Finite Group Databasebeta

← #14667457

Subgroups — #14667457

Order 2816.

298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081509C211yesmaximal, characteristic, complemented
2#13070841C211yesmaximal, characteristic
3#13070657C211yesmaximal, characteristic
4#13067977C211yesmaximal, characteristic
5#13066594C211yesmaximal, characteristic, complemented
6#13066579C211yesmaximal, characteristic, complemented
7C11×#1364C211yesmaximal, characteristic, complemented
8#10623252—21no—
9C11×#500C2211yescharacteristic
10#10622707—21no—
11C2×#66864—21no—
12#10622491—21no—
13#10622490—22no—
14#10622486—21no—
15#10622461—21no—
16C4×Dic44C2211yescharacteristic
17#10622308C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#335C2211yescharacteristic
21#10622147—21no—
22#10622129—22no—
23#10622123—21no—
24C4×C11⋊C16C2211yescharacteristic
25C11×C4⋊Q8—21no—
26Q8×Dic11—41no—
27#66997—41no—
28C2×Dic44D411yescharacteristic
29C2×D88—21no—
30C2×D88—21no—
31C2×#4314—41no—
32#66943—22no—
33#66942—42no—
34#66940—22no—
35#66927—21no—
36C4×Dic22—21no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107D412yes—
41C11×C4⋊C8—21no—
42C4×C8×C11C2311yescharacteristic
43#66885—41no—
44#66882D411yescharacteristic
45#66880—21no—
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66874—22no—
50#66872—22no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#66864—42no—
53#12353—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×D44—41no—
56C2×D44—41no—
57C2×D44—41no—
58C2×Dic22—21no—
59C2×Dic22D811yescharacteristic
60C2×C8×C11—41no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—22no—
64C11×C4⋊C4—41no—
65C42×C11C2×D411yescharacteristic
66C4⋊Dic11—21no—
67C4⋊Dic11—42no—
68C4⋊Dic11D811yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—42no—
71Dic11⋊C4—42no—
72Dic11⋊C4—41no—
73C4×Dic11—21no—
74C4×Dic11—42no—
75C4×Dic11—41no—
76C2×C11⋊C8—21no—
77Dic44—21no—
78Dic44SD1612yescomplemented
79D88—42no—
80D88—41no—
81D88—41no—
82#4314—82no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3383—111no—
86#2240—111no—
87#2207—111no—
88#1668—111no—
89#1364D1111yescharacteristic, complemented
90Q8⋊C16—111no—
91#1332—111no—
92C22×D11—81no—
93Q8×C11—81no—
94Q8×C11—81no—
95C2×C4×C11—42no—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—41no—
102C2×Dic11—41no—
103D44—81no—
104D44—81no—
105D44—81no—
106D44—81no—
107D44—161no—
108Dic22—22no—
109Dic22—21no—
110Dic22—21no—
111Dic22—41no—
112C8×C11—21no—
113C8×C11—81no—
114C8×C11C2×SD1611yescharacteristic
115C8×C11#13711yescharacteristic
116C11⋊C8—41no—
117#557—221no—
118C2×SD32—221no—
119#500C2×D1111yescharacteristic
120#499—221no—
121#493—111no—
122#479—222no—
123#475—221no—
124#460—221no—
125C8×Q8—111no—
126C4×Q16—111no—
127C4×Q16—221no—
128C4⋊C16C2×D1111yescharacteristic
129#357—221no—
130#357—222no—
131C4×C16—111no—
132#335C2×D1111yescharacteristic
133#331—221no—
134C22×C11#44711yescharacteristic
135C2×D11—161no—
136C2×D11—161no—
137C2×D11—161no—
138C4×C11—21no—
139C4×C11—82no—
140C4×C11#44811yescharacteristic
141C4×C11#45411yescharacteristic
142C4×C11#50811yescharacteristic
143C4×C11#50911yescharacteristic
144Dic11—42no—
145Dic11—41no—
146Dic11—41no—
147Dic11—81no—
148C2×Q16—111no—
149C2×SD16—441no—
150C2×D8—221no—
151C2×D8—221no—
152C4⋊Q8—21no—
153C4⋊Q8—441no—
154#127—221no—
155#125—222no—
156#125—442no—
157C4×Q8—111no—
158C4×Q8—222no—
159C4×Q8—221no—
160C4×Q8—441no—
161SD32—442no—
162C2×C16—21no—
163C2×C16—221no—
164#107—21no—
165#107—111no—
166#107D4412yes—
167#106—222no—
168C4⋊C8—21no—
169C4⋊C8—111no—
170C4⋊C8—221no—
171#103—222no—
172#103—221no—
173#102—441no—
174C4×C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162711yescharacteristic
177C2×C11#218611yescharacteristic
178C2×C11#219311yescharacteristic
179D11—321no—
180C2×Q8—41no—
181C2×Q8—111no—
182C2×Q8—221no—
183C2×D4—441no—
184C2×D4—441no—
185C2×D4—441no—
186Q16—112no—
187Q16—221no—
188SD16—882no—
189D8—442no—
190D8—441no—
191D8—441no—
192C2×C8—41no—
193C2×C8—221no—
194C2×C8C2×D4411yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—111no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—441no—
205C42—221no—
206C42—442no—
207C42—441no—
208C42D4×D1111yescharacteristic
209C16—41no—
210C16—441no—
211C11#1235311yescharacteristic, complemented, Sylow
212C23—881no—
213Q8—81no—
214Q8—81no—
215Q8—221no—
216Q8—221no—
217Q8—222no—
218Q8—441no—
219D4—881no—
220D4—881no—
221D4—881no—
222D4—881no—
223D4—1761no—
224C2×C4—42no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4#6693511yescharacteristic
230C2×C4D8×D1111yescharacteristic
231C2×C4#6696711yescharacteristic
232C8—21no—
233C8—81no—
234C8—441no—
235C8SD16×D1111yescharacteristic
236C8#6697111yescharacteristic
237C22—1761no—
238C22—1761no—
239C22—1761no—
240C22#1062238611yescharacteristic
241C4—21no—
242C4—82no—
243C4—442no—
244C4—441no—
245C4—441no—
246C4—881no—
247C4#1062236611yescharacteristic
248C4#1062241911yescharacteristic
249C4#1062252411yescharacteristic
250C4#1062252911yescharacteristic
251C2—3521no—
252C2#1306772011yescharacteristic
253C2#1307054011yescharacteristic
254C2#1307058311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1364C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1364D11
hypocenterC11#12353
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #13081509C2semidirect
5. #13066594C2semidirect
6. #13066579C2semidirect
7. C11×#1364C2semidirect
78. Dic44SD16semidirect
89. #1364D11semidirect
211. C11#12353semidirect

Maximal subgroups

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

subgroupindex
#130815092
#130708412
#130706572
#130679772
#130665942
#130665792
C11×#13642
#1235311