Finite Group Databasebeta

← #13069850

Subgroups — #13069850

Order 1408.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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×#66927C211yesmaximal, characteristic
2C11×#389C211yesmaximal, characteristic, complemented
3C2×#66873C212yesmaximal, complemented
4C2×#66873C212yesmaximal, complemented
5#10622162C211yesmaximal, characteristic, complemented
6C22×D44—21no—
7C22×D44—21no—
8C22×D44C2212yes—
9C2×C11×C4⋊C4—21no—
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13C22×C11⋊C8C2212yes—
14#66927—24no—
15C11×#95—21no—
16#66873—24no—
17#66873—24no—
18C23×D11—22no—
19C22×C4×C11—21no—
20C22×C4×C11—21no—
21C22×C4×C11D411yescharacteristic
22C22×C4×C11D411yescharacteristic
23C22×C4×C11C2311yescharacteristic
24C2×D44—24no—
25C2×D44—24no—
26C2×D44—22no—
27C2×D44—22no—
28C2×D44—22no—
29C2×D44—22no—
30C2×D44—22no—
31C2×D44—42no—
32C2×D44—42no—
33C2×D44—42no—
34C2×D44—42no—
35C2×D44D414yes—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—22no—
38C11×C4⋊C4—42no—
39C11×C4⋊C4D412yescomplemented
40C42×C11—22no—
41C2×C11⋊C8—22no—
42C2×C11⋊C8—22no—
43C2×C11⋊C8—22no—
44#2041—111nomaximal, Sylow
45C23×C11C2×D411yescharacteristic
46C22×D11—24no—
47C22×D11—42no—
48C22×D11—42no—
49C22×D11—42no—
50C22×D11—42no—
51C22×D11—42no—
52C22×D11—42no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
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×C11D812yes—
64C2×C4×C11SD1612yes—
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×D412yes—
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4112yes—
69D44—24no—
70D44—24no—
71D44—48no—
72D44—48no—
73D44—42no—
74D44—42no—
75C11⋊C8—42no—
76C2×#127—111no—
77C2×#102—112no—
78C2×#102—112no—
79#389D1111yescharacteristic, complemented
80#336—111no—
81C22×C11#12011yescharacteristic
82C22×C11#12111yescharacteristic
83C22×C11#12411yescharacteristic
84C22×C11C2×D811yescharacteristic
85C22×C11C2×SD1611yescharacteristic
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C22×C11AGL(1,ℤ/8)11yescharacteristic
88C2×D11—44no—
89C2×D11—44no—
90C2×D11—44no—
91C2×D11—82no—
92C2×D11—82no—
93C2×D11—82no—
94C2×D11—82no—
95C4×C11—22no—
96C4×C11—22no—
97C4×C11—42no—
98C4×C11—81no—
99C4×C11#12112yes—
100C4×C11#12312yes—
101C22×D4—112no—
102C22×D4—221no—
103C22×D4—221no—
104C22×C8—112no—
105#127—224no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4C2×D1111yescharacteristic
108C2×C4⋊C4C2×D1111yescharacteristic
109C2×C42C2×D1111yescharacteristic
110#102—224no—
111#102—224no—
112#95—21no—
113C2×C11#39411yescharacteristic
114C2×C11#44711yescharacteristic
115C2×C11#45011yescharacteristic
116C2×C11#45911yescharacteristic
117C2×C11#46011yescharacteristic
118C2×C11#48611yescharacteristic
119C2×C11#49011yescharacteristic
120D11—84no—
121C24—222no—
122C2×D4—114no—
123C2×D4—224no—
124C2×D4—224no—
125C2×D4—222no—
126C2×D4—222no—
127C2×D4—222no—
128C2×D4—222no—
129C2×D4—222no—
130C2×D4—442no—
131C2×D4—442no—
132C2×D4—442no—
133C2×D4—442no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D1111yescharacteristic
137C22×C4C22⋊D1111yescharacteristic
138C22×C4C22×D1111yescharacteristic
139C2×C8—222no—
140C2×C8—222no—
141C2×C8—222no—
142C4⋊C4—21no—
143C4⋊C4—22no—
144C4⋊C4—42no—
145C4⋊C4D4412yescomplemented
146C42—22no—
147C11#204111yescharacteristic, complemented, Sylow
148C23—224no—
149C23—442no—
150C23—442no—
151C23—442no—
152C23—442no—
153C23—442no—
154C23—442no—
155C23C2×C22⋊D1111yescharacteristic
156D4—224no—
157D4—224no—
158D4—448no—
159D4—448no—
160D4—442no—
161D4—442no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4#432312yes—
173C2×C4#432512yes—
174C2×C4C2×D4411yescharacteristic
175C2×C4#433911yescharacteristic
176C2×C4D4×D1112yes—
177C2×C4#434312yes—
178C8—442no—
179C22—444no—
180C22—444no—
181C22—444no—
182C22—882no—
183C22—882no—
184C22—882no—
185C22—882no—
186C22#6698311yescharacteristic
187C22C2×#432311yescharacteristic
188C22#6699011yescharacteristic
189C22C2×#432511yescharacteristic
190C22#6700011yescharacteristic
191C22#6700211yescharacteristic
192C22#6700211yescharacteristic
193C4—22no—
194C4—22no—
195C4—42no—
196C4—81no—
197C4#6694712yes—
198C4#6694812yes—
199C2—884no—
200C2#1062260411yescharacteristic
201C2#1062262811yescharacteristic
202C2#1062264011yescharacteristic
203C2#1062264911yescharacteristic
204C2#1062265911yescharacteristic
205C2#1062268011yescharacteristic
206C2#1062270111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#389C2
socleC23×C11C2×D4
prime radicalC2×#66927C2
hypercenter#389D11
hypocenterC11#2041
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C11×#389C2semidirect
3. C2×#66873C2semidirect
4. C2×#66873C2semidirect
5. #10622162C2semidirect
39. C11×C4⋊C4D4semidirect
79. #389D11semidirect
145. C4⋊C4D44semidirect
147. C11#2041semidirect

Maximal subgroups

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

subgroupindex
C2×#669272
C11×#3892
C2×#668732
#106221622
#204111