Finite Group Databasebeta

← #14667678

Subgroups — #14667678

Order 2816.

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

normal subgroups only

This group has 282 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#13081621C211yesmaximal, characteristic
2#13070845C211yesmaximal, characteristic
3#13068017C211yesmaximal, characteristic
4#13066666C211yesmaximal, characteristic
5#13066594C211yesmaximal, characteristic
6#13066580C211yesmaximal, characteristic
7C11×#2227C211yesmaximal, characteristic
8#10623098—21no—
9C11×#500C2211yescharacteristic
10C4×C11×Q16C2211yescharacteristic
11#10622794—21no—
12#10622704—21no—
13#10622644—21no—
14#10622486—21no—
15#10622406—22no—
16#10622312C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C11×#366—21no—
19C11×C4⋊C16C2211yescharacteristic
20C11×#358—21no—
21#10622184—21no—
22#10622130—22no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C11×C4⋊Q8—21no—
27C4×Q8×C11—21no—
28#66997—22no—
29C2×#4326—22no—
30C2×Dic44—21no—
31C2×Dic44D412yes—
32#66942—42no—
33#66940—22no—
34#66923—41no—
35#66922—21no—
36C4×Dic22—41no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107—21no—
41C11×#107D411yescharacteristic
42C11×#103—21no—
43C4×C8×C11C2311yescharacteristic
44Dic11⋊C8—21no—
45C8×Dic11—21no—
46C2×C11⋊C16—21no—
47#66874—22no—
48#66874—41no—
49#66871—41no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12386—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Q8×C11—41no—
55C2×Dic22—22no—
56C2×Dic22D811yescharacteristic
57C11×Q16—21no—
58C11×Q16—21no—
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61C11×C4⋊C4—21no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C42×C11—41no—
66C42×C11C2×D411yescharacteristic
67#4326—82no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11D811yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75C4×Dic11—21no—
76C4×Dic11—42no—
77C2×C11⋊C8—21no—
78C2×C11⋊C8—41no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3395—111no—
85#2241—111no—
86#2227D1111yescharacteristic
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—41no—
92Q8×C11—41no—
93Q8×C11—161no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—81no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—42no—
103Dic22—21no—
104Dic22—42no—
105Dic22—42no—
106Dic22Q3212yes—
107C8×C11—21no—
108C8×C11#13511yescharacteristic
109C8×C11#13711yescharacteristic
110C11⋊C8—41no—
111C11⋊C8—81no—
112#557—221no—
113#500C2×D1111yescharacteristic
114#494—111no—
115#494—221no—
116#477—221no—
117#462—222no—
118#462—221no—
119C8×Q8—111no—
120C4×Q16—221no—
121C4×Q16C2×D1111yescharacteristic
122#366—21no—
123C4⋊C16C2×D1111yescharacteristic
124#358—21no—
125#358—222no—
126C4×C16—111no—
127#335—111no—
128#333—221no—
129C22×C11#44711yescharacteristic
130C4×C11—21no—
131C4×C11—81no—
132C4×C11—81no—
133C4×C11—161no—
134C4×C11#45211yescharacteristic
135C4×C11#45511yescharacteristic
136C4×C11C2×Q3211yescharacteristic
137C4×C11#51011yescharacteristic
138Dic11—22no—
139Dic11—41no—
140Dic11—82no—
141C2×Q16—112no—
142C2×Q16—222no—
143C2×Q16—221no—
144C2×Q16C22⋊D1111yescharacteristic
145C4⋊Q8—21no—
146C4⋊Q8—222no—
147C4⋊Q8—221no—
148#125—441no—
149#125—442no—
150C4×Q8—21no—
151C4×Q8—111no—
152C4×Q8—222no—
153C4×Q8—441no—
154C2×C16—21no—
155C2×C16—221no—
156#107—21no—
157#107—21no—
158#107—441no—
159#107C22⋊D1111yescharacteristic
160C4⋊C8—111no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163#103—21no—
164#103—222no—
165#103—441no—
166C4×C8—221no—
167C4×C8C22×D1111yescharacteristic
168C2×C11#164111yescharacteristic
169C2×C11#218811yescharacteristic
170C2×C11#219311yescharacteristic
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—111no—
174C2×Q8—222no—
175Q16—21no—
176Q16—21no—
177Q16—442no—
178Q16—441no—
179Q16—441no—
180Q16—882no—
181C2×C8—221no—
182C2×C8—441no—
183C2×C8D4×D1111yescharacteristic
184C2×C8C2×C22⋊D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—111no—
190C4⋊C4—221no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C42—41no—
197C42—221no—
198C42—442no—
199C42D4×D1111yescharacteristic
200C16—41no—
201C16—441no—
202C11#1238611yescharacteristic, complemented, Sylow
203Q8—41no—
204Q8—41no—
205Q8—112no—
206Q8—161no—
207Q8—221no—
208Q8—442no—
209Q8—442no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—442no—
216C2×C4D8×D1111yescharacteristic
217C2×C4#6696411yescharacteristic
218C2×C4#6699011yescharacteristic
219C8—21no—
220C8—441no—
221C8—881no—
222C8#6699511yescharacteristic
223C8#6700311yescharacteristic
224C22#1062276911yescharacteristic
225C4—21no—
226C4—81no—
227C4—81no—
228C4—161no—
229C4—222no—
230C4—441no—
231C4—882no—
232C4D11×Q3211yescharacteristic
233C4#1062253111yescharacteristic
234C4#1062266011yescharacteristic
235C4#1062281511yescharacteristic
236C2#1306780811yescharacteristic
237C2#1307054811yescharacteristic
238C2#1307057711yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2227C2
socle, prime radicalC22×C11#447
hypercenter#2227D11
hypocenterC11#12386
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
202. C11#12386semidirect

Maximal subgroups

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

subgroupindex
#130816212
#130708452
#130680172
#130666662
#130665942
#130665802
C11×#22272
#1238611