Finite Group Databasebeta

← #14673598

Subgroups — #14673598

Order 2816.

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

normal subgroups only

This group has 338 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
1C2×#10622201C212yesmaximal
2#13068791C211yesmaximal, characteristic, complemented
3#13066714C212yesmaximal, complemented
4#13066700C211yesmaximal, characteristic, complemented
5C11×#1972C211yesmaximal, characteristic
6C22×C11×D8C2211yescharacteristic
7C2×C11×#106C2211yescharacteristic
8C2×C11×#102—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#390—21no—
11C2×#66883—21no—
12C2×#66883C2212yes—
13C2×#66876C2212yes—
14#10622537—21no—
15#10622201—24no—
16C22×D4×C11—21no—
17C2×C11×D8—22no—
18C2×C11×D8—22no—
19C2×C11×D8—21no—
20C2×C11×D8D412yes—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C11×C4⋊C4—21no—
24C2×C11×C22⋊C4—42no—
25C2×C42×C11D411yescharacteristic
26C2×#4318—22no—
27C11×#106—22no—
28C11×#102—42no—
29C11×#97—22no—
30#66883—22no—
31#66883—22no—
32#66883—42no—
33#66876—22no—
34#66876—22no—
35C2×C11⋊C16—22no—
36C4⋊(C11⋊C8)—42no—
37#13487—111nomaximal, Sylow
38C24×C11—41no—
39C2×D4×C11—22no—
40C2×D4×C11—41no—
41C2×D4×C11—41no—
42C2×D4×C11—41no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11SD1612yes—
47C22×C4×C11C2×D411yescharacteristic
48C11×D8—24no—
49C11×D8—42no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11D812yes—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C2×C8×C11#4112yes—
56C2×C8×C11#4112yes—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C11×C22⋊C4—84no—
60C42×C11—21no—
61C42×C11—21no—
62#4318—42no—
63#4318—42no—
64C2×C11⋊C8—42no—
65C11⋊C16—42no—
66C2×#361—112no—
67#1972D1111yescharacteristic
68#1849—111no—
69#1383—112no—
70#1377—111no—
71C23×C11—42no—
72C23×C11—82no—
73C23×C11—82no—
74C23×C11—81no—
75C23×C11—81no—
76C23×C11C2×SD1611yescharacteristic
77D4×C11—42no—
78D4×C11—42no—
79D4×C11—81no—
80D4×C11—81no—
81C2×C4×C11—22no—
82C2×C4×C11—42no—
83C2×C4×C11—82no—
84C2×C4×C11—81no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11#12311yescharacteristic
87C2×C4×C11#12411yescharacteristic
88C2×C4×C11C2×D811yescharacteristic
89C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
90C2×C4×C11#13711yescharacteristic
91C8×C11—22no—
92C8×C11#12312yes—
93C8×C11#12612yes—
94C11⋊C8—82no—
95C22×D8C2×D1111yescharacteristic
96C2×M32—112no—
97C2×#108—112no—
98C2×#108—221no—
99C2×#106C2×D1111yescharacteristic
100#423—221no—
101C2×#102—21no—
102C2×#97C2×D1111yescharacteristic
103#390—21no—
104#361—224no—
105C22×C11—22no—
106C22×C11—84no—
107C22×C11—82no—
108C22×C11—161no—
109C22×C11—161no—
110C22×C11—162no—
111C22×C11#46111yescharacteristic
112C22×C11#48111yescharacteristic
113C22×C11#48611yescharacteristic
114C4×C11—42no—
115C4×C11—161no—
116C4×C11#39711yescharacteristic
117C4×C11#45911yescharacteristic
118C4×C11#48011yescharacteristic
119C4×C11#48911yescharacteristic
120C22×D4—21no—
121C2×D8—21no—
122C2×D8—22no—
123C2×D8—22no—
124C2×D8D4412yes—
125C2×M16—222no—
126C22×C8C22⋊D1111yescharacteristic
127C22×C8C22×D1111yescharacteristic
128C2×C4⋊C4—21no—
129C2×C22⋊C4—42no—
130C2×C42C22⋊D1111yescharacteristic
131M32—222no—
132M32—222no—
133C2×C16—222no—
134#108—222no—
135#108—222no—
136#108—442no—
137#106—22no—
138C4⋊C8—442no—
139#102—42no—
140#97—22no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11—162no—
144C2×C11#207111yescharacteristic
145C2×C11#223812yes—
146C24—41no—
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C2×D4—41no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4—41no—
154C22×C4#432412yes—
155C22×C4C2×C22⋊D1111yescharacteristic
156D8—24no—
157D8—42no—
158M16—442no—
159M16—442no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—442no—
163C2×C8#432312yes—
164C2×C8C2×D4411yescharacteristic
165C2×C8#433911yescharacteristic
166C2×C8#434112yes—
167C2×C8#434112yes—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C22⋊C4—84no—
171C42—21no—
172C42—21no—
173C16—442no—
174C11#1348711yescharacteristic, complemented, Sylow
175C23—42no—
176C23—82no—
177C23—82no—
178C23—81no—
179C23—81no—
180C23C2×#432411yescharacteristic
181D4—42no—
182D4—42no—
183D4—81no—
184D4—81no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—82no—
188C2×C4—81no—
189C2×C4#6698311yescharacteristic
190C2×C4C2×#432311yescharacteristic
191C2×C4#6698811yescharacteristic
192C2×C4#6698911yescharacteristic
193C2×C4#6700211yescharacteristic
194C2×C4#6700411yescharacteristic
195C8—22no—
196C8—882no—
197C8#6693212yes—
198C8#6693912yes—
199C22—22no—
200C22—84no—
201C22—82no—
202C22—161no—
203C22—161no—
204C22—162no—
205C22#1062263211yescharacteristic
206C22#1062264711yescharacteristic
207C22#1062268311yescharacteristic
208C4—42no—
209C4—161no—
210C4#1062256611yescharacteristic
211C4#1062262811yescharacteristic
212C4#1062264611yescharacteristic
213C4#1062266811yescharacteristic
214C2—21no—
215C2—21no—
216C2—162no—
217C2#1307001911yescharacteristic
218C2#1307082812yes—
subgroupG/H
centerC22#10622647
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1972C2
socleC22×C11#481
prime radicalC22×C11×D8C22
hypercenter#1972D11
hypocenterC11#13487
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #13068791C2semidirect
3. #13066714C2semidirect
4. #13066700C2semidirect
174. C11#13487semidirect

Maximal subgroups

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

subgroupindex
C2×#106222012
#130687912
#130667142
#130667002
C11×#19722
#1348711