Finite Group Databasebeta

← #30595657

Subgroups — #30595657

Order 15616.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461735C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3#21460638C214yesmaximal
4#21448386C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519844—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12C2×#14519742—21no—
13#16839667—21no—
14#16839658—21no—
15#16839658C2212yes—
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61C412yes—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519844—42no—
24C22×Dic122—21no—
25#14519777—24no—
26#14519742—42no—
27#14519742—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C412yes—
30C2×#11758196—22no—
31C2×C4×Dic61—22no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61C2311yescharacteristic
38#14519684—22no—
39#14519684—22no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61C2×C412yes—
43C2×C42×C61C2×C411yescharacteristic
44C22×C4×C61—22no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—22no—
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C2×D411yescharacteristic
52C22×Dic61C2×D411yescharacteristic
53C2×Dic122—24no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×#92420—42no—
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—22no—
68C4⋊Dic61M1614yes—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C4×Dic61—41no—
74C4×Dic61—41no—
75C4×Dic61—44no—
76C4×Dic61D812yes—
77C4×Dic61SD1612yes—
78C4×Dic61SD1612yes—
79C4×Dic61Q1612yes—
80C23×C61C2×C22⋊C411yescharacteristic
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61#10212yes—
91C2×C4×C61#10312yes—
92C2×C4×C61C2×M1612yes—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—24no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61#10112yes—
104C2×Dic61#10212yes—
105C2×Dic61#10312yes—
106C2×Dic61C2×D811yescharacteristic
107C2×Dic61C2×SD1611yescharacteristic
108C2×Dic61C2×SD1611yescharacteristic
109C2×Dic61C2×Q1611yescharacteristic
110Dic122—48no—
111#92420—82no—
112#92420—82no—
113#7652—611nomaximal, Sylow
114C22×C61#40711yescharacteristic
115C22×C61#41011yescharacteristic
116C22×C61C2×#10111yescharacteristic
117C22×C61C2×#10211yescharacteristic
118C22×C61C2×#10311yescharacteristic
119C22×C61#42111yescharacteristic
120C22×C61#42111yescharacteristic
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—22no—
124C4×C61—82no—
125Dic61—21no—
126Dic61—21no—
127Dic61—21no—
128Dic61—21no—
129Dic61—41no—
130Dic61—44no—
131Dic61#33214yes—
132C4×C4⋊Q8—611no—
133#1831—611no—
134#1831—611no—
135#1271—614no—
136C2×C61#146711yescharacteristic
137C2×C61#148611yescharacteristic
138C2×C61#148711yescharacteristic
139C2×C61#151711yescharacteristic
140C2×C61#151811yescharacteristic
141C2×C61#153711yescharacteristic
142C2×C61C2×#33211yescharacteristic
143C2×C4⋊Q8—611no—
144C2×C4×Q8—1221no—
145C2×C4⋊C8—1221no—
146C2×C4⋊C8—1221no—
147#391—1221no—
148#389—612no—
149#389—1221no—
150#384#692311yescharacteristic
151C4×C4⋊C4—612no—
152C4×C4⋊C4—1221no—
153C43—611no—
154#336—612no—
155#336—612no—
156#336—1221no—
157#336—1221no—
158C61#765211yescharacteristic, complemented, Sylow
159C22×Q8—1221no—
160C22×C8—1222no—
161C22×C8—1222no—
162C4⋊Q8—1224no—
163C4×Q8—2442no—
164C4×Q8—2442no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4C2×#692312yes—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42—611no—
174C2×C42—611no—
175C2×C42—611no—
176C2×C42—611no—
177C2×C42—1222no—
178C2×C42C2×#692311yescharacteristic
179C4⋊C8—2442no—
180C4⋊C8—2442no—
181#95—1222no—
182#95—1222no—
183C2×Q8—1224no—
184C2×Q8—2442no—
185C2×Q8—2442no—
186C22×C4—22no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—1222no—
192C22×C4C22⋊#692311yescharacteristic
193C22×C4C22⋊#692311yescharacteristic
194C22×C4C22×#692311yescharacteristic
195C2×C8—2442no—
196C2×C8—2442no—
197C2×C8—2442no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2442no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—614no—
205C4⋊C4—1224no—
206C4⋊C4—1222no—
207C4⋊C4—2442no—
208C4⋊C4—2442no—
209C42—22no—
210C42—612no—
211C42—612no—
212C42—612no—
213C42—612no—
214C42—1222no—
215C42—2441no—
216C42—2441no—
217C42—2441no—
218C42—2444no—
219C23C2×C22⋊#692311yescharacteristic
220Q8—2448no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—612no—
231C2×C4—612no—
232C2×C4—612no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1224no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4#1451983912yes—
248C2×C4#1451984012yes—
249C2×C4D61⋊M1612yes—
250C8—4882no—
251C8—4882no—
252C22#1684073411yescharacteristic
253C22#1684074211yescharacteristic
254C22D61⋊#10111yescharacteristic
255C22C2×#1451983911yescharacteristic
256C22C2×#1451984011yescharacteristic
257C22#1684076011yescharacteristic
258C22#1684076111yescharacteristic
259C4—22no—
260C4—22no—
261C4—22no—
262C4—82no—
263C4—614no—
264C4—1221no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—2441no—
269C4—2444no—
270C2#2146108311yescharacteristic
271C2#2146114611yescharacteristic
272C2#2146114911yescharacteristic
273C2#2146124811yescharacteristic
274C2#2146125311yescharacteristic
275C2#2146131111yescharacteristic
276C2D61⋊#33211yescharacteristic
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#7652
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
158. C61#7652semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606382
#214483862
#765261