Finite Group Databasebeta

← #14666996

Subgroups — #14666996

Order 2816.

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

normal subgroups only

This group has 344 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#13070816C212yesmaximal, complemented
2#13070044C211yesmaximal, characteristic
3#13066628C212yesmaximal, complemented
4#13066540C211yesmaximal, characteristic
5C11×#3189C211yesmaximal, characteristic
6C2×C11×C22⋊Q8—21no—
7C11×#484—22no—
8C11×#467—21no—
9C11×#467C2212yes—
10C11×#451—22no—
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622825—21no—
13C2×#66882C2211yescharacteristic
14#10622202—22no—
15#10622189—21no—
16#10622189C2211yescharacteristic
17C22⋊(C11⋊C16)C2212yes—
18#10622127—22no—
19C22×Q8×C11—21no—
20C23×C4×C11D411yescharacteristic
21C2×C11×Q16—21no—
22C2×C11×Q16D412yes—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C11×C22⋊Q8—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—41no—
28C11×C22⋊Q8—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C22⋊C4—41no—
32C2×C22⋊Dic11—41no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C11×#107—21no—
36C11×#107D412yes—
37C11×#103—22no—
38C11×#103—22no—
39C11×C22⋊C8—22no—
40C11⋊#95—41no—
41#66882—22no—
42C2×C11⋊C16—22no—
43#12282—111nomaximal, Sylow
44C24×C11D811yescharacteristic
45C2×Q8×C11—22no—
46C2×Q8×C11—41no—
47C2×Q8×C11—81no—
48C2×Q8×C11—81no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11D811yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C22×Dic11—41no—
59C11×Q16—42no—
60C11×Q16—81no—
61C2×C8×C11—21no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C2×C8×C11C2×D412yes—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C22⋊C4—42no—
70C11×C22⋊C4—42no—
71C22⋊Dic11—82no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76C11⋊C16—42no—
77#3189D1111yescharacteristic
78#2236—112no—
79#2076—111no—
80#1348—112no—
81#1314—111no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—41no—
85C23×C11—41no—
86C23×C11Q3212yes—
87C23×C11C2×D811yescharacteristic
88Q8×C11—42no—
89Q8×C11—42no—
90Q8×C11—82no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—81no—
100C2×C4×C11—82no—
101C2×C4×C11—82no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—81no—
105C2×Dic11—81no—
106C2×Dic11—81no—
107C2×Dic11—81no—
108C2×Dic11—81no—
109C2×Dic11—81no—
110C8×C11—22no—
111C8×C11—41no—
112C2×C22⋊Q8—21no—
113#484—22no—
114#467—21no—
115#467C2×D1112yes—
116#451—22no—
117C2×#107—111no—
118C2×C22⋊C8C2×D1111yescharacteristic
119#380—221no—
120#366—222no—
121#358—222no—
122C22⋊C16—112no—
123#340—111no—
124#340—221no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—22no—
128C22×C11—42no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—81no—
132C22×C11#44711yescharacteristic
133C22×C11C2×Q3211yescharacteristic
134C22×C11#51011yescharacteristic
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—82no—
138C4×C11—82no—
139C4×C11#45511yescharacteristic
140C4×C11#45811yescharacteristic
141Dic11—161no—
142Dic11—161no—
143C22×Q8—21no—
144C23×C4C22⋊D1111yescharacteristic
145C2×Q16—21no—
146C2×Q16C22⋊D1112yes—
147C22×C8C22⋊D1111yescharacteristic
148C22×C8C22×D1111yescharacteristic
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—41no—
152C22⋊Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—441no—
159C2×C16—222no—
160#107—21no—
161#107—222no—
162#107C22⋊D1112yes—
163#103—22no—
164#103—22no—
165C22⋊C8—22no—
166#95—441no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—42no—
170C2×C11#160711yescharacteristic
171C2×C11#218811yescharacteristic
172C2×C11#219011yescharacteristic
173C24#432311yescharacteristic
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—81no—
177C2×Q8—81no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—441no—
185C22×C4—441no—
186C22×C4#432311yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188Q16—42no—
189Q16—81no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8C2×C22⋊D1112yes—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—441no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—882no—
205C16—442no—
206C11#1228211yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#6689312yes—
212C23C2×#432311yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—82no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—881no—
228C2×C4—881no—
229C2×C4—881no—
230C2×C4—881no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4#6698511yescharacteristic
234C2×C4#6700611yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1062279211yescharacteristic
245C22C2×#6689311yescharacteristic
246C22#1062283011yescharacteristic
247C4—21no—
248C4—41no—
249C4—82no—
250C4—82no—
251C4—1761no—
252C4—1761no—
253C4#1062285511yescharacteristic
254C4#1062285611yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#1306760211yescharacteristic
259C2#1307055011yescharacteristic
260C2#1307056211yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#3189C2
socleC22×C11#447
prime radicalC24×C11D8
hypercenter#3189D11
hypocenterC11#12282
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. #13070816C2semidirect
3. #13066628C2semidirect
206. C11#12282semidirect

Maximal subgroups

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

subgroupindex
#130708162
#130700442
#130666282
#130665402
C11×#31892
#1228211