Finite Group Databasebeta

← #14667498

Subgroups — #14667498

Order 2816.

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

normal subgroups only

This group has 296 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#13070845C211yesmaximal, characteristic, complemented
2#13070661C211yesmaximal, characteristic
3#13067986C211yesmaximal, characteristic, complemented
4#13066674C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#3380C211yesmaximal, characteristic
8C11×#554—21no—
9C11×#500C2211yescharacteristic
10C11×#499—21no—
11C11×#478—22no—
12C11×#476—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×D8—21no—
15C4×C11×D8C2211yescharacteristic
16C2×#66891—21no—
17#10622633—21no—
18#10622312C2211yescharacteristic
19#10622130—21no—
20#10622130—22no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×D8D411yescharacteristic
26C11×C4⋊Q8—21no—
27C11×#125—22no—
28C11×C22⋊Q8—42no—
29C11×C22⋊Q8—41no—
30C4×Q8×C11D411yescharacteristic
31C4×D4×C11—22no—
32C4×D4×C11—21no—
33C2×C11×C4⋊C4—41no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36#66922—21no—
37C11×#107—21no—
38C11×#107D411yescharacteristic
39C11×#107D412yes—
40C11×#106—22no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×#102—22no—
44C11×#102—21no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—41no—
48#66891—42no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51#66872—41no—
52C4⋊(C11⋊C8)—21no—
53#12359—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11D811yescharacteristic
56C2×D4×C11—21no—
57C22×C4×C11—42no—
58C22×C4×C11—41no—
59C2×Dic22—41no—
60C11×D8—21no—
61C11×D8SD1612yes—
62C2×C8×C11—21no—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4D811yescharacteristic
72C11×C22⋊C4—42no—
73C11×C22⋊C4—41no—
74C42×C11—21no—
75C42×C11C2×D411yescharacteristic
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3380D1111yescharacteristic
85#2241—111no—
86#2208—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1331—111no—
91C23×C11—41no—
92Q8×C11—21no—
93Q8×C11—21no—
94Q8×C11—161no—
95D4×C11—22no—
96D4×C11—41no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—81no—
102C2×C4×C11—81no—
103C2×C4×C11—162no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×Dic11—81no—
108Dic22—81no—
109Dic22—81no—
110C8×C11—21no—
111C8×C11—41no—
112C8×C11C2×SD1611yescharacteristic
113C8×C11#13711yescharacteristic
114C11⋊C8—81no—
115#554—21no—
116C2×SD32—221no—
117#500C2×D1111yescharacteristic
118#499—21no—
119#494—111no—
120#478—22no—
121#476—21no—
122#475—221no—
123C8×Q8C2×D1111yescharacteristic
124C4×D8—21no—
125C4×D8C2×D1111yescharacteristic
126C4⋊C16—111no—
127#358—221no—
128#358—222no—
129C4×C16—111no—
130#335—111no—
131#332—221no—
132C22×C11—42no—
133C22×C11—81no—
134C22×C11—81no—
135C22×C11#44711yescharacteristic
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—81no—
140C4×C11—82no—
141C4×C11#44811yescharacteristic
142C4×C11#45411yescharacteristic
143C4×C11#50811yescharacteristic
144C4×C11#51011yescharacteristic
145Dic11—161no—
146C2×Q16—221no—
147C2×Q16—221no—
148C2×D8C22⋊D1111yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—221no—
151#125—22no—
152C22⋊Q8—42no—
153C22⋊Q8—41no—
154C4×Q8C22⋊D1111yescharacteristic
155C4×D4—22no—
156C4×D4—21no—
157C2×C4⋊C4—41no—
158SD32—442no—
159C2×C16—221no—
160C2×C16—221no—
161#107—21no—
162#107C22⋊D1111yescharacteristic
163#107C22⋊D1112yes—
164#106—22no—
165#106—441no—
166C4⋊C8—21no—
167C4⋊C8—221no—
168C4⋊C8C22⋊D1111yescharacteristic
169#103—441no—
170#102—22no—
171#102—21no—
172C4×C8—21no—
173C4×C8C22×D1111yescharacteristic
174C2×C11—82no—
175C2×C11#162711yescharacteristic
176C2×C11#218911yescharacteristic
177C2×C11#219411yescharacteristic
178C2×Q8—41no—
179C2×Q8—441no—
180C2×Q8#432311yescharacteristic
181C2×D4—21no—
182C22×C4—42no—
183C22×C4—41no—
184Q16—442no—
185Q16—441no—
186Q16—441no—
187D8—21no—
188D8#432512yes—
189C2×C8—21no—
190C2×C8—441no—
191C2×C8C2×C22⋊D1111yescharacteristic
192C2×C8C2×C22⋊D1111yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4#432311yescharacteristic
202C22⋊C4—42no—
203C22⋊C4—41no—
204C42—21no—
205C42C2×C22⋊D1111yescharacteristic
206C16—441no—
207C16—441no—
208C11#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—21no—
211Q8—21no—
212Q8—161no—
213Q8—881no—
214Q8—881no—
215D4—22no—
216D4—41no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—162no—
224C2×C4—881no—
225C2×C4C2×#432311yescharacteristic
226C2×C4#6698511yescharacteristic
227C2×C4#6700611yescharacteristic
228C8—21no—
229C8—41no—
230C8—881no—
231C8C2×#432511yescharacteristic
232C8#6699511yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1062283011yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—81no—
241C4—82no—
242C4—1761no—
243C4#1062280711yescharacteristic
244C4#1062280811yescharacteristic
245C4#1062284011yescharacteristic
246C4#1062285811yescharacteristic
247C2—82no—
248C2#1306771911yescharacteristic
249C2#1307055611yescharacteristic
250C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3380C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#3380D11
hypocenterC11#12359
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #13070845C2semidirect
3. #13067986C2semidirect
4. #13066674C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
208. C11#12359semidirect

Maximal subgroups

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

subgroupindex
#130708452
#130706612
#130679862
#130666742
Q8⋊(C11⋊C16)2
#130665772
C11×#33802
#1235911