Finite Group Databasebeta

← #14667787

Subgroups — #14667787

Order 2816.

274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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#13081192C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070758C211yesmaximal, characteristic, complemented
4#13068140C211yesmaximal, characteristic
5#13066669C211yesmaximal, characteristic, complemented
6#13066575C211yesmaximal, characteristic
7C11×#1334C211yesmaximal, characteristic, complemented
8#10623112—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622802—21no—
11#10622635—21no—
12#10622494—21no—
13#10622455—21no—
14#10622427—21no—
15#10622422—21no—
16#10622301C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×#346C2211yescharacteristic
20C11×#334C2211yescharacteristic
21#10622202—21no—
22#10622143—21no—
23#10622142—21no—
24#10622128—21no—
25#10622119—21no—
26C4⋊(C11⋊C16)C2211yescharacteristic
27C2×C11×Q16D411yescharacteristic
28C4×Q8×C11—21no—
29#66999—21no—
30#66999—21no—
31C2×#4313—21no—
32#66947—41no—
33#66945—21no—
34C4⋊C4×D11—21no—
35#66942—41no—
36#66929—41no—
37C4×D44D411yescharacteristic
38#66925—41no—
39#66923—21no—
40#66922—21no—
41C2×C11×C16—21no—
42C11×#107D411yescharacteristic
43C11×C4⋊C8—21no—
44C11×#103—21no—
45C4×C8×C11C2311yescharacteristic
46#66899—21no—
47#66899—21no—
48#66885—41no—
49(C2×D11)⋊C8—21no—
50#66882—21no—
51#66882—21no—
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66881—41no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)D411yescharacteristic
60#12401—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C2×D44D811yescharacteristic
63C2×C4×D11—21no—
64C2×C4×D11—41no—
65C2×Dic22—41no—
66C11×Q16—21no—
67C11×Q16—21no—
68C2×C8×C11—41no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C42×C11—41no—
74C42×C11C2×D411yescharacteristic
75(C2×D11)⋊C4—21no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11D811yescharacteristic
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C2×C11⋊C8—21no—
91#4313—41no—
92#4313—41no—
93C11×C16—22no—
94C11⋊C16—41no—
95#3352—111no—
96#2255—111no—
97#2225—111no—
98#1695—111no—
99#1363—111no—
100#1334D1111yescharacteristic, complemented
101#1330—111no—
102C22×D11—21no—
103Q8×C11—41no—
104Q8×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—21no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—81no—
114D44—41no—
115C4×D11—41no—
116C4×D11—41no—
117C4×D11—82no—
118Dic22—161no—
119C8×C11—21no—
120C8×C11—81no—
121C8×C11#13511yescharacteristic
122C8×C11#13711yescharacteristic
123C11⋊C8—41no—
124#552—221no—
125#500—111no—
126#499—111no—
127#485—221no—
128#484—221no—
129#479—221no—
130#476—221no—
131#470—221no—
132C4×Q16C2×D1111yescharacteristic
133#436—111no—
134#428—221no—
135#367—221no—
136#367—221no—
137#366—221no—
138C4⋊C16—111no—
139#358—221no—
140#346C2×D1111yescharacteristic
141#334C2×D1111yescharacteristic
142#333—221no—
143C22×C11#44711yescharacteristic
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—41no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—81no—
150C4×C11—81no—
151C4×C11#45211yescharacteristic
152C4×C11#45611yescharacteristic
153Dic11—41no—
154Dic11—81no—
155Dic11—81no—
156Dic11—161no—
157C2×Q16D4411yescharacteristic
158C2×M16—221no—
159C4⋊Q8—221no—
160#126—441no—
161#125—221no—
162#125—441no—
163#123—441no—
164C22⋊Q8—221no—
165C22⋊Q8—221no—
166C4×Q8—21no—
167C4×D4—111no—
168#117—221no—
169#117—441no—
170C2×C4⋊C4—221no—
171C2×C16—21no—
172C2×C16—221no—
173#107—111no—
174#107—111no—
175#107—221no—
176#107—221no—
177#107—221no—
178#107D4411yescharacteristic
179#106—221no—
180#106—221no—
181#106—441no—
182C4⋊C8—21no—
183C4⋊C8—111no—
184#103—21no—
185#103—221no—
186#103—221no—
187#102—441no—
188C22⋊C8—221no—
189C4×C8C22×D1111yescharacteristic
190C2×C11#164711yescharacteristic
191C2×C11#219111yescharacteristic
192C2×C11#219311yescharacteristic
193D11—81no—
194C2×Q8—21no—
195C2×Q8—441no—
196C2×D4—111no—
197C22×C4—221no—
198C22×C4—441no—
199Q16—21no—
200Q16—21no—
201M16—441no—
202M16—441no—
203C2×C8—41no—
204C2×C8—221no—
205C2×C8C2×D4411yescharacteristic
206C2×C8D4×D1111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—111no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C22⋊C4—221no—
220C22⋊C4—441no—
221C22⋊C4—441no—
222C22⋊C4—441no—
223C42—41no—
224C42—441no—
225C42D4×D1111yescharacteristic
226C16—22no—
227C16—441no—
228C11#1240111yescharacteristic, complemented, Sylow
229C23—221no—
230Q8—41no—
231Q8—41no—
232Q8—1761no—
233D4—441no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—221no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—882no—
242C2×C4—881no—
243C2×C4#6693511yescharacteristic
244C2×C4D8×D1111yescharacteristic
245C2×C4#6696711yescharacteristic
246C8—21no—
247C8—81no—
248C8—441no—
249C8#6695711yescharacteristic
250C8#6696211yescharacteristic
251C22—441no—
252C22—441no—
253C22—441no—
254C22#1062238611yescharacteristic
255C4—21no—
256C4—21no—
257C4—81no—
258C4—81no—
259C4—441no—
260C4—881no—
261C4—881no—
262C4—1761no—
263C4#1062234611yescharacteristic
264C4#1062243911yescharacteristic
265C2—881no—
266C2#1306785411yescharacteristic
267C2#1307056811yescharacteristic
268C2#1307058311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1334C2
socleC22×C11#447
prime radicalC2×D44D8
hypercenter#1334D11
hypocenterC11#12401
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

Complements

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

NH ≅ G/Ntype
2. #13070902C2semidirect
3. #13070758C2semidirect
5. #13066669C2semidirect
7. C11×#1334C2semidirect
100. #1334D11semidirect
228. C11#12401semidirect

Maximal subgroups

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

subgroupindex
#130811922
#130709022
#130707582
#130681402
#130666692
#130665752
C11×#13342
#1240111