Finite Group Databasebeta

← #13070112

Subgroups — #13070112

Order 1408.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C11×#389C211yesmaximal, characteristic
2C2×#66871C211yesmaximal, characteristic
3#10622541C211yesmaximal, characteristic
4C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic
5#10622167C211yesmaximal, characteristic
6#10622167C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C2×C11×C4⋊C4—21no—
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15C22×C11⋊C8C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11×#95—21no—
18C11⋊#95—21no—
19#66871—22no—
20C4⋊(C11⋊C8)—22no—
21C22×C4×C11—21no—
22C22×C4×C11—21no—
23C22×C4×C11D411yescharacteristic
24C22×C4×C11D411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C22×Dic11—21no—
27C22×Dic11—21no—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—21no—
30C11×C4⋊C4—21no—
31C11×C4⋊C4—42no—
32C11×C4⋊C4Q812yes—
33C42×C11—21no—
34C42×C11—21no—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4⋊Dic11—21no—
38C4⋊Dic11Q812yes—
39Dic11⋊C4—42no—
40C2×C11⋊C8—21no—
41C2×C11⋊C8—21no—
42C2×C11⋊C8—21no—
43C2×C11⋊C8—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8D412yes—
46#2087—111nomaximal, Sylow
47C23×C11C2×D411yescharacteristic
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—22no—
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11Q1612yes—
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11C2×Q811yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×C4×C11#4111yescharacteristic
66C2×Dic11—22no—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C11⋊C8—22no—
73C11⋊C8—41no—
74C2×#107—111no—
75C2×C4⋊C8—111no—
76#389—111no—
77#389D1111yescharacteristic
78#340—111no—
79#340—111no—
80#340—111no—
81C22×C11#12111yescharacteristic
82C22×C11C22⋊Q811yescharacteristic
83C22×C11C22⋊Q811yescharacteristic
84C22×C11C2×Q1611yescharacteristic
85C22×C11#13511yescharacteristic
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C22×C11AGL(1,ℤ/8)11yescharacteristic
88C4×C11—22no—
89C4×C11—41no—
90C4×C11—42no—
91C4×C11—81no—
92C4×C11#12311yescharacteristic
93C4×C11#12511yescharacteristic
94C4×C11#12511yescharacteristic
95C4×C11C4⋊Q811yescharacteristic
96Dic11—42no—
97Dic11—81no—
98C22×C8—111no—
99C22×C8—111no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—221no—
104C2×C4⋊C4C2×D1111yescharacteristic
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C42C2×D1111yescharacteristic
107#107—222no—
108C4⋊C8—222no—
109#95—21no—
110#95—221no—
111C2×C11#39811yescharacteristic
112C2×C11#46711yescharacteristic
113C2×C11#46911yescharacteristic
114C2×C11#47711yescharacteristic
115C2×C11#47711yescharacteristic
116C2×C11#47811yescharacteristic
117C2×C11#47811yescharacteristic
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—221no—
121C22×C4—221no—
122C22×C4C22⋊D1111yescharacteristic
123C22×C4C22⋊D1111yescharacteristic
124C22×C4C22×D1111yescharacteristic
125C2×C8—112no—
126C2×C8—221no—
127C2×C8—221no—
128C2×C8—221no—
129C2×C8—221no—
130C2×C8—221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—42no—
135C4⋊C4—112no—
136C4⋊C4—221no—
137C4⋊C4—221no—
138C4⋊C4—221no—
139C4⋊C4—442no—
140C4⋊C4Dic2212yes—
141C42—21no—
142C42—21no—
143C11#208711yescharacteristic, complemented, Sylow
144C23C2×C22⋊D1111yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—222no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4—441no—
162C2×C4#432612yes—
163C2×C4C2×Dic2211yescharacteristic
164C2×C4#433911yescharacteristic
165C2×C4D4×D1111yescharacteristic
166C2×C4#434111yescharacteristic
167C2×C4Q8×D1111yescharacteristic
168C2×C4#434311yescharacteristic
169C8—222no—
170C8—441no—
171C22#6697711yescharacteristic
172C22#6698511yescharacteristic
173C22#6699211yescharacteristic
174C22C2×#432611yescharacteristic
175C22#6699911yescharacteristic
176C22#6700211yescharacteristic
177C22#6700311yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4—81no—
182C4—442no—
183C4—881no—
184C4#6694111yescharacteristic
185C4#6694211yescharacteristic
186C4#6694311yescharacteristic
187C4#6694711yescharacteristic
188C2#1062259711yescharacteristic
189C2#1062262211yescharacteristic
190C2#1062263411yescharacteristic
191C2#1062265211yescharacteristic
192C2#1062266411yescharacteristic
193C2#1062267911yescharacteristic
194C2#1062270411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#389C2
socle, prime radicalC23×C11C2×D4
hypercenter#389D11
hypocenterC11#2087
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
143. C11#2087semidirect

Maximal subgroups

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

subgroupindex
C11×#3892
C2×#668712
#106225412
C2×C4⋊(C11⋊C8)2
#106221672
#208711