Finite Group Databasebeta

← #30598793

Subgroups — #30598793

Order 15616.

1026 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461653C212yesmaximal
2#21461067C214yesmaximal
3C22×#14519777C211yesmaximal, characteristic
4C2×#14519838—24no—
5#16840732C2214yes—
6#16840607—28no—
7C23×Dic122C411yescharacteristic
8C23×Dic122C2211yescharacteristic
9C2×#14519777—28no—
10C2×#14519777—24no—
11C22×C4⋊Dic61C412yes—
12C22×C4⋊Dic61C2212yes—
13C22×C42×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519838—48no—
16C22⋊#92420—28no—
17C22×Dic122—22no—
18C22×Dic122—24no—
19C22×Dic122—24no—
20C22×Dic122—44no—
21C22×Dic122—44no—
22C22×Dic122D414yes—
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C412yes—
25C23×Dic61C2311yescharacteristic
26#14519777—232no—
27C2×C4⋊Dic61—24no—
28C2×C4⋊Dic61—24no—
29C2×C4⋊Dic61—24no—
30C2×C4⋊Dic61—24no—
31C2×C4⋊Dic61—24no—
32C2×C4⋊Dic61D418yes—
33C23×C4×C61C2×C412yes—
34C23×C4×C61C2×C411yescharacteristic
35C2×C42×C61—24no—
36C2×C42×C61—22no—
37C24×C61C22×C411yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—24no—
42C22×C4×C61—28no—
43C22×C4×C61C22⋊C412yes—
44C22×C4×C61C22⋊C414yes—
45C22×Dic61—22no—
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—42no—
49C22×Dic61—42no—
50C22×Dic61—44no—
51C22×Dic61C22⋊C412yes—
52C22×Dic61C22⋊C414yes—
53C22×Dic61C2×D412yes—
54C22×Dic61C2×D414yes—
55C2×Dic122—28no—
56C2×Dic122—28no—
57C2×Dic122—28no—
58C2×Dic122—44no—
59C2×Dic122—416no—
60C2×Dic122—416no—
61C2×Dic122—44no—
62C2×Dic122—44no—
63#11758217—48no—
64C2×#92420—44no—
65C42×C61—28no—
66C4⋊Dic61—216no—
67C4⋊Dic61—216no—
68C23×C61—22no—
69C23×C61—24no—
70C23×C61C2×C22⋊C411yescharacteristic
71C23×C61C2×C22⋊C412yes—
72C2×C4×C61—28no—
73C2×C4×C61—28no—
74C2×C4×C61—28no—
75C2×C4×C61—24no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—24no—
79C2×C4×C61#9914yes—
80C2×C4×C61#10118yescomplemented
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—24no—
85C2×Dic61—44no—
86C2×Dic61—44no—
87C2×Dic61—44no—
88C2×Dic61—44no—
89C2×Dic61—44no—
90C2×Dic61#12014yes—
91Dic122—416no—
92Dic122—416no—
93#92420—84no—
94#8551—611nomaximal, Sylow
95C22×C61—28no—
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61#37911yescharacteristic
100C22×C61C2×#9912yes—
101C22×C61C2×#10114yes—
102C4×C61—24no—
103C4×C61—28no—
104Dic61—24no—
105Dic61—42no—
106Dic61—44no—
107C22×C4⋊Q8—611no—
108#1784—612no—
109#1463—614no—
110C2×C61—22no—
111C2×C61—24no—
112C2×C61#178111yescharacteristic
113C2×C61#178412yes—
114C23×Q8—611no—
115C23×Q8—611no—
116C2×C4⋊Q8—1228no—
117C2×C4⋊Q8—1224no—
118C22×C4⋊C4—612no—
119C22×C4⋊C4—612no—
120C22×C42#692311yescharacteristic
121C2×#101—1224no—
122#407—614no—
123#324—1228no—
124C61#855111yescharacteristic, complemented, Sylow
125C22×Q8—614no—
126C22×Q8—1224no—
127C22×Q8—1224no—
128C22×Q8—1222no—
129C22×Q8—2444no—
130C22×Q8—2444no—
131C23×C4—611no—
132C23×C4—611no—
133C23×C4—612no—
134C23×C4C2×#692312yes—
135C23×C4C2×#692311yescharacteristic
136C2×M16—1224no—
137C4⋊Q8—12232no—
138C2×C4⋊C4—618no—
139C2×C4⋊C4—1224no—
140C2×C4⋊C4—1224no—
141C2×C4⋊C4—1224no—
142C2×C4⋊C4—1224no—
143C2×C4⋊C4—1224no—
144C2×C42—22no—
145C2×C42—24no—
146#101—2448no—
147C22⋊C8—1228no—
148C24C22×#692311yescharacteristic
149C2×Q8—1228no—
150C2×Q8—1228no—
151C2×Q8—1228no—
152C2×Q8—2444no—
153C2×Q8—24416no—
154C2×Q8—24416no—
155C2×Q8—2444no—
156C2×Q8—2444no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—28no—
162C22×C4—612no—
163C22×C4—614no—
164C22×C4—612no—
165C22×C4—614no—
166C22×C4—1222no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4—2442no—
170C22×C4—2442no—
171C22×C4—2444no—
172C22×C4C22⋊#692312yes—
173C22×C4C22⋊#692314yes—
174M16—2448no—
175C2×C8—2444no—
176C4⋊C4—12216no—
177C4⋊C4—12216no—
178C42—28no—
179C23—22no—
180C23—24no—
181C23C2×C22⋊#692311yescharacteristic
182C23C2×C22⋊#692312yes—
183Q8—24416no—
184Q8—24416no—
185C2×C4—28no—
186C2×C4—28no—
187C2×C4—28no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—614no—
193C2×C4—1224no—
194C2×C4—1224no—
195C2×C4—1222no—
196C2×C4—1224no—
197C2×C4—2444no—
198C2×C4—2444no—
199C2×C4—2444no—
200C2×C4—2444no—
201C2×C4—2444no—
202C2×C4#1451983614yes—
203C2×C4#1451983818yescomplemented
204C8—4884no—
205C22—28no—
206C22—22no—
207C22—22no—
208C22—22no—
209C22#1684070311yescharacteristic
210C22C2×#1451983612yes—
211C22C2×#1451983814yes—
212C4—24no—
213C4—28no—
214C4—1224no—
215C4—2442no—
216C4—2444no—
217C2—22no—
218C2—24no—
219C2#2146164711yescharacteristic
220C2#2146165312yes—
subgroupG/H
centerC22#16840703
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C42×C61C4
socleC22×C61#379
cosocleC23×Dic61C23
hypercenterC22×C42#6923
hypocenterC61#8551
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
80. C2×C4×C61#101semidirect
124. C61#8551semidirect
203. C2×C4#14519838semidirect

Maximal subgroups

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

subgroupindex
#214616532
#214610672
C22×#145197772
#855161