Finite Group Databasebeta

← #14673873

Subgroups — #14673873

Order 2816.

346 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10622132C212yesmaximal, complemented
2C2×#10622204C212yesmaximal
3#13068773C211yesmaximal, characteristic, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C11×#1974C211yesmaximal, characteristic
6C2×C11×#135C2211yescharacteristic
7C2×C11×#108C2211yescharacteristic
8C2×C11×#104—21no—
9C11×#408—21no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66881—21no—
12C2×#66881C2212yes—
13C2×#66876C2212yes—
14#10622548—21no—
15#10622204—24no—
16#10622132—24no—
17C2×C11×#41—21no—
18C11×#135—22no—
19C11×#135—22no—
20C2×C11×Q16Q811yescharacteristic
21C2×C11×SD16—21no—
22C2×C11×D8Q811yescharacteristic
23C2×C11×M16—21no—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—42no—
29C11×#108—22no—
30C11×#104—42no—
31C11×C22⋊C8—42no—
32C4×C8×C11—22no—
33#66881—22no—
34#66881—22no—
35#66881—42no—
36#66876—22no—
37#66876D414yes—
38C2×C11⋊C16—22no—
39#13533—111nomaximal, Sylow
40C11×#41—41no—
41C11×#41—41no—
42C11×#41—41no—
43C11×#41—41no—
44C2×Q8×C11—21no—
45C2×D4×C11—21no—
46C2×D4×C11—41no—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×Dic11—42no—
51C11×Q16—22no—
52C11×SD16—42no—
53C11×D8—22no—
54C11×M16—41no—
55C11×M16—41no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11SD1612yes—
60C2×C8×C11C2×D412yes—
61C2×C8×C11C2×Q811yescharacteristic
62C2×C8×C11#4111yescharacteristic
63C2×C8×C11#4112yes—
64C42×C11—21no—
65C42×C11SD1612yes—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—84no—
69C11⋊C16—24no—
70C2×#365—112no—
71C2×#360—112no—
72#1974D1111yescharacteristic
73#1844—111no—
74#1376—111no—
75C23×C11—41no—
76C23×C11AGL(1,ℤ/8)11yescharacteristic
77Q8×C11—41no—
78Q8×C11—41no—
79D4×C11—41no—
80D4×C11—41no—
81D4×C11—81no—
82D4×C11—81no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11—41no—
86C2×C4×C11—81no—
87C2×C4×C11—81no—
88C2×C4×C11C22⋊Q811yescharacteristic
89C2×C4×C11#12311yescharacteristic
90C2×C4×C11#12711yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C2×C4×C11C2×SD1611yescharacteristic
93C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
94C2×Dic11—84no—
95C2×Dic11—82no—
96C8×C11—22no—
97C8×C11—81no—
98C8×C11C22⋊Q812yes—
99C8×C11#12312yes—
100C2×#135C2×D1111yescharacteristic
101C2×M32—112no—
102C2×#108C2×D1111yescharacteristic
103C2×#106—112no—
104C2×#106—221no—
105C2×#104—21no—
106#408—21no—
107C2×C4×C8C2×D1111yescharacteristic
108#384—221no—
109#365—224no—
110#360—224no—
111C22×C11—22no—
112C22×C11—81no—
113C22×C11—82no—
114C22×C11#47611yescharacteristic
115C22×C11#48111yescharacteristic
116C22×C11#49611yescharacteristic
117C4×C11—24no—
118C4×C11—81no—
119C4×C11#39911yescharacteristic
120C4×C11#47611yescharacteristic
121C4×C11#48111yescharacteristic
122C4×C11#49211yescharacteristic
123Dic11—162no—
124C2×#41—21no—
125#135—22no—
126#135—22no—
127C2×Q16Dic2211yescharacteristic
128C2×SD16—21no—
129C2×D8Dic2211yescharacteristic
130C2×M16—21no—
131C22×C8C22⋊D1111yescharacteristic
132C22×C8C22×D1111yescharacteristic
133C2×C4⋊C4—222no—
134C2×C4⋊C4—442no—
135C2×C42C22⋊D1111yescharacteristic
136M32—114no—
137M32—222no—
138C2×C16—222no—
139#108—22no—
140#106—222no—
141#106—222no—
142#106—442no—
143#104—42no—
144C22⋊C8—42no—
145C4×C8—22no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11—161no—
149C2×C11#209411yescharacteristic
150C2×C11#223012yes—
151#41—41no—
152#41—41no—
153#41—41no—
154#41—41no—
155C2×Q8—21no—
156C2×D4—21no—
157C2×D4—41no—
158C22×C4—21no—
159C22×C4—41no—
160C22×C4—442no—
161C22×C4C2×C22⋊D1111yescharacteristic
162Q16—22no—
163SD16—42no—
164D8—22no—
165M16—41no—
166M16—41no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8#432412yes—
171C2×C8C2×Dic2211yescharacteristic
172C2×C8#433911yescharacteristic
173C2×C8D4×D1112yes—
174C2×C8#434112yes—
175C4⋊C4—442no—
176C4⋊C4—442no—
177C4⋊C4—884no—
178C42—21no—
179C42#432412yes—
180C16—224no—
181C11#1353311yescharacteristic, complemented, Sylow
182C23—41no—
183C23#6700211yescharacteristic
184Q8—41no—
185Q8—41no—
186D4—41no—
187D4—41no—
188D4—81no—
189D4—81no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—884no—
196C2×C4—882no—
197C2×C4#6697711yescharacteristic
198C2×C4C2×#432411yescharacteristic
199C2×C4C2×#432411yescharacteristic
200C2×C4#6698811yescharacteristic
201C2×C4#6699311yescharacteristic
202C2×C4#6700211yescharacteristic
203C8—22no—
204C8—81no—
205C8#6693112yes—
206C8#6693612yes—
207C22—22no—
208C22—81no—
209C22—82no—
210C22#1062262111yescharacteristic
211C22#1062264711yescharacteristic
212C22#1062267111yescharacteristic
213C4—24no—
214C4—81no—
215C4—1762no—
216C4#1062256211yescharacteristic
217C4#1062262111yescharacteristic
218C4#1062264711yescharacteristic
219C4#1062268911yescharacteristic
220C2—21no—
221C2—21no—
222C2—161no—
223C2#1307014911yescharacteristic
224C2#1307078712yes—
subgroupG/H
centerC22#10622621
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1974C2
socleC22×C11#476
prime radicalC2×C11×#135C22
hypercenter#1974D11
hypocenterC11#13533
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
1. C2×#10622132C2semidirect
3. #13068773C2semidirect
4. #13066698C2semidirect
181. C11#13533semidirect

Maximal subgroups

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

subgroupindex
C2×#106221322
C2×#106222042
#130687732
#130666982
C11×#19742
#1353311