Finite Group Databasebeta

← #14667507

Subgroups — #14667507

Order 2816.

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

normal subgroups only

This group has 308 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, complemented
2#13070858C211yesmaximal, characteristic, complemented
3#13070652C211yesmaximal, characteristic
4#13068100C211yesmaximal, characteristic, complemented
5#13066667C211yesmaximal, characteristic, complemented
6#13066584C211yesmaximal, characteristic, complemented
7C11×#1338C211yesmaximal, characteristic, complemented
8#10623110—21no—
9C11×#446C2211yescharacteristic
10#10622640—21no—
11C2×D176—21no—
12#10622460—21no—
13#10622460—21no—
14#10622459—21no—
15#10622324—21no—
16#10622315—21no—
17#10622308C2211yescharacteristic
18C4×D88C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#346C2211yescharacteristic
22#10622147—21no—
23#10622147—21no—
24#10622147—21no—
25#10622123—21no—
26#10622095C2211yescharacteristic
27C4×Q8×C11D411yescharacteristic
28#66999—41no—
29C2×#4325—41no—
30C2×D88—21no—
31C2×D88—21no—
32C2×D88D411yescharacteristic
33#66949—41no—
34#66949—41no—
35C4⋊C4×D11—41no—
36#66927—21no—
37C4×D44—21no—
38C4×D44—21no—
39C4×D44—21no—
40#66923—21no—
41#66923—21no—
42#66922—21no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D411yescharacteristic
47C11×#97—21no—
48C4×C8×C11C2311yescharacteristic
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#66873—41no—
59C4⋊(C11⋊C8)—21no—
60D176—42no—
61#12360—111nomaximal, Sylow
62C2×Q8×C11D811yescharacteristic
63C2×D44—21no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×C4×D11—41no—
68C2×C4×D11—41no—
69C2×C4×D11—41no—
70C2×Dic22—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4D811yescharacteristic
76C42×C11—21no—
77C42×C11C2×D411yescharacteristic
78#4325—82no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C2×C11⋊C8—41no—
91D88—21no—
92D88—42no—
93D88—41no—
94D88—41no—
95D88SD1612yescomplemented
96C11×C16—41no—
97C11×C16—41no—
98#3389—111no—
99#2244—111no—
100#2206—111no—
101#1688—111no—
102#1363—111no—
103#1338D1111yescharacteristic, complemented
104#1333—111no—
105C22×D11—41no—
106C22×D11—81no—
107Q8×C11—41no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116D44—22no—
117D44—41no—
118D44—81no—
119D44—81no—
120D44—81no—
121D44—81no—
122D44—161no—
123C4×D11—82no—
124C4×D11—161no—
125C4×D11—161no—
126Dic22—161no—
127C8×C11—21no—
128C8×C11—41no—
129C8×C11C2×SD1611yescharacteristic
130C8×C11#13711yescharacteristic
131C11⋊C8—81no—
132#554—221no—
133C2×D16—221no—
134#501—221no—
135#499—111no—
136#493—111no—
137#478—221no—
138#478—221no—
139#474—221no—
140#460—221no—
141#446C2×D1111yescharacteristic
142#442—221no—
143C4×D8—111no—
144C4⋊C16C2×D1111yescharacteristic
145#357—221no—
146#357—221no—
147#357—221no—
148#346C2×D1111yescharacteristic
149#334—111no—
150#331—221no—
151C22×C11#44711yescharacteristic
152C2×D11—42no—
153C2×D11—81no—
154C2×D11—81no—
155C2×D11—161no—
156C2×D11—161no—
157C2×D11—161no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11#44811yescharacteristic
163C4×C11#45411yescharacteristic
164Dic11—81no—
165Dic11—81no—
166Dic11—81no—
167C2×SD16—441no—
168C2×D8—111no—
169C2×D8—221no—
170C2×D8—221no—
171C4⋊Q8—221no—
172#127—221no—
173#125—221no—
174#125—221no—
175C22⋊Q8—441no—
176C22⋊Q8—441no—
177C22⋊Q8—441no—
178C4×Q8D4411yescharacteristic
179C4×D4—221no—
180C4×D4—221no—
181C4×D4—221no—
182C2×C4⋊C4—441no—
183D16—442no—
184C2×C16—21no—
185C2×C16—21no—
186#107—111no—
187#107—111no—
188#107—111no—
189#107—221no—
190#106—221no—
191#106—221no—
192C4⋊C8—21no—
193C4⋊C8—221no—
194C4⋊C8D4411yescharacteristic
195#102—221no—
196#102—221no—
197#102—221no—
198#102—441no—
199#97—21no—
200C4×C8C22×D1111yescharacteristic
201C2×C11#162711yescharacteristic
202C2×C11#219011yescharacteristic
203C2×C11#219211yescharacteristic
204D11—82no—
205D11—321no—
206C2×Q8—441no—
207C2×Q8D8811yescharacteristic
208C2×D4—221no—
209C2×D4—441no—
210C2×D4—441no—
211C2×D4—441no—
212C22×C4—441no—
213C22×C4—441no—
214C22×C4—441no—
215SD16—882no—
216D8—112no—
217D8—221no—
218D8—442no—
219D8—441no—
220D8—441no—
221C2×C8—21no—
222C2×C8—441no—
223C2×C8D4×D1111yescharacteristic
224C2×C8D4×D1111yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—221no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4D8811yescharacteristic
235C22⋊C4—441no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C42—21no—
239C42C2×D4411yescharacteristic
240C16—41no—
241C16—41no—
242C11#1236011yescharacteristic, complemented, Sylow
243C23—441no—
244C23—881no—
245Q8—41no—
246Q8—1761no—
247D4—222no—
248D4—441no—
249D4—881no—
250D4—881no—
251D4—881no—
252D4—881no—
253D4—1761no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—882no—
260C2×C4—1761no—
261C2×C4—1761no—
262C2×C4#6693511yescharacteristic
263C2×C4C2×D8811yescharacteristic
264C2×C4#6696111yescharacteristic
265C8—21no—
266C8—41no—
267C8—881no—
268C8SD16×D1111yescharacteristic
269C8#6697111yescharacteristic
270C22—442no—
271C22—881no—
272C22—881no—
273C22—1761no—
274C22—1761no—
275C22—1761no—
276C22#1062234511yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—881no—
282C4—881no—
283C4—881no—
284C4#1062241911yescharacteristic
285C4#1062244011yescharacteristic
286C2—882no—
287C2—3521no—
288C2#1306772111yescharacteristic
289C2#1307056411yescharacteristic
290C2#1307057511yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1338C2
socleC22×C11#447
prime radical#13070652C2
hypercenter#1338D11
hypocenterC11#12360
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
1. #13081576C2semidirect
2. #13070858C2semidirect
4. #13068100C2semidirect
5. #13066667C2semidirect
6. #13066584C2semidirect
7. C11×#1338C2semidirect
95. D88SD16semidirect
103. #1338D11semidirect
242. C11#12360semidirect

Maximal subgroups

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

subgroupindex
#130815762
#130708582
#130706522
#130681002
#130666672
#130665842
C11×#13382
#1236011