Finite Group Databasebeta

← #14666184

Subgroups — #14666184

Order 2816.

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

normal subgroups only

This group has 424 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#13073989C211yesmaximal, characteristic, complemented
2#13067619C212yesmaximal
3#13066621C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic
6C11×#537C2211yescharacteristic
7C2×C4×Dic22—21no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C11×#384C2211yescharacteristic
11#10622646—22no—
12#10622598—22no—
13#10622596—21no—
14#10622596C2212yes—
15#10622587—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×Dic22—21no—
21C2×C11×M16—21no—
22C11×C22⋊Q8—41no—
23C11×#121—22no—
24C11×#121—41no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—22no—
34C4×Dic22—42no—
35C4×Dic22—42no—
36C11×#104—42no—
37C11×#103—41no—
38C11×#102—41no—
39#66896—42no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66871—42no—
46#12153—111nomaximal, Sylow
47C11×#41—41no—
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C2×Q8×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D412yes—
60C22×Dic11—22no—
61C22×Dic11—22no—
62C2×Dic22—24no—
63C2×Dic22—42no—
64C2×Dic22—42no—
65C11×M16—41no—
66C11×M16—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—44no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—42no—
73C42×C11—21no—
74C42×C11D812yes—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—81no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80C4×Dic11—44no—
81C2×C11⋊C8—42no—
82#2582—111no—
83#2039D1111yescharacteristic
84#1610—112no—
85#1346—112no—
86#1325—111no—
87C23×C11—41no—
88C23×C11#12011yescharacteristic
89Q8×C11—41no—
90Q8×C11—41no—
91D4×C11—41no—
92D4×C11—41no—
93D4×C11—82no—
94D4×C11—81no—
95D4×C11—81no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—81no—
107C2×C4×C11—81no—
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—24no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116Dic22—48no—
117C8×C11—81no—
118C11⋊C8—82no—
119#537C2×D1111yescharacteristic
120C2×C4×Q8—221no—
121#480—222no—
122C2×#104—21no—
123#417—21no—
124#398—112no—
125#398—221no—
126#391—222no—
127#389—222no—
128#384C2×D1111yescharacteristic
129#343C2×D1111yescharacteristic
130#327—222no—
131#324—112no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—81no—
135C22×C11—81no—
136C22×C11—81no—
137C22×C11#44711yescharacteristic
138C22×C11#45411yescharacteristic
139C22×C11B(4,𝔽2)11yescharacteristic
140C4×C11—24no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11—81no—
145C4×C11—81no—
146Dic11—44no—
147Dic11—82no—
148C2×#41—21no—
149C22×Q8—221no—
150C2×M16—21no—
151C22⋊Q8—41no—
152#121—22no—
153#121—41no—
154C4×Q8—442no—
155C4×Q8—442no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—221no—
159C2×C4⋊C4—222no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4C22⋊D1111yescharacteristic
162C2×C4⋊C4C22×D1111yescharacteristic
163C2×C42—222no—
164C2×C42C22⋊D1111yescharacteristic
165#107—442no—
166#104—42no—
167#103—41no—
168#102—41no—
169#102—442no—
170C22⋊C8—222no—
171#95—112no—
172#95—222no—
173#95—221no—
174#95—222no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11—161no—
178C2×C11#159811yescharacteristic
179C2×C11#219811yescharacteristic
180C2×C11#220511yescharacteristic
181#41—41no—
182#41—41no—
183#41—41no—
184#41—41no—
185C2×Q8—21no—
186C2×Q8—224no—
187C2×Q8—442no—
188C2×Q8—442no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—41no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4D4×D1112yes—
198C22×C4C2×C22⋊D1111yescharacteristic
199M16—41no—
200M16—41no—
201C2×C8—41no—
202C2×C8—442no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—44no—
207C4⋊C4—442no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C4⋊C4—881no—
212C22⋊C4—42no—
213C42—21no—
214C42—444no—
215C42#432312yes—
216C11#1215311yescharacteristic, complemented, Sylow
217C23—41no—
218C23#6699011yescharacteristic
219Q8—41no—
220Q8—41no—
221Q8—448no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—224no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4C2×#432311yescharacteristic
246C2×C4#6700211yescharacteristic
247C8—81no—
248C8—882no—
249C22—21no—
250C22—21no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1062264511yescharacteristic
255C22#1062264911yescharacteristic
256C22#1062267511yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—81no—
262C4—81no—
263C4—444no—
264C4—882no—
265C2—21no—
266C2—21no—
267C2—161no—
268C2#1306755011yescharacteristic
269C2#1307061111yescharacteristic
270C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2039D11
hypocenterC11#12153
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13073989C2semidirect
3. #13066621C2semidirect
4. #13066562C2semidirect
216. C11#12153semidirect

Maximal subgroups

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

subgroupindex
#130739892
#130676192
#130666212
#130665622
C11×#20392
#1215311