Finite Group Databasebeta

← #14658566

Subgroups — #14658566

Order 2816.

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

normal subgroups only

This group has 310 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
1#13068791C211yesmaximal, characteristic
2#13067288C212yesmaximal
3#13066474C212yesmaximal
4#13066461C211yesmaximal, characteristic
5C11×#1960C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#103—21no—
8C2×C11×#103—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66883—21no—
12C2×#66883—21no—
13#10622538C2212yes—
14#10622537C2212yes—
15#10622185—24no—
16C22×Q8×C11—21no—
17C22×C8×C11D411yescharacteristic
18C22×C8×C11D411yescharacteristic
19C11×C4⋊Q8—22no—
20C11×C4⋊Q8—21no—
21C11×C4⋊Q8D412yes—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—21no—
24C2×C42×C11C2311yescharacteristic
25C2×#4318—22no—
26C11×#103—42no—
27C11×#103—42no—
28C11×#97—22no—
29C11×#95—22no—
30C22⋊(C11⋊C8)—22no—
31#66883—42no—
32#66883—42no—
33C4⋊(C11⋊C8)—22no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)—22no—
36C4×C11⋊C8—22no—
37#10632—111nomaximal, Sylow
38C2×Q8×C11—22no—
39C2×Q8×C11—41no—
40C2×Q8×C11—41no—
41C2×Q8×C11—41no—
42C2×Q8×C11—41no—
43C2×Q8×C11—41no—
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11#4112yes—
48C2×C8×C11—21no—
49C2×C8×C11—21no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11D812yes—
53C2×C8×C11SD1612yes—
54C11×C4⋊C4—24no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C42×C11C2×D411yescharacteristic
59C42×C11#4111yescharacteristic
60C42×C11#4112yes—
61#4318—42no—
62#4318—42no—
63C2×C11⋊C8—42no—
64C2×C11⋊C8—42no—
65#1960D1111yescharacteristic
66#1849—111no—
67#1546—112no—
68#1286—112no—
69#1281—111no—
70C23×C11#12411yescharacteristic
71Q8×C11—42no—
72Q8×C11—42no—
73Q8×C11—81no—
74Q8×C11—81no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11—81no—
78C2×C4×C11—81no—
79C2×C4×C11—82no—
80C2×C4×C11—81no—
81C2×C4×C11#12111yescharacteristic
82C2×C4×C11#12312yes—
83C2×C4×C11#12311yescharacteristic
84C2×C4×C11#12612yes—
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11C2×SD1611yescharacteristic
87C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C11#13711yescharacteristic
89C8×C11—22no—
90C8×C11—22no—
91C11⋊C8—82no—
92C11⋊C8—82no—
93C2×C4⋊Q8C2×D1111yescharacteristic
94#431—112no—
95C2×#108—221no—
96C2×#108—221no—
97#423—112no—
98C2×#103—21no—
99C2×#103—21no—
100C2×#97C2×D1111yescharacteristic
101#382C2×D1111yescharacteristic
102#332—224no—
103C22×C11—22no—
104C22×C11#39711yescharacteristic
105C22×C11#48611yescharacteristic
106C22×C11#48911yescharacteristic
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—82no—
110C4×C11—161no—
111C4×C11#45911yescharacteristic
112C4×C11#46111yescharacteristic
113C4×C11#48011yescharacteristic
114C4×C11#48111yescharacteristic
115C22×Q8—21no—
116C2×M16—222no—
117C22×C8C22⋊D1111yescharacteristic
118C22×C8C22⋊D1111yescharacteristic
119C4⋊Q8—21no—
120C4⋊Q8—22no—
121C4⋊Q8D4412yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—21no—
124C2×C42C22×D1111yescharacteristic
125#108—442no—
126#108—442no—
127C4⋊C8—222no—
128C4⋊C8—222no—
129C4⋊C8—222no—
130#103—42no—
131#103—42no—
132C22⋊C8—222no—
133#97—22no—
134C4×C8—222no—
135#95—22no—
136C2×C11—21no—
137C2×C11—21no—
138C2×C11#207111yescharacteristic
139C2×C11#208212yes—
140C2×Q8—22no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4#434112yes—
149C22×C4C2×C22⋊D1111yescharacteristic
150M16—442no—
151M16—442no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—442no—
157C2×C8—442no—
158C2×C8#432312yes—
159C2×C8#432412yes—
160C4⋊C4—24no—
161C4⋊C4—42no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C42C2×D4411yescharacteristic
165C42#433911yescharacteristic
166C42#434112yes—
167C11#1063211yescharacteristic, complemented, Sylow
168C23#6698911yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—81no—
172Q8—81no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4#6693212yes—
180C2×C4#6693912yes—
181C2×C4#6698311yescharacteristic
182C2×C4C2×#432311yescharacteristic
183C2×C4C2×#432411yescharacteristic
184C2×C4#6698811yescharacteristic
185C2×C4#6700211yescharacteristic
186C2×C4#6700411yescharacteristic
187C8—22no—
188C8—22no—
189C8—882no—
190C8—882no—
191C22—22no—
192C22#1062256611yescharacteristic
193C22#1062266811yescharacteristic
194C22#1062268311yescharacteristic
195C4—22no—
196C4—22no—
197C4—82no—
198C4—161no—
199C4#1062262811yescharacteristic
200C4#1062263211yescharacteristic
201C4#1062264611yescharacteristic
202C4#1062264711yescharacteristic
203C2—21no—
204C2—21no—
205C2#1307001911yescharacteristic
206C2#1307008012yes—
subgroupG/H
centerC22#10622566
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1960C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1960D11
hypocenterC11#10632
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
167. C11#10632semidirect

Maximal subgroups

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

subgroupindex
#130687912
#130672882
#130664742
#130664612
C11×#19602
#1063211