Finite Group Databasebeta

← #14673126

Subgroups — #14673126

Order 2816.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10622202C212yesmaximal
2C2×#10622202C212yesmaximal
3#13069349C211yesmaximal, characteristic
4#13066694C211yesmaximal, characteristic
5C2×C11×#494C211yesmaximal, characteristic
6C22×C11×Q16—21no—
7C22×C11×Q16C2212yes—
8C2×C11×C4⋊Q8—21no—
9C11×#494—24no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66882C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13C22×C11⋊C16C2212yes—
14#10622541—21no—
15#10622202—24no—
16#10622202—24no—
17#10622189—21no—
18C22×Q8×C11—22no—
19C2×C11×Q16—24no—
20C2×C11×Q16—22no—
21C2×C11×Q16—22no—
22C2×C11×Q16—22no—
23C2×C11×Q16—22no—
24C2×C11×Q16—22no—
25C2×C11×Q16—42no—
26C2×C11×Q16—42no—
27C2×C11×Q16D414yes—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×C4⋊Q8—24no—
31C11×C4⋊Q8—42no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4—41no—
34C2×C42×C11D411yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—41no—
38C4×C8×C11—22no—
39C11⋊#95—41no—
40#66882—21no—
41#66882—22no—
42#66882D412yes—
43C2×C11⋊C16—22no—
44C2×C11⋊C16—22no—
45C2×C11⋊C16—22no—
46#13409—111nomaximal, Sylow
47C2×Q8×C11—24no—
48C2×Q8×C11—42no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C22×C4×C11—42no—
54C22×C4×C11D811yescharacteristic
55C22×C4×C11D811yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C22×Dic11—41no—
59C11×Q16—24no—
60C11×Q16—24no—
61C11×Q16—48no—
62C11×Q16—42no—
63C11×Q16—42no—
64C2×C8×C11—21no—
65C2×C8×C11—21no—
66C2×C8×C11SD1612yes—
67C2×C8×C11C2×D412yes—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11#4111yescharacteristic
70C2×C8×C11#4112yes—
71C11×C4⋊C4—44no—
72C11×C4⋊C4—44no—
73C42×C11—21no—
74C42×C11—21no—
75C4⋊Dic11—22no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—82no—
80C11⋊C16—42no—
81C2×#494D1111yescharacteristic
82C2×#358—112no—
83C2×#358—112no—
84#1942—111no—
85#1374—111no—
86C23×C11C2×D811yescharacteristic
87Q8×C11—44no—
88Q8×C11—44no—
89Q8×C11—82no—
90Q8×C11—82no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—44no—
96C2×C4×C11—82no—
97C2×C4×C11—82no—
98C2×C4×C11SD3212yes—
99C2×C4×C11Q3212yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12111yescharacteristic
102C2×C4×C11#12411yescharacteristic
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×Dic11—42no—
107C2×Dic11—81no—
108C2×Dic11—81no—
109C2×Dic11—81no—
110C2×Dic11—81no—
111C2×Dic11—81no—
112C8×C11—22no—
113C8×C11#12112yes—
114C8×C11#12312yes—
115C22×Q16—21no—
116C22×Q16C2×D1112yes—
117C2×C4⋊Q8—21no—
118C22×C16—112no—
119#494—24no—
120C2×#107—111no—
121C2×#107—111no—
122C2×C4×C8C2×D1111yescharacteristic
123#389—221no—
124#358—224no—
125#358—224no—
126#340—221no—
127C22×C11#44711yescharacteristic
128C22×C11#45911yescharacteristic
129C22×C11#48611yescharacteristic
130C22×C11C2×SD3211yescharacteristic
131C22×C11C2×Q3211yescharacteristic
132C22×C11#51011yescharacteristic
133C22×C11#51011yescharacteristic
134C4×C11—22no—
135C4×C11—22no—
136C4×C11—84no—
137C4×C11#39411yescharacteristic
138C4×C11#45011yescharacteristic
139C4×C11#46011yescharacteristic
140C4×C11#49011yescharacteristic
141Dic11—82no—
142Dic11—161no—
143C22×Q8—22no—
144C2×Q16—24no—
145C2×Q16—22no—
146C2×Q16—22no—
147C2×Q16—22no—
148C2×Q16—22no—
149C2×Q16—22no—
150C2×Q16—42no—
151C2×Q16—42no—
152C2×Q16C22⋊D1114yes—
153C22×C8C22⋊D1111yescharacteristic
154C22×C8C22×D1111yescharacteristic
155C4⋊Q8—24no—
156C4⋊Q8—42no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—441no—
162C2×C42C22⋊D1111yescharacteristic
163C2×C16—222no—
164C2×C16—222no—
165C2×C16—222no—
166#107—112no—
167#107—221no—
168#107—222no—
169C4×C8—22no—
170#95—441no—
171C2×C11#204111yescharacteristic
172C2×C11#218511yescharacteristic
173C2×C11#218811yescharacteristic
174C2×C11#220811yescharacteristic
175C2×C11#220911yescharacteristic
176C2×C11#224111yescharacteristic
177C2×C11#224511yescharacteristic
178C2×Q8—24no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—42no—
184C22×C4—42no—
185C22×C4—441no—
186C22×C4—441no—
187C22×C4#432311yescharacteristic
188C22×C4#432311yescharacteristic
189C22×C4C2×C22⋊D1111yescharacteristic
190Q16—24no—
191Q16—24no—
192Q16—48no—
193Q16—42no—
194Q16—42no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8#432412yes—
198C2×C8D4×D1111yescharacteristic
199C2×C8#434111yescharacteristic
200C2×C8#434112yes—
201C2×C8C2×C22⋊D1112yes—
202C4⋊C4—44no—
203C4⋊C4—44no—
204C4⋊C4—222no—
205C4⋊C4—441no—
206C4⋊C4—441no—
207C4⋊C4—441no—
208C4⋊C4—882no—
209C42—21no—
210C42—21no—
211C16—442no—
212C11#1340911yescharacteristic, complemented, Sylow
213C23C2×#432311yescharacteristic
214Q8—44no—
215Q8—44no—
216Q8—82no—
217Q8—82no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—44no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—442no—
226C2×C4—881no—
227C2×C4—881no—
228C2×C4—881no—
229C2×C4—881no—
230C2×C4—881no—
231C2×C4#6689212yes—
232C2×C4#6689312yes—
233C2×C4#6698511yescharacteristic
234C2×C4#6698511yescharacteristic
235C2×C4C2×#432411yescharacteristic
236C2×C4#6698911yescharacteristic
237C2×C4#6699111yescharacteristic
238C2×C4#6700611yescharacteristic
239C8—22no—
240C8#6698812yes—
241C8#6699212yes—
242C22#1062268311yescharacteristic
243C22#1062268511yescharacteristic
244C22C2×#6689211yescharacteristic
245C22#1062279211yescharacteristic
246C22#1062279211yescharacteristic
247C22C2×#6689311yescharacteristic
248C22#1062283011yescharacteristic
249C4—22no—
250C4—22no—
251C4—84no—
252C4—882no—
253C4—1761no—
254C4#1062268411yescharacteristic
255C4#1062268811yescharacteristic
256C4#1062283111yescharacteristic
257C4#1062283511yescharacteristic
258C2#1306984711yescharacteristic
259C2#1307053311yescharacteristic
260C2#1307055011yescharacteristic
261C2#1307065811yescharacteristic
262C2#1307066311yescharacteristic
263C2#1307084311yescharacteristic
264C2#1307086111yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#494C2
socle, prime radicalC23×C11C2×D8
hypercenterC2×#494D11
hypocenterC11#13409
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
212. C11#13409semidirect

Maximal subgroups

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

subgroupindex
C2×#106222022
#130693492
#130666942
C2×C11×#4942
#1340911