Finite Group Databasebeta

← #13079808

Subgroups — #13079808

Order 1408.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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#10623008C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3C11×#432C211yesmaximal, characteristic, complemented
4#10622460C214yesmaximal, complemented
5#10622349C212yesmaximal, complemented
6#10622348C212yesmaximal, complemented
7#10622326C212yesmaximal, complemented
8#10622315C212yesmaximal, complemented
9C2×#4339—21no—
10C2×C42×C11C2211yescharacteristic
11#66983—21no—
12#66983C2212yes—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4—21no—
16C2×Dic11⋊C4—21no—
17#66928—21no—
18#66927C2211yescharacteristic
19C4×D44—21no—
20C4×D44C2212yes—
21#66923—21no—
22#66923—21no—
23#66923C2212yes—
24#66923C2212yes—
25#66922C2211yescharacteristic
26C11×C4⋊C8C2212yes—
27C11×C22⋊C8C2212yes—
28C11×#97C2212yes—
29#66885C2214yes—
30#66885C2214yes—
31#66882C2214yes—
32#66881C2214yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C22×Dic11—21no—
38C22×Dic11—21no—
39#4339—44no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×Dic22—21no—
45C2×C8×C11C2314yes—
46C42×C11D411yescharacteristic
47C42×C11D411yescharacteristic
48C42×C11C2311yescharacteristic
49C42×C11C2311yescharacteristic
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—22no—
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C4⋊Dic11C2312yes—
56C4⋊Dic11C2312yes—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62#3234—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64C22×D11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—41no—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2411yescharacteristic
74C22⋊D11—44no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—42no—
79C2×Dic11—42no—
80D44—24no—
81D44—42no—
82D44—42no—
83C4×D11—44no—
84Dic22—42no—
85C8×C11—24no—
86#532—111no—
87C2×#125—111no—
88#501—112no—
89#490—112no—
90#481—112no—
91#480—112no—
92#478—114no—
93#432D1111yescharacteristic, complemented
94C22×C11—21no—
95C22×C11—21no—
96C22×C11AGL(1,ℤ/8)12yes—
97C22×C11C22×D411yescharacteristic
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—42no—
101C4×C11—21no—
102C4×C11—21no—
103C4×C11—21no—
104C4×C11—21no—
105C4×C11—21no—
106C4×C112−1+412yes—
107Dic11—42no—
108Dic11—42no—
109Dic11—42no—
110C2×#41—221no—
111C4⋊Q8—111no—
112#127—111no—
113#125—112no—
114#125—112no—
115#125—221no—
116#125—221no—
117#124—221no—
118#121—112no—
119#121—221no—
120C4×D4—112no—
121C4×D4—221no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—111no—
124C2×C4⋊C4—221no—
125C2×C4⋊C4—221no—
126C2×C42C2×D1111yescharacteristic
127#107—114no—
128#106—114no—
129C4⋊C8C2×D1112yes—
130#102—114no—
131#102—114no—
132C22⋊C8C2×D1112yes—
133#97C2×D1112yes—
134C2×C11—22no—
135C2×C11#53611yescharacteristic
136C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C11#57511yescharacteristic
138D11—82no—
139#41—444no—
140C2×Q8—221no—
141C2×D4—112no—
142C2×D4—222no—
143C2×D4—221no—
144C2×D4—221no—
145C22×C4—221no—
146C22×C4—221no—
147C22×C4—222no—
148C22×C4D4411yescharacteristic
149C22×C4D4411yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C2×C8C22×D1114yes—
152C4⋊C4—112no—
153C4⋊C4—112no—
154C4⋊C4—112no—
155C4⋊C4—221no—
156C4⋊C4—221no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—222no—
161C4⋊C4—221no—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C42D4411yescharacteristic
165C42D4411yescharacteristic
166C42C22×D1111yescharacteristic
167C42C22×D1111yescharacteristic
168C11#323411yescharacteristic, complemented, Sylow
169C23—222no—
170C23C2×D4411yescharacteristic
171Q8—442no—
172D4—224no—
173D4—442no—
174D4—442no—
175D4—444no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—444no—
183C2×C4—442no—
184C2×C4—442no—
185C2×C4C2×D4411yescharacteristic
186C2×C4C2×D4411yescharacteristic
187C2×C4C2×D4411yescharacteristic
188C2×C4C2×D4411yescharacteristic
189C2×C4C2×D4411yescharacteristic
190C2×C4C23×D1111yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—442no—
195C22—442no—
196C22—442no—
197C22#6696112yes—
198C22C22×D4411yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—442no—
205C4—442no—
206C4—442no—
207C4#6704312yes—
208C2—22no—
209C2—882no—
210C2#1062305711yescharacteristic
211C2C2×#6696111yescharacteristic
212C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#432C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenter#432D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. C11×#432C2semidirect
4. #10622460C2semidirect
5. #10622349C2semidirect
6. #10622348C2semidirect
7. #10622326C2semidirect
8. #10622315C2semidirect
93. #432D11semidirect
168. C11#3234semidirect

Maximal subgroups

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

subgroupindex
#106230082
C2×#669232
C11×#4322
#106224602
#106223492
#106223482
#106223262
#106223152
#323411