Finite Group Databasebeta

← #14667455

Subgroups — #14667455

Order 2816.

298 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081505C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic
3#13067973C211yesmaximal, characteristic
4#13066670C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066580C211yesmaximal, characteristic, complemented
7C11×#2207C211yesmaximal, characteristic
8#10623101—21no—
9C2×C11×SD32—21no—
10C11×#493C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12Q16×Dic11—21no—
13#10622688—21no—
14#10622633—21no—
15#10622491—21no—
16#10622409—22no—
17#10622295C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#357—21no—
21#10622200—22no—
22#10622182—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C11×#127—21no—
29C4×Q8×C11—21no—
30Q8×Dic11—22no—
31C2×#4324—41no—
32#66943—22no—
33#66943—42no—
34#66922—21no—
35#66922—41no—
36C4×Dic22—41no—
37C4×Dic22D411yescharacteristic
38C11×SD32—42no—
39C2×C11×C16—21no—
40C11×#107D411yescharacteristic
41C11×#103—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—22no—
44#66896—41no—
45#66882—21no—
46#66882D412yes—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50#66872—22no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12353—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×Dic22—41no—
59C2×Dic22D811yescharacteristic
60C11×Q16—21no—
61C11×Q16SD1612yescomplemented
62C11×D8—42no—
63C11×D8—41no—
64C11×D8—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C42×C11—41no—
70C42×C11C2×D411yescharacteristic
71#4324—82no—
72C4⋊Dic11—22no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11D811yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—42no—
79C4×Dic11—21no—
80C4×Dic11—42no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—41no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3383—111no—
86#2240—111no—
87#2207D1111yescharacteristic
88#1668—111no—
89#1364—111no—
90Q8⋊C16—111no—
91#1332—111no—
92C23×C11—81no—
93Q8×C11—22no—
94Q8×C11—41no—
95D4×C11—81no—
96D4×C11—81no—
97D4×C11—81no—
98D4×C11—81no—
99D4×C11—161no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—42no—
108Dic22—21no—
109Dic22—21no—
110Dic22—81no—
111Dic22—81no—
112C8×C11—21no—
113C8×C11C2×SD1611yescharacteristic
114C8×C11#13711yescharacteristic
115C11⋊C8—41no—
116C11⋊C8—81no—
117#557—221no—
118C2×SD32—21no—
119#500—111no—
120#499—221no—
121#493C2×D1111yescharacteristic
122#479—222no—
123#475—221no—
124#460—221no—
125C8×Q8—111no—
126C4×Q16—221no—
127C4×Q16C2×D1111yescharacteristic
128C4⋊C16C2×D1111yescharacteristic
129#357—21no—
130#357—222no—
131C4×C16—111no—
132#335—111no—
133#331—221no—
134C22×C11—161no—
135C22×C11—161no—
136C22×C11—161no—
137C22×C11#44711yescharacteristic
138C4×C11—21no—
139C4×C11—42no—
140C4×C11—81no—
141C4×C11#44811yescharacteristic
142C4×C11#45411yescharacteristic
143C4×C11#50811yescharacteristic
144C4×C11#50911yescharacteristic
145Dic11—41no—
146Dic11—41no—
147Dic11—82no—
148C2×Q16C22⋊D1111yescharacteristic
149C2×SD16—441no—
150C2×D8—21no—
151C2×D8—21no—
152C4⋊Q8—221no—
153C4⋊Q8—441no—
154#127—21no—
155#125—222no—
156#125—442no—
157C4×Q8—21no—
158C4×Q8—111no—
159C4×Q8—222no—
160C4×Q8—441no—
161SD32—42no—
162C2×C16—21no—
163C2×C16—221no—
164#107—112no—
165#107—221no—
166#107C22⋊D1111yescharacteristic
167#106—222no—
168C4⋊C8—111no—
169C4⋊C8—221no—
170C4⋊C8—221no—
171#103—21no—
172#103—222no—
173#102—441no—
174C4×C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11—321no—
177C2×C11#162711yescharacteristic
178C2×C11#218611yescharacteristic
179C2×C11#219311yescharacteristic
180C2×Q8—21no—
181C2×Q8—111no—
182C2×Q8—441no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4—41no—
186Q16—21no—
187Q16#432412yescomplemented
188SD16—882no—
189D8—42no—
190D8—41no—
191D8—41no—
192C2×C8—221no—
193C2×C8—441no—
194C2×C8D4×D1111yescharacteristic
195C2×C8C2×C22⋊D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—41no—
198C4⋊C4—111no—
199C4⋊C4—221no—
200C4⋊C4—222no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—441no—
205C42—41no—
206C42—221no—
207C42—442no—
208C42D4×D1111yescharacteristic
209C16—41no—
210C16—441no—
211C11#1235311yescharacteristic, complemented, Sylow
212C23—81no—
213Q8—22no—
214Q8—41no—
215Q8—221no—
216Q8—221no—
217Q8—881no—
218Q8—881no—
219D4—81no—
220D4—81no—
221D4—81no—
222D4—81no—
223D4—161no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—442no—
229C2×C4D8×D1111yescharacteristic
230C2×C4#6696411yescharacteristic
231C2×C4#6699011yescharacteristic
232C8—21no—
233C8—441no—
234C8—881no—
235C8C2×#432411yescharacteristic
236C8#6700411yescharacteristic
237C22—161no—
238C22—161no—
239C22—161no—
240C22#1062276911yescharacteristic
241C4—21no—
242C4—42no—
243C4—81no—
244C4—441no—
245C4—441no—
246C4—882no—
247C4#1062252711yescharacteristic
248C4#1062252911yescharacteristic
249C4#1062265311yescharacteristic
250C4#1062281411yescharacteristic
251C2—321no—
252C2#1306771811yescharacteristic
253C2#1307053811yescharacteristic
254C2#1307057711yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2207C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#2207D11
hypocenterC11#12353
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13081505C2semidirect
4. #13066670C2semidirect
5. #13066594C2semidirect
6. #13066580C2semidirect
61. C11×Q16SD16semidirect
187. Q16#4324semidirect
211. C11#12353semidirect

Maximal subgroups

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

subgroupindex
#130815052
#130708392
#130679732
#130666702
#130665942
#130665802
C11×#22072
#1235311