Finite Group Databasebeta

← #13081419

Subgroups — #13081419

Order 1408.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#557C211yesmaximal, characteristic
2#10623101C211yesmaximal, characteristic
3#10622707C211yesmaximal, characteristic
4#10622706C211yesmaximal, characteristic
5#10622682C212yesmaximal
6#10622676C212yesmaximal
7#10622644C212yesmaximal
8#10622644C211yesmaximal, characteristic
9#10622643C212yesmaximal
10C4×#4326C211yesmaximal, characteristic
11#10622637C211yesmaximal, characteristic
12C11×C4⋊Q8—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125—22no—
15C11×#125C2212yes—
16C4×Q8×C11—21no—
17C4×Q8×C11C2211yescharacteristic
18C4×Q8×C11C2212yes—
19C4×Q8×C11C2211yescharacteristic
20Q8×Dic11—21no—
21C2×#4326C2211yescharacteristic
22C2×#4326C2212yes—
23#66943—21no—
24#66943—22no—
25#66922C2212yes—
26#66922C2211yescharacteristic
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2212yes—
29#66899C2211yescharacteristic
30#66874C2211yescharacteristic
31#66874C2212yes—
32#66874C2212yes—
33#66874C2212yes—
34#66874C2212yes—
35#66872C2212yes—
36#66871C2211yescharacteristic
37C4⋊(C11⋊C8)C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39#66867C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11D411yescharacteristic
43C2×Q8×C11C2311yescharacteristic
44C2×Dic22C2311yescharacteristic
45C2×Dic22C2312yes—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4D411yescharacteristic
52C11×C4⋊C4D412yes—
53C11×C4⋊C4C2311yescharacteristic
54C11×C4⋊C4C2312yes—
55C42×C11—22no—
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58C42×C11C2312yes—
59#4326—22no—
60#4326—24no—
61C4⋊Dic11—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2311yescharacteristic
66Dic11⋊C4—22no—
67Dic11⋊C4—21no—
68C4×Dic11—22no—
69C4×Dic11—21no—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2312yes—
73#3374—111nomaximal, Sylow
74Q8×C11—22no—
75Q8×C11—21no—
76Q8×C11—42no—
77Q8×C11#4112yes—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D412yes—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—21no—
87C2×Dic11—22no—
88C2×Dic11—21no—
89Dic22—21no—
90Dic22—22no—
91Dic22—21no—
92Dic22—22no—
93C11⋊C8—21no—
94C11⋊C8—22no—
95C11⋊C8—21no—
96#557—111no—
97#557D1111yescharacteristic
98#491—112no—
99#487—111no—
100#479—112no—
101#475—111no—
102#462—112no—
103#462—111no—
104#446—111no—
105#441—112no—
106C4×Q16—111no—
107C22×C11C22×D411yescharacteristic
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—22no—
111C4×C11—21no—
112C4×C11—42no—
113C4×C11—41no—
114C4×C11#13712yes—
115C4×C11C2×#4111yescharacteristic
116C4×C112−1+411yescharacteristic
117Dic11—41no—
118Dic11—42no—
119Dic11—41no—
120C2×Q16—111no—
121C2×Q16—112no—
122C4⋊Q8—21no—
123C4⋊Q8—111no—
124C4⋊Q8—112no—
125C4⋊Q8C2×D1111yescharacteristic
126#125—22no—
127#125—221no—
128#125—222no—
129#125C2×D1112yes—
130C4×Q8—21no—
131C4×Q8—111no—
132C4×Q8—112no—
133C4×Q8—221no—
134C4×Q8C2×D1111yescharacteristic
135C4×Q8C2×D1112yes—
136C4×Q8C2×D1111yescharacteristic
137#107—111no—
138#106—112no—
139C4⋊C8—111no—
140C4⋊C8—112no—
141#103—111no—
142#103—111no—
143#103—112no—
144#103—112no—
145#103—112no—
146#103—112no—
147#97—112no—
148C4×C8—111no—
149C2×C11#54811yescharacteristic
150C2×C11C2×#13711yescharacteristic
151C2×C11#57811yescharacteristic
152C2×Q8—21no—
153C2×Q8—111no—
154C2×Q8—112no—
155C2×Q8C22⋊D1111yescharacteristic
156C2×Q8C22×D1111yescharacteristic
157Q16—222no—
158Q16—224no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8—112no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—21no—
166C4⋊C4—22no—
167C4⋊C4—111no—
168C4⋊C4—222no—
169C4⋊C4—221no—
170C4⋊C4—222no—
171C4⋊C4—221no—
172C4⋊C4—222no—
173C4⋊C4—221no—
174C4⋊C4C22⋊D1111yescharacteristic
175C4⋊C4C22⋊D1112yes—
176C4⋊C4C22×D1112yes—
177C4⋊C4C22×D1111yescharacteristic
178C42—22no—
179C42—21no—
180C42—222no—
181C42—221no—
182C42C22×D1111yescharacteristic
183C42C22×D1112yes—
184C11#337411yescharacteristic, complemented, Sylow
185Q8—22no—
186Q8—21no—
187Q8—42no—
188Q8—221no—
189Q8—222no—
190Q8—221no—
191Q8—222no—
192Q8#434312yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—221no—
197C2×C4—222no—
198C2×C4—221no—
199C2×C4C2×C22⋊D1112yes—
200C2×C4C2×C22⋊D1112yes—
201C2×C4C2×C22⋊D1111yescharacteristic
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—221no—
205C8—222no—
206C8—221no—
207C22C22×C22⋊D1111yescharacteristic
208C4—22no—
209C4—22no—
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—442no—
215C4—441no—
216C4—441no—
217C4#6700412yes—
218C4C2×#434311yescharacteristic
219C4#6704011yescharacteristic
220C2#1062334811yescharacteristic
221C2C2×#6700411yescharacteristic
222C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#557C2
socle, prime radicalC22×C11C22×D4
hypercenter#557D11
hypocenterC11#3374
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
184. C11#3374semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106231012
#106227072
#106227062
#106226822
#106226762
#106226442
#106226432
C4×#43262
#106226372
#337411