Finite Group Databasebeta

← #13070138

Subgroups — #13070138

Order 1408.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#106C211yesmaximal, characteristic, complemented
2C2×#66885C211yesmaximal, characteristic
3#10622601C211yesmaximal, characteristic
4#10622590C211yesmaximal, characteristic, complemented
5C2×#66873C211yesmaximal, characteristic
6C2×#66871C211yesmaximal, characteristic, complemented
7#10622188C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×(C2×D11)⋊C4—22no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4×Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C11×#106—22no—
17C11⋊#95—22no—
18#66885—22no—
19#66873—22no—
20#66871—22no—
21C23×D11—21no—
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C22×Dic11—21no—
26C22×Dic11D412yes—
27C2×D44—21no—
28C2×D44—21no—
29C2×D44—21no—
30C2×D44—21no—
31C2×D44—21no—
32C2×D44Q812yes—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11D412yes—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40(C2×D11)⋊C4—44no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4×Dic11—21no—
44C4×Dic11—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8D412yes—
48#2092—111nomaximal, Sylow
49C23×C11C2×D411yescharacteristic
50C22×D11—22no—
51C22×D11—41no—
52C22×D11—41no—
53C22×D11—42no—
54C22×D11—42no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—42no—
58C2×C4×C11—42no—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—22no—
68C2×Dic11—41no—
69C2×Dic11—42no—
70D44—22no—
71D44—22no—
72D44—41no—
73D44—41no—
74C8×C11—22no—
75C11⋊C8—22no—
76C2×#107—111no—
77C2×#106D1111yescharacteristic, complemented
78C2×#102—111no—
79C2×#102—111no—
80#390—111no—
81#382—111no—
82#336—111no—
83C22×C11C22⋊Q811yescharacteristic
84C22×C11#12311yescharacteristic
85C22×C11#12711yescharacteristic
86C22×C11#13512yes—
87C22×C11AGL(1,ℤ/8)12yes—
88C2×D11—42no—
89C2×D11—44no—
90C2×D11—82no—
91C2×D11—81no—
92C2×D11—81no—
93C4×C11—81no—
94C4×C11—81no—
95C4×C11C22⋊Q811yescharacteristic
96C4×C11C22⋊Q811yescharacteristic
97C4×C11#12311yescharacteristic
98C4×C11#12311yescharacteristic
99Dic11—42no—
100Dic11—81no—
101C22×D4—111no—
102C22×C8—111no—
103C22×C8C2×D1111yescharacteristic
104C2×C4⋊C4—111no—
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C22⋊C4—222no—
108C2×C42—111no—
109#107—222no—
110#106—22no—
111#102—222no—
112#102—222no—
113#95—222no—
114C2×C11#39911yescharacteristic
115C2×C11#47812yes—
116C2×C11#48212yes—
117C2×C11#49511yescharacteristic
118C2×C11#49611yescharacteristic
119D11—82no—
120C24—221no—
121C2×D4—112no—
122C2×D4—221no—
123C2×D4—221no—
124C2×D4—221no—
125C2×D4—221no—
126C2×D4—221no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—112no—
130C22×C4—221no—
131C22×C4C22×D1111yescharacteristic
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—112no—
135C2×C8—221no—
136C2×C8—221no—
137C2×C8C22⋊D1112yes—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C22⋊C4—444no—
145C42—221no—
146C42—221no—
147C11#209211yescharacteristic, complemented, Sylow
148C23—222no—
149C23—441no—
150C23—442no—
151C23—442no—
152C23—441no—
153C23D4×D1111yescharacteristic
154D4—222no—
155D4—222no—
156D4—441no—
157D4—441no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—222no—
165C2×C4—442no—
166C2×C4—441no—
167C2×C4#433911yescharacteristic
168C2×C4#433911yescharacteristic
169C2×C4D4×D1111yescharacteristic
170C2×C4Q8×D1111yescharacteristic
171C2×C4#434311yescharacteristic
172C2×C4C2×C22⋊D1111yescharacteristic
173C8—22no—
174C8—222no—
175C22—444no—
176C22—442no—
177C22—882no—
178C22—881no—
179C22—881no—
180C22#6694711yescharacteristic
181C22#6694911yescharacteristic
182C22#6696712yes—
183C22#6696912yes—
184C22#6699311yescharacteristic
185C4—81no—
186C4—81no—
187C4—442no—
188C4—881no—
189C4#6694711yescharacteristic
190C4#6694911yescharacteristic
191C4#6698211yescharacteristic
192C4#6699911yescharacteristic
193C2—882no—
194C2#1062247912yes—
195C2#1062248412yes—
196C2#1062260511yescharacteristic
197C2#1062278111yescharacteristic
198C2#1062278911yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#106C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenterC2×#106D11
hypocenterC11#2092
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×C11×#106C2semidirect
4. #10622590C2semidirect
6. C2×#66871C2semidirect
7. #10622188C2semidirect
77. C2×#106D11semidirect
147. C11#2092semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1062
C2×#668852
#106226012
#106225902
C2×#668732
C2×#668712
#106221882
#209211