Finite Group Databasebeta

← #29569146

Subgroups — #29569146

Order 15616.

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

normal subgroups only

This group has 366 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#21453807C211yesmaximal, characteristic
2#21447362C211yesmaximal, characteristic
3#21447292C212yesmaximal
4#21443643C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519711—22no—
7C2×#14519708—21no—
8C2×#14519701—21no—
9#16839701—21no—
10#16839694—22no—
11#16839669—21no—
12#16839660C2212yes—
13#16839649—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×#92418—21no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×C4×Dic61—21no—
28#14519711—44no—
29#14519708—42no—
30#14519701—42no—
31#14519684—22no—
32#14519684—22no—
33#14519684—21no—
34#14519684—22no—
35C22×Q8×C61D411yescharacteristic
36C22×C8×C61—22no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C42×C61C2311yescharacteristic
39#95×C61—22no—
40C2×Q8×C61—21no—
41C2×Q8×C61—41no—
42C2×Q8×C61—41no—
43C2×Q8×C61Q1612yes—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2×D411yescharacteristic
47C22×C4×C61C2×D412yes—
48C22×Dic61—22no—
49C22×Dic61—22no—
50C22×Dic61—41no—
51C2×C8×C61—24no—
52C2×C8×C61—42no—
53C2×C8×C61—42no—
54C4⋊C4×C61—41no—
55C42×C61—41no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—42no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63C4⋊Dic61—81no—
64C4⋊Dic61—81no—
65#11758196—42no—
66#11758196—42no—
67C4×Dic61—81no—
68C2×#92418—22no—
69C2×#92418—41no—
70C2×#92418—41no—
71C23×C61#12011yescharacteristic
72Q8×C61—42no—
73Q8×C61—81no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—42no—
83C2×C4×C61C2×Q1611yescharacteristic
84C2×C4×C61#13512yes—
85C2×C4×C61AGL(1,ℤ/8)12yes—
86C2×C4×C61#13711yescharacteristic
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—82no—
94C2×Dic61—81no—
95C8×C61—44no—
96#92418—42no—
97#7802—611nomaximal, Sylow
98C22×C61#44912yes—
99C22×C61#45111yescharacteristic
100C22×C61#45311yescharacteristic
101C22×C61#45612yes—
102C22×C61#45811yescharacteristic
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—42no—
108C4×C61—81no—
109Dic61—82no—
110Dic61—82no—
111Dic61—161no—
112#2809—611no—
113#2096—611no—
114#2083—612no—
115#1272D6111yescharacteristic
116#1271—612no—
117C2×C61#160912yes—
118C2×C61#161411yescharacteristic
119C2×C61#162411yescharacteristic
120C2×C61#164812yes—
121C2×C61#166011yescharacteristic
122C2×#107—1222no—
123C2×#106—1221no—
124C2×#103—1221no—
125#400—1221no—
126#398—1222no—
127#391—1221no—
128#391C2×D6111yescharacteristic
129#389—612no—
130#387—1222no—
131#384—611no—
132#340—1222no—
133#336—611no—
134#336C2×D6112yes—
135C61#780211yescharacteristic, complemented, Sylow
136C22×Q8D24411yescharacteristic
137C22×C8—22no—
138C22×C8—1221no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—1221no—
142C2×C4⋊C4—1221no—
143C2×C4⋊C4—1222no—
144C2×C4⋊C4—1221no—
145C2×C4⋊C4—1222no—
146C2×C4⋊C4D24411yescharacteristic
147C2×C42—1221no—
148C2×C42C22×D6111yescharacteristic
149#107—2444no—
150#106—2442no—
151#103—2442no—
152#95—22no—
153#95—1221no—
154#95—1222no—
155#95—1222no—
156#95—1222no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8Dic24412yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—1222no—
164C22×C4—1222no—
165C22×C4—2441no—
166C22×C4C2×D24411yescharacteristic
167C22×C4D4×D6112yes—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—1222no—
172C2×C8—2441no—
173C2×C8—2441no—
174C4⋊C4—41no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—4881no—
178C4⋊C4—4881no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C4⋊C4—2442no—
185C4⋊C4—2442no—
186C42—41no—
187C42—4881no—
188C23#1451974711yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—4882no—
201C2×C4—4881no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4C2×Dic24411yescharacteristic
209C2×C4#1451980012yes—
210C2×C4#1451980412yes—
211C2×C4#1451981011yescharacteristic
212C8—44no—
213C8—2442no—
214C22#1683991012yes—
215C22#1683992011yescharacteristic
216C22#1683993211yescharacteristic
217C22#1683994612yes—
218C22#1683995311yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—81no—
225C4—9761no—
226C4—4882no—
227C4—4882no—
228C2#2144481912yes—
229C2#2144484611yescharacteristic
230C2#2144490311yescharacteristic
231C2#2144506412yes—
232C2#2144513111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7802
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
135. C61#7802semidirect

Maximal subgroups

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

subgroupindex
#214538072
#214473622
#214472922
#214436432
C61×#12722
#780261