Finite Group Databasebeta

← #30595561

Subgroups — #30595561

Order 15616.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461747C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3#21460640C214yesmaximal
4#21448386C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519832—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12C2×#14519742C412yes—
13#16839667C2212yes—
14#16839658—21no—
15#16839658—21no—
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61—21no—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—24no—
23#14519832—42no—
24C22×Dic122C2×C412yes—
25#14519777—24no—
26#14519742—44no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—22no—
30C2×C4×Dic61—22no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61C2311yescharacteristic
37#14519684—22no—
38#14519684—22no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61C2×C412yes—
42C2×C42×C61C2×C411yescharacteristic
43C22×C4×C61—22no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C22×Dic61—22no—
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C2×D411yescharacteristic
51C22×Dic61C2×D411yescharacteristic
52C2×Dic122—22no—
53C2×Dic122—42no—
54C2×Dic122—42no—
55C2×Dic122M1614yes—
56C2×#92420—24no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C2×#92420—42no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—42no—
65C42×C61—22no—
66C4⋊Dic61—24no—
67C4⋊Dic61—24no—
68#11758196—44no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C4×Dic61—41no—
74C4×Dic61—44no—
75C4×Dic61SD1612yes—
76C4×Dic61Q1612yes—
77C23×C61C2×C22⋊C411yescharacteristic
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61#10312yes—
88C2×C4×C61#10412yes—
89C2×C4×C61C2×M1612yes—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—24no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61#10012yes—
102C2×Dic61#10312yes—
103C2×Dic61C2×SD1611yescharacteristic
104C2×Dic61C2×Q1611yescharacteristic
105C2×Dic61#13712yes—
106Dic122—44no—
107Dic122—44no—
108#92420—44no—
109#92420—82no—
110#7624—611nomaximal, Sylow
111C22×C61#40711yescharacteristic
112C22×C61#41011yescharacteristic
113C22×C61C2×#10011yescharacteristic
114C22×C61C2×#10311yescharacteristic
115C22×C61#41911yescharacteristic
116C22×C61C2×#10411yescharacteristic
117C22×C61#42111yescharacteristic
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—82no—
122Dic61—22no—
123Dic61—21no—
124Dic61—21no—
125Dic61—22no—
126Dic61—22no—
127Dic61—44no—
128C4×C4⋊Q8—611no—
129#1839—611no—
130#1767—611no—
131#1272—614no—
132C2×C61#146611yescharacteristic
133C2×C61#148711yescharacteristic
134C2×C61#149111yescharacteristic
135C2×C61#150311yescharacteristic
136C2×C61#151511yescharacteristic
137C2×C61#153011yescharacteristic
138C2×C61#154811yescharacteristic
139C2×C4⋊Q8—611no—
140C2×C4×Q8—612no—
141C2×C4⋊C8—1221no—
142C2×#97—1221no—
143#391—612no—
144#389—1221no—
145#389—1221no—
146#384#692311yescharacteristic
147C4×C4⋊C4—1221no—
148C4×C4⋊C4—1221no—
149C43—611no—
150#336—612no—
151#336—612no—
152#336—1221no—
153#336—1221no—
154C61#762411yescharacteristic, complemented, Sylow
155C22×Q8—612no—
156C22×C8—1222no—
157C22×C8—1222no—
158C4⋊Q8—1224no—
159C4×Q8—2444no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4C2×#692312yes—
166C2×C42—611no—
167C2×C42—611no—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—611no—
172C2×C42—1222no—
173C2×C42C2×#692311yescharacteristic
174C4⋊C8—1224no—
175#97—2442no—
176#95—1222no—
177#95—1222no—
178C2×Q8—614no—
179C2×Q8—1222no—
180C2×Q8—2442no—
181C2×Q8—2442no—
182C22×C4—22no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—1222no—
188C22×C4C22⋊#692311yescharacteristic
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22×#692311yescharacteristic
191C2×C8—1224no—
192C2×C8—2442no—
193C2×C8—2442no—
194C2×C8—2442no—
195C2×C8—2442no—
196C2×C8—2442no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—1224no—
201C4⋊C4—1224no—
202C4⋊C4—2444no—
203C42—22no—
204C42—612no—
205C42—612no—
206C42—1222no—
207C42—1222no—
208C42—1222no—
209C42—2441no—
210C42—2441no—
211C42—2444no—
212C23C2×C22⋊#692311yescharacteristic
213Q8—2444no—
214Q8—2444no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—612no—
225C2×C4—612no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—612no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1224no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4#1451984012yes—
241C2×C4#1451984112yes—
242C2×C4D61⋊M1612yes—
243C8—4882no—
244C8—2444no—
245C22#1684073411yescharacteristic
246C22#1684074311yescharacteristic
247C22D61⋊#10011yescharacteristic
248C22C2×#1451984011yescharacteristic
249C22#1684075511yescharacteristic
250C22C2×#1451984111yescharacteristic
251C22#1684076011yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—82no—
256C4—1222no—
257C4—1222no—
258C4—1221no—
259C4—1221no—
260C4—1222no—
261C4—2444no—
262C2#2146108011yescharacteristic
263C2#2146114911yescharacteristic
264C2#2146116311yescharacteristic
265C2#2146120211yescharacteristic
266C2#2146124211yescharacteristic
267C2#2146128911yescharacteristic
268C2#2146133311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7624
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
154. C61#7624semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214616042
#214606402
#214483862
#762461