Finite Group Databasebeta

← #13069293

Subgroups — #13069293

Order 1408.

256 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 95 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×#66880C211yesmaximal, characteristic
2C2×C8×Dic11C211yesmaximal, characteristic
3#10622598C211yesmaximal, characteristic
4#10622587C211yesmaximal, characteristic
5C2×#66874C211yesmaximal, characteristic
6C11×#340C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C22×Dic22C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4×Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C11⋊#95—21no—
17C11⋊#95—21no—
18C11⋊#95—21no—
19#66880—22no—
20C8×Dic11—22no—
21#66874C414yescomplemented
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C22×Dic11—21no—
26C22×Dic11—21no—
27C22×Dic11D411yescharacteristic
28C22×Dic11D411yescharacteristic
29C2×Dic22—21no—
30C2×Dic22—21no—
31C2×Dic22—21no—
32C2×Dic22—21no—
33C2×Dic22—21no—
34C2×Dic22C2×C412yes—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C2×C8×C11D412yes—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C11×C4⋊C4C2×C412yes—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C4⋊Dic11—42no—
45C4×Dic11—21no—
46C4×Dic11—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8C2×C412yes—
50#1933—111nomaximal, Sylow
51C23×C11C2×D411yescharacteristic
52C2×C4×C11—22no—
53C2×C4×C11—41no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11C22×C411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11#4111yescharacteristic
61C2×C4×C11#4111yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—22no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73C2×Dic11—41no—
74C2×Dic11SD1612yes—
75C2×Dic11Q1612yes—
76Dic22—22no—
77Dic22—22no—
78Dic22—41no—
79Dic22—41no—
80C8×C11—22no—
81C11⋊C8—22no—
82C2×#103—111no—
83C2×#103—111no—
84C2×C4×C8—111no—
85#391—111no—
86#389—111no—
87#340—111no—
88#340D1111yescharacteristic
89C22×C11C4×D411yescharacteristic
90C22×C11#12111yescharacteristic
91C22×C11#12411yescharacteristic
92C22×C11C2×SD1611yescharacteristic
93C22×C11C2×Q1611yescharacteristic
94C22×C11#13511yescharacteristic
95C22×C11#13511yescharacteristic
96C4×C11—42no—
97C4×C11—81no—
98C4×C11#11711yescharacteristic
99C4×C11C4×D411yescharacteristic
100C4×C11#12311yescharacteristic
101C4×C11#12611yescharacteristic
102Dic11—22no—
103Dic11—22no—
104Dic11—42no—
105Dic11—81no—
106C22×Q8—111no—
107C22×C8—111no—
108C22×C8C2×D1111yescharacteristic
109C2×C4⋊C4—111no—
110C2×C4⋊C4—221no—
111C2×C4⋊C4C2×D1111yescharacteristic
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C42—111no—
114#103—114no—
115#103—222no—
116C4×C8—222no—
117#95—221no—
118#95—221no—
119#95—221no—
120C2×C11#38811yescharacteristic
121C2×C11C4×SD1611yescharacteristic
122C2×C11C4×Q1611yescharacteristic
123C2×C11#46511yescharacteristic
124C2×C11#46711yescharacteristic
125C2×C11#48711yescharacteristic
126C2×C11#48811yescharacteristic
127C2×Q8—112no—
128C2×Q8—221no—
129C2×Q8—221no—
130C2×Q8—221no—
131C2×Q8—221no—
132C2×Q8—221no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—111no—
136C22×C4—111no—
137C22×C4—221no—
138C22×C4—221no—
139C22×C4C22×D1111yescharacteristic
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—112no—
143C2×C8—221no—
144C2×C8—221no—
145C2×C8D4412yes—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—221no—
150C4⋊C4—221no—
151C4⋊C4—442no—
152C4⋊C4C4×D1112yes—
153C42—221no—
154C42—221no—
155C11#193311yescharacteristic, complemented, Sylow
156C23D4×D1111yescharacteristic
157Q8—222no—
158Q8—222no—
159Q8—441no—
160Q8—441no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—112no—
168C2×C4—112no—
169C2×C4—221no—
170C2×C4—221no—
171C2×C4—221no—
172C2×C4—221no—
173C2×C4—222no—
174C2×C4—441no—
175C2×C4—441no—
176C2×C4—441no—
177C2×C4—441no—
178C2×C4—441no—
179C2×C4C2×C4×D1111yescharacteristic
180C2×C4C2×D4411yescharacteristic
181C2×C4#433911yescharacteristic
182C2×C4#434111yescharacteristic
183C2×C4#434111yescharacteristic
184C2×C4#434311yescharacteristic
185C8—22no—
186C8—222no—
187C22(C22⋊D11)⋊C411yescharacteristic
188C22#6693811yescharacteristic
189C22#6694811yescharacteristic
190C22#6696511yescharacteristic
191C22SD16×D1111yescharacteristic
192C22#6696911yescharacteristic
193C22Q16×D1111yescharacteristic
194C4—42no—
195C4—81no—
196C4—222no—
197C4—222no—
198C4—442no—
199C4—881no—
200C4C4×D4411yescharacteristic
201C4#6693911yescharacteristic
202C4#6694511yescharacteristic
203C4#6695111yescharacteristic
204C2#1062228311yescharacteristic
205C2#1062237111yescharacteristic
206C2#1062238111yescharacteristic
207C2#1062240311yescharacteristic
208C2#1062240511yescharacteristic
209C2#1062247711yescharacteristic
210C2#1062250011yescharacteristic
subgroupG/H
centerC23D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#340C2
socle, prime radicalC23×C11C2×D4
cosocleC22×C4×C11C23
hypercenter#340D11
hypocenterC11#1933
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
21. #66874C4semidirect
155. C11#1933semidirect

Maximal subgroups

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

subgroupindex
C2×#668802
C2×C8×Dic112
#106225982
#106225872
C2×#668742
C11×#3402
#106221672
#193311