Finite Group Databasebeta

← #14667688

Subgroups — #14667688

Order 2816.

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

normal subgroups only

This group has 288 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#13081605C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070764C211yesmaximal, characteristic
4#13068020C211yesmaximal, characteristic, complemented
5#13066666C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic
7C11×Q8⋊C16C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622634—21no—
11#10622458—22no—
12#10622454—21no—
13#10622312C2211yescharacteristic
14C4×Dic44—21no—
15#10622309—21no—
16C4×D88C2211yescharacteristic
17#10622295C2211yescharacteristic
18C11×C4⋊C16C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20#10622147—21no—
21#10622143—21no—
22#10622141—22no—
23#10622119—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26#66999—41no—
27C2×Dic44—21no—
28C2×Dic44D412yes—
29C2×D88D411yescharacteristic
30C2×#4314—22no—
31#66951—42no—
32#66945—41no—
33#66928—22no—
34C4×D44—21no—
35#66922—21no—
36#66922—21no—
37C4×Dic22—22no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—41no—
45#66885—21no—
46#66882—21no—
47#66882—21no—
48#66882D411yescharacteristic
49#66880—22no—
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52#12387—111nomaximal, Sylow
53C2×Q8×C11D811yescharacteristic
54C2×D44—21no—
55C2×C4×D11—41no—
56C2×Dic22—22no—
57C2×Dic22—41no—
58C2×C8×C11—21no—
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61C11×C4⋊C4—21no—
62C11×C4⋊C4D811yescharacteristic
63C42×C11—21no—
64C42×C11C2×D411yescharacteristic
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—41no—
68C4⋊Dic11—21no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73Dic11⋊C4—42no—
74C4×Dic11—42no—
75C2×C11⋊C8—41no—
76Dic44—42no—
77Dic44—41no—
78Dic44—41no—
79D88—21no—
80D88—21no—
81#4314—82no—
82C11×C16—41no—
83C11×C16—41no—
84#3393—111no—
85#2241—111no—
86#2226—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16D1111yescharacteristic, complemented
90#1331—111no—
91C22×D11—41no—
92Q8×C11—21no—
93Q8×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—81no—
102D44—41no—
103D44—41no—
104C4×D11—81no—
105C4×D11—81no—
106Dic22—42no—
107Dic22—42no—
108Dic22—161no—
109C8×C11—21no—
110C8×C11—41no—
111C8×C11#13511yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—81no—
114#556—221no—
115#500—111no—
116#495—221no—
117#494—111no—
118#477—221no—
119#464—222no—
120#461—221no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—221no—
123C4×D8—111no—
124#367—221no—
125C4⋊C16C2×D1111yescharacteristic
126#358—222no—
127#357—221no—
128C4×C16C2×D1111yescharacteristic
129#335—111no—
130#333—221no—
131C22×C11#44711yescharacteristic
132C2×D11—81no—
133C2×D11—81no—
134C2×D11—81no—
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—41no—
138C4×C11#45211yescharacteristic
139C4×C11#45511yescharacteristic
140C4×C11#50811yescharacteristic
141C4×C11#51011yescharacteristic
142Dic11—82no—
143Dic11—81no—
144Dic11—161no—
145C2×Q16—112no—
146C2×Q16—221no—
147C2×SD16—222no—
148C2×D8—111no—
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151#126—442no—
152#124—222no—
153C22⋊Q8—441no—
154C4×Q8—222no—
155C4×Q8D4411yescharacteristic
156C4×D4—221no—
157#117—441no—
158C2×C16—21no—
159C2×C16—21no—
160#107—111no—
161#107—221no—
162#107—221no—
163#107—441no—
164C4⋊C8—21no—
165C4⋊C8—221no—
166C4⋊C8D4411yescharacteristic
167#103—222no—
168#103—441no—
169#102—221no—
170C4×C8—21no—
171C4×C8C22×D1111yescharacteristic
172C2×C11#164111yescharacteristic
173C2×C11#218911yescharacteristic
174C2×C11#219311yescharacteristic
175D11—161no—
176C2×Q8—222no—
177C2×Q8—441no—
178C2×Q8D8811yescharacteristic
179C2×D4—221no—
180C22×C4—441no—
181Q16—442no—
182Q16—441no—
183Q16—441no—
184SD16—882no—
185D8—221no—
186D8—221no—
187C2×C8—21no—
188C2×C8—441no—
189C2×C8D4×D1111yescharacteristic
190C2×C8D4×D1111yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—221no—
193C4⋊C4—442no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4D8811yescharacteristic
199C22⋊C4—442no—
200C22⋊C4—442no—
201C22⋊C4—441no—
202C42—21no—
203C42—442no—
204C42C2×D4411yescharacteristic
205C16—41no—
206C16—41no—
207C11#1238711yescharacteristic, complemented, Sylow
208C23—441no—
209Q8—21no—
210Q8—21no—
211Q8—442no—
212Q8—442no—
213Q8—1761no—
214D4—441no—
215D4—441no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—441no—
219C2×C4—442no—
220C2×C4—881no—
221C2×C4—881no—
222C2×C4—881no—
223C2×C4#6693511yescharacteristic
224C2×C4C2×D8811yescharacteristic
225C2×C4#6696111yescharacteristic
226C8—21no—
227C8—41no—
228C8—881no—
229C8#6696911yescharacteristic
230C8#6697111yescharacteristic
231C22—881no—
232C22—881no—
233C22—881no—
234C22#1062234511yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—882no—
239C4—881no—
240C4—1761no—
241C4#1062242311yescharacteristic
242C4#1062243811yescharacteristic
243C4#1062251711yescharacteristic
244C4#1062252211yescharacteristic
245C2—1761no—
246C2#1306781111yescharacteristic
247C2#1307055811yescharacteristic
248C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenterQ8⋊C16D11
hypocenterC11#12387
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
4. #13068020C2semidirect
5. #13066666C2semidirect
7. C11×Q8⋊C16C2semidirect
89. Q8⋊C16D11semidirect
207. C11#12387semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708442
#130707642
#130680202
#130666662
#130665782
C11×Q8⋊C162
#1238711