Finite Group Databasebeta

← #14647650

Subgroups — #14647650

Order 2816.

386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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#13069553C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic
3#13067369C212yesmaximal
4#13066452C212yesmaximal
5C11×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#446—22no—
8C11×#446—22no—
9C11×#432—22no—
10C11×#431C2212yes—
11C2×#66900C412yes—
12C2×C4⋊(C11⋊C8)C2211yescharacteristic
13C4×#4318C2212yes—
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622168C411yescharacteristic
16#10622168C411yescharacteristic
17#10622162—22no—
18#10622118—22no—
19#10622117—22no—
20C22×Q8×C11C2×C411yescharacteristic
21C4×Q8×C11—22no—
22C4×Q8×C11—22no—
23C2×C11×C4⋊C4C2×C411yescharacteristic
24C2×C11×C4⋊C4Q812yes—
25C2×C42×C11D412yes—
26C2×C42×C11C2311yescharacteristic
27C2×#4318C2×C412yes—
28C2×#4318C2×C412yes—
29C22×C11⋊C8—21no—
30C22×C11⋊C8—21no—
31C11×C4⋊C8—22no—
32C11×C4⋊C8—22no—
33C11×C4⋊C8D412yes—
34C11×C4⋊C8D412yes—
35C11×C22⋊C8—22no—
36C11×#97—24no—
37C4×C8×C11—22no—
38#66900—24no—
39C4⋊(C11⋊C8)—22no—
40#66867—22no—
41C4×C11⋊C8—22no—
42C4×C11⋊C8—22no—
43#8838—111nomaximal, Sylow
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11—21no—
47C2×Q8×C11—21no—
48C22×C4×C11C4⋊C412yes—
49C22×C4×C11C4⋊C412yes—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×Q811yescharacteristic
53C2×C8×C11—22no—
54C2×C8×C11—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—24no—
57C42×C11—22no—
58C42×C11—22no—
59C42×C11C2×D412yes—
60C42×C11#4112yes—
61#4318—22no—
62#4318—22no—
63#4318—22no—
64#4318M1614yes—
65C2×C11⋊C8—22no—
66C2×C11⋊C8—22no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—41no—
69C2×C11⋊C8—42no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72#2983D1111yescharacteristic
73#1984—111no—
74C4×#101—111no—
75#1565—112no—
76#1278—112no—
77C23×C11C2×C4⋊C411yescharacteristic
78Q8×C11—42no—
79Q8×C11—42no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—41no—
87C2×C4×C11—42no—
88C2×C4×C11C4×D412yes—
89C2×C4×C11#12011yescharacteristic
90C2×C4×C11C22⋊Q812yes—
91C2×C4×C11#12311yescharacteristic
92C2×C4×C11C2×M1612yes—
93C2×C4×C11#13111yescharacteristic
94C2×C4×C11#13111yescharacteristic
95C8×C11—42no—
96C8×C11—42no—
97C11⋊C8—24no—
98C11⋊C8—42no—
99C11⋊C8—42no—
100C11⋊C8—81no—
101C2×C4×Q8C2×D1111yescharacteristic
102#446—22no—
103#446—22no—
104#432—22no—
105#431C2×D1112yes—
106C2×C4⋊C8—111no—
107C2×#101—112no—
108C4×M16—112no—
109C2×C4×C8—111no—
110#343—111no—
111#343—111no—
112#336—222no—
113#335—222no—
114#334—222no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11#38511yescharacteristic
118C22×C11#42311yescharacteristic
119C22×C11#42411yescharacteristic
120C4×C11—21no—
121C4×C11—22no—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11#43512yes—
125C4×C11#43612yes—
126C4×C11#45411yescharacteristic
127C4×C11#45611yescharacteristic
128C22×Q8C4×D1111yescharacteristic
129C2×M16—112no—
130C2×M16—112no—
131C22×C8—221no—
132C22×C8—221no—
133C4×Q8—22no—
134C4×Q8—22no—
135C2×C4⋊C4Dic2212yes—
136C2×C4⋊C4C4×D1111yescharacteristic
137C2×C42C22⋊D1112yes—
138C2×C42C22×D1111yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—222no—
142C4⋊C8C22⋊D1112yes—
143C4⋊C8C22⋊D1112yes—
144#101—224no—
145C22⋊C8—22no—
146#97—24no—
147#97—222no—
148C4×C8—22no—
149C4×C8—222no—
150C4×C8—222no—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11#185111yescharacteristic
154C2×C11#185711yescharacteristic
155C2×C11#185811yescharacteristic
156C2×Q8—22no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—22no—
160C22×C4Dic11⋊C412yes—
161C22×C4Dic11⋊C412yes—
162C22×C4C2×Dic2211yescharacteristic
163C22×C4C2×C4×D1111yescharacteristic
164C22×C4C2×C22⋊D1111yescharacteristic
165M16—114no—
166M16—222no—
167M16—222no—
168M16—222no—
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—222no—
172C2×C8—222no—
173C2×C8—222no—
174C2×C8—441no—
175C2×C8—441no—
176C2×C8—442no—
177C2×C8—441no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C42—22no—
181C42—22no—
182C42#433912yes—
183C42C2×C22⋊D1112yes—
184C11#883811yescharacteristic, complemented, Sylow
185C23C2×Dic11⋊C411yescharacteristic
186Q8—42no—
187Q8—42no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4M16×D1112yes—
197C2×C4#6696011yescharacteristic
198C2×C4#6696011yescharacteristic
199C2×C4#6697712yes—
200C2×C4C4×C22⋊D1112yes—
201C2×C4#6698211yescharacteristic
202C2×C4#6700611yescharacteristic
203C8—42no—
204C8—42no—
205C8—224no—
206C8—442no—
207C8—442no—
208C8—881no—
209C22—21no—
210C22—21no—
211C22#1062273111yescharacteristic
212C22#1062273211yescharacteristic
213C22#1062282311yescharacteristic
214C4—21no—
215C4—22no—
216C4—42no—
217C4—42no—
218C4#1062274012yes—
219C4#1062274112yes—
220C4#1062285811yescharacteristic
221C4#1062285911yescharacteristic
222C2—21no—
223C2—21no—
224C2#1306879911yescharacteristic
225C2#1306883111yescharacteristic
226C2#1306883611yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#385
prime radicalC23×C11C2×C4⋊C4
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#8838
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
184. C11#8838semidirect

Maximal subgroups

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

subgroupindex
#130695532
C4×#669002
#130673692
#130664522
C11×#29832
#883811