Finite Group Databasebeta

← #14667682

Subgroups — #14667682

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#13070844C211yesmaximal, characteristic
3#13070768C211yesmaximal, characteristic
4#13068021C211yesmaximal, characteristic
5#13066664C211yesmaximal, characteristic
6#13066596C211yesmaximal, characteristic
7C11×#1332C211yesmaximal, characteristic
8#10623098—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622794—21no—
11#10622644—21no—
12#10622486—21no—
13#10622463—21no—
14#10622406—22no—
15#10622312C2211yescharacteristic
16#10622295C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C4×C11×C16C2211yescharacteristic
19C11×#335C2211yescharacteristic
20#10622202—21no—
21#10622141—22no—
22#10622127—21no—
23#10622119—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27#66997—22no—
28C2×#4326—22no—
29C2×Dic44—21no—
30C2×Dic44D412yes—
31#66942—42no—
32#66940—22no—
33#66923—41no—
34#66922—21no—
35#66922—21no—
36C4×Dic22—41no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×C4⋊C8—21no—
41C11×#103—21no—
42C4×C8×C11C2311yescharacteristic
43#66882—21no—
44#66882—21no—
45#66882—41no—
46#66880—41no—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50#66874—22no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12386—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Dic22—22no—
55C2×Dic22—41no—
56C2×Dic22D811yescharacteristic
57C11×Q16—21no—
58C11×Q16—21no—
59C2×C8×C11—41no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4—41no—
64C42×C11—41no—
65C42×C11C2×D411yescharacteristic
66#4326—82no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11D811yescharacteristic
72Dic11⋊C4—21no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C2×C11⋊C8—21no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3395—111no—
85#2241—111no—
86#2227—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1332D1111yescharacteristic
91Q8×C11—41no—
92Q8×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—42no—
101C2×Dic11—81no—
102Dic22—21no—
103Dic22—42no—
104Dic22—42no—
105Dic22—161no—
106Dic22Q3212yes—
107C8×C11—21no—
108C8×C11—81no—
109C8×C11#13511yescharacteristic
110C8×C11#13711yescharacteristic
111C11⋊C8—41no—
112#557—221no—
113#500—111no—
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—221no—
123C4⋊C16—111no—
124#358—222no—
125#358—221no—
126C4×C16C2×D1111yescharacteristic
127#335C2×D1111yescharacteristic
128#333—221no—
129C22×C11#44711yescharacteristic
130C4×C11—21no—
131C4×C11—81no—
132C4×C11—81no—
133C4×C11#45211yescharacteristic
134C4×C11#45511yescharacteristic
135C4×C11C2×Q3211yescharacteristic
136C4×C11#51011yescharacteristic
137Dic11—22no—
138Dic11—41no—
139Dic11—82no—
140Dic11—161no—
141C2×Q16—112no—
142C2×Q16—222no—
143C2×Q16—221no—
144C2×Q16D4411yescharacteristic
145C4⋊Q8—222no—
146C4⋊Q8—221no—
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—221no—
157#107—221no—
158#107—441no—
159#107D4411yescharacteristic
160C4⋊C8—21no—
161C4⋊C8—111no—
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—111no—
173C2×Q8—222no—
174C2×Q8—441no—
175Q16—21no—
176Q16—21no—
177Q16—442no—
178Q16—441no—
179Q16—441no—
180Q16—882no—
181C2×C8—41no—
182C2×C8—221no—
183C2×C8C2×D4411yescharacteristic
184C2×C8D4×D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—111no—
188C4⋊C4—221no—
189C4⋊C4—442no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—441no—
193C4⋊C4—441no—
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—221no—
207Q8—442no—
208Q8—442no—
209Q8—1761no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—442no—
215C2×C4—881no—
216C2×C4#6693511yescharacteristic
217C2×C4D8×D1111yescharacteristic
218C2×C4#6696711yescharacteristic
219C8—21no—
220C8—81no—
221C8—441no—
222C8#6695711yescharacteristic
223C8#6696211yescharacteristic
224C22#1062238611yescharacteristic
225C4—21no—
226C4—81no—
227C4—81no—
228C4—222no—
229C4—441no—
230C4—882no—
231C4—1761no—
232C4#1062234611yescharacteristic
233C4#1062243811yescharacteristic
234C4#1062252811yescharacteristic
235C4D11×Q3211yescharacteristic
236C2#1306781211yescharacteristic
237C2#1307055111yescharacteristic
238C2#1307058111yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socle, prime radicalC22×C11#447
hypercenter#1332D11
hypocenterC11#12386
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

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
#130708442
#130707682
#130680212
#130666642
#130665962
C11×#13322
#1238611