Finite Group Databasebeta

← #13069995

Subgroups — #13069995

Order 1408.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×C11×#103C211yesmaximal, characteristic
2#10622843C211yesmaximal, characteristic
3C2×#66899C211yesmaximal, characteristic
4C2×#66881C211yesmaximal, characteristic
5C2×Dic11⋊C8C211yesmaximal, characteristic
6#10622586C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×Dic11⋊C4—21no—
14C2×C4×Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C11×#103—22no—
17#66899—22no—
18C11⋊#95—21no—
19C11⋊#95—21no—
20C11⋊#95—21no—
21#66881—22no—
22Dic11⋊C8—22no—
23C2×Q8×C11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11Q812yes—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C22×Dic11—21no—
34C22×Dic11D411yescharacteristic
35C22×Dic11D411yescharacteristic
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C2×C8×C11D412yes—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C4⋊Dic11D412yes—
45Dic11⋊C4—42no—
46C4×Dic11—21no—
47C4×Dic11—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51#2066—111nomaximal, Sylow
52C23×C11C2×D411yescharacteristic
53Q8×C11—22no—
54Q8×C11—22no—
55Q8×C11—41no—
56Q8×C11—41no—
57C2×C4×C11—22no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×Q811yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×Dic11—21no—
70C2×Dic11—21no—
71C2×Dic11—21no—
72C2×Dic11—22no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—41no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11SD1612yes—
81C8×C11—22no—
82C11⋊C8—41no—
83C2×#106—111no—
84C2×C4⋊C8—111no—
85C2×#103—111no—
86C2×#103D1111yescharacteristic
87#391—111no—
88#389—111no—
89#340—111no—
90C22×C11#12111yescharacteristic
91C22×C11#12111yescharacteristic
92C22×C11C22⋊Q811yescharacteristic
93C22×C11C2×SD1611yescharacteristic
94C22×C11#13511yescharacteristic
95C22×C11#13711yescharacteristic
96C22×C11#13711yescharacteristic
97C4×C11—42no—
98C4×C11—81no—
99C4×C11#12111yescharacteristic
100C4×C11C22⋊Q811yescharacteristic
101C4×C11C22⋊Q811yescharacteristic
102C4×C11#12611yescharacteristic
103Dic11—22no—
104Dic11—42no—
105Dic11—41no—
106Dic11—81no—
107C22×Q8C2×D1111yescharacteristic
108C22×C8—111no—
109C22×C8C2×D1111yescharacteristic
110C2×C4⋊C4—111no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—221no—
113C2×C4⋊C4C2×D1111yescharacteristic
114C2×C42—111no—
115#106—222no—
116C4⋊C8—222no—
117#103—22no—
118#103—222no—
119#95—221no—
120#95—221no—
121#95—221no—
122C2×C11#39611yescharacteristic
123C2×C11#46111yescharacteristic
124C2×C11#46411yescharacteristic
125C2×C11#46511yescharacteristic
126C2×C11#47011yescharacteristic
127C2×C11#47511yescharacteristic
128C2×C11#47911yescharacteristic
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8Dic2212yes—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—111no—
138C22×C4—111no—
139C22×C4—221no—
140C22×C4—221no—
141C22×C4C22×D1111yescharacteristic
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—221no—
145C2×C8—221no—
146C2×C8—221no—
147C2×C8C22⋊D1112yes—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—112no—
151C4⋊C4—221no—
152C4⋊C4—221no—
153C4⋊C4—221no—
154C4⋊C4—442no—
155C42—221no—
156C42—221no—
157C11#206611yescharacteristic, complemented, Sylow
158C23D4×D1111yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—112no—
170C2×C4—221no—
171C2×C4—221no—
172C2×C4—222no—
173C2×C4—221no—
174C2×C4—221no—
175C2×C4—221no—
176C2×C4—441no—
177C2×C4—441no—
178C2×C4—441no—
179C2×C4—441no—
180C2×C4—441no—
181C2×C4C2×Dic2211yescharacteristic
182C2×C4#433911yescharacteristic
183C2×C4D4×D1111yescharacteristic
184C2×C4#434111yescharacteristic
185C2×C4#434111yescharacteristic
186C2×C4C2×C22⋊D1111yescharacteristic
187C8—22no—
188C8—441no—
189C22#6693111yescharacteristic
190C22#6693711yescharacteristic
191C22SD16×D1111yescharacteristic
192C22#6696911yescharacteristic
193C22#6697111yescharacteristic
194C22#6697111yescharacteristic
195C22#6699111yescharacteristic
196C4—42no—
197C4—81no—
198C4—222no—
199C4—441no—
200C4—442no—
201C4—881no—
202C4#6693111yescharacteristic
203C4#6693211yescharacteristic
204C4#6697711yescharacteristic
205C4#6699211yescharacteristic
206C2#1062240411yescharacteristic
207C2#1062241111yescharacteristic
208C2#1062241211yescharacteristic
209C2#1062243111yescharacteristic
210C2#1062256111yescharacteristic
211C2#1062278411yescharacteristic
212C2#1062280211yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#103D11
hypocenterC11#2066
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
157. C11#2066semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1032
#106228432
C2×#668992
C2×#668812
C2×Dic11⋊C82
#106225862
#106221672
#206611