Finite Group Databasebeta

← #14643091

Subgroups — #14643091

Order 2816.

438 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070154C212yesmaximal, complemented
2#13070149C211yesmaximal, characteristic
3#13066442C212yesmaximal, complemented
4#13066437C211yesmaximal, characteristic
5C11×#2804C211yesmaximal, characteristic
6C11×#400—21no—
7C11×#393—22no—
8C11×#391C2212yes—
9C11×#390C2211yescharacteristic
10C11×#386—21no—
11C11×#385—22no—
12C2×#66899—22no—
13C2×#66896—21no—
14C2×#66872—21no—
15C2×#66871—22no—
16#10622548C2211yescharacteristic
17#10622162C2211yescharacteristic
18#10622162C2212yes—
19C22×Q8×C11D412yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—22no—
31C22×C11⋊C8—21no—
32C22×C11⋊C8—22no—
33C11×#95—22no—
34C11×#95—21no—
35C11×#95—22no—
36C11×#95—22no—
37#66899—44no—
38#66896—42no—
39#66872—42no—
40#66871—44no—
41#7833—111nomaximal, Sylow
42C24×C11—21no—
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11—42no—
46C2×Q8×C11—42no—
47C2×D4×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11Q1612yes—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—82no—
55C22×C4×C11—81no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×Dic11—41no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—81no—
62C11×C22⋊C4—42no—
63C11×C22⋊C4—42no—
64C11×C22⋊C4—82no—
65C11×C22⋊C4—81no—
66C42×C11—41no—
67C4⋊Dic11—42no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—42no—
71C2×C11⋊C8—24no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77#2804D1111yescharacteristic
78#2095—112no—
79#2094—111no—
80#1272—112no—
81#1270—111no—
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11—41no—
87C23×C11#12011yescharacteristic
88Q8×C11—44no—
89Q8×C11—82no—
90D4×C11—42no—
91D4×C11—81no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—84no—
105C2×C4×C11C2×Q1611yescharacteristic
106C2×C4×C11#13512yes—
107C2×C4×C11#13711yescharacteristic
108C2×C4×C11#13712yes—
109C2×Dic11—81no—
110C2×Dic11—82no—
111C11⋊C8—42no—
112C11⋊C8—44no—
113C2×#107—222no—
114C2×#106—221no—
115C2×#103—222no—
116C2×#102—221no—
117#400—21no—
118#393—22no—
119#391C2×D1112yes—
120#390C2×D1111yescharacteristic
121#386—21no—
122#385—22no—
123#384—111no—
124#336—111no—
125#336—112no—
126C22×C11—42no—
127C22×C11—44no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#45111yescharacteristic
132C22×C11#45212yes—
133C22×C11#45311yescharacteristic
134C22×C11#45312yes—
135C22×C11#45811yescharacteristic
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11—82no—
143Dic11—161no—
144C22×Q8C22⋊D1112yes—
145C22×D4C22⋊D1111yescharacteristic
146C23×C4—21no—
147C22×C8—221no—
148C22×C8—222no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—222no—
152C2×C4⋊C4C22⋊D1112yes—
153C2×C4⋊C4C22⋊D1111yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C42C22×D1111yescharacteristic
158#107—444no—
159#106—442no—
160#103—444no—
161#102—442no—
162#95—22no—
163#95—21no—
164#95—22no—
165#95—22no—
166C2×C11—82no—
167C2×C11#161411yescharacteristic
168C2×C11#161812yes—
169C2×C11#163011yescharacteristic
170C2×C11#163212yes—
171C2×C11#165511yescharacteristic
172C24—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#432612yes—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—82no—
185C22×C4—81no—
186C22×C4—441no—
187C22×C4C2×C22⋊D1111yescharacteristic
188C22×C4C2×C22⋊D1112yes—
189C2×C8—222no—
190C2×C8—224no—
191C2×C8—441no—
192C2×C8—442no—
193C2×C8—441no—
194C2×C8—442no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—441no—
199C4⋊C4—442no—
200C4⋊C4—441no—
201C4⋊C4—442no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—82no—
205C22⋊C4—81no—
206C42—41no—
207C11#783311yescharacteristic, complemented, Sylow
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#6700611yescharacteristic
214Q8—44no—
215Q8—82no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—881no—
232C2×C4—882no—
233C2×C4#6699511yescharacteristic
234C2×C4C2×#432611yescharacteristic
235C2×C4#6700312yes—
236C2×C4#6700412yes—
237C8—442no—
238C8—444no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#1062284111yescharacteristic
245C22#1062285212yes—
246C22#1062285411yescharacteristic
247C22#1062285412yes—
248C22#1062285611yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—1761no—
257C2—82no—
258C2#1306764111yescharacteristic
259C2#1306766412yes—
260C2#1306773711yescharacteristic
261C2#1306775012yes—
262C2#1306790511yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2804C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2804D11
hypocenterC11#7833
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2804

Complements

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

NH ≅ G/Ntype
1. #13070154C2semidirect
3. #13066442C2semidirect
207. C11#7833semidirect

Maximal subgroups

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

subgroupindex
#130701542
#130701492
#130664422
#130664372
C11×#28042
#783311