Finite Group Databasebeta

← #14658561

Subgroups — #14658561

Order 2816.

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

normal subgroups only

This group has 362 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, complemented
2#13067284C212yesmaximal
3#13066474C212yesmaximal, complemented
4#13066461C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#102—21no—
8C2×C11×#102—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66883—21no—
12C2×#66883—21no—
13#10622538C2212yes—
14#10622537C2212yes—
15#10622182—24no—
16C22×D4×C11—21no—
17C22×D4×C11—22no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11D411yescharacteristic
20C11×#127—21no—
21C11×#127—22no—
22C11×#127D412yes—
23C2×C11×C4⋊C4—21no—
24C2×C42×C11C2311yescharacteristic
25C2×#4318—22no—
26C11×#102—42no—
27C11×#102—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#10631—111nomaximal, Sylow
38C24×C11—41no—
39C2×D4×C11—22no—
40C2×D4×C11—24no—
41C2×D4×C11—41no—
42C2×D4×C11—42no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11—84no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11#4112yes—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11D812yes—
56C2×C8×C11SD1612yes—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C42×C11C2×D411yescharacteristic
60C42×C11#4111yescharacteristic
61C42×C11#4112yes—
62#4318—42no—
63#4318—42no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—42no—
66#1961D1111yescharacteristic
67#1849—111no—
68#1545—112no—
69#1286—112no—
70#1281—111no—
71C23×C11—42no—
72C23×C11—84no—
73C23×C11—81no—
74C23×C11—81no—
75C23×C11#12411yescharacteristic
76D4×C11—42no—
77D4×C11—42no—
78D4×C11—84no—
79D4×C11—84no—
80D4×C11—81no—
81D4×C11—81no—
82C2×C4×C11—42no—
83C2×C4×C11—82no—
84C2×C4×C11—81no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11#12312yes—
87C2×C4×C11#12311yescharacteristic
88C2×C4×C11#12612yes—
89C2×C4×C11C2×D811yescharacteristic
90C2×C4×C11C2×SD1611yescharacteristic
91C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
92C2×C4×C11#13711yescharacteristic
93C8×C11—22no—
94C8×C11—22no—
95C11⋊C8—82no—
96C11⋊C8—82no—
97C2×#127C2×D1111yescharacteristic
98#431—112no—
99C2×#108—221no—
100C2×#108—221no—
101#423—112no—
102C2×#102—21no—
103C2×#102—21no—
104C2×#97C2×D1111yescharacteristic
105#382C2×D1111yescharacteristic
106#331—224no—
107C22×C11—22no—
108C22×C11—82no—
109C22×C11—84no—
110C22×C11—162no—
111C22×C11—162no—
112C22×C11#39711yescharacteristic
113C22×C11#48611yescharacteristic
114C22×C11#48911yescharacteristic
115C4×C11—22no—
116C4×C11—22no—
117C4×C11—161no—
118C4×C11#45911yescharacteristic
119C4×C11#46111yescharacteristic
120C4×C11#48011yescharacteristic
121C4×C11#48111yescharacteristic
122C22×D4—22no—
123C22×D4—21no—
124C2×M16—222no—
125C22×C8C22⋊D1111yescharacteristic
126C22×C8C22⋊D1111yescharacteristic
127#127—21no—
128#127—22no—
129#127D4412yes—
130C2×C4⋊C4—21no—
131C2×C42C22×D1111yescharacteristic
132#108—442no—
133#108—442no—
134C4⋊C8—222no—
135C4⋊C8—222no—
136C4⋊C8—222no—
137#102—42no—
138#102—42no—
139C22⋊C8—222no—
140#97—22no—
141C4×C8—222no—
142#95—22no—
143C2×C11—21no—
144C2×C11—21no—
145C2×C11—162no—
146C2×C11#207111yescharacteristic
147C2×C11#208112yes—
148C24—41no—
149C2×D4—24no—
150C2×D4—22no—
151C2×D4—42no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—84no—
158C22×C4—41no—
159C22×C4#434112yes—
160C22×C4C2×C22⋊D1111yescharacteristic
161M16—442no—
162M16—442no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—442no—
168C2×C8—442no—
169C2×C8#432312yes—
170C2×C8#432412yes—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C42C2×D4411yescharacteristic
174C42#433911yescharacteristic
175C42#434112yes—
176C11#1063111yescharacteristic, complemented, Sylow
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#6698911yescharacteristic
182D4—42no—
183D4—42no—
184D4—84no—
185D4—84no—
186D4—81no—
187D4—81no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4#6693212yes—
192C2×C4#6693912yes—
193C2×C4#6698311yescharacteristic
194C2×C4C2×#432311yescharacteristic
195C2×C4C2×#432411yescharacteristic
196C2×C4#6698811yescharacteristic
197C2×C4#6700211yescharacteristic
198C2×C4#6700411yescharacteristic
199C8—22no—
200C8—22no—
201C8—882no—
202C8—882no—
203C22—22no—
204C22—82no—
205C22—84no—
206C22—162no—
207C22—162no—
208C22#1062256611yescharacteristic
209C22#1062266811yescharacteristic
210C22#1062268311yescharacteristic
211C4—22no—
212C4—22no—
213C4—161no—
214C4#1062262811yescharacteristic
215C4#1062263211yescharacteristic
216C4#1062264611yescharacteristic
217C4#1062264711yescharacteristic
218C2—21no—
219C2—21no—
220C2—162no—
221C2#1307001911yescharacteristic
222C2#1307007312yes—
subgroupG/H
centerC22#10622566
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1961C2
socleC22×C11#397
prime radicalC2×C11×#127C22
hypercenter#1961D11
hypocenterC11#10631
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #13068791C2semidirect
3. #13066474C2semidirect
4. #13066461C2semidirect
176. C11#10631semidirect

Maximal subgroups

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

subgroupindex
#130687912
#130672842
#130664742
#130664612
C11×#19612
#1063111