Finite Group Databasebeta

← #14667653

Subgroups — #14667653

Order 2816.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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#13081622C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic
3#13070759C211yesmaximal, characteristic
4#13068010C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×Q8⋊C16C211yesmaximal, characteristic
8#10623101—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622644—21no—
11#10622462—22no—
12#10622462—21no—
13#10622312—21no—
14#10622312C2211yescharacteristic
15C4×Dic44—21no—
16C4×Dic44C2211yescharacteristic
17#10622295C2211yescharacteristic
18C11×C4⋊C16C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20#10622143—21no—
21#10622141—21no—
22#10622141—22no—
23#10622124—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×#4326—41no—
28C2×Dic44—21no—
29C2×Dic44—22no—
30C2×Dic44D411yescharacteristic
31C2×Dic44D412yes—
32#66943—42no—
33#66943—41no—
34#66922—22no—
35#66922—21no—
36#66922—21no—
37C4×Dic22—22no—
38C4×Dic22—21no—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C4×C8×C11—21no—
44C4×C8×C11C2311yescharacteristic
45#66882—21no—
46#66882—21no—
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66874—41no—
51C4⋊(C11⋊C8)—21no—
52#12382—111nomaximal, Sylow
53C2×Q8×C11D811yescharacteristic
54C2×Dic22—21no—
55C2×Dic22—22no—
56C2×Dic22—41no—
57C2×C8×C11—21no—
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—21no—
61C11×C4⋊C4D811yescharacteristic
62C42×C11—21no—
63C42×C11C2×D411yescharacteristic
64#4326—82no—
65C4⋊Dic11—21no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72Dic11⋊C4—42no—
73Dic11⋊C4—41no—
74C4×Dic11—42no—
75C4×Dic11—41no—
76C2×C11⋊C8—41no—
77Dic44—21no—
78Dic44—21no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82Dic44—82no—
83C11×C16—41no—
84C11×C16—41no—
85#3395—111no—
86#2241—111no—
87#2225—111no—
88#1674—111no—
89#1362—111no—
90Q8⋊C16D1111yescharacteristic
91#1332—111no—
92Q8×C11—21no—
93Q8×C11SD3212yes—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—41no—
102C2×Dic11—81no—
103Dic22—41no—
104Dic22—42no—
105Dic22—42no—
106Dic22—41no—
107Dic22—81no—
108Dic22—81no—
109C8×C11—21no—
110C8×C11—41no—
111C8×C11#13511yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—81no—
114#557—221no—
115#500—111no—
116#494—111no—
117#494—221no—
118#462—222no—
119#462—221no—
120#462—221no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—111no—
123C4×Q16—221no—
124#367—221no—
125C4⋊C16C2×D1111yescharacteristic
126#358—221no—
127#358—222no—
128C4×C16C2×D1111yescharacteristic
129#335—111no—
130#332—221no—
131C22×C11#44711yescharacteristic
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11#45211yescharacteristic
136C4×C11#45511yescharacteristic
137C4×C11C2×SD3211yescharacteristic
138C4×C11#51011yescharacteristic
139Dic11—81no—
140Dic11—82no—
141Dic11—81no—
142Dic11—161no—
143C2×Q16—111no—
144C2×Q16—112no—
145C2×Q16—222no—
146C2×Q16—221no—
147C2×Q16—441no—
148C4⋊Q8—222no—
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151#125—442no—
152#125—441no—
153C4×Q8—222no—
154C4×Q8—221no—
155C4×Q8—441no—
156C4×Q8D4411yescharacteristic
157C2×C16—21no—
158C2×C16—21no—
159#107—111no—
160#107—221no—
161#107—221no—
162C4⋊C8—21no—
163C4⋊C8—221no—
164C4⋊C8D4411yescharacteristic
165#103—222no—
166#103—221no—
167#103—441no—
168C4×C8—21no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#164111yescharacteristic
171C2×C11#218511yescharacteristic
172C2×C11#219511yescharacteristic
173C2×Q8—221no—
174C2×Q8—222no—
175C2×Q8—441no—
176C2×Q8D8811yescharacteristic
177Q16—221no—
178Q16—221no—
179Q16—442no—
180Q16—441no—
181Q16—441no—
182Q16—882no—
183Q16—882no—
184C2×C8—21no—
185C2×C8—441no—
186C2×C8D4×D1111yescharacteristic
187C2×C8D4×D1111yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—221no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4D8811yescharacteristic
199C42—21no—
200C42—442no—
201C42—441no—
202C42C2×D4411yescharacteristic
203C16—41no—
204C16—41no—
205C11#1238211yescharacteristic, complemented, Sylow
206Q8—21no—
207Q8—441no—
208Q8—442no—
209Q8—442no—
210Q8—441no—
211Q8—881no—
212Q8—881no—
213Q8#6686412yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—441no—
217C2×C4—442no—
218C2×C4—441no—
219C2×C4—881no—
220C2×C4#6693511yescharacteristic
221C2×C4C2×D8811yescharacteristic
222C2×C4#6696111yescharacteristic
223C8—21no—
224C8—41no—
225C8—881no—
226C8#6696911yescharacteristic
227C8#6697111yescharacteristic
228C22#1062234511yescharacteristic
229C4—21no—
230C4—22no—
231C4—41no—
232C4—881no—
233C4—881no—
234C4—882no—
235C4—1761no—
236C4#1062242311yescharacteristic
237C4#1062243811yescharacteristic
238C4C2×#6686411yescharacteristic
239C4#1062252211yescharacteristic
240C2#1306781111yescharacteristic
241C2#1307053511yescharacteristic
242C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socle, prime radicalC22×C11#447
hypercenterQ8⋊C16D11
hypocenterC11#12382
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
205. C11#12382semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708442
#130707592
#130680102
#130666662
#130665812
C11×Q8⋊C162
#1238211