Finite Group Databasebeta

← #14656391

Subgroups — #14656391

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×#10622697C212yesmaximal
2#13069410C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C2×C11×#500C211yesmaximal, characteristic, complemented
6C2×C11×C4⋊Q8C2212yes—
7C2×C4×D44C2211yescharacteristic
8C11×#500—24no—
9C2×C11×#107—22no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12#10622697—24no—
13#10622697—24no—
14C2×#66873—22no—
15C2×#66872—22no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2212yes—
18#10622184—24no—
19C22×Q8×C11—22no—
20C22×D44D411yescharacteristic
21C22×C4×D11—21no—
22C22×C8×C11D412yes—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8D414yes—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C42×C11C2311yescharacteristic
30C2×(C2×D11)⋊C4—21no—
31C2×C4⋊Dic11D411yescharacteristic
32C22×C11⋊C8—22no—
33C22×C11⋊C8—21no—
34C4×D44—22no—
35C4×D44—22no—
36C11×#107—28no—
37C4×C8×C11—22no—
38(C2×D11)⋊C8—44no—
39#66873—28no—
40#66872—28no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)D414yes—
44#10278—111nomaximal, Sylow
45C23×D11—21no—
46C2×Q8×C11—24no—
47C2×Q8×C11—42no—
48C2×Q8×C11—84no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×Dic11—21no—
54C2×D44—22no—
55C2×D44—21no—
56C2×D44—22no—
57C2×D44Q1612yes—
58C2×C4×D11—41no—
59C2×C4×D11—41no—
60C2×C4×D11—42no—
61C2×C4×D11—42no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11SD1614yes—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C42×C11C2×D412yes—
70C42×C11C2×D412yes—
71(C2×D11)⋊C4—42no—
72C4⋊Dic11—22no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×#500D1111yescharacteristic, complemented
79C2×#476—112no—
80#1954—111no—
81C2×#333—112no—
82#1277—111no—
83C23×C11#12111yescharacteristic
84C22×D11—22no—
85C22×D11—41no—
86C22×D11—42no—
87C22×D11—41no—
88C22×D11—42no—
89Q8×C11—84no—
90Q8×C11—84no—
91C2×C4×C11—22no—
92C2×C4×C11—44no—
93C2×C4×C11—84no—
94C2×C4×C11#12012yes—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11#12112yes—
97C2×C4×C11#12711yescharacteristic
98C2×C4×C11C2×SD1612yes—
99C2×C4×C11C2×Q1611yescharacteristic
100C2×C4×C11#13511yescharacteristic
101C2×C4×C11#13712yes—
102C2×C4×C11#13712yes—
103C2×Dic11—41no—
104C2×Dic11—42no—
105D44—24no—
106D44—42no—
107C4×D11—82no—
108C4×D11—81no—
109C4×D11—81no—
110C8×C11—24no—
111C11⋊C8—44no—
112C11⋊C8—81no—
113C2×C4⋊Q8C2×D1112yes—
114C2×C4×D4—111no—
115#500—24no—
116#476—224no—
117#476—224no—
118C2×#107—22no—
119C2×#106—222no—
120C2×C4⋊C8—112no—
121C2×C4⋊C8—111no—
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—84no—
138C4×C11#44812yes—
139C4×C11#45112yes—
140C4×C11#45212yes—
141C4×C11#49211yescharacteristic
142C4×C11#49711yescharacteristic
143Dic11—81no—
144C22×Q8—22no—
145C22×D4—111no—
146C23×C4—221no—
147C22×C8—222no—
148C22×C8—221no—
149C22×C8C22⋊D1112yes—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4⋊Q8—22no—
153C4⋊Q8C22⋊D1114yes—
154C4×D4—222no—
155C4×D4—222no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—111no—
159C2×C22⋊C4—221no—
160C2×C42C22×D1111yescharacteristic
161#107—28no—
162#106—228no—
163C4⋊C8—114no—
164C4⋊C8—222no—
165C4⋊C8—222no—
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—24no—
177C2×Q8—42no—
178C2×Q8—84no—
179C2×D4—112no—
180C2×D4—222no—
181C2×D4—221no—
182C2×D4—222no—
183C22×C4—42no—
184C22×C4—221no—
185C22×C4—441no—
186C22×C4—442no—
187C22×C4—442no—
188C22×C4—441no—
189C22×C4D4×D1111yescharacteristic
190C22×C4#434111yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—224no—
195C2×C8—442no—
196C2×C8—442no—
197C2×C8—441no—
198C2×C8—442no—
199C2×C8#432514yes—
200C4⋊C4—24no—
201C4⋊C4—24no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—222no—
205C22⋊C4—442no—
206C42D4×D1112yes—
207C42C2×C22⋊D1112yes—
208C11#1027811yescharacteristic, complemented, Sylow
209C23—222no—
210C23—442no—
211C23—441no—
212C23—441no—
213C23—442no—
214C23#6699111yescharacteristic
215Q8—84no—
216Q8—84no—
217D4—224no—
218D4—442no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—84no—
222C2×C4—441no—
223C2×C4—442no—
224C2×C4—882no—
225C2×C4—881no—
226C2×C4—881no—
227C2×C4Q16×D1111yescharacteristic
228C2×C4#6697112yes—
229C2×C4#6697211yescharacteristic
230C2×C4#6699012yes—
231C2×C4#6699212yes—
232C2×C4#6699311yescharacteristic
233C2×C4C2×#432512yes—
234C2×C4#6699512yes—
235C2×C4#6700611yescharacteristic
236C8—24no—
237C8—444no—
238C8—881no—
239C22—442no—
240C22—444no—
241C22—882no—
242C22—881no—
243C22—881no—
244C22#1062269612yes—
245C22#1062277312yes—
246C22#1062280111yescharacteristic
247C22#1062280211yescharacteristic
248C22#1062283611yescharacteristic
249C4—22no—
250C4—84no—
251C4—881no—
252C4#1062269811yescharacteristic
253C4#1062269911yescharacteristic
254C4#1062279912yes—
255C4#1062280012yes—
256C4#1062284012yes—
257C2—882no—
258C2#1306801212yes—
259C2#1306813612yes—
260C2#1306962311yescharacteristic
261C2#1306969911yescharacteristic
262C2#1306972311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#500D11
hypocenterC11#10278
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. C2×#10622184C2semidirect
4. #13066451C2semidirect
5. C2×C11×#500C2semidirect
78. C2×#500D11semidirect
208. C11#10278semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130694102
C2×#106221842
#130664512
C2×C11×#5002
#1027811