Finite Group Databasebeta

← #14667303

Subgroups — #14667303

Order 2816.

328 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081606C211yesmaximal, characteristic, complemented
2#13070873C211yesmaximal, characteristic, complemented
3#13070652C211yesmaximal, characteristic
4#13067977C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic, complemented
7C11×#1362C211yesmaximal, characteristic, complemented
8#10623263—21no—
9C11×#494C2211yescharacteristic
10#10622804—21no—
11#10622798—22no—
12Q16×Dic11—21no—
13C2×#66892—22no—
14#10622696—21no—
15C2×D176—21no—
16#10622461—21no—
17#10622308C2211yescharacteristic
18C4×D88C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622147—21no—
23#10622123—21no—
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C11×C4⋊Q8—21no—
28#67000—22no—
29Q8×Dic11—22no—
30C2×#4325—22no—
31C2×D88—21no—
32C2×D88—21no—
33C2×D88D411yescharacteristic
34C2×#4314—41no—
35#66951—42no—
36#66950—41no—
37#66945—41no—
38#66927—21no—
39C4×D44—21no—
40C4×Dic22D411yescharacteristic
41C2×C11×C16—21no—
42C11×C4⋊C8—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—22no—
45#66892—44no—
46#66885—21no—
47#66885—41no—
48#66882D411yescharacteristic
49Dic11⋊C8—21no—
50C8×Dic11—21no—
51C2×C11⋊C16—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53D176—42no—
54#12331—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×D44—21no—
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—41no—
60C2×C4×D11—41no—
61C2×Dic22D811yescharacteristic
62C11×Q16—41no—
63C11×Q16—41no—
64C11×Q16—42no—
65C2×C8×C11—41no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11C2×D411yescharacteristic
71#4325—82no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11—42no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80C4×Dic11—42no—
81C2×C11⋊C8—21no—
82D88—21no—
83D88—21no—
84D88—42no—
85D88—41no—
86D88—41no—
87#4314—82no—
88C11×C16—41no—
89C11⋊C16—22no—
90#3393—111no—
91#2248—111no—
92#2206—111no—
93#1668—111no—
94#1362D1111yescharacteristic, complemented
95Q8⋊C16—111no—
96#1331—111no—
97C22×D11—41no—
98C22×D11—81no—
99Q8×C11—42no—
100Q8×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—41no—
108D44—41no—
109D44—41no—
110D44—81no—
111D44—81no—
112D44—81no—
113D44—81no—
114D44—161no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—21no—
118Dic22—21no—
119C8×C11—21no—
120C8×C11—81no—
121C8×C11#13511yescharacteristic
122C8×C11AGL(1,ℤ/8)11yescharacteristic
123C11⋊C8—41no—
124#556—221no—
125C2×SD32—222no—
126C2×D16—221no—
127#495—221no—
128#494C2×D1111yescharacteristic
129#493—111no—
130#464—222no—
131#461—221no—
132#460—221no—
133C8×Q8—111no—
134C4×Q16—221no—
135C4×D8—111no—
136C4⋊C16C2×D1111yescharacteristic
137#357—221no—
138C4×C16—111no—
139#335C2×D1111yescharacteristic
140#331—221no—
141C22×C11#44711yescharacteristic
142C2×D11—81no—
143C2×D11—81no—
144C2×D11—81no—
145C2×D11—161no—
146C2×D11—161no—
147C2×D11—161no—
148C4×C11—21no—
149C4×C11—82no—
150C4×C11#44911yescharacteristic
151C4×C11#45311yescharacteristic
152C4×C11#50811yescharacteristic
153C4×C11#50911yescharacteristic
154Dic11—41no—
155Dic11—41no—
156Dic11—81no—
157C2×Q16—21no—
158C2×Q16D4412yes—
159C2×SD16—222no—
160C2×SD16—441no—
161C2×D8—111no—
162C2×D8—221no—
163C2×D8—221no—
164C4⋊Q8—21no—
165#127—221no—
166#126—442no—
167#124—222no—
168C22⋊Q8—441no—
169C4×Q8—111no—
170C4×Q8—222no—
171C4×D4—221no—
172#117—441no—
173SD32—444no—
174D16—442no—
175C2×C16—21no—
176C2×C16—221no—
177#107—111no—
178C4⋊C8—21no—
179C4⋊C8—111no—
180C4⋊C8—221no—
181#103—222no—
182#102—221no—
183#102—441no—
184C4×C8—221no—
185C4×C8C22×D1111yescharacteristic
186C2×C11#162111yescharacteristic
187C2×C11#218611yescharacteristic
188C2×C11#219311yescharacteristic
189D11—161no—
190D11—321no—
191C2×Q8—22no—
192C2×Q8—111no—
193C2×D4—221no—
194C2×D4—441no—
195C2×D4—441no—
196C2×D4—441no—
197C22×C4—441no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201SD16—882no—
202SD16—882no—
203D8—221no—
204D8—221no—
205D8—442no—
206D8—441no—
207D8—441no—
208C2×C8—41no—
209C2×C8—221no—
210C2×C8C2×D4411yescharacteristic
211C2×C8D4×D1111yescharacteristic
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—111no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—441no—
221C42—221no—
222C42—442no—
223C42D4×D1111yescharacteristic
224C16—41no—
225C16—222no—
226C11#1233111yescharacteristic, complemented, Sylow
227C23—441no—
228C23—881no—
229Q8—42no—
230Q8—42no—
231Q8—221no—
232Q8—221no—
233D4—441no—
234D4—441no—
235D4—881no—
236D4—881no—
237D4—881no—
238D4—881no—
239D4—1761no—
240C2×C4—42no—
241C2×C4—221no—
242C2×C4—221no—
243C2×C4—441no—
244C2×C4—881no—
245C2×C4—881no—
246C2×C4#6693511yescharacteristic
247C2×C4D8×D1111yescharacteristic
248C2×C4#6696711yescharacteristic
249C8—21no—
250C8—81no—
251C8—441no—
252C8#6696411yescharacteristic
253C8#6696911yescharacteristic
254C22—881no—
255C22—881no—
256C22—881no—
257C22—1761no—
258C22—1761no—
259C22—1761no—
260C22#1062238611yescharacteristic
261C4—21no—
262C4—82no—
263C4—441no—
264C4—441no—
265C4—881no—
266C4#1062236011yescharacteristic
267C4#1062239411yescharacteristic
268C4#1062252711yescharacteristic
269C4#1062253211yescharacteristic
270C2—3521no—
271C2—1761no—
272C2#1306768211yescharacteristic
273C2#1307054211yescharacteristic
274C2#1307058311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socleC22×C11#447
prime radical#13070652C2
hypercenter#1362D11
hypocenterC11#12331
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13081606C2semidirect
2. #13070873C2semidirect
4. #13067977C2semidirect
5. #13066594C2semidirect
6. #13066576C2semidirect
7. C11×#1362C2semidirect
94. #1362D11semidirect
226. C11#12331semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130708732
#130706522
#130679772
#130665942
#130665762
C11×#13622
#1233111