Finite Group Databasebeta

← #14654740

Subgroups — #14654740

Order 2816.

636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079062C211yesmaximal, characteristic, complemented
2#13078617C212yesmaximal, complemented
3#13069414C211yesmaximal, characteristic, complemented
4#13067016C212yesmaximal, complemented
5C11×#1275C211yesmaximal, characteristic, complemented
6C2×#66957—22no—
7#10623008C2212yes—
8C2×C4×D44C2211yescharacteristic
9C11×#431C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12C2×C4⋊(C11⋊C8)C2211yescharacteristic
13#10622459—22no—
14#10622456—22no—
15#10622349—22no—
16#10622345—22no—
17#10622328—22no—
18#10622325—22no—
19C4×D88—24no—
20#10622097—24no—
21C2×#4339—22no—
22C22×D44D411yescharacteristic
23C22×C4×D11—21no—
24C22×C8×C11D412yes—
25C2×C42×C11C2311yescharacteristic
26#66983—22no—
27#66983—22no—
28C2×(C2×D11)⋊C4—21no—
29C2×C4⋊Dic11D411yescharacteristic
30C22×C11⋊C8—21no—
31C2×Dic44—22no—
32#66957—44no—
33#66957—44no—
34C2×D88—22no—
35C2×D88—24no—
36C2×#4314—24no—
37#66928—22no—
38#66927D412yes—
39C4×D44—22no—
40C4×D44—22no—
41C4×D44—22no—
42C4×D44—22no—
43#66922D412yes—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×#97—22no—
47C4×C8×C11D414yes—
48#66885—24no—
49#66885—24no—
50(C2×D11)⋊C8—44no—
51#66882—24no—
52C4⋊(C11⋊C8)—22no—
53#10032—111nomaximal, Sylow
54C23×D11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C2×C22⋊D11—42no—
59C22×Dic11—21no—
60#4339—44no—
61#4339—44no—
62C2×D44—22no—
63C2×D44—22no—
64C2×D44—22no—
65C2×D44—22no—
66C2×D44—42no—
67C2×C4×D11—41no—
68C2×C4×D11—41no—
69C2×C4×D11—42no—
70C2×C4×D11—42no—
71C2×C4×D11—42no—
72C2×Dic22—22no—
73C2×C8×C11—22no—
74C2×C8×C11—24no—
75C2×C8×C11—22no—
76C2×C8×C11D814yescomplemented
77C42×C11C2×D412yes—
78C42×C11C2×D412yes—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—42no—
81(C2×D11)⋊C4—42no—
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—42no—
87Dic44—44no—
88D88—44no—
89D88—48no—
90#4314—48no—
91#3150—111no—
92#3100—112no—
93#1955—111no—
94#1480—112no—
95#1275D1111yescharacteristic, complemented
96C23×C11#12111yescharacteristic
97C22×D11—22no—
98C22×D11—41no—
99C22×D11—42no—
100C22×D11—41no—
101C22×D11—42no—
102C22×D11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11#12012yes—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11#12112yes—
108C2×C4×C11#12711yescharacteristic
109C2×C4×C11C2×D812yes—
110C2×C4×C11AGL(1,ℤ/8)12yes—
111C22⋊D11—84no—
112C2×Dic11—42no—
113C2×Dic11—41no—
114C2×Dic11—42no—
115D44—24no—
116D44—42no—
117D44—44no—
118D44—44no—
119D44—44no—
120C4×D11—82no—
121C4×D11—81no—
122C4×D11—82no—
123C4×D11—81no—
124C4×D11—82no—
125Dic22—44no—
126C8×C11—24no—
127C8×C11—44no—
128C11⋊C8—81no—
129C2×#135—222no—
130#532—112no—
131C2×C4×D4—111no—
132#497—222no—
133#496—222no—
134#480—222no—
135#474—222no—
136#459—222no—
137#447—222no—
138C4×D8—224no—
139#431C2×D1112yes—
140C2×C4⋊C8—111no—
141C2×C22⋊C8—222no—
142C2×#97C2×D1111yescharacteristic
143D4⋊C8—224no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#39211yescharacteristic
147C22×C11#45912yes—
148C2×D11—44no—
149C2×D11—42no—
150C2×D11—82no—
151C2×D11—81no—
152C2×D11—81no—
153C2×D11—82no—
154C2×D11—82no—
155C2×D11—82no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11#44712yes—
159C4×C11#49311yescharacteristic
160C4×C11#49611yescharacteristic
161Dic11—82no—
162Dic11—81no—
163C2×#41—222no—
164C22×D4—111no—
165C23×C4—221no—
166#135—444no—
167#135—444no—
168C2×Q16—222no—
169C2×SD16—224no—
170C2×D8—222no—
171C2×D8—224no—
172C22×C8—221no—
173C22×C8D4412yes—
174C4⋊Q8—112no—
175#127—112no—
176#124—222no—
177#121—222no—
178#121—222no—
179C4×D4—222no—
180C4×D4—222no—
181C4×D4—222no—
182C4×D4—222no—
183C2×C4⋊C4—111no—
184C2×C22⋊C4—221no—
185C2×C42C22×D1111yescharacteristic
186#107—224no—
187C4⋊C8—22no—
188C4⋊C8—222no—
189#102—224no—
190#102—224no—
191C22⋊C8—22no—
192C22⋊C8—444no—
193#97—22no—
194C4×C8D4414yes—
195C2×C11—22no—
196C2×C11#201011yescharacteristic
197C2×C11#201111yescharacteristic
198C2×C11#201711yescharacteristic
199D11—82no—
200D11—162no—
201C24—221no—
202#41—444no—
203#41—444no—
204C2×Q8—222no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—222no—
209C2×D4—442no—
210C2×D4—442no—
211C22×C4—221no—
212C22×C4—441no—
213C22×C4—442no—
214C22×C4—441no—
215C22×C4—442no—
216C22×C4—442no—
217C22×C4C2×D4411yescharacteristic
218C22×C4D4×D1111yescharacteristic
219C22×C4#434311yescharacteristic
220Q16—444no—
221SD16—448no—
222D8—444no—
223D8—448no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—24no—
227C2×C8—441no—
228C2×C8—442no—
229C2×C8D8814yescomplemented
230C4⋊C4—222no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C22⋊C4—442no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C42C2×D4412yes—
237C42D4×D1112yes—
238C11#1003211yescharacteristic, complemented, Sylow
239C23—222no—
240C23—441no—
241C23—442no—
242C23—441no—
243C23—442no—
244C23—442no—
245C23#6694811yescharacteristic
246Q8—444no—
247D4—224no—
248D4—442no—
249D4—444no—
250D4—444no—
251D4—444no—
252D4—884no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—441no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—881no—
259C2×C4—882no—
260C2×C4—881no—
261C2×C4—882no—
262C2×C4—882no—
263C2×C4#6692711yescharacteristic
264C2×C4#6693512yes—
265C2×C4#6693511yescharacteristic
266C2×C4#6694812yes—
267C2×C4C2×D8812yes—
268C2×C4#6696112yes—
269C8—24no—
270C8—44no—
271C8—881no—
272C22—21no—
273C22—21no—
274C22—444no—
275C22—442no—
276C22—882no—
277C22—881no—
278C22—881no—
279C22—882no—
280C22—882no—
281C22—882no—
282C22#1062228411yescharacteristic
283C22#1062245612yes—
284C4—22no—
285C4—22no—
286C4—881no—
287C4—882no—
288C4#1062230811yescharacteristic
289C4#1062232511yescharacteristic
290C4#1062234512yes—
291C2—22no—
292C2—882no—
293C2—1762no—
294C2#1306968411yescharacteristic
295C2#1306968911yescharacteristic
296C2#1306972111yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#392
hypercenter#1275D11
hypocenterC11#10032
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
1. #13079062C2semidirect
2. #13078617C2semidirect
3. #13069414C2semidirect
4. #13067016C2semidirect
5. C11×#1275C2semidirect
76. C2×C8×C11D8semidirect
95. #1275D11semidirect
229. C2×C8D88semidirect
238. C11#10032semidirect

Maximal subgroups

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

subgroupindex
#130790622
#130786172
#130694142
#130670162
C11×#12752
#1003211