Finite Group Databasebeta

← #30596865

Subgroups — #30596865

Order 15616.

778 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 184 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
1C2×C4×#11758217C212yesmaximal
2#21460695C214yesmaximal, complemented
3#21448222C211yesmaximal, characteristic
4C22×#11758217—22no—
5C4×#11758217—24no—
6C4×#11758217C418yescomplemented
7C2×#14519832C2214yes—
8C2×C4×#92420—22no—
9C2×#14519736C411yescharacteristic
10C22×C4×Dic61C2211yescharacteristic
11#16839631C412yes—
12#16839627C2212yes—
13#16839620—22no—
14C4×#11758196—22no—
15C2×#117×C61C411yescharacteristic
16C2×#11758217—216no—
17C2×#11758217—28no—
18C22×#92420—24no—
19#14519832—24no—
20#14519832C2×C418yes—
21C4×#92420—28no—
22C23×Dic61D412yes—
23#14519736—42no—
24C2×C4⋊Dic61C2×C412yes—
25C2×#11758196—24no—
26C2×C22⋊Dic61—21no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61C2×C414yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61D412yes—
32C2×C4×Dic61Q812yes—
33C2×C4×Dic61C2311yescharacteristic
34#14519684—24no—
35C23×C4×C61C2×C411yescharacteristic
36#117×C61—42no—
37C2×C4⋊C4×C61C2×C412yes—
38C2×C22⋊C4×C61—21no—
39C2×C42×C61—21no—
40C24×C61C22⋊C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61C4212yes—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C4⋊C412yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—28no—
49C22×Dic61—22no—
50C22×Dic61C22⋊C414yes—
51C22×Dic61C22⋊C412yes—
52C22×Dic61C4⋊C414yes—
53C22×Dic61C2×D412yes—
54#11758217—232no—
55C2×#92420—216no—
56C2×#92420—28no—
57C4⋊C4×C61—42no—
58C22⋊C4×C61—42no—
59C42×C61—42no—
60C22⋊Dic61—42no—
61C4⋊Dic61—42no—
62#11758196—48no—
63C4×Dic61—42no—
64C4×Dic61C4212yes—
65C4×Dic61C22⋊C414yes—
66C4×Dic61C4⋊C412yes—
67C4×Dic61C4⋊C414yes—
68C4×Dic61C22×C412yes—
69C4×Dic61C2×D411yescharacteristic
70C4×Dic61C2×Q811yescharacteristic
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—24no—
74C23×C61#9512yes—
75C23×C61C2×C22⋊C411yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—24no—
79C2×C4×C61—24no—
80C2×C4×C61—42no—
81C2×C4×C61—44no—
82C2×C4×C61#9512yes—
83C2×C4×C61#10012yes—
84C2×C4×C61#10112yes—
85C2×C4×C61C2×C4211yescharacteristic
86C2×C4×C61C2×C4⋊C411yescharacteristic
87C2×Dic61—24no—
88C2×Dic61—28no—
89C2×Dic61—28no—
90C2×Dic61—42no—
91C2×Dic61—44no—
92C2×Dic61#9514yes—
93C2×Dic61#10418yes—
94C2×Dic61C2×C22⋊C412yes—
95C2×Dic61C2×C4⋊C412yes—
96#92420—216no—
97#8028—611nomaximal, Sylow
98C22×C61—24no—
99C22×C61—22no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61C2×#9511yescharacteristic
103C22×C61C2×#10011yescharacteristic
104C22×C61C2×#10111yescharacteristic
105C22×C61C2×#10414yes—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—82no—
109C4×C61#34314yes—
110Dic61—22no—
111Dic61—22no—
112Dic61—82no—
113Dic61#33918yes—
114C2×C4×M16—612no—
115#2285—611no—
116#1295—614no—
117C2×C61—42no—
118C2×C61#152512yes—
119C2×C61#152612yes—
120C2×C61C2×#33912yes—
121C2×C61C2×#34311yescharacteristic
122C22×M16—1222no—
123C2×#117—611no—
124C2×#117#692311yescharacteristic
125C22×C42—611no—
126C4×M16—618no—
127C4×M16—1224no—
128C2×#97—614no—
129C2×C4×C8—1222no—
130#384—612no—
131#382—612no—
132#380—1222no—
133C4×C4⋊C4—1222no—
134C61#802811yescharacteristic, complemented, Sylow
135C23×C4—612no—
136C23×C4C2×#692311yescharacteristic
137C2×M16—1228no—
138C2×M16—12216no—
139C22×C8—1224no—
140#117—42no—
141#117—2442no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—1224no—
144C2×C4⋊C4C2×#692312yes—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—1221no—
147C2×C42—21no—
148C2×C42—614no—
149C2×C42—612no—
150C2×C42—612no—
151C2×C42—612no—
152C2×C42—611no—
153C2×C42—611no—
154C2×C42—1221no—
155#97—618no—
156#97—1224no—
157C4×C8—1228no—
158#95—1224no—
159C24C22⋊#692311yescharacteristic
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—612no—
164C22×C4—614no—
165C22×C4—614no—
166C22×C4—612no—
167C22×C4—1228no—
168C22×C4—1222no—
169C22×C4C4×#692312yes—
170C22×C4C4⋊#692312yes—
171C22×C4C22⋊#692311yescharacteristic
172C22×C4C22×#692311yescharacteristic
173M16—12232no—
174C2×C8—1228no—
175C2×C8—12216no—
176C4⋊C4—42no—
177C4⋊C4—2442no—
178C4⋊C4—2448no—
179C22⋊C4—42no—
180C22⋊C4—2442no—
181C42—42no—
182C42—614no—
183C42—614no—
184C42—612no—
185C42—612no—
186C42—611no—
187C42—612no—
188C42—611no—
189C42—2442no—
190C23—21no—
191C23—21no—
192C23—24no—
193C23(C2×#6923)⋊C412yes—
194C23C2×C22⋊#692311yescharacteristic
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—618no—
202C2×C4—614no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—1228no—
206C2×C4—1228no—
207C2×C4—1224no—
208C2×C4—2442no—
209C2×C4—2444no—
210C2×C4(C2×#6923)⋊C412yes—
211C2×C4#1451983712yes—
212C2×C4#1451983812yes—
213C2×C4C2×C4×#692311yescharacteristic
214C2×C4C2×C4⋊#692311yescharacteristic
215C8—12216no—
216C22—22no—
217C22—24no—
218C22—42no—
219C22—42no—
220C22C2×(C2×#6923)⋊C411yescharacteristic
221C22C2×#1451983711yescharacteristic
222C22C2×#1451983811yescharacteristic
223C22D61⋊#10414yes—
224C4—21no—
225C4—21no—
226C4—82no—
227C4—618no—
228C4—1222no—
229C4—1222no—
230C4—4882no—
231C4#1684064214yes—
232C2—42no—
233C2#2146127312yes—
234C2#2146127612yes—
235C2#2146149512yes—
236C2C2×#1684064211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8028
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
6. C4×#11758217C4semidirect
134. C61#8028semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582172
#214606952
#214482222
#802861