Finite Group Databasebeta

← #14673430

Subgroups — #14673430

Order 2816.

318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 97 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#13079139C211yesmaximal, characteristic
2#13070389C211yesmaximal, characteristic
3#13070388C211yesmaximal, characteristic
4#13069370C211yesmaximal, characteristic
5#13066717C211yesmaximal, characteristic
6#13066695C211yesmaximal, characteristic
7C11×#1384C211yesmaximal, characteristic
8#10623048—21no—
9C2×C11×M32C2211yescharacteristic
10C11×#427C2211yescharacteristic
11C11×#427C2211yescharacteristic
12C2×#66883C2211yescharacteristic
13#10622719C2211yescharacteristic
14C2×#66879C2211yescharacteristic
15C2×#66876C2211yescharacteristic
16#10622612—21no—
17#10622611—21no—
18#10622489—22no—
19#10622469—22no—
20#10622170—21no—
21#10622151—22no—
22#10622125—22no—
23C22×C8×C11C2311yescharacteristic
24C11×#117—21no—
25C11×#117—21no—
26#66979—21no—
27C2×C4×Dic11D411yescharacteristic
28C2×#4318—21no—
29C22×C11⋊C8D411yescharacteristic
30#66943—22no—
31#66941—22no—
32#66931—42no—
33C4×Dic22—42no—
34C11×M32—21no—
35C11×M32—21no—
36C2×C11×C16Q812yescomplemented
37C11×#107—21no—
38C11×#107—21no—
39C11×#106D412yes—
40C11×#106Q812yescomplemented
41#66883—21no—
42#66883—21no—
43#66882—21no—
44#66881D412yes—
45#66879—21no—
46#66879—21no—
47#66876—21no—
48#66876—21no—
49C2×C11⋊C16Q812yescomplemented
50#66872—22no—
51#66871—22no—
52C4⋊(C11⋊C8)—42no—
53#13459—111nomaximal, Sylow
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—21no—
56C2×Dic22—42no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2×Q811yescharacteristic
60C2×C8×C11C2×Q811yescharacteristic
61C2×C8×C11C2×Q811yescharacteristic
62C2×C8×C11#4111yescharacteristic
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—41no—
67C42×C11—41no—
68C42×C11—41no—
69C22⋊Dic11—41no—
70C4⋊Dic11—22no—
71C4⋊Dic11—42no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74C4×Dic11—21no—
75C4×Dic11—41no—
76C4×Dic11SD1612yes—
77#4318—41no—
78#4318—41no—
79C2×C11⋊C8—21no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8SD1612yes—
83C11×C16—22no—
84C11⋊C16—22no—
85#3162—111no—
86#2155—111no—
87#2155—111no—
88#1946—111no—
89#1384—111no—
90#1384D1111yescharacteristic
91#1375—111no—
92C23×C11AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11C4⋊Q811yescharacteristic
98C2×C4×C11C2×SD1611yescharacteristic
99C2×C4×C11C2×SD1611yescharacteristic
100C2×C4×C11#13711yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—42no—
103C2×Dic11—81no—
104Dic22—84no—
105C8×C11C22⋊Q811yescharacteristic
106C8×C11C22⋊Q811yescharacteristic
107C8×C11C4⋊Q811yescharacteristic
108C8×C11C4⋊Q811yescharacteristic
109C11⋊C8—22no—
110C11⋊C8—81no—
111#533—221no—
112C2×M32—111no—
113C2×M32C2×D1111yescharacteristic
114#501—222no—
115#501—222no—
116C2×#108—111no—
117#427—111no—
118#427—221no—
119#427C2×D1111yescharacteristic
120#427C2×D1111yescharacteristic
121#424—221no—
122C2×#97—111no—
123#365—222no—
124#365—222no—
125#339—221no—
126C22×C11—41no—
127C22×C11#45011yescharacteristic
128C22×C11#47611yescharacteristic
129C22×C11#50111yescharacteristic
130C4×C11—82no—
131C4×C11—82no—
132C4×C11#39511yescharacteristic
133C4×C11#44811yescharacteristic
134C4×C11#47511yescharacteristic
135C4×C11#49811yescharacteristic
136Dic11—42no—
137Dic11—82no—
138C2×M16—221no—
139C22×C8—111no—
140C22×C8C22×D1111yescharacteristic
141C4⋊Q8—222no—
142#125—222no—
143C22⋊Q8—442no—
144C4×Q8—442no—
145#117—21no—
146#117—21no—
147#117—221no—
148C2×C42—111no—
149M32—21no—
150M32—21no—
151M32—221no—
152M32—221no—
153C2×C16—112no—
154C2×C16Dic2212yescomplemented
155#108—221no—
156#108—221no—
157#107—21no—
158#107—21no—
159#107—222no—
160#107—221no—
161#106—112no—
162#106—222no—
163#106Dic2212yescomplemented
164#106D4412yes—
165C4⋊C8—442no—
166#97—221no—
167#97—221no—
168C2×C11—21no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#205811yescharacteristic
172C2×Q8—442no—
173C22×C4—221no—
174C22×C4D4×D1111yescharacteristic
175M16—441no—
176M16—441no—
177C2×C8—112no—
178C2×C8—221no—
179C2×C8—221no—
180C2×C8—441no—
181C2×C8C2×Dic2211yescharacteristic
182C2×C8C2×Dic2211yescharacteristic
183C2×C8C2×D4411yescharacteristic
184C2×C8D4×D1111yescharacteristic
185C2×C8#434111yescharacteristic
186C2×C8Q8×D1111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—222no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—441no—
196C42—41no—
197C42—41no—
198C42—112no—
199C42—221no—
200C42—441no—
201C16—22no—
202C16—222no—
203C11#1345911yescharacteristic, complemented, Sylow
204C23#6696411yescharacteristic
205Q8—884no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—222no—
209C2×C4—442no—
210C2×C4—881no—
211C2×C4#6693111yescharacteristic
212C2×C4#6693511yescharacteristic
213C2×C4#6694111yescharacteristic
214C2×C4SD16×D1111yescharacteristic
215C2×C4SD16×D1111yescharacteristic
216C2×C4#6697111yescharacteristic
217C8—222no—
218C8—881no—
219C8#6692211yescharacteristic
220C8#6693111yescharacteristic
221C8#6694111yescharacteristic
222C8#6695011yescharacteristic
223C22—41no—
224C22#1062237411yescharacteristic
225C22#1062238911yescharacteristic
226C22#1062248911yescharacteristic
227C4—82no—
228C4—82no—
229C4—442no—
230C4—882no—
231C4#1062226911yescharacteristic
232C4#1062240411yescharacteristic
233C4#1062241911yescharacteristic
234C4#1062246811yescharacteristic
235C2—21no—
236C2—21no—
237C2—21no—
238C2#1306994811yescharacteristic
subgroupG/H
centerC4#10622468
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1384C2
socleC2×C11#2058
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1384D11
hypocenterC11#13459
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1384

Complements

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

NH ≅ G/Ntype
36. C2×C11×C16Q8semidirect
40. C11×#106Q8semidirect
49. C2×C11⋊C16Q8semidirect
154. C2×C16Dic22semidirect
163. #106Dic22semidirect
203. C11#13459semidirect

Maximal subgroups

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

subgroupindex
#130791392
#130703892
#130703882
#130693702
#130667172
#130666952
C11×#13842
#1345911