Finite Group Databasebeta

← #14656394

Subgroups — #14656394

Order 2816.

562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622295C211yesmaximal, characteristic, complemented
2C2×#10622455C212yesmaximal
3#13069410C211yesmaximal, characteristic
4C2×#10622119C212yesmaximal, complemented
5C11×#1277C211yesmaximal, characteristic, complemented
6C2×C4×D44C2211yescharacteristic
7C2×#66922C2212yes—
8C2×C11×C4⋊C8C2212yes—
9C2×C4×C8×C11C2211yescharacteristic
10C2×#66885—22no—
11C2×(C2×D11)⋊C8—22no—
12C2×#66882—22no—
13C2×#66881—22no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622455—24no—
16#10622455—24no—
17#10622295—24no—
18#10622119—24no—
19C22×D44D411yescharacteristic
20C22×C4×D11—21no—
21C22×Dic22—22no—
22C22×C8×C11—22no—
23C22×C8×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×(C2×D11)⋊C4—21no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11D411yescharacteristic
29C22×C11⋊C8—21no—
30C4×D44—22no—
31C4×D44—22no—
32#66922—22no—
33#66922—22no—
34#66922—22no—
35#66922D414yes—
36C11×C4⋊C8—22no—
37C11×C4⋊C8D414yes—
38C4×C8×C11—22no—
39#66885—28no—
40(C2×D11)⋊C8—44no—
41#66882—28no—
42#66881—28no—
43C4⋊(C11⋊C8)—22no—
44#10278—111nomaximal, Sylow
45C23×D11—21no—
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11#4111yescharacteristic
49C22×Dic11—21no—
50C22×Dic11—42no—
51C2×D44—22no—
52C2×D44—21no—
53C2×D44—22no—
54C2×D44Q1612yes—
55C2×C4×D11—41no—
56C2×C4×D11—41no—
57C2×C4×D11—42no—
58C2×C4×D11—42no—
59C2×Dic22—24no—
60C2×Dic22—42no—
61C2×Dic22—84no—
62C2×C8×C11—22no—
63C2×C8×C11—24no—
64C2×C8×C11—22no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C2×C8×C11SD1614yes—
68C42×C11C2×D412yes—
69C42×C11C2×D412yes—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—22no—
72C4⋊Dic11—24no—
73C4⋊Dic11—24no—
74C4⋊Dic11—42no—
75C4⋊Dic11—42no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—42no—
78C2×#500—111no—
79C2×#476—112no—
80#1954—111no—
81C2×#333—112no—
82#1277D1111yescharacteristic, complemented
83C23×C11#12111yescharacteristic
84C22×D11—22no—
85C22×D11—41no—
86C22×D11—42no—
87C22×D11—41no—
88C22×D11—42no—
89C2×C4×C11—22no—
90C2×C4×C11#12011yescharacteristic
91C2×C4×C11#12012yes—
92C2×C4×C11#12112yes—
93C2×C4×C11#12711yescharacteristic
94C2×C4×C11C2×SD1612yes—
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13511yescharacteristic
97C2×C4×C11#13712yes—
98C2×C4×C11#13712yes—
99C2×Dic11—44no—
100C2×Dic11—41no—
101C2×Dic11—42no—
102C2×Dic11—84no—
103D44—24no—
104D44—42no—
105C4×D11—82no—
106C4×D11—81no—
107C4×D11—81no—
108Dic22—84no—
109Dic22—84no—
110C8×C11—24no—
111C8×C11—44no—
112C11⋊C8—81no—
113C2×C4⋊Q8—112no—
114C2×C4×D4—111no—
115#500—224no—
116#476—224no—
117#476—224no—
118C2×#107—222no—
119C2×#106—222no—
120C2×C4⋊C8—111no—
121C2×C4⋊C8C2×D1112yes—
122C2×#102—222no—
123C2×C22⋊C8—222no—
124C2×C4×C8C2×D1111yescharacteristic
125#333—224no—
126C22×C11#39211yescharacteristic
127C22×C11#46112yes—
128C22×C11#46711yescharacteristic
129C22×C11#47011yescharacteristic
130C22×C11#47212yes—
131C2×D11—44no—
132C2×D11—42no—
133C2×D11—82no—
134C2×D11—81no—
135C2×D11—81no—
136C4×C11—22no—
137C4×C11#44812yes—
138C4×C11#45112yes—
139C4×C11#45212yes—
140C4×C11#49211yescharacteristic
141C4×C11#49711yescharacteristic
142Dic11—81no—
143Dic11—84no—
144C22×Q8—222no—
145C22×D4—111no—
146C23×C4—221no—
147C22×C8—22no—
148C22×C8—221no—
149C22×C8D4412yes—
150C4⋊Q8—114no—
151C4⋊Q8—222no—
152C4⋊Q8—222no—
153C4⋊Q8—222no—
154C4×D4—222no—
155C4×D4—222no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4—222no—
159C2×C22⋊C4—221no—
160C2×C42C22×D1111yescharacteristic
161#107—228no—
162#106—228no—
163C4⋊C8—22no—
164C4⋊C8—222no—
165C4⋊C8D4414yes—
166#102—228no—
167C22⋊C8—444no—
168C4×C8—22no—
169C2×C11#167512yes—
170C2×C11#169512yes—
171C2×C11#200111yescharacteristic
172C2×C11#201311yescharacteristic
173C2×C11#201811yescharacteristic
174D11—82no—
175C24—221no—
176C2×Q8—224no—
177C2×Q8—442no—
178C2×Q8—884no—
179C2×D4—112no—
180C2×D4—222no—
181C2×D4—221no—
182C2×D4—222no—
183C22×C4—221no—
184C22×C4—442no—
185C22×C4—441no—
186C22×C4—441no—
187C22×C4—442no—
188C22×C4—442no—
189C22×C4C2×D4411yescharacteristic
190C22×C4D4×D1111yescharacteristic
191C22×C4#434311yescharacteristic
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—24no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—441no—
198C2×C8—442no—
199C2×C8#431414yes—
200C4⋊C4—224no—
201C4⋊C4—222no—
202C4⋊C4—224no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—442no—
206C42C2×D4412yes—
207C42D4×D1112yes—
208C11#1027811yescharacteristic, complemented, Sylow
209C23—222no—
210C23—441no—
211C23—442no—
212C23—441no—
213C23—442no—
214C23#6694811yescharacteristic
215Q8—884no—
216Q8—884no—
217D4—224no—
218D4—442no—
219C2×C4—22no—
220C2×C4—441no—
221C2×C4—444no—
222C2×C4—442no—
223C2×C4—884no—
224C2×C4—881no—
225C2×C4—881no—
226C2×C4—882no—
227C2×C4#6692711yescharacteristic
228C2×C4#6693511yescharacteristic
229C2×C4#6693512yes—
230C2×C4#6694812yes—
231C2×C4C2×#431412yes—
232C2×C4#6696212yes—
233C2×C4#6696511yescharacteristic
234C2×C4#6696812yes—
235C2×C4Q16×D1111yescharacteristic
236C8—24no—
237C8—44no—
238C8—881no—
239C22—442no—
240C22—444no—
241C22—882no—
242C22—881no—
243C22—881no—
244C22#1062228411yescharacteristic
245C22#1062245412yes—
246C22#1062248111yescharacteristic
247C22#1062250011yescharacteristic
248C22#1062251012yes—
249C4—22no—
250C4—881no—
251C4—884no—
252C4#1062230611yescharacteristic
253C4#1062232811yescharacteristic
254C4#1062235112yes—
255C4#1062239612yes—
256C4#1062242112yes—
257C2—882no—
258C2#1306801612yes—
259C2#1306814012yes—
260C2#1306962711yescharacteristic
261C2#1306970111yescharacteristic
262C2#1306972611yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1277D11
hypocenterC11#10278
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#10622295C2semidirect
4. C2×#10622119C2semidirect
5. C11×#1277C2semidirect
82. #1277D11semidirect
208. C11#10278semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106224552
#130694102
C2×#106221192
C11×#12772
#1027811