Finite Group Databasebeta

← #29569200

Subgroups — #29569200

Order 15616.

478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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#21452845C211yesmaximal, characteristic
2#21447362C211yesmaximal, characteristic, complemented
3#21447224C212yesmaximal, complemented
4#21443639C212yesmaximal, complemented
5C61×#1272C211yesmaximal, characteristic, complemented
6C2×#14519766—21no—
7C2×#14519708—21no—
8C2×#14519701—21no—
9C2×#14519699—22no—
10#16839679—21no—
11#16839672—22no—
12#16839664C2212yes—
13#16839654—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×D244—21no—
20C22×D244—21no—
21C22×D244D412yes—
22C22×#92418—21no—
23#14519766—42no—
24#14519766—42no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×C4×Dic61—21no—
33#14519708—42no—
34#14519701—42no—
35#14519699—44no—
36#14519684—21no—
37C22×Q8×C61D411yescharacteristic
38C22×C8×C61—22no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41#95×C61—22no—
42C23×D61—22no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61SD1612yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—22no—
52C22×Dic61—41no—
53C2×D244—22no—
54C2×D244—22no—
55C2×D244—42no—
56C2×D244—42no—
57C2×D244—42no—
58C2×D244—81no—
59C2×D244—81no—
60C2×D244—81no—
61C2×D244—82no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C2×C8×C61—42no—
65C4⋊C4×C61—41no—
66C42×C61—41no—
67#11758198—44no—
68#11758198—42no—
69#11758198—42no—
70#11758198—42no—
71#11758198—42no—
72#11758198—82no—
73C4⋊Dic61—42no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4⋊Dic61—42no—
77C4⋊Dic61—42no—
78C4×Dic61—42no—
79C2×#92418—22no—
80C2×#92418—41no—
81C2×#92418—41no—
82C23×C61#12011yescharacteristic
83C22×D61—42no—
84C22×D61—42no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—42no—
90Q8×C61—42no—
91Q8×C61—81no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61C2×SD1611yescharacteristic
102C2×C4×C61#13512yes—
103C2×C4×C61AGL(1,ℤ/8)12yes—
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—82no—
109C2×Dic61—81no—
110D244—44no—
111D244—82no—
112D244—84no—
113D244—84no—
114C8×C61—82no—
115#92418—42no—
116#7810—611nomaximal, Sylow
117C22×C61#44912yes—
118C22×C61#45011yescharacteristic
119C22×C61#45311yescharacteristic
120C22×C61#45512yes—
121C22×C61#45811yescharacteristic
122C2×D61—82no—
123C2×D61—82no—
124C2×D61—82no—
125C2×D61—82no—
126C2×D61—82no—
127C2×D61—82no—
128C2×D61—82no—
129C4×C61—22no—
130C4×C61—22no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61—81no—
135Dic61—82no—
136Dic61—161no—
137#2733—611no—
138#2096—611no—
139#2071—612no—
140#1272D6111yescharacteristic, complemented
141#1270—612no—
142C2×C61#161212yes—
143C2×C61#161311yescharacteristic
144C2×C61#162411yescharacteristic
145C2×C61#164212yes—
146C2×C61#165911yescharacteristic
147D61—162no—
148C2×#124—1221no—
149C2×#106—1221no—
150C2×#103—1221no—
151C2×#102—1222no—
152#394—1221no—
153#392—1222no—
154#391C2×D6111yescharacteristic
155#390—612no—
156#388—1222no—
157#384—611no—
158#340—1222no—
159#336—611no—
160#336C2×D6112yes—
161C61#781011yescharacteristic, complemented, Sylow
162C22×Q8D24411yescharacteristic
163C22×D4—612no—
164C22×D4—1221no—
165C22×D4—1221no—
166C22×C8—22no—
167C22×C8—1221no—
168#124—2442no—
169#124—2442no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1222no—
173C2×C4⋊C4D24411yescharacteristic
174C2×C22⋊C4—1222no—
175C2×C22⋊C4—1222no—
176C2×C22⋊C4—1222no—
177C2×C22⋊C4—1222no—
178C2×C42—1221no—
179C2×C42C22×D6111yescharacteristic
180#106—2442no—
181#103—2442no—
182#102—2444no—
183#95—22no—
184#95—1221no—
185C24—1222no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#1175819012yes—
190C2×D4—1222no—
191C2×D4—1222no—
192C2×D4—4881no—
193C2×D4—4881no—
194C2×D4—4882no—
195C2×D4—4881no—
196C2×D4—2442no—
197C2×D4—2442no—
198C2×D4—2442no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—1222no—
202C22×C4—2441no—
203C22×C4C2×D24411yescharacteristic
204C22×C4D4×D6112yes—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—1222no—
209C2×C8—2441no—
210C2×C8—2441no—
211C4⋊C4—41no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2442no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C22⋊C4—4882no—
218C22⋊C4—2444no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C42—41no—
224C42—2442no—
225C23—2442no—
226C23—2442no—
227C23—2442no—
228C23—2442no—
229C23—2442no—
230C23—2442no—
231C23—2442no—
232C23#1451974711yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—4882no—
236D4—4884no—
237D4—4884no—
238D4—2444no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—4882no—
249C2×C4—4881no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4C2×#1175819011yescharacteristic
254C2×C4#1451980012yes—
255C2×C4#1451980412yes—
256C2×C4#1451980511yescharacteristic
257C8—82no—
258C8—2442no—
259C22—4882no—
260C22—4882no—
261C22—4882no—
262C22—4882no—
263C22—4882no—
264C22—4882no—
265C22—4882no—
266C22#1683991012yes—
267C22#1683991511yescharacteristic
268C22#1683993211yescharacteristic
269C22#1683994112yes—
270C22#1683995311yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—9761no—
278C4—4882no—
279C2—9762no—
280C2#2144483612yes—
281C2#2144484111yescharacteristic
282C2#2144490311yescharacteristic
283C2#2144502212yes—
284C2#2144512611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61#120
prime radical#21452845C2
hypercenter#1272D61
hypocenterC61#7810
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21447362C2semidirect
3. #21447224C2semidirect
4. #21443639C2semidirect
5. C61×#1272C2semidirect
140. #1272D61semidirect
161. C61#7810semidirect

Maximal subgroups

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

subgroupindex
#214528452
#214473622
#214472242
#214436392
C61×#12722
#781061