Finite Group Databasebeta

← #14666252

Subgroups — #14666252

Order 2816.

350 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 59 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#13080070C211yesmaximal, characteristic, complemented
2#13070545C212yesmaximal
3#13066633C212yesmaximal, complemented
4#13066558C211yesmaximal, characteristic, complemented
5C11×#2045C211yesmaximal, characteristic
6C22×C11×D8C2211yescharacteristic
7#10623049—21no—
8C11×#424C2211yescharacteristic
9C11×#418—21no—
10C2×C11×#100—21no—
11C2×#66891—22no—
12#10622750—21no—
13#10622729C2212yes—
14#10622462—22no—
15#10622442—22no—
16C11×#341C2211yescharacteristic
17#10622200—22no—
18C22⋊(C11⋊C16)C2212yes—
19C22×D4×C11—21no—
20C2×C11×D8—22no—
21C2×C11×D8—42no—
22C2×C11×M16—21no—
23C2×C11×M16D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C11×#117D411yescharacteristic
26#66977—22no—
27C2×Dic44—21no—
28C2×Dic44D412yes—
29#66942—42no—
30#66932—42no—
31#66923—21no—
32#66922—21no—
33C4×Dic22—22no—
34C11×C4⋊C8—22no—
35C11×#102—42no—
36C11×#100—42no—
37#66891—44no—
38#66882D412yes—
39#66881—21no—
40#66880—22no—
41#66880—22no—
42C2×C11⋊C16—22no—
43#12165—111nomaximal, Sylow
44C24×C11—41no—
45C2×D4×C11—22no—
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C22×C4×C11C2×D411yescharacteristic
52C2×Dic22—22no—
53C11×D8—24no—
54C11×D8—42no—
55C11×M16—41no—
56C11×M16—41no—
57C11×M16—41no—
58C2×C8×C11—21no—
59C2×C8×C11—41no—
60C2×C8×C11—41no—
61C2×C8×C11C2×D412yes—
62C11×C4⋊C4D812yes—
63C11×C22⋊C4—21no—
64C42×C11—21no—
65C22⋊Dic11—42no—
66C4⋊Dic11—22no—
67C4⋊Dic11—42no—
68Dic11⋊C4—42no—
69Dic11⋊C4—42no—
70Dic11⋊C4—42no—
71C4×Dic11—42no—
72Dic44—42no—
73Dic44—81no—
74C11⋊C16—42no—
75#3261—111no—
76#2187—112no—
77#2045D1111yescharacteristic
78#1350—112no—
79#1323—111no—
80C23×C11—42no—
81C23×C11—81no—
82C23×C11—81no—
83C23×C11—162no—
84C23×C11AGL(1,ℤ/8)11yescharacteristic
85D4×C11—42no—
86D4×C11—42no—
87D4×C11—81no—
88D4×C11—81no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11C2×D811yescharacteristic
94C2×Dic11—42no—
95C2×Dic11—42no—
96Dic22—42no—
97Dic22—42no—
98C8×C11—22no—
99C8×C11—41no—
100C8×C11—81no—
101C22×D8C2×D1111yescharacteristic
102#541—221no—
103C2×SD32—222no—
104#479—222no—
105#470—221no—
106#467—112no—
107#462—222no—
108#424C2×D1111yescharacteristic
109#418—21no—
110C2×#100—21no—
111#357—222no—
112C22⋊C16—112no—
113#341C2×D1111yescharacteristic
114C22×C11—21no—
115C22×C11—22no—
116C22×C11—82no—
117C22×C11—162no—
118C22×C11—162no—
119C22×C11—162no—
120C22×C11#44711yescharacteristic
121C4×C11—21no—
122C4×C11—42no—
123C4×C11#45411yescharacteristic
124C4×C11B(4,𝔽2)11yescharacteristic
125Dic11—82no—
126Dic11—82no—
127C22×D4—21no—
128C2×Q16—112no—
129C2×Q16—221no—
130C2×D8—22no—
131C2×D8—42no—
132C2×M16—21no—
133C2×M16C22⋊D1111yescharacteristic
134C22×C8C22×D1111yescharacteristic
135C4⋊Q8—221no—
136#126—442no—
137#125—221no—
138#125—442no—
139C22⋊Q8—222no—
140C4×Q8—222no—
141#117C22⋊D1111yescharacteristic
142SD32—444no—
143C2×C16—222no—
144#107—112no—
145#106—221no—
146C4⋊C8—22no—
147#103—222no—
148#103—222no—
149#102—42no—
150#100—42no—
151C2×C11—41no—
152C2×C11—162no—
153C2×C11#159811yescharacteristic
154C2×C11#219312yes—
155C24—41no—
156C2×Q8—222no—
157C2×D4—22no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—442no—
165Q16—881no—
166D8—24no—
167D8—42no—
168M16—41no—
169M16—41no—
170M16—41no—
171C2×C8—21no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8D4×D1112yes—
175C4⋊C4—222no—
176C4⋊C4—442no—
177C4⋊C4—442no—
178C4⋊C4—442no—
179C4⋊C4—442no—
180C4⋊C4#432312yes—
181C22⋊C4—21no—
182C22⋊C4—442no—
183C42—21no—
184C42—442no—
185C16—442no—
186C11#1216511yescharacteristic, complemented, Sylow
187C23—42no—
188C23—81no—
189C23—81no—
190C23—162no—
191C23#6700211yescharacteristic
192Q8—442no—
193Q8—442no—
194D4—42no—
195D4—42no—
196D4—81no—
197D4—81no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4C2×#432311yescharacteristic
204C2×C4#6699011yescharacteristic
205C8—22no—
206C8—41no—
207C8—81no—
208C22—21no—
209C22—22no—
210C22—82no—
211C22—162no—
212C22—162no—
213C22—162no—
214C22#1062264911yescharacteristic
215C4—21no—
216C4—42no—
217C4—882no—
218C4—882no—
219C4#1062264511yescharacteristic
220C4#1062267511yescharacteristic
221C2—41no—
222C2—162no—
223C2#1306755011yescharacteristic
224C2#1307057812yes—
subgroupG/H
centerC22#10622649
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2045C2
socleC22×C11#447
prime radicalC22×C11×D8C22
hypercenter#2045D11
hypocenterC11#12165
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #2045

Complements

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

NH ≅ G/Ntype
1. #13080070C2semidirect
3. #13066633C2semidirect
4. #13066558C2semidirect
186. C11#12165semidirect

Maximal subgroups

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

subgroupindex
#130800702
#130705452
#130666332
#130665582
C11×#20452
#1216511