Finite Group Databasebeta

← #14656292

Subgroups — #14656292

Order 2816.

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

normal subgroups only

This group has 742 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×#10622308C211yesmaximal, characteristic
2C2×#10622461C212yesmaximal, complemented
3#13069552C211yesmaximal, characteristic, complemented
4C2×#10622123C212yesmaximal, complemented
5C11×#1277C211yesmaximal, characteristic, complemented
6C22×D88—22no—
7C22×#4314—22no—
8C2×#66927C2212yes—
9C2×C4×Dic22C2211yescharacteristic
10C2×C11×C4⋊C8C2212yes—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66885—22no—
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14#10622461—24no—
15#10622461—24no—
16#10622308—24no—
17#10622188—22no—
18#10622123—24no—
19C22×D44—22no—
20C22×D44—22no—
21C22×D44—22no—
22C22×Dic22D411yescharacteristic
23C22×C8×C11—22no—
24C22×C8×C11D412yes—
25C2×C42×C11C2311yescharacteristic
26C2×C4⋊Dic11D411yescharacteristic
27C2×Dic11⋊C4—21no—
28C2×C4×Dic11—21no—
29C22×C11⋊C8—21no—
30C2×D88—28no—
31C2×D88—44no—
32C2×D88—44no—
33C2×#4314—28no—
34C2×#4314—44no—
35C2×#4314—44no—
36#66927—22no—
37#66927—22no—
38#66927—22no—
39#66927D414yes—
40C4×Dic22—22no—
41C4×Dic22—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8D414yes—
44C4×C8×C11—22no—
45#66885—28no—
46C4⋊(C11⋊C8)—22no—
47#10262—111nomaximal, Sylow
48C23×D11—42no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C22×Dic11—21no—
53C22×Dic11—21no—
54C2×D44—24no—
55C2×D44—24no—
56C2×D44—24no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44—42no—
61C2×D44—44no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—44no—
65C2×D44—42no—
66C2×D44—84no—
67C2×Dic22—22no—
68C2×Dic22—21no—
69C2×Dic22—22no—
70C2×Dic22D812yescomplemented
71C2×C8×C11—22no—
72C2×C8×C11—24no—
73C2×C8×C11—22no—
74C2×C8×C11—42no—
75C2×C8×C11—42no—
76C2×C8×C11SD1614yescomplemented
77C42×C11C2×D412yes—
78C42×C11C2×D412yes—
79C4⋊Dic11—22no—
80Dic11⋊C4—42no—
81C4×Dic11—41no—
82C4×Dic11—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—42no—
85D88—416no—
86#4314—416no—
87C2×#493—111no—
88C2×#460—112no—
89#1984—111no—
90C2×#331—112no—
91#1277D1111yescharacteristic, complemented
92C23×C11#12111yescharacteristic
93C22×D11—44no—
94C22×D11—84no—
95C22×D11—82no—
96C22×D11—82no—
97C22×D11—84no—
98C2×C4×C11—22no—
99C2×C4×C11#12012yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12711yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11C2×SD1612yes—
105C2×C4×C11#13511yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×C4×C11AGL(1,ℤ/8)12yes—
108C2×Dic11—22no—
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113D44—44no—
114D44—44no—
115D44—48no—
116D44—84no—
117D44—84no—
118D44—82no—
119D44—82no—
120D44—82no—
121D44—82no—
122Dic22—24no—
123Dic22—42no—
124C8×C11—24no—
125C8×C11—44no—
126C11⋊C8—81no—
127C22×SD16—222no—
128C22×D8—222no—
129C2×#127—112no—
130C2×C4×Q8—111no—
131#493—224no—
132#460—224no—
133#460—224no—
134C2×C4⋊C8—111no—
135C2×C4⋊C8C2×D1112yes—
136C2×#102—222no—
137C2×C4×C8C2×D1111yescharacteristic
138#336—222no—
139#331—224no—
140C22×C11#39211yescharacteristic
141C22×C11#46012yes—
142C22×C11#46611yescharacteristic
143C22×C11#46911yescharacteristic
144C22×C11#47212yes—
145C2×D11—84no—
146C2×D11—84no—
147C2×D11—84no—
148C2×D11—164no—
149C2×D11—164no—
150C4×C11—22no—
151C4×C11#44712yes—
152C4×C11#44912yes—
153C4×C11#45012yes—
154C4×C11#49211yescharacteristic
155C4×C11#49611yescharacteristic
156Dic11—42no—
157Dic11—81no—
158C22×Q8—111no—
159C22×D4—222no—
160C22×D4—222no—
161C22×D4—222no—
162C2×SD16—228no—
163C2×SD16—444no—
164C2×SD16—444no—
165C2×D8—228no—
166C2×D8—444no—
167C2×D8—444no—
168C22×C8—22no—
169C22×C8—221no—
170C22×C8D4412yes—
171#127—114no—
172#127—222no—
173#127—222no—
174#127—222no—
175C4×Q8—222no—
176C4×Q8—222no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—221no—
179C2×C42—221no—
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—22no—
182C4⋊C8—222no—
183C4⋊C8D4414yes—
184#102—228no—
185C4×C8—22no—
186C2×C11#166812yes—
187C2×C11#168812yes—
188C2×C11#199911yescharacteristic
189C2×C11#201411yescharacteristic
190C2×C11#201811yescharacteristic
191D11—164no—
192C24—442no—
193C2×Q8—112no—
194C2×Q8—221no—
195C2×Q8—222no—
196C2×Q8—222no—
197C2×D4—224no—
198C2×D4—224no—
199C2×D4—224no—
200C2×D4—442no—
201C2×D4—442no—
202C2×D4—442no—
203C2×D4—444no—
204C2×D4—444no—
205C2×D4—442no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—884no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4C2×D4411yescharacteristic
213C22×C4D4×D1111yescharacteristic
214C22×C4#434311yescharacteristic
215SD16—4416no—
216D8—4416no—
217C2×C8—22no—
218C2×C8—22no—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—441no—
223C2×C8—442no—
224C2×C8#431414yescomplemented
225C4⋊C4—222no—
226C4⋊C4—442no—
227C42—441no—
228C42—441no—
229C42C2×D4412yes—
230C42D4×D1112yes—
231C11#1026211yescharacteristic, complemented, Sylow
232C23—444no—
233C23—882no—
234C23—882no—
235C23—884no—
236C23—884no—
237C23#6694811yescharacteristic
238Q8—224no—
239Q8—442no—
240D4—448no—
241D4—444no—
242D4—444no—
243D4—884no—
244D4—884no—
245D4—882no—
246D4—882no—
247D4—882no—
248D4—882no—
249C2×C4—22no—
250C2×C4—222no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—442no—
254C2×C4—441no—
255C2×C4#6692711yescharacteristic
256C2×C4#6693511yescharacteristic
257C2×C4#6693512yes—
258C2×C4#6694812yes—
259C2×C4C2×#431412yes—
260C2×C4#6696112yes—
261C2×C4D8×D1111yescharacteristic
262C2×C4#6696712yes—
263C2×C4#6697211yescharacteristic
264C8—24no—
265C8—44no—
266C8—881no—
267C22—884no—
268C22—884no—
269C22—884no—
270C22—1764no—
271C22—1764no—
272C22#1062228411yescharacteristic
273C22#1062246112yes—
274C22#1062247811yescharacteristic
275C22#1062249611yescharacteristic
276C22#1062251012yes—
277C4—22no—
278C4—442no—
279C4—881no—
280C4#1062230611yescharacteristic
281C4#1062232511yescharacteristic
282C4#1062234412yes—
283C4#1062238612yes—
284C4#1062242412yes—
285C2—1764no—
286C2#1306797712yes—
287C2#1306810112yes—
288C2#1306961511yescharacteristic
289C2#1306970611yescharacteristic
290C2#1306972611yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC2×#10622308C2
hypercenter#1277D11
hypocenterC11#10262
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
2. C2×#10622461C2semidirect
3. #13069552C2semidirect
4. C2×#10622123C2semidirect
5. C11×#1277C2semidirect
70. C2×Dic22D8semidirect
76. C2×C8×C11SD16semidirect
91. #1277D11semidirect
224. C2×C8#4314semidirect
231. C11#10262semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
C2×#106224612
#130695522
C2×#106221232
C11×#12772
#1026211