Finite Group Databasebeta

← #14653268

Subgroups — #14653268

Order 2816.

390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#10622691C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic
5#13067297C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic
7C11×#1549C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622691—21no—
13#10622691—21no—
14#10622691C414yes—
15C2×#66871—22no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#332—22no—
20#10622196—22no—
21#10622184—22no—
22#10622120—22no—
23#10622119—22no—
24#10622093—21no—
25#10622092—21no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×#4318—21no—
39C22×C11⋊C8D412yes—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50#66871—24no—
51#66871—24no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)D412yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8C2×C412yes—
57C4×C11⋊C8D411yescharacteristic
58C4×C11⋊C8D411yescharacteristic
59#9778—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11—82no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—41no—
68C2×Dic22—22no—
69C2×Dic22—41no—
70C2×Dic22—82no—
71C11×M16—42no—
72C2×C8×C11—22no—
73C2×C8×C11—41no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11C22×C411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86#4318—42no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8C22⋊C412yes—
92C2×C11⋊C8C22⋊C412yes—
93C2×#500—111no—
94#1837—111no—
95#1549—111no—
96#1549D1111yescharacteristic
97#1548—111no—
98#1548—111no—
99#1452—111no—
100C23×C11#12411yescharacteristic
101Q8×C11—82no—
102Q8×C11—82no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—42no—
106C2×C4×C11—82no—
107C2×C4×C11C2×C22⋊C411yescharacteristic
108C2×C4×C11C4×D411yescharacteristic
109C2×C4×C11C4×D411yescharacteristic
110C2×C4×C11#12111yescharacteristic
111C2×C4×C11#12111yescharacteristic
112C2×C4×C11#12711yescharacteristic
113C2×C4×C11#13712yes—
114C2×C4×C11#13712yes—
115C2×Dic11—42no—
116C2×Dic11—82no—
117Dic22—82no—
118Dic22—82no—
119C8×C11—42no—
120C8×C11—81no—
121C11⋊C8—22no—
122C11⋊C8—22no—
123C11⋊C8—42no—
124C11⋊C8—81no—
125C2×C4⋊Q8—111no—
126C2×C4⋊Q8C2×D1111yescharacteristic
127#500—114no—
128#500—221no—
129#500—221no—
130#431—111no—
131#431C2×D1111yescharacteristic
132C2×#107—222no—
133#423—111no—
134#423C2×D1111yescharacteristic
135C2×C4×C8—111no—
136#341—222no—
137#333—222no—
138#333—222no—
139#332—22no—
140#332—222no—
141#322—221no—
142#322—221no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11#39011yescharacteristic
146C22×C11#49112yes—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—82no—
150C4×C11#41912yes—
151C4×C11#47212yes—
152C4×C11#47312yes—
153C4×C11#49711yescharacteristic
154C4×C11#49711yescharacteristic
155Dic11—82no—
156C22×Q8—21no—
157C22×Q8—221no—
158C2×M16—21no—
159C2×M16—221no—
160C22×C8—112no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—112no—
165C4⋊Q8—221no—
166C4⋊Q8—221no—
167C4⋊Q8—221no—
168C4⋊Q8C4×D1112yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C42C22×D1111yescharacteristic
174#107—224no—
175#107—224no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—112no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C4⋊C8C22⋊D1112yes—
182C22⋊C8—21no—
183C22⋊C8—221no—
184C4×C8—21no—
185C4×C8—112no—
186C4×C8—111no—
187C4×C8—111no—
188C4×C8—221no—
189C2×C11—22no—
190C2×C11#196011yescharacteristic
191C2×C11#197811yescharacteristic
192C2×C11#197911yescharacteristic
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—82no—
196C2×Q8—222no—
197C2×Q8—441no—
198C2×Q8—882no—
199C22×C4—41no—
200C22×C4—441no—
201C22×C4#433911yescharacteristic
202C22×C4D4×D1111yescharacteristic
203C22×C4#434111yescharacteristic
204M16—42no—
205M16—442no—
206C2×C8—22no—
207C2×C8—41no—
208C2×C8—112no—
209C2×C8—112no—
210C2×C8—222no—
211C2×C8—222no—
212C2×C8—222no—
213C2×C8—441no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C42C2×C4×D1111yescharacteristic
223C42D4×D1111yescharacteristic
224C42D4×D1111yescharacteristic
225C42C2×C22⋊D1111yescharacteristic
226C11#977811yescharacteristic, complemented, Sylow
227C23#6693811yescharacteristic
228Q8—82no—
229Q8—82no—
230Q8—882no—
231Q8—882no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—442no—
237C2×C4—882no—
238C2×C4C22⋊C4×D1111yescharacteristic
239C2×C4(C22⋊D11)⋊C411yescharacteristic
240C2×C4#6693711yescharacteristic
241C2×C4#6696812yes—
242C2×C4#6697112yes—
243C2×C4C4×C22⋊D1111yescharacteristic
244C2×C4#6699211yescharacteristic
245C2×C4#6699311yescharacteristic
246C8—42no—
247C8—81no—
248C8—222no—
249C8—222no—
250C8—442no—
251C8—881no—
252C22—21no—
253C22—21no—
254C22#1062241012yes—
255C22#1062257011yescharacteristic
256C4—21no—
257C4—21no—
258C4—82no—
259C4—882no—
260C4#1062236812yes—
261C4#1062241512yes—
262C4#1062278011yescharacteristic
263C4#1062280311yescharacteristic
264C4#1062281212yes—
265C2—22no—
266C2#1306943411yescharacteristic
267C2#1306952511yescharacteristic
268C2#1306952811yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenter#1549D11
hypocenterC11#9778
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
226. C11#9778semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
#130687532
#130673002
#130672982
#130672972
#130669092
C11×#15492
#977811