Finite Group Databasebeta

← #14667508

Subgroups — #14667508

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#13081572C211yesmaximal, characteristic, complemented
2#13070858C211yesmaximal, characteristic, complemented
3#13070651C211yesmaximal, characteristic
4#13068101C211yesmaximal, characteristic, complemented
5#13066669C211yesmaximal, characteristic, complemented
6#13066599C211yesmaximal, characteristic, complemented
7C11×#1333C211yesmaximal, characteristic, complemented
8#10623070—21no—
9C4×C11×D8C2211yescharacteristic
10#10622765—21no—
11C2×#66890—21no—
12#10622622—21no—
13#10622489—21no—
14#10622461—21no—
15#10622379—21no—
16#10622372—21no—
17#10622308C2211yescharacteristic
18#10622296C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×#346C2211yescharacteristic
21C11×#334C2211yescharacteristic
22#10622147—21no—
23#10622147—21no—
24#10622129—21no—
25#10622123—21no—
26C4⋊(C11⋊C16)C2211yescharacteristic
27C2×C11×D8D411yescharacteristic
28C4×D4×C11—21no—
29D4×Dic11—21no—
30D4×Dic11—21no—
31#66977—41no—
32C2×Dic11⋊C4—41no—
33C2×D88—21no—
34C2×D88—21no—
35C2×#4314—41no—
36#66943—21no—
37#66941—21no—
38#66931—41no—
39#66931—41no—
40#66927—21no—
41#66923—21no—
42C4×Dic22D411yescharacteristic
43C2×C11×C16—21no—
44C11×#107D411yescharacteristic
45C11×C4⋊C8—21no—
46C11×#102—21no—
47C4×C8×C11C2311yescharacteristic
48#66896—21no—
49#66896—21no—
50#66890—42no—
51#66885—41no—
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66879—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66872—21no—
59#66871—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12360—111nomaximal, Sylow
62C2×D4×C11—21no—
63C22×C4×C11—41no—
64C22×Dic11—41no—
65C22×Dic11—41no—
66C2×D44—41no—
67C2×D44—41no—
68C2×D44—41no—
69C2×Dic22—41no—
70C2×Dic22D811yescharacteristic
71C11×D8—21no—
72C11×D8SD1612yescomplemented
73C2×C8×C11—41no—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—21no—
77C11×C22⋊C4—41no—
78C42×C11C2×D411yescharacteristic
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—41no—
84C4⋊Dic11D811yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—21no—
91C2×C11⋊C8—21no—
92D88—42no—
93D88—41no—
94D88—41no—
95#4314—82no—
96C11×C16—41no—
97C11⋊C16—41no—
98#3389—111no—
99#2244—111no—
100#2206—111no—
101#1688—111no—
102#1363—111no—
103#1338—111no—
104#1333D1111yescharacteristic, complemented
105C23×C11—41no—
106C22×D11—81no—
107D4×C11—22no—
108D4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—161no—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—82no—
119C2×Dic11—161no—
120D44—81no—
121D44—81no—
122D44—81no—
123D44—81no—
124D44—161no—
125Dic22—41no—
126Dic22—161no—
127C8×C11—21no—
128C8×C11—81no—
129C8×C11C2×SD1611yescharacteristic
130C8×C11#13711yescharacteristic
131C11⋊C8—41no—
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#446—111no—
142#442—221no—
143C4×D8C2×D1111yescharacteristic
144C4⋊C16—111no—
145#357—221no—
146#357—221no—
147#357—221no—
148#346C2×D1111yescharacteristic
149#334C2×D1111yescharacteristic
150#331—221no—
151C22×C11—42no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11#44711yescharacteristic
155C2×D11—161no—
156C2×D11—161no—
157C2×D11—161no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—81no—
161C4×C11#44811yescharacteristic
162C4×C11#45411yescharacteristic
163Dic11—41no—
164Dic11—41no—
165Dic11—81no—
166Dic11—81no—
167C2×SD16—441no—
168C2×D8—221no—
169C2×D8—221no—
170C2×D8D4411yescharacteristic
171C4⋊Q8—221no—
172#127—221no—
173#125—221no—
174#125—221no—
175C22⋊Q8—441no—
176C22⋊Q8—441no—
177C22⋊Q8—441no—
178C4×Q8—111no—
179C4×D4—21no—
180C4×D4—221no—
181C4×D4—221no—
182C2×C4⋊C4—441no—
183D16—442no—
184C2×C16—21no—
185C2×C16—221no—
186#107—111no—
187#107—111no—
188#107—221no—
189#107D4411yescharacteristic
190#106—221no—
191#106—221no—
192C4⋊C8—21no—
193C4⋊C8—111no—
194C4⋊C8—221no—
195#102—21no—
196#102—221no—
197#102—221no—
198#102—441no—
199#97—221no—
200C4×C8C22×D1111yescharacteristic
201C2×C11—82no—
202C2×C11#162711yescharacteristic
203C2×C11#219011yescharacteristic
204C2×C11#219211yescharacteristic
205D11—321no—
206C2×Q8—111no—
207C2×Q8—441no—
208C2×D4—21no—
209C2×D4—441no—
210C2×D4—441no—
211C2×D4—441no—
212C22×C4—41no—
213C22×C4—441no—
214C22×C4—441no—
215SD16—882no—
216D8—21no—
217D8—442no—
218D8—441no—
219D8—441no—
220D8#431412yescomplemented
221C2×C8—41no—
222C2×C8—221no—
223C2×C8C2×D4411yescharacteristic
224C2×C8D4×D1111yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—111no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C22⋊C4—41no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C42—221no—
239C42D4×D1111yescharacteristic
240C16—41no—
241C16—441no—
242C11#1236011yescharacteristic, complemented, Sylow
243C23—41no—
244C23—881no—
245Q8—441no—
246Q8—1761no—
247D4—22no—
248D4—41no—
249D4—881no—
250D4—881no—
251D4—881no—
252D4—881no—
253D4—1761no—
254C2×C4—41no—
255C2×C4—161no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—882no—
261C2×C4—1761no—
262C2×C4#6693511yescharacteristic
263C2×C4D8×D1111yescharacteristic
264C2×C4#6696711yescharacteristic
265C8—21no—
266C8—81no—
267C8—441no—
268C8C2×#431411yescharacteristic
269C8#6696211yescharacteristic
270C22—42no—
271C22—81no—
272C22—81no—
273C22—1761no—
274C22—1761no—
275C22—1761no—
276C22#1062238611yescharacteristic
277C4—21no—
278C4—21no—
279C4—81no—
280C4—441no—
281C4—441no—
282C4—881no—
283C4—881no—
284C4#1062235111yescharacteristic
285C4#1062244011yescharacteristic
286C2—82no—
287C2—3521no—
288C2#1306772211yescharacteristic
289C2#1307056311yescharacteristic
290C2#1307057611yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1333C2
socleC22×C11#447
prime radical#13070651C2
hypercenter#1333D11
hypocenterC11#12360
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
1. #13081572C2semidirect
2. #13070858C2semidirect
4. #13068101C2semidirect
5. #13066669C2semidirect
6. #13066599C2semidirect
7. C11×#1333C2semidirect
72. C11×D8SD16semidirect
104. #1333D11semidirect
220. D8#4314semidirect
242. C11#12360semidirect

Maximal subgroups

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

subgroupindex
#130815722
#130708582
#130706512
#130681012
#130666692
#130665992
C11×#13332
#1236011