Finite Group Databasebeta

← #14667676

Subgroups — #14667676

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#13081620C211yesmaximal, characteristic
2#13070765C211yesmaximal, characteristic
3#13068017C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic
5#13066596C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×#2241C211yesmaximal, characteristic
8#10623252—21no—
9C11×#500C2211yescharacteristic
10C11×#494C2211yescharacteristic
11Q16×Dic11—21no—
12#10622795—22no—
13#10622794—21no—
14#10622704—21no—
15#10622703—21no—
16C4×Dic44C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C11×#358—22no—
19C4×C11×C16C2211yescharacteristic
20#10622184—21no—
21#10622130—21no—
22#10622127—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29Q8×Dic11—22no—
30#66997—22no—
31C2×#4326—22no—
32C2×Dic44D411yescharacteristic
33#66943—41no—
34#66942—42no—
35#66940—41no—
36C4×Dic22—21no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107—21no—
41C4×C8×C11C2311yescharacteristic
42#66899—22no—
43#66882D411yescharacteristic
44#66880—21no—
45Dic11⋊C8—21no—
46C8×Dic11—21no—
47C2×C11⋊C16—21no—
48#66874—41no—
49#66871—41no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12386—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11—41no—
55C2×Dic22—21no—
56C2×Dic22D811yescharacteristic
57C11×Q16—41no—
58C11×Q16—41no—
59C11×Q16—42no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C42×C11C2×D411yescharacteristic
67#4326—82no—
68C4⋊Dic11—21no—
69C4⋊Dic11—42no—
70C4⋊Dic11D811yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic11⋊C4—41no—
75C4×Dic11—21no—
76C4×Dic11—42no—
77C4×Dic11—41no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80Dic44—21no—
81Dic44—21no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3395—111no—
85#2241D1111yescharacteristic
86#2227—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—42no—
92Q8×C11—42no—
93Q8×C11—161no—
94C2×C4×C11—42no—
95C2×C4×C11—81no—
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—
103Dic22—21no—
104Dic22—41no—
105Dic22—41no—
106Dic22Q3212yes—
107C8×C11—21no—
108C8×C11#13511yescharacteristic
109C8×C11#13711yescharacteristic
110C11⋊C8—41no—
111C11⋊C8—81no—
112#557—221no—
113#500C2×D1111yescharacteristic
114#494—221no—
115#494C2×D1111yescharacteristic
116#477—221no—
117#462—221no—
118#462—222no—
119C8×Q8—111no—
120C4×Q16—111no—
121C4×Q16—221no—
122#366—221no—
123C4⋊C16—111no—
124#358—22no—
125#358—221no—
126C4×C16C2×D1111yescharacteristic
127#335—111no—
128#333—221no—
129C22×C11#44711yescharacteristic
130C4×C11—21no—
131C4×C11—82no—
132C4×C11—161no—
133C4×C11#45211yescharacteristic
134C4×C11#45511yescharacteristic
135C4×C11C2×Q3211yescharacteristic
136C4×C11#51011yescharacteristic
137Dic11—22no—
138Dic11—41no—
139Dic11—81no—
140Dic11—81no—
141C2×Q16—21no—
142C2×Q16—111no—
143C2×Q16—222no—
144C2×Q16C22⋊D1112yes—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147C4⋊Q8—222no—
148#125—441no—
149#125—442no—
150C4×Q8—111no—
151C4×Q8—222no—
152C4×Q8—221no—
153C4×Q8—441no—
154C2×C16—21no—
155C2×C16—221no—
156#107—21no—
157#107—21no—
158#107—111no—
159#107—441no—
160C4⋊C8—111no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163#103—222no—
164#103—221no—
165#103—441no—
166C4×C8—221no—
167C4×C8C22×D1111yescharacteristic
168C2×C11#164111yescharacteristic
169C2×C11#218811yescharacteristic
170C2×C11#219311yescharacteristic
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—111no—
174C2×Q8—221no—
175Q16—42no—
176Q16—41no—
177Q16—41no—
178Q16—221no—
179Q16—221no—
180Q16—882no—
181C2×C8—221no—
182C2×C8—441no—
183C2×C8D4×D1111yescharacteristic
184C2×C8C2×C22⋊D1111yescharacteristic
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—111no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—441no—
196C42—221no—
197C42—442no—
198C42—441no—
199C42D4×D1111yescharacteristic
200C16—41no—
201C16—441no—
202C11#1238611yescharacteristic, complemented, Sylow
203Q8—42no—
204Q8—42no—
205Q8—112no—
206Q8—161no—
207Q8—221no—
208Q8—441no—
209Q8—441no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4D8×D1111yescharacteristic
217C2×C4#6696411yescharacteristic
218C2×C4#6699011yescharacteristic
219C8—21no—
220C8—441no—
221C8—881no—
222C8#6696811yescharacteristic
223C8#6696911yescharacteristic
224C22#1062276911yescharacteristic
225C4—21no—
226C4—82no—
227C4—161no—
228C4—222no—
229C4—441no—
230C4—881no—
231C4—881no—
232C4D11×Q3211yescharacteristic
233C4#1062253111yescharacteristic
234C4#1062267411yescharacteristic
235C4#1062278611yescharacteristic
236C2#1306780611yescharacteristic
237C2#1307054811yescharacteristic
238C2#1307057911yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2241C2
socle, prime radicalC22×C11#447
hypercenter#2241D11
hypocenterC11#12386
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

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
#130816202
#130707652
#130680172
#130666652
#130665962
#130665812
C11×#22412
#1238611