Finite Group Databasebeta

← #14667686

Subgroups — #14667686

Order 2816.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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, complemented
2#13070763C211yesmaximal, characteristic
3#13068020C211yesmaximal, characteristic, complemented
4#13066665C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#3393C211yesmaximal, characteristic
8C11×#556—21no—
9C11×#495—21no—
10C11×#494C2211yescharacteristic
11C11×#464—22no—
12C11×#461—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×D8C2211yescharacteristic
16#10622634—21no—
17#10622295C2211yescharacteristic
18#10622202—22no—
19#10622200—21no—
20#10622128—21no—
21#10622119—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×SD16—22no—
28C2×C11×D8D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×#126—42no—
31C11×#124—22no—
32C11×C22⋊Q8—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C11×#117—41no—
37#66922—21no—
38C11×#107D411yescharacteristic
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#103—22no—
42C11×#102—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#12387—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11D811yescharacteristic
55C2×D4×C11—21no—
56C22×C4×C11—41no—
57C2×Dic22—41no—
58C11×Q16—41no—
59C11×Q16—41no—
60C11×Q16—42no—
61C11×SD16—82no—
62C11×D8—21no—
63C11×D8—21no—
64C2×C8×C11—21no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4D811yescharacteristic
73C11×C22⋊C4—42no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—41no—
76C42×C11—21no—
77C42×C11—42no—
78C42×C11C2×D411yescharacteristic
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C2×C11⋊C8—41no—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3393D1111yescharacteristic
85#2241—111no—
86#2226—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1331—111no—
91C23×C11—41no—
92Q8×C11—21no—
93Q8×C11—21no—
94Q8×C11—42no—
95Q8×C11—42no—
96D4×C11—41no—
97D4×C11—41no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—81no—
103C2×C4×C11—81no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×Dic11—81no—
108Dic22—161no—
109C8×C11—21no—
110C8×C11—41no—
111C8×C11#13511yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—81no—
114#556—21no—
115#500—111no—
116#495—21no—
117#494C2×D1111yescharacteristic
118#477—221no—
119#464—22no—
120#461—21no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—21no—
123C4×D8C2×D1111yescharacteristic
124#367—221no—
125C4⋊C16—111no—
126#358—222no—
127#357—221no—
128C4×C16—111no—
129#335—111no—
130#333—221no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11—81no—
134C22×C11#44711yescharacteristic
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—41no—
138C4×C11—82no—
139C4×C11—81no—
140C4×C11#45211yescharacteristic
141C4×C11#45511yescharacteristic
142C4×C11#50811yescharacteristic
143C4×C11#51011yescharacteristic
144Dic11—161no—
145C2×Q16—21no—
146C2×Q16C22⋊D1112yes—
147C2×SD16—22no—
148C2×D8C22⋊D1111yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—221no—
151#126—42no—
152#124—22no—
153C22⋊Q8—41no—
154C4×Q8—22no—
155C4×Q8C22⋊D1111yescharacteristic
156C4×D4—21no—
157#117—41no—
158C2×C16—221no—
159C2×C16—221no—
160#107—221no—
161#107—221no—
162#107—441no—
163#107C22⋊D1111yescharacteristic
164C4⋊C8—21no—
165C4⋊C8—221no—
166C4⋊C8C22⋊D1111yescharacteristic
167#103—22no—
168#103—441no—
169#102—21no—
170C4×C8—21no—
171C4×C8C22×D1111yescharacteristic
172C2×C11—161no—
173C2×C11#164111yescharacteristic
174C2×C11#218911yescharacteristic
175C2×C11#219311yescharacteristic
176C2×Q8—22no—
177C2×Q8—441no—
178C2×Q8#432311yescharacteristic
179C2×D4—21no—
180C22×C4—41no—
181Q16—42no—
182Q16—41no—
183Q16—41no—
184SD16—82no—
185D8—21no—
186D8—21no—
187C2×C8—21no—
188C2×C8—441no—
189C2×C8C2×C22⋊D1111yescharacteristic
190C2×C8C2×C22⋊D1111yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4#432311yescharacteristic
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—41no—
202C42—21no—
203C42—42no—
204C42C2×C22⋊D1111yescharacteristic
205C16—441no—
206C16—441no—
207C11#1238711yescharacteristic, complemented, Sylow
208C23—41no—
209Q8—21no—
210Q8—21no—
211Q8—42no—
212Q8—42no—
213Q8—1761no—
214D4—41no—
215D4—41no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—881no—
223C2×C4C2×#432311yescharacteristic
224C2×C4#6698511yescharacteristic
225C2×C4#6700611yescharacteristic
226C8—21no—
227C8—41no—
228C8—881no—
229C8#6700311yescharacteristic
230C8#6700411yescharacteristic
231C22—81no—
232C22—81no—
233C22—81no—
234C22#1062283011yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—82no—
239C4—81no—
240C4—1761no—
241C4#1062280711yescharacteristic
242C4#1062280811yescharacteristic
243C4#1062285211yescharacteristic
244C4#1062285511yescharacteristic
245C2—161no—
246C2#1306780911yescharacteristic
247C2#1307055611yescharacteristic
248C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3393C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#3393D11
hypocenterC11#12387
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13070843C2semidirect
3. #13068020C2semidirect
4. #13066665C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
207. C11#12387semidirect

Maximal subgroups

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

subgroupindex
#130708432
#130707632
#130680202
#130666652
Q8⋊(C11⋊C16)2
#130665772
C11×#33932
#1238711