Finite Group Databasebeta

← #14667521

Subgroups — #14667521

Order 2816.

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

normal subgroups only

This group has 292 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#13081576C211yesmaximal, characteristic
2#13070862C211yesmaximal, characteristic, complemented
3#13070662C211yesmaximal, characteristic
4#13068110C211yesmaximal, characteristic, complemented
5#13066667C211yesmaximal, characteristic, complemented
6#13066584C211yesmaximal, characteristic
7C11×#1338C211yesmaximal, characteristic, complemented
8#10623110—21no—
9C11×#446C2211yescharacteristic
10#10622633—21no—
11C2×#66864—21no—
12#10622460—21no—
13#10622460—21no—
14#10622459—21no—
15#10622324—21no—
16#10622315—21no—
17#10622312C2211yescharacteristic
18C4×D88C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#346C2211yescharacteristic
22#10622141—21no—
23#10622141—21no—
24#10622141—21no—
25#10622120—21no—
26#10622095C2211yescharacteristic
27C4×Q8×C11D411yescharacteristic
28#66999—41no—
29C2×Dic44—21no—
30C2×Dic44—21no—
31C2×D88D411yescharacteristic
32#66949—41no—
33#66949—41no—
34C4⋊C4×D11—41no—
35C4×D44—21no—
36C4×D44—21no—
37C4×D44—21no—
38#66923—21no—
39#66923—21no—
40#66922—21no—
41#66922—21no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×#97—21no—
47C4×C8×C11C2311yescharacteristic
48#66899—41no—
49#66885—21no—
50#66885—21no—
51#66885—21no—
52#66882—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66882D411yescharacteristic
56#66881—21no—
57#66881—21no—
58#66872—41no—
59C4⋊(C11⋊C8)—21no—
60#66864—42no—
61#12362—111nomaximal, Sylow
62C2×Q8×C11D811yescharacteristic
63C2×D44—21no—
64C2×C4×D11—41no—
65C2×C4×D11—41no—
66C2×C4×D11—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×C8×C11—21no—
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4D811yescharacteristic
74C42×C11—21no—
75C42×C11C2×D411yescharacteristic
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C2×C11⋊C8—41no—
90Dic44—42no—
91Dic44—41no—
92Dic44—41no—
93D88—21no—
94D88SD1612yes—
95C11×C16—41no—
96C11×C16—41no—
97#3389—111no—
98#2245—111no—
99#2208—111no—
100#1690—111no—
101#1363—111no—
102#1338D1111yescharacteristic, complemented
103#1333—111no—
104C22×D11—41no—
105Q8×C11—41no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—81no—
115D44—22no—
116D44—41no—
117C4×D11—82no—
118C4×D11—161no—
119C4×D11—161no—
120Dic22—81no—
121Dic22—81no—
122Dic22—161no—
123C8×C11—21no—
124C8×C11—41no—
125C8×C11C2×SD1611yescharacteristic
126C8×C11#13711yescharacteristic
127C11⋊C8—81no—
128#554—221no—
129C2×SD32—221no—
130#501—221no—
131#499—111no—
132#494—111no—
133#478—221no—
134#478—221no—
135#475—221no—
136#474—221no—
137#446C2×D1111yescharacteristic
138#442—221no—
139C4×D8—111no—
140C4⋊C16C2×D1111yescharacteristic
141#358—221no—
142#358—221no—
143#358—221no—
144#346C2×D1111yescharacteristic
145#334—111no—
146#332—221no—
147C22×C11#44711yescharacteristic
148C2×D11—42no—
149C2×D11—81no—
150C2×D11—81no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11#44811yescharacteristic
156C4×C11#45411yescharacteristic
157Dic11—81no—
158Dic11—81no—
159Dic11—81no—
160Dic11—161no—
161C2×Q16—221no—
162C2×Q16—221no—
163C2×D8—111no—
164C4⋊Q8—221no—
165C4⋊Q8—221no—
166#125—221no—
167#125—221no—
168C22⋊Q8—441no—
169C22⋊Q8—441no—
170C22⋊Q8—441no—
171C4×Q8D4411yescharacteristic
172C4×D4—221no—
173C4×D4—221no—
174C4×D4—221no—
175C2×C4⋊C4—441no—
176SD32—442no—
177C2×C16—21no—
178C2×C16—21no—
179#107—111no—
180#107—111no—
181#107—111no—
182#107—221no—
183#106—221no—
184#106—221no—
185#106—441no—
186C4⋊C8—21no—
187C4⋊C8—221no—
188C4⋊C8D4411yescharacteristic
189#103—441no—
190#102—221no—
191#102—221no—
192#102—221no—
193#97—21no—
194C4×C8C22×D1111yescharacteristic
195C2×C11#162711yescharacteristic
196C2×C11#219111yescharacteristic
197C2×C11#219411yescharacteristic
198D11—82no—
199C2×Q8—441no—
200C2×Q8—441no—
201C2×Q8D8811yescharacteristic
202C2×D4—221no—
203C22×C4—441no—
204C22×C4—441no—
205C22×C4—441no—
206Q16—442no—
207Q16—441no—
208Q16—441no—
209D8—112no—
210D8—221no—
211C2×C8—21no—
212C2×C8—441no—
213C2×C8D4×D1111yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—221no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4D8811yescharacteristic
227C22⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—441no—
230C42—21no—
231C42C2×D4411yescharacteristic
232C16—41no—
233C16—41no—
234C11#1236211yescharacteristic, complemented, Sylow
235C23—441no—
236Q8—41no—
237Q8—881no—
238Q8—881no—
239Q8—1761no—
240D4—222no—
241D4—441no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—441no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4—882no—
248C2×C4—881no—
249C2×C4—1761no—
250C2×C4—1761no—
251C2×C4#6693511yescharacteristic
252C2×C4C2×D8811yescharacteristic
253C2×C4#6696111yescharacteristic
254C8—21no—
255C8—41no—
256C8—881no—
257C8SD16×D1111yescharacteristic
258C8#6697111yescharacteristic
259C22—442no—
260C22—881no—
261C22—881no—
262C22#1062234511yescharacteristic
263C4—21no—
264C4—21no—
265C4—41no—
266C4—41no—
267C4—881no—
268C4—881no—
269C4—881no—
270C4—1761no—
271C4#1062241911yescharacteristic
272C4#1062244011yescharacteristic
273C2—882no—
274C2#1306772111yescharacteristic
275C2#1307056911yescharacteristic
276C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1338C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#1338D11
hypocenterC11#12362
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #13070862C2semidirect
4. #13068110C2semidirect
5. #13066667C2semidirect
7. C11×#1338C2semidirect
102. #1338D11semidirect
234. C11#12362semidirect

Maximal subgroups

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

subgroupindex
#130815762
#130708622
#130706622
#130681102
#130666672
#130665842
C11×#13382
#1236211