Finite Group Databasebeta

← #13081289

Subgroups — #13081289

Order 1408.

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

normal subgroups only

This group has 336 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
1#10623252C211yesmaximal, characteristic
2Q8×Dic22C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic
4Q16×Dic11C212yesmaximal
5#10622795C212yesmaximal
6#10622694C211yesmaximal, characteristic
7C4×#4326C211yesmaximal, characteristic
8#10622463C211yesmaximal, characteristic
9#10622443C211yesmaximal, characteristic
10#10622407C212yesmaximal
11#10622405C212yesmaximal
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15Q8×Dic11C2212yes—
16Q8×Dic11C2212yes—
17#66997C2212yes—
18C2×#4326C2211yescharacteristic
19#66943—21no—
20#66942—22no—
21#66941—22no—
22#66941C2212yes—
23#66940—21no—
24#66922—21no—
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×C4⋊C8C2211yescharacteristic
30C11×#103C2212yes—
31#66899C2212yes—
32#66899C2211yescharacteristic
33#66899C2212yes—
34#66882C2212yes—
35#66880C2212yes—
36Dic11⋊C8C2212yes—
37C8×Dic11C2212yes—
38#66874C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2312yes—
42C2×Q8×C11C2311yescharacteristic
43C2×Dic22—22no—
44C2×Dic22—21no—
45C2×Dic22D411yescharacteristic
46C2×Dic22C2311yescharacteristic
47C11×Q16—24no—
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—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11—21no—
59C4⋊Dic11D411yescharacteristic
60C4⋊Dic11C2311yescharacteristic
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—21no—
66Dic11⋊C4D412yes—
67C4×Dic11—22no—
68C4×Dic11—22no—
69C4×Dic11—21no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#3363—111nomaximal, Sylow
74Q8×C11—21no—
75Q8×C11—22no—
76Q8×C11—22no—
77Q8×C11#4112yes—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
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—21no—
90Dic22—21no—
91Dic22—82no—
92Dic22—81no—
93Dic22Q1614yescomplemented
94C8×C11—22no—
95C11⋊C8—21no—
96C11⋊C8—21no—
97Q82—111no—
98#557—111no—
99#487—111no—
100#487—112no—
101#477—111no—
102#477—112no—
103#462—112no—
104#462D1111yescharacteristic
105C8×Q8—111no—
106C4×Q16—112no—
107C4×Q16—111no—
108C22×C11C22×D411yescharacteristic
109C4×C11—22no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11—41no—
113C4×C11C2×Q1612yes—
114C4×C11C2×#4111yescharacteristic
115C4×C112−1+411yescharacteristic
116Dic11—22no—
117Dic11—41no—
118Dic11—42no—
119Dic11—41no—
120Dic11C2×Q1614yes—
121C2×Q16—111no—
122C2×Q16C2×D1112yes—
123C4⋊Q8—112no—
124C4⋊Q8—112no—
125C4⋊Q8—111no—
126C4⋊Q8—221no—
127C4⋊Q8—222no—
128C4⋊Q8C2×D1111yescharacteristic
129#125—222no—
130#125—221no—
131C4×Q8—111no—
132C4×Q8—112no—
133C4×Q8—112no—
134C4×Q8—111no—
135C4×Q8—221no—
136C4×Q8—221no—
137C4×Q8C2×D1111yescharacteristic
138#107—112no—
139#107—111no—
140C4⋊C8—112no—
141C4⋊C8C2×D1111yescharacteristic
142#103—111no—
143#103—112no—
144#103—112no—
145#103—112no—
146#103—111no—
147#103C2×D1112yes—
148C4×C8—112no—
149C4×C8—111no—
150C2×C11#54811yescharacteristic
151C2×C11C22×Q1611yescharacteristic
152C2×C11#57711yescharacteristic
153C2×Q8—111no—
154C2×Q8—111no—
155C2×Q8—222no—
156C2×Q8—221no—
157C2×Q8C22×D1112yes—
158C2×Q8C22×D1111yescharacteristic
159Q16—24no—
160Q16—222no—
161C2×C8—111no—
162C2×C8—111no—
163C2×C8C22×D1112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—112no—
168C4⋊C4—111no—
169C4⋊C4—112no—
170C4⋊C4—111no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—221no—
177C4⋊C4—221no—
178C4⋊C4C22×D1111yescharacteristic
179C42—21no—
180C42—112no—
181C42—222no—
182C42—222no—
183C42—221no—
184C42C22×D1111yescharacteristic
185C11#336311yescharacteristic, complemented, Sylow
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—114no—
190Q8—221no—
191Q8—221no—
192Q8—881no—
193Q8—882no—
194Q8#434112yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—112no—
199C2×C4—112no—
200C2×C4—221no—
201C2×C4—222no—
202C2×C4—221no—
203C2×C4D4×D1111yescharacteristic
204C2×C4D4×D1111yescharacteristic
205C2×C4C23×D1111yescharacteristic
206C8—22no—
207C8—221no—
208C8—221no—
209C22C2×D4×D1111yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—114no—
215C4—222no—
216C4—442no—
217C4—441no—
218C4—441no—
219C4Q16×D1112yes—
220C4C2×#434111yescharacteristic
221C4#6704311yescharacteristic
222C2#1062312911yescharacteristic
223C2C2×Q16×D1111yescharacteristic
224C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socle, prime radicalC22×C11C22×D4
hypercenter#462D11
hypocenterC11#3363
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
93. Dic22Q16semidirect
185. C11#3363semidirect

Maximal subgroups

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

subgroupindex
#106232522
Q8×Dic222
C11×#4622
Q16×Dic112
#106227952
#106226942
C4×#43262
#106224632
#106224432
#106224072
#106224052
#336311