Finite Group Databasebeta

← #30594111

Subgroups — #30594111

Order 15616.

368 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 76 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#21460657C212yesmaximal
2#21444088C211yesmaximal, characteristic
3C2×C22⋊#92420—22no—
4C22×C4⋊Dic61C411yescharacteristic
5C2×#14519684—22no—
6C2×#14519684C2211yescharacteristic
7C2×#95×C61C411yescharacteristic
8C22×#92420—42no—
9C22⋊#92420—24no—
10C22⋊#92420—42no—
11C23×Dic61—21no—
12C23×Dic61D412yes—
13C2×C4⋊Dic61—21no—
14C2×C4⋊Dic61—41no—
15C2×C4⋊Dic61—41no—
16C2×C4⋊Dic61C812yescomplemented
17#14519684—41no—
18#14519684—42no—
19#14519684—42no—
20C23×C4×C61—21no—
21C23×C4×C61C2×C411yescharacteristic
22#95×C61—41no—
23C24×C61C22⋊C411yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—22no—
27C22×C4×C61—42no—
28C22×C4×C61—42no—
29C22×C4×C61—41no—
30C22×C4×C61—41no—
31C22×C4×C61—42no—
32C22×C4×C61C2×C811yescharacteristic
33C22×C4×C61M1611yescharacteristic
34C22×Dic61—22no—
35C22×Dic61—22no—
36C22×Dic61—22no—
37C22×Dic61—42no—
38C22×Dic61—42no—
39C22×Dic61—41no—
40C22×Dic61—41no—
41C22×Dic61—42no—
42C22×Dic61—42no—
43C22×Dic61D812yes—
44C22×Dic61SD1612yes—
45C2×#92420—44no—
46C2×#92420—82no—
47C2×#92420—82no—
48C4⋊Dic61—42no—
49C4⋊Dic61—42no—
50C23×C61—22no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61C22⋊C811yescharacteristic
54C23×C61#9911yescharacteristic
55C23×C61#10011yescharacteristic
56C23×C61#10212yes—
57C23×C61#10412yes—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—42no—
61C2×C4×C61—42no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—42no—
65C2×C4×C61—44no—
66C2×C4×C61—81no—
67C2×C4×C61—82no—
68C2×C4×C61—81no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—44no—
77C2×Dic61—82no—
78C2×Dic61—82no—
79C2×Dic61—81no—
80C2×Dic61—81no—
81#92420—84no—
82#7104—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61#32311yescharacteristic
92C22×C61D4⋊C812yes—
93C22×C61#32712yes—
94C22×C61#32911yescharacteristic
95C22×C61#33111yescharacteristic
96C22×C61#35212yes—
97C22×C61#35411yescharacteristic
98C22×C61#35611yescharacteristic
99C4×C61—41no—
100C4×C61—41no—
101C4×C61—82no—
102Dic61—42no—
103Dic61—42no—
104Dic61—82no—
105#1445—611no—
106#1280—612no—
107C2×C61—21no—
108C2×C61—22no—
109C2×C61—21no—
110C2×C61#127011yescharacteristic
111C2×C61#131711yescharacteristic
112C2×C61#131911yescharacteristic
113C2×C61#134412yes—
114C2×C61#134612yes—
115C22×C4⋊C4—611no—
116C2×C22⋊C8—1222no—
117C2×#95—611no—
118C2×#95—1222no—
119C2×#95#692311yescharacteristic
120C61#710411yescharacteristic, complemented, Sylow
121C23×C4—21no—
122C23×C4—612no—
123C23×C4—1221no—
124C23×C4C2×#692311yescharacteristic
125C22×C8—2442no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—1221no—
128C2×C4⋊C4—2441no—
129C2×C4⋊C4—2441no—
130C22⋊C8—1224no—
131C22⋊C8—2442no—
132#95—41no—
133#95—2441no—
134#95—2442no—
135#95—2442no—
136C24C22⋊#692311yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—22no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—42no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4—1222no—
149C22×C4—1222no—
150C22×C4—2441no—
151C22×C4—2441no—
152C22×C4—2442no—
153C22×C4—2442no—
154C22×C4—2442no—
155C22×C4—2442no—
156C22×C4D61⋊C811yescharacteristic
157C22×C4#1175821311yescharacteristic
158C2×C8—4882no—
159C2×C8—4882no—
160C2×C8—2444no—
161C4⋊C4—2442no—
162C4⋊C4—2442no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23#1451983411yescharacteristic
167C23#1451983611yescharacteristic
168C23#1451983711yescharacteristic
169C23#1451983912yes—
170C23#1451984212yes—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—81no—
180C2×C4—82no—
181C2×C4—81no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—4882no—
185C2×C4—4881no—
186C2×C4—4881no—
187C2×C4—4882no—
188C2×C4—2442no—
189C2×C4—2444no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2442no—
194C8—4884no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22#1684060611yescharacteristic
204C22#1684061012yes—
205C22#1684061412yes—
206C22#1684061811yescharacteristic
207C22#1684062011yescharacteristic
208C22#1684066512yes—
209C22#1684066911yescharacteristic
210C22#1684067311yescharacteristic
211C4—41no—
212C4—41no—
213C4—82no—
214C4—4882no—
215C4—2442no—
216C4—2442no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2#2146063611yescharacteristic
221C2#2146074611yescharacteristic
222C2#2146075011yescharacteristic
223C2#2146080012yes—
224C2#2146080412yes—
subgroupG/H
centerC23#14519836
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#14519684C22
hypercenterC2×#95#6923
hypocenterC61#7104
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic61C8semidirect
120. C61#7104semidirect

Maximal subgroups

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

subgroupindex
#214606572
#214440882
#710461