461—111no—
109#446—111no—
110#441—112no—
111C4×SD16—111no—
112C22×C11C22×D411yescharacteristic
113C2×D11—41no—
114C2×D11—41no—
115C2×D11—41no—
116C4×C11—21no—
117C4×C11—42no—
118C4×C11—41no—
119C4×C11—41no—
120C4×C11#13712yes—
121C4×C11C2×#4111yescharacteristic
122C4×C11H(5,𝔽2)11yescharacteristic
123Dic11—22no—
124Dic11—22no—
125Dic11—42no—
126Dic11—41no—
127C2×Q16—112no—
128C2×Q16—112no—
129C2×Q16C2×D1112yes—
130C2×SD16—111no—
131C2×SD16—112no—
132C4⋊Q8—112no—
133C4⋊Q8—111no—
134C4⋊Q8C2×D1111yescharacteristic
135#126—222no—
136#125—221no—
137#125—222no—
138#124—112no—
139C22⋊Q8—221no—
140C4×Q8—111no—
141C4×Q8—112no—
142C4×Q8—112no—
143C4×Q8—221no—
144C4×Q8C2×D1111yescharacteristic
145C4×D4—111no—
146#117—221no—
147#106—111no—
148C4⋊C8—112no—
149C4⋊C8C2×D1111yescharacteristic
150#103—111no—
151#103—112no—
152#103C2×D1112yes—
153#102—111no—
154#97—112no—
155C4×C8—111no—
156C2×C11#55011yescharacteristic
157C2×C11C2×#13711yescharacteristic
158C2×C11#57811yescharacteristic
159D11—81no—
160C2×Q8—111no—
161C2×Q8—112no—
162C2×Q8C22×D1111yescharacteristic
163C2×Q8C22×D1112yes—
164C2×D4—111no—
165C22×C4—221no—
166Q16—42no—
167Q16—224no—
168Q16—442no—
169SD16—222no—
170SD16—442no—
171C2×C8—111no—
172C2×C8—111no—
173C2×C8C22×D1112yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—111no—
178C4⋊C4—112no—
179C4⋊C4—111no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4C22×D1111yescharacteristic
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—221no—
190C42—21no—
191C42—112no—
192C42—222no—
193C42—222no—
194C42C22×D1111yescharacteristic
195C11#339811yescharacteristic, complemented, Sylow
196C23—221no—
197Q8—21no—
198Q8—22no—
199Q8—21no—
200Q8—22no—
201Q8—222no—
202Q8—222no—
203Q8—222no—
204D4—221no—
205D4—221no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—112no—
210C2×C4—112no—
211C2×C4—221no—
212C2×C4—222no—
213C2×C4—442no—
214C2×C4D4×D1111yescharacteristic
215C2×C4D4×D1111yescharacteristic
216C2×C4C23×D1111yescharacteristic
217C8—22no—
218C8—112no—
219C8—221no—
220C22—441no—
221C22—441no—
222C22—441no—
223C22C2×D4×D1111yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—222no—
229C4—222no—
230C4—441no—
231C4—442no—
232C4#6697112yes—
233C4#6703711yescharacteristic
234C4#41×D1111yescharacteristic
235C2—881no—
236C2#1062313011yescharacteristic
237C2C2×#6697111yescharacteristic
238C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#462D11
hypocenterC11#3398
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. #10623098C2semidirect
3. C11×#462C2semidirect
5. #10622795C2semidirect
6. #10622705C2semidirect
9. #10622444C2semidirect
11. #10622402C2semidirect
107. #462D11semidirect
195. C11#3398semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106230982
C11×#4622
#106228032
#106227952
#106227052
C4×#43252
#106224542
#106224442
#106224112
#106224022
#339811