Finite Group Databasebeta

← #14673883

Subgroups — #14673883

Order 2816.

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

normal subgroups only

This group has 354 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×#10622125C212yesmaximal, complemented
2C2×#10622201C212yesmaximal
3#13068791C211yesmaximal, characteristic, 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—
16#10622125—24no—
17C22×D4×C11—21no—
18C2×C11×D8—22no—
19C2×C11×D8—22no—
20C2×C11×D8—21no—
21C2×C11×D8Q812yes—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C2×C11×C4⋊C4—21no—
25C2×C11×C22⋊C4—42no—
26C2×C42×C11D411yescharacteristic
27C2×#4318—22no—
28C11×#106—22no—
29C11×#102—42no—
30C11×#97—22no—
31#66883—22no—
32#66883—22no—
33#66883—42no—
34#66876—22no—
35#66876D414yes—
36C2×C11⋊C16—22no—
37C4⋊(C11⋊C8)—42no—
38#13535—111nomaximal, Sylow
39C24×C11—41no—
40C2×D4×C11—22no—
41C2×D4×C11—41no—
42C2×D4×C11—41no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C2×D4×C11—41no—
46C22×C4×C11—41no—
47C22×C4×C11SD1612yes—
48C22×C4×C11C2×D411yescharacteristic
49C11×D8—24no—
50C11×D8—42no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11SD1612yes—
54C2×C8×C11C2×D412yes—
55C2×C8×C11C2×Q811yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C2×C8×C11#4112yes—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C11×C22⋊C4—84no—
61C42×C11—21no—
62C42×C11—21no—
63#4318—42no—
64#4318—42no—
65C2×C11⋊C8—42no—
66C11⋊C16—24no—
67C2×#365—112no—
68C2×#361—112no—
69#1972D1111yescharacteristic
70#1849—111no—
71#1377—111no—
72C23×C11—42no—
73C23×C11—82no—
74C23×C11—82no—
75C23×C11—81no—
76C23×C11—81no—
77C23×C11C2×SD1611yescharacteristic
78D4×C11—42no—
79D4×C11—42no—
80D4×C11—81no—
81D4×C11—81no—
82C2×C4×C11—22no—
83C2×C4×C11—42no—
84C2×C4×C11—82no—
85C2×C4×C11—81no—
86C2×C4×C11C22⋊Q811yescharacteristic
87C2×C4×C11#12311yescharacteristic
88C2×C4×C11#12711yescharacteristic
89C2×C4×C11C2×SD1611yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
92C8×C11—22no—
93C8×C11C22⋊Q812yes—
94C8×C11#12312yes—
95C11⋊C8—82no—
96C22×D8C2×D1111yescharacteristic
97C2×M32—112no—
98C2×#108—112no—
99C2×#108—221no—
100C2×#106C2×D1111yescharacteristic
101#423—221no—
102C2×#102—21no—
103C2×#97C2×D1111yescharacteristic
104#390—21no—
105#365—224no—
106#361—224no—
107C22×C11—22no—
108C22×C11—84no—
109C22×C11—82no—
110C22×C11—161no—
111C22×C11—161no—
112C22×C11—162no—
113C22×C11#47611yescharacteristic
114C22×C11#48111yescharacteristic
115C22×C11#49211yescharacteristic
116C4×C11—42no—
117C4×C11—161no—
118C4×C11#39911yescharacteristic
119C4×C11#47611yescharacteristic
120C4×C11#48111yescharacteristic
121C4×C11#49611yescharacteristic
122C22×D4—21no—
123C2×D8—21no—
124C2×D8—22no—
125C2×D8—22no—
126C2×D8Dic2212yes—
127C2×M16—222no—
128C22×C8C22⋊D1111yescharacteristic
129C22×C8C22×D1111yescharacteristic
130C2×C4⋊C4—21no—
131C2×C22⋊C4—42no—
132C2×C42C22⋊D1111yescharacteristic
133M32—114no—
134M32—222no—
135C2×C16—222no—
136#108—222no—
137#108—222no—
138#108—442no—
139#106—22no—
140C4⋊C8—442no—
141#102—42no—
142#97—22no—
143C2×C11—21no—
144C2×C11—21no—
145C2×C11—162no—
146C2×C11#209411yescharacteristic
147C2×C11#223812yes—
148C24—41no—
149C2×D4—22no—
150C2×D4—41no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155C22×C4—41no—
156C22×C4#432412yes—
157C22×C4C2×C22⋊D1111yescharacteristic
158D8—24no—
159D8—42no—
160M16—442no—
161M16—442no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—442no—
165C2×C8#432412yes—
166C2×C8C2×Dic2211yescharacteristic
167C2×C8#433911yescharacteristic
168C2×C8D4×D1112yes—
169C2×C8#434112yes—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C22⋊C4—84no—
173C42—21no—
174C42—21no—
175C16—224no—
176C11#1353511yescharacteristic, complemented, Sylow
177C23—42no—
178C23—82no—
179C23—82no—
180C23—81no—
181C23—81no—
182C23C2×#432411yescharacteristic
183D4—42no—
184D4—42no—
185D4—81no—
186D4—81no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4#6697711yescharacteristic
192C2×C4C2×#432411yescharacteristic
193C2×C4#6698811yescharacteristic
194C2×C4#6699311yescharacteristic
195C2×C4#6700211yescharacteristic
196C2×C4#6700211yescharacteristic
197C8—22no—
198C8—882no—
199C8#6693112yes—
200C8#6693612yes—
201C22—22no—
202C22—84no—
203C22—82no—
204C22—161no—
205C22—161no—
206C22—162no—
207C22#1062262111yescharacteristic
208C22#1062264711yescharacteristic
209C22#1062268911yescharacteristic
210C4—42no—
211C4—161no—
212C4#1062256211yescharacteristic
213C4#1062262111yescharacteristic
214C4#1062264711yescharacteristic
215C4#1062267111yescharacteristic
216C2—21no—
217C2—21no—
218C2—162no—
219C2#1307014911yescharacteristic
220C2#1307082812yes—
subgroupG/H
centerC22#10622647
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1972C2
socleC22×C11#481
prime radicalC22×C11×D8C22
hypercenter#1972D11
hypocenterC11#13535
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
1. C2×#10622125C2semidirect
3. #13068791C2semidirect
4. #13066700C2semidirect
176. C11#13535semidirect

Maximal subgroups

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

subgroupindex
C2×#106221252
C2×#106222012
#130687912
#130667002
C11×#19722
#1353511