Finite Group Databasebeta

← #14667679

Subgroups — #14667679

Order 2816.

282 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070843C211yesmaximal, characteristic
2#13070768C211yesmaximal, characteristic
3#13068020C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic
6#13066580C211yesmaximal, characteristic
7C11×#3395C211yesmaximal, characteristic
8C11×#557—21no—
9C11×#494—21no—
10C11×#494C2211yescharacteristic
11C11×#462—22no—
12C11×#462—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×Q16C2211yescharacteristic
16#10622634—21no—
17#10622295C2211yescharacteristic
18#10622202—21no—
19#10622202—22no—
20#10622127—21no—
21#10622119—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—22no—
26C2×C11×Q16—21no—
27C2×C11×Q16D411yescharacteristic
28C2×C11×Q16D412yes—
29C11×C4⋊Q8—22no—
30C11×C4⋊Q8—21no—
31C11×#125—42no—
32C11×#125—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11—21no—
35C4×Q8×C11—41no—
36C4×Q8×C11D411yescharacteristic
37#66922—21no—
38C11×#107D411yescharacteristic
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#103—22no—
42C11×#103—21no—
43C4×C8×C11—21no—
44C4×C8×C11C2311yescharacteristic
45#66899—41no—
46#66882—21no—
47#66882—21no—
48C2×C11⋊C16—21no—
49C2×C11⋊C16—21no—
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52#12386—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Q8×C11—22no—
55C2×Q8×C11D811yescharacteristic
56C2×Dic22—41no—
57C11×Q16—21no—
58C11×Q16—21no—
59C11×Q16—41no—
60C11×Q16—41no—
61C11×Q16—42no—
62C11×Q16—82no—
63C2×C8×C11—21no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4D811yescharacteristic
75C42×C11—21no—
76C42×C11—42no—
77C42×C11—41no—
78C42×C11C2×D411yescharacteristic
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C2×C11⋊C8—41no—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3395D1111yescharacteristic
85#2241—111no—
86#2227—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—21no—
92Q8×C11—41no—
93Q8×C11—42no—
94Q8×C11—42no—
95Q8×C11—41no—
96Q8×C11Q3212yes—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—81no—
106Dic22—161no—
107C8×C11—21no—
108C8×C11—41no—
109C8×C11#13511yescharacteristic
110C8×C11#13711yescharacteristic
111C11⋊C8—81no—
112#557—21no—
113#500—111no—
114#494—21no—
115#494C2×D1111yescharacteristic
116#477—221no—
117#462—22no—
118#462—21no—
119C8×Q8C2×D1111yescharacteristic
120C4×Q16—21no—
121C4×Q16C2×D1111yescharacteristic
122#366—221no—
123C4⋊C16—111no—
124#358—221no—
125#358—222no—
126C4×C16—111no—
127#335—111no—
128#333—221no—
129C22×C11#44711yescharacteristic
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—41no—
133C4×C11—81no—
134C4×C11—82no—
135C4×C11—81no—
136C4×C11#45211yescharacteristic
137C4×C11#45511yescharacteristic
138C4×C11C2×Q3211yescharacteristic
139C4×C11#51011yescharacteristic
140Dic11—161no—
141C2×Q16—22no—
142C2×Q16—21no—
143C2×Q16C22⋊D1111yescharacteristic
144C2×Q16C22⋊D1112yes—
145C4⋊Q8—22no—
146C4⋊Q8—21no—
147C4⋊Q8—221no—
148#125—42no—
149#125—41no—
150C4×Q8—22no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8C22⋊D1111yescharacteristic
154C2×C16—221no—
155C2×C16—221no—
156#107—221no—
157#107—221no—
158#107—441no—
159#107C22⋊D1111yescharacteristic
160C4⋊C8—21no—
161C4⋊C8—221no—
162C4⋊C8C22⋊D1111yescharacteristic
163#103—22no—
164#103—21no—
165#103—441no—
166C4×C8—21no—
167C4×C8C22×D1111yescharacteristic
168C2×C11#164111yescharacteristic
169C2×C11#218811yescharacteristic
170C2×C11#219311yescharacteristic
171C2×Q8—21no—
172C2×Q8—22no—
173C2×Q8—441no—
174C2×Q8#432311yescharacteristic
175Q16—21no—
176Q16—21no—
177Q16—42no—
178Q16—41no—
179Q16—41no—
180Q16—82no—
181C2×C8—21no—
182C2×C8—441no—
183C2×C8C2×C22⋊D1111yescharacteristic
184C2×C8C2×C22⋊D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C4⋊C4#432311yescharacteristic
196C42—21no—
197C42—42no—
198C42—41no—
199C42C2×C22⋊D1111yescharacteristic
200C16—441no—
201C16—441no—
202C11#1238611yescharacteristic, complemented, Sylow
203Q8—21no—
204Q8—41no—
205Q8—42no—
206Q8—42no—
207Q8—41no—
208Q8—1761no—
209Q8#6689312yes—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—881no—
216C2×C4C2×#432311yescharacteristic
217C2×C4#6698511yescharacteristic
218C2×C4#6700611yescharacteristic
219C8—21no—
220C8—41no—
221C8—881no—
222C8#6700311yescharacteristic
223C8#6700411yescharacteristic
224C22#1062283011yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—81no—
229C4—82no—
230C4—81no—
231C4—1761no—
232C4#1062279211yescharacteristic
233C4C2×#6689311yescharacteristic
234C4#1062285211yescharacteristic
235C4#1062285511yescharacteristic
236C2#1306780911yescharacteristic
237C2#1307055011yescharacteristic
238C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3395C2
socle, prime radicalC22×C11#447
hypercenter#3395D11
hypocenterC11#12386
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

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
#130708432
#130707682
#130680202
#130666652
Q8⋊(C11⋊C16)2
#130665802
C11×#33952
#1238611