Finite Group Databasebeta

← #14667648

Subgroups — #14667648

Order 2816.

288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081620C211yesmaximal, characteristic
2#13070755C211yesmaximal, characteristic
3#13068007C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic
5#13066596C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×#2241C211yesmaximal, characteristic
8#10623252—21no—
9C11×#500C2211yescharacteristic
10C11×#494C2211yescharacteristic
11Q16×Dic11—21no—
12#10622795—22no—
13#10622794—21no—
14#10622703—21no—
15#10622703—21no—
16C4×Dic44C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C11×#358—22no—
19C4×C11×C16C2211yescharacteristic
20#10622185—21no—
21#10622130—21no—
22#10622128—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29Q8×Dic11—22no—
30#66997—22no—
31C2×#4326—22no—
32C2×#4326—41no—
33C2×Dic44D411yescharacteristic
34#66943—41no—
35#66942—42no—
36#66940—41no—
37C4×Dic22—21no—
38C4×Dic22D411yescharacteristic
39C2×C11×C16—21no—
40C11×#107—21no—
41C11×#107—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—22no—
44#66899—41no—
45#66882D411yescharacteristic
46#66880—21no—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12382—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11—41no—
55C2×Dic22—21no—
56C2×Dic22D811yescharacteristic
57C11×Q16—41no—
58C11×Q16—41no—
59C11×Q16—42no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C42×C11C2×D411yescharacteristic
67#4326—82no—
68#4326—82no—
69C4⋊Dic11—21no—
70C4⋊Dic11—42no—
71C4⋊Dic11D811yescharacteristic
72Dic11⋊C4—21no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75Dic11⋊C4—41no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C4×Dic11—41no—
79C2×C11⋊C8—21no—
80C2×C11⋊C8—41no—
81Dic44—21no—
82Dic44—21no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3395—111no—
86#2241D1111yescharacteristic
87#2225—111no—
88#1674—111no—
89#1362—111no—
90Q8⋊C16—111no—
91#1332—111no—
92Q8×C11—42no—
93Q8×C11—42no—
94Q8×C11—81no—
95Q8×C11—81no—
96C2×C4×C11—42no—
97C2×C4×C11—81no—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—41no—
104C2×Dic11—41no—
105Dic22—21no—
106Dic22—41no—
107Dic22—41no—
108Dic22SD3212yes—
109C8×C11—21no—
110C8×C11#13511yescharacteristic
111C8×C11#13711yescharacteristic
112C11⋊C8—41no—
113C11⋊C8—81no—
114#557—221no—
115#500C2×D1111yescharacteristic
116#494—221no—
117#494C2×D1111yescharacteristic
118#462—221no—
119#462—222no—
120#462—221no—
121C8×Q8—111no—
122C4×Q16—111no—
123C4×Q16—221no—
124#367—221no—
125C4⋊C16—111no—
126#358—22no—
127#358—221no—
128C4×C16C2×D1111yescharacteristic
129#335—111no—
130#332—221no—
131C22×C11#44711yescharacteristic
132C4×C11—21no—
133C4×C11—82no—
134C4×C11—161no—
135C4×C11#45211yescharacteristic
136C4×C11#45511yescharacteristic
137C4×C11C2×SD3211yescharacteristic
138C4×C11#51011yescharacteristic
139Dic11—22no—
140Dic11—41no—
141Dic11—81no—
142Dic11—81no—
143C2×Q16—21no—
144C2×Q16—111no—
145C2×Q16—222no—
146C2×Q16—441no—
147C2×Q16C22⋊D1112yes—
148C4⋊Q8—21no—
149C4⋊Q8—21no—
150C4⋊Q8—222no—
151#125—441no—
152#125—442no—
153C4×Q8—111no—
154C4×Q8—222no—
155C4×Q8—221no—
156C4×Q8—441no—
157C2×C16—21no—
158C2×C16—221no—
159#107—21no—
160#107—21no—
161#107—111no—
162C4⋊C8—111no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#103—222no—
166#103—221no—
167#103—441no—
168C4×C8—221no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#164111yescharacteristic
171C2×C11#218511yescharacteristic
172C2×C11#219511yescharacteristic
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—111no—
176C2×Q8—221no—
177Q16—42no—
178Q16—41no—
179Q16—41no—
180Q16—221no—
181Q16—221no—
182Q16—882no—
183Q16—882no—
184C2×C8—221no—
185C2×C8—441no—
186C2×C8D4×D1111yescharacteristic
187C2×C8C2×C22⋊D1111yescharacteristic
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—111no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—441no—
199C42—221no—
200C42—442no—
201C42—441no—
202C42D4×D1111yescharacteristic
203C16—41no—
204C16—441no—
205C11#1238211yescharacteristic, complemented, Sylow
206Q8—42no—
207Q8—42no—
208Q8—81no—
209Q8—81no—
210Q8—112no—
211Q8—221no—
212Q8—441no—
213Q8—441no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4D8×D1111yescharacteristic
221C2×C4#6696411yescharacteristic
222C2×C4#6699011yescharacteristic
223C8—21no—
224C8—441no—
225C8—881no—
226C8#6696811yescharacteristic
227C8#6696911yescharacteristic
228C22#1062276911yescharacteristic
229C4—21no—
230C4—82no—
231C4—161no—
232C4—222no—
233C4—441no—
234C4—881no—
235C4—881no—
236C4D11×SD3211yescharacteristic
237C4#1062252811yescharacteristic
238C4#1062267411yescharacteristic
239C4#1062278611yescharacteristic
240C2#1306780611yescharacteristic
241C2#1307053111yescharacteristic
242C2#1307059311yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2241C2
socle, prime radicalC22×C11#447
hypercenter#2241D11
hypocenterC11#12382
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

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
#130816202
#130707552
#130680072
#130666652
#130665962
#130665812
C11×#22412
#1238211