Finite Group Databasebeta

← #14656369

Subgroups — #14656369

Order 2816.

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

normal subgroups only

This group has 626 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×#10622312C211yesmaximal, characteristic, complemented
2C2×#10622620C212yesmaximal
3C2×#10622120C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×Dic44—22no—
8C2×#66922C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C22⋊C8—22no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66896—22no—
13#10622620—24no—
14#10622620—24no—
15C2×#66871—22no—
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622312—24no—
18#10622120—24no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11—21no—
21C22×Dic22—22no—
22C22×C8×C11—21no—
23C22×C8×C11D412yes—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—22no—
31C22×C11⋊C8—22no—
32C2×Dic44—28no—
33C2×Dic44—44no—
34C2×Dic44—44no—
35#66922—22no—
36#66922—22no—
37#66922—22no—
38#66922D414yes—
39C11×C4⋊C8—22no—
40C11×C22⋊C8—44no—
41C4×C8×C11—22no—
42#66896—28no—
43#66871—28no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46#10274—111nomaximal, Sylow
47C24×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—21no—
50C2×D4×C11—22no—
51C2×D4×C11Q1612yescomplemented
52C22×C4×C11—21no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—42no—
61C2×Dic22—24no—
62C2×Dic22—42no—
63C2×Dic22—44no—
64C2×Dic22—44no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—41no—
68C2×C8×C11—42no—
69C2×C8×C11D814yes—
70C11×C4⋊C4—22no—
71C11×C22⋊C4—42no—
72C42×C11C2×D412yes—
73C42×C11C2×D412yes—
74C4⋊Dic11—24no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81Dic44—416no—
82C2×#494—111no—
83C2×#474—112no—
84#1954D1111yescharacteristic
85C2×#332—112no—
86#1277—111no—
87C23×C11—22no—
88C23×C11—41no—
89C23×C11—42no—
90C23×C11—41no—
91C23×C11—42no—
92C23×C11#12111yescharacteristic
93D4×C11—24no—
94D4×C11—42no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—82no—
99C2×C4×C11—81no—
100C2×C4×C11—81no—
101C2×C4×C11#12012yes—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11#12112yes—
104C2×C4×C11#12711yescharacteristic
105C2×C4×C11C2×D812yes—
106C2×C4×C11C2×Q1611yescharacteristic
107C2×C4×C11#13511yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×C4×C11#13712yes—
110C2×Dic11—44no—
111C2×Dic11—84no—
112Dic22—48no—
113Dic22—82no—
114Dic22—82no—
115C8×C11—24no—
116C8×C11—81no—
117C11⋊C8—44no—
118C22×Q16—222no—
119C2×C4⋊Q8—112no—
120C2×C4×D4C2×D1111yescharacteristic
121#494—224no—
122#474—224no—
123#474—224no—
124C2×#107—222no—
125C2×C4⋊C8—112no—
126C2×C4⋊C8C2×D1111yescharacteristic
127C2×#102—222no—
128C2×C22⋊C8—22no—
129C2×C4×C8C2×D1111yescharacteristic
130#332—224no—
131C22×C11—44no—
132C22×C11—42no—
133C22×C11—82no—
134C22×C11—81no—
135C22×C11—81no—
136C22×C11#39211yescharacteristic
137C22×C11#45912yes—
138C22×C11#46711yescharacteristic
139C22×C11#47011yescharacteristic
140C22×C11#47312yes—
141C4×C11—22no—
142C4×C11—81no—
143C4×C11#44712yes—
144C4×C11#45112yes—
145C4×C11#45212yes—
146C4×C11#49311yescharacteristic
147C4×C11#49611yescharacteristic
148Dic11—84no—
149C22×Q8—222no—
150C22×D4D4411yescharacteristic
151C23×C4—21no—
152C2×Q16—228no—
153C2×Q16—444no—
154C2×Q16—444no—
155C22×C8—21no—
156C22×C8—222no—
157C22×C8C22⋊D1112yes—
158C4⋊Q8—114no—
159C4⋊Q8—222no—
160C4⋊Q8—222no—
161C4⋊Q8—222no—
162C4×D4—22no—
163C4×D4—22no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4D4411yescharacteristic
167C2×C22⋊C4—21no—
168C2×C42C22×D1111yescharacteristic
169#107—228no—
170C4⋊C8—22no—
171C4⋊C8—114no—
172C4⋊C8—222no—
173#102—228no—
174C22⋊C8—44no—
175C4×C8—22no—
176C2×C11—82no—
177C2×C11#166912yes—
178C2×C11#168912yes—
179C2×C11#200111yescharacteristic
180C2×C11#201111yescharacteristic
181C2×C11#202011yescharacteristic
182C24—21no—
183C2×Q8—224no—
184C2×Q8—442no—
185C2×Q8—444no—
186C2×Q8—444no—
187C2×D4—22no—
188C2×D4—21no—
189C2×D4—22no—
190C2×D4Dic4412yescomplemented
191C22×C4—21no—
192C22×C4—42no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—42no—
196C22×C4—442no—
197C22×C4C2×D4411yescharacteristic
198C22×C4#433911yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200Q16—4416no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—42no—
204C2×C8—41no—
205C2×C8—224no—
206C2×C8—442no—
207C2×C8—442no—
208C2×C8#432314yes—
209C4⋊C4—22no—
210C4⋊C4—224no—
211C4⋊C4—224no—
212C4⋊C4—442no—
213C4⋊C4—442no—
214C22⋊C4—42no—
215C42D4×D1112yes—
216C42D4×D1112yes—
217C11#1027411yescharacteristic, complemented, Sylow
218C23—22no—
219C23—41no—
220C23—42no—
221C23—41no—
222C23—42no—
223C23#6698311yescharacteristic
224Q8—448no—
225Q8—882no—
226Q8—882no—
227D4—24no—
228D4—42no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—444no—
236C2×C4—884no—
237C2×C4#6693512yes—
238C2×C4#6693712yes—
239C2×C4#6695711yescharacteristic
240C2×C4C2×Dic4411yescharacteristic
241C2×C4#6696212yes—
242C2×C4C2×#432312yes—
243C2×C4#6699011yescharacteristic
244C2×C4#6699311yescharacteristic
245C2×C4#6700212yes—
246C8—24no—
247C8—81no—
248C8—444no—
249C22—42no—
250C22—44no—
251C22—82no—
252C22—81no—
253C22—81no—
254C22#1062257311yescharacteristic
255C22#1062262812yes—
256C22#1062272911yescharacteristic
257C22#1062275011yescharacteristic
258C22#1062275612yes—
259C4—22no—
260C4—81no—
261C4—884no—
262C4#1062234612yes—
263C4#1062235212yes—
264C4#1062264912yes—
265C4#1062267111yescharacteristic
266C4#1062268611yescharacteristic
267C2—82no—
268C2#1306798112yes—
269C2#1306810512yes—
270C2#1306962611yescharacteristic
271C2#1306968611yescharacteristic
272C2#1306973711yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#10274
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622312C2semidirect
3. C2×#10622120C2semidirect
4. #13066451C2semidirect
51. C2×D4×C11Q16semidirect
190. C2×D4Dic44semidirect
217. C11#10274semidirect

Maximal subgroups

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

subgroupindex
C2×#106223122
C2×#106226202
C2×#106221202
#130664512
C11×#19542
#1027411