Finite Group Databasebeta

← #30599271

Subgroups — #30599271

Order 15616.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461546C212yesmaximal
2#21460695C214yesmaximal, complemented
3#382×D61C211yesmaximal, characteristic
4C2×#14519834—22no—
5C2×#14519832C2214yes—
6#16840628—22no—
7C2×C4⋊C4×D61C412yes—
8C2×C42×D61C2211yescharacteristic
9#16839628C411yescharacteristic
10#16839627C2212yes—
11#16839626—22no—
12#95×D61—22no—
13C61×#382C411yescharacteristic
14C22×#92420—24no—
15#14519834—28no—
16#14519832—28no—
17C22×C4×D61—22no—
18C22×C4×D61C2×C411yescharacteristic
19C22×C4×D61D412yes—
20C2×C4⋊Dic61C2×C412yes—
21C2×#11758196—22no—
22C4⋊C4×D61—44no—
23C2×C4×Dic61D412yes—
24C2×C4×Dic61C2311yescharacteristic
25C42×D61—24no—
26#14519684—22no—
27#14519684—24no—
28C2×C4⋊C4×C61C2×C412yes—
29C2×C42×C61C2×C411yescharacteristic
30#95×C61—22no—
31C23×D61C22⋊C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61C22⋊C412yes—
34C22×C4×C61C22×C411yescharacteristic
35C22×Dic61—22no—
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61—24no—
42C2×C4×D61—24no—
43C2×C4×D61—42no—
44C2×C4×D61—44no—
45C2×C4×D61—44no—
46C2×C4×D61—44no—
47C2×#92420—28no—
48C2×#92420—44no—
49C2×#92420—44no—
50C4⋊C4×C61—42no—
51C42×C61—22no—
52C4⋊Dic61—42no—
53#11758196—44no—
54C4×Dic61—24no—
55C4×Dic61#4114yes—
56C23×C61C2×C22⋊C411yescharacteristic
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—22no—
60C22×D61#10112yes—
61C22×D61#10414yes—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61#11712yes—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61#10012yes—
79C2×Dic61#12314yes—
80C4×D61—28no—
81C4×D61—48no—
82C4×D61—88no—
83#92420—48no—
84#8719—611nomaximal, Sylow
85C22×C61#38111yescharacteristic
86C22×C61C2×#10011yescharacteristic
87C22×C61C2×#10111yescharacteristic
88C22×C61C2×#10412yes—
89C22×C61#42112yes—
90C2×D61—22no—
91C2×D61—24no—
92C2×D61—24no—
93C2×D61—22no—
94C2×D61#33014yes—
95C4×C61—22no—
96C4×C61—42no—
97C4×C61—82no—
98Dic61—22no—
99Dic61—24no—
100Dic61—82no—
101C2×#382—611no—
102#1749—612no—
103#1295—614no—
104C2×C61C2×#33011yescharacteristic
105C2×C61#152712yes—
106C2×C61#153411yescharacteristic
107C2×C61#182111yescharacteristic
108C2×C61#182612yes—
109D61—24no—
110C22×C4⋊C4—612no—
111C22×C42—611no—
112C2×C22⋊C8—1222no—
113C2×#97—614no—
114#382—612no—
115#382—611no—
116#382—1222no—
117#382#692311yescharacteristic
118C2×#95—1222no—
119#336—1222no—
120C61#871911yescharacteristic, complemented, Sylow
121C23×C4—611no—
122C23×C4—612no—
123C23×C4—1222no—
124C22×C8—1224no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—1222no—
127C2×C4⋊C4—2444no—
128C2×C4⋊C4C2×#692312yes—
129C2×C42—611no—
130C2×C42—612no—
131C2×C42—1224no—
132C2×C42C2×#692311yescharacteristic
133C22⋊C8—1228no—
134#97—1228no—
135#95—22no—
136#95—1224no—
137#95—1222no—
138C24—611no—
139C22×C4—22no—
140C22×C4—612no—
141C22×C4—611no—
142C22×C4—1222no—
143C22×C4—1224no—
144C22×C4—1222no—
145C22×C4—1224no—
146C22×C4—1222no—
147C22×C4—1222no—
148C22×C4—2442no—
149C22×C4—2444no—
150C22×C4—2444no—
151C22×C4—2444no—
152C22×C4C22⋊#692312yes—
153C22×C4C22×#692311yescharacteristic
154C2×C8—1228no—
155C2×C8—2444no—
156C2×C8—2444no—
157C4⋊C4—42no—
158C4⋊C4—2442no—
159C4⋊C4—2444no—
160C42—22no—
161C42—614no—
162C42—1224no—
163C23—612no—
164C23—614no—
165C23—1221no—
166C23—1221no—
167C23—1222no—
168C23C2×C22⋊#692311yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—614no—
178C2×C4—612no—
179C2×C4—1228no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—4888no—
185C2×C4—2448no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4#1451985612yes—
190C8—2448no—
191C22—614no—
192C22—1224no—
193C22—1222no—
194C22—1222no—
195C22—1224no—
196C22#1684070511yescharacteristic
197C22D61⋊#10011yescharacteristic
198C22D61⋊#10111yescharacteristic
199C22D61⋊#10412yes—
200C22#1684075912yes—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—1222no—
205C4—1224no—
206C4—4882no—
207C2—1224no—
208C2D61⋊#33011yescharacteristic
209C2#2146127912yes—
210C2#2146130211yescharacteristic
211C2#2146171911yescharacteristic
212C2#2146172712yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8719
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
120. C61#8719semidirect

Maximal subgroups

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

subgroupindex
#214615462
#214606952
#382×D612
#871961