Finite Group Databasebeta

← #13081355

Subgroups — #13081355

Order 1408.

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

normal subgroups only

This group has 338 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#10623253C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic
3C11×#476C211yesmaximal, characteristic
4#10622706C211yesmaximal, characteristic, complemented
5C4×#4324C211yesmaximal, characteristic
6#10622467C212yesmaximal, complemented
7#10622466C212yesmaximal, complemented
8#10622462C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622380C212yesmaximal
11#10622378C212yesmaximal
12C11×C4⋊Q8C2211yescharacteristic
13C4×D4×C11C2211yescharacteristic
14#66997—22no—
15#66989C2212yes—
16C2×#4324C2211yescharacteristic
17#66979—21no—
18#66977—21no—
19C2×Dic44C2212yes—
20#66941—21no—
21#66941C2212yes—
22#66940—21no—
23#66940C2212yes—
24#66940C2212yes—
25#66932—22no—
26#66922C2211yescharacteristic
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#106C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#102C2212yes—
32#66896C2211yescharacteristic
33#66880C2212yes—
34#66879C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2211yescharacteristic
37#66874C2212yes—
38#66874C2212yes—
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C2×Dic22—22no—
45C2×Dic22D411yescharacteristic
46C2×Dic22C2312yes—
47C2×Dic22C2311yescharacteristic
48C2×C8×C11C2312yes—
49C11×C4⋊C4—21no—
50C11×C4⋊C4C2311yescharacteristic
51C11×C4⋊C4C2312yes—
52C11×C22⋊C4—21no—
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55C22⋊Dic11—22no—
56#4324—22no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11D411yescharacteristic
60C4⋊Dic11C2311yescharacteristic
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—21no—
65Dic11⋊C4D412yes—
66C4×Dic11—22no—
67C4×Dic11—22no—
68C4×Dic11—21no—
69C4×Dic11C2312yes—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72Dic44—24no—
73#3369—111nomaximal, Sylow
74C23×C11—21no—
75Q8×C11—81no—
76D4×C11—21no—
77D4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—42no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2411yescharacteristic
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89Dic22—22no—
90Dic22—21no—
91Dic22—22no—
92Dic22—22no—
93Dic22—82no—
94Dic22#4112yes—
95C8×C11—22no—
96C11⋊C8—21no—
97C11⋊C8—21no—
98Q82—111no—
99#556—111no—
100#489—112no—
101#487—111no—
102#476D1111yescharacteristic
103#475—112no—
104#464—112no—
105#462—111no—
106#446—111no—
107#441—112no—
108C4×SD16—111no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11C22×D411yescharacteristic
113C4×C11—21no—
114C4×C11—41no—
115C4×C11—42no—
116C4×C11#13712yes—
117C4×C11C2×#4111yescharacteristic
118C4×C112−1+411yescharacteristic
119Dic11—22no—
120Dic11—22no—
121Dic11—22no—
122Dic11—42no—
123Dic11—41no—
124C2×Q16—112no—
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—111no—
138C4×Q8—221no—
139C4×D4C2×D1111yescharacteristic
140#117—221no—
141#106—111no—
142#106C2×D1112yes—
143C4⋊C8—112no—
144C4⋊C8C2×D1111yescharacteristic
145#103—112no—
146#103—111no—
147#103—112no—
148#103—112no—
149#102—111no—
150#102C2×D1112yes—
151#97—112no—
152C4×C8—111no—
153C2×C11—81no—
154C2×C11#54811yescharacteristic
155C2×C11C2×#13711yescharacteristic
156C2×C11#57711yescharacteristic
157C2×Q8—21no—
158C2×Q8—111no—
159C2×Q8—111no—
160C2×Q8—112no—
161C2×Q8—222no—
162C2×D4C22×D1111yescharacteristic
163C22×C4—21no—
164Q16—224no—
165SD16—222no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8C22×D1112yes—
169C4⋊C4—21no—
170C4⋊C4—111no—
171C4⋊C4—112no—
172C4⋊C4—111no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—221no—
177C4⋊C4—221no—
178C4⋊C4—221no—
179C4⋊C4C22×D1112yes—
180C4⋊C4C22×D1111yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C42—112no—
185C42—222no—
186C42—222no—
187C42—221no—
188C42C22×D1111yescharacteristic
189C11#336911yescharacteristic, complemented, Sylow
190C23—21no—
191Q8—81no—
192Q8—112no—
193Q8—222no—
194Q8—221no—
195Q8—222no—
196Q8—222no—
197Q8—882no—
198D4—21no—
199D4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—112no—
204C2×C4—112no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—221no—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—221no—
213C8—221no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—222no—
222C4—222no—
223C4—222no—
224C4—441no—
225C4—442no—
226C4#6696812yes—
227C4#6704011yescharacteristic
228C4#41×D1111yescharacteristic
229C2—81no—
230C2#1062316411yescharacteristic
231C2C2×#6696811yescharacteristic
232C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#476D11
hypocenterC11#3369
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. #10623253C2semidirect
4. #10622706C2semidirect
6. #10622467C2semidirect
7. #10622466C2semidirect
8. #10622462C2semidirect
9. #10622444C2semidirect
189. C11#3369semidirect

Maximal subgroups

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

subgroupindex
#106232532
#106230732
C11×#4762
#106227062
C4×#43242
#106224672
#106224662
#106224622
#106224442
#106223802
#106223782
#336911