Finite Group Databasebeta

← #14666615

Subgroups — #14666615

Order 2816.

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

normal subgroups only

This group has 380 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#13076609C211yesmaximal, characteristic
2#13067590C212yesmaximal
3#13066645C212yesmaximal
4#13066550C211yesmaximal, characteristic
5C11×#2028C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C11×#419—21no—
8C11×#391C2211yescharacteristic
9#10622843—21no—
10#10622663—22no—
11#10622592C2212yes—
12#10622542—21no—
13#10622269—22no—
14#10622259—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—21no—
21C22×Dic22D412yes—
22C2×C11×M16—21no—
23C11×C4⋊Q8—41no—
24C11×#125—41no—
25C11×C22⋊Q8—22no—
26C11×#117—21no—
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×#4326—42no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—21no—
34C11×#103—41no—
35C11×#103—41no—
36C11×#95—22no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41C22⋊(C11⋊C8)—22no—
42#66874—42no—
43#12224—111nomaximal, Sylow
44C2×Q8×C11—21no—
45C2×Q8×C11—22no—
46C2×Q8×C11—41no—
47C2×Q8×C11—41no—
48C2×Q8×C11Q1612yescomplemented
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C2×Dic22—24no—
56C2×Dic22—42no—
57C2×Dic22—82no—
58C2×Dic22—81no—
59C2×Dic22—81no—
60C11×M16—41no—
61C11×M16—41no—
62C2×C8×C11—41no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—42no—
68C11×C22⋊C4—41no—
69C42×C11—41no—
70C42×C11—41no—
71#4326—84no—
72C4⋊Dic11—81no—
73C4⋊Dic11—81no—
74Dic11⋊C4—82no—
75C4×Dic11—81no—
76C2×C11⋊C8—42no—
77#2811—111no—
78#2028D1111yescharacteristic
79#1605—112no—
80#1354—112no—
81#1319—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—42no—
84Q8×C11—81no—
85Q8×C11—82no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11C2×Q1611yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C2×Dic11—24no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106Dic22—44no—
107Dic22—84no—
108Dic22—82no—
109C8×C11—81no—
110C11⋊C8—82no—
111#544C2×D1111yescharacteristic
112#451—222no—
113#419—21no—
114#395—112no—
115#395—222no—
116#391—222no—
117#391—221no—
118#391—221no—
119#391C2×D1111yescharacteristic
120#343C2×D1111yescharacteristic
121#339—21no—
122#328—222no—
123#324—112no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11#45111yescharacteristic
127C22×C11#45511yescharacteristic
128C22×C11B(4,𝔽2)11yescharacteristic
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—42no—
132C4×C11—42no—
133C4×C11—42no—
134C4×C11—81no—
135C4×C11—81no—
136Dic11—44no—
137Dic11—82no—
138C22×Q8—112no—
139C22×Q8—221no—
140C22×Q8C22⋊D1111yescharacteristic
141C2×Q16—442no—
142C2×M16—21no—
143C4⋊Q8—41no—
144#125—41no—
145C22⋊Q8—22no—
146#117—21no—
147C2×C4⋊C4—221no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4C22×D1111yescharacteristic
151C2×C42—221no—
152C2×C42C22⋊D1111yescharacteristic
153#103—41no—
154#103—41no—
155#103—442no—
156C22⋊C8—222no—
157#95—22no—
158#95—112no—
159#95—222no—
160#95—222no—
161#95—222no—
162C2×C11—21no—
163C2×C11—21no—
164C2×C11#160211yescharacteristic
165C2×C11#219911yescharacteristic
166C2×C11#220511yescharacteristic
167C2×Q8—21no—
168C2×Q8—22no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—224no—
172C2×Q8—442no—
173C2×Q8—882no—
174C2×Q8—881no—
175C2×Q8—881no—
176C2×Q8#432612yescomplemented
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4D4×D1112yes—
182C22×C4C2×C22⋊D1111yescharacteristic
183Q16—884no—
184M16—41no—
185M16—41no—
186C2×C8—41no—
187C2×C8—442no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—882no—
194C4⋊C4—881no—
195C4⋊C4—881no—
196C22⋊C4—41no—
197C42—41no—
198C42—41no—
199C42—881no—
200C11#1222411yescharacteristic, complemented, Sylow
201C23#6699011yescharacteristic
202Q8—42no—
203Q8—81no—
204Q8—82no—
205Q8—444no—
206Q8—884no—
207Q8—882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—224no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4C2×#432611yescharacteristic
227C2×C4#6700411yescharacteristic
228C8—81no—
229C8—882no—
230C22—21no—
231C22—21no—
232C22#1062264511yescharacteristic
233C22#1062266311yescharacteristic
234C22#1062267411yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—81no—
241C4—81no—
242C4—444no—
243C4—882no—
244C2—21no—
245C2—21no—
246C2#1306757211yescharacteristic
247C2#1307061611yescharacteristic
248C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2028C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2028D11
hypocenterC11#12224
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
48. C2×Q8×C11Q16semidirect
176. C2×Q8#4326semidirect
200. C11#12224semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130675902
#130666452
#130665502
C11×#20282
#1222411