Finite Group Databasebeta

← #30595696

Subgroups — #30595696

Order 15616.

426 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 120 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#21461736C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3#21460638C214yesmaximal
4#21454180C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519768—21no—
12#16839661—21no—
13#16839661C412yes—
14#16839658—21no—
15#16839658C2212yes—
16#16839632C411yescharacteristic
17#16839627—21no—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—24no—
23C4⋊#92420—42no—
24C4×#92420—42no—
25#14519768—42no—
26#14519768—42no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61C2×C412yes—
31C2×#11758196—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×#92420—24no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C42×C61—22no—
63C4⋊Dic61—24no—
64C4⋊Dic61—42no—
65C4⋊Dic61—42no—
66C4⋊Dic61—44no—
67#11758196—42no—
68#11758196—42no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—41no—
72C4×Dic61—41no—
73C4×Dic61D812yes—
74C4×Dic61SD1612yes—
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—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61#10112yes—
86C2×C4×C61#10212yes—
87C2×C4×C61#10312yes—
88C2×C4×C61#10412yes—
89C2×C4×C61#13112yes—
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—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61#10212yes—
102C2×Dic61#10312yes—
103C2×Dic61C2×D811yescharacteristic
104C2×Dic61C2×SD1611yescharacteristic
105C2×Dic61C2×SD1611yescharacteristic
106C2×Dic61C2×Q1611yescharacteristic
107#92420—44no—
108#92420—82no—
109#7663—611nomaximal, Sylow
110C22×C61#40811yescharacteristic
111C22×C61#41011yescharacteristic
112C22×C61C2×#10111yescharacteristic
113C22×C61C2×#10211yescharacteristic
114C22×C61C2×#10311yescharacteristic
115C22×C61C2×#10411yescharacteristic
116C22×C61#42111yescharacteristic
117C4×C61—22no—
118C4×C61—22no—
119C4×C61—82no—
120C4×C61#33214yes—
121Dic61—22no—
122Dic61—22no—
123Dic61—21no—
124Dic61—21no—
125Dic61—21no—
126Dic61—21no—
127Dic61—82no—
128#2859—611no—
129#1831—611no—
130C4×C4⋊C8—611no—
131#1271—614no—
132C2×C61#147011yescharacteristic
133C2×C61#148011yescharacteristic
134C2×C61#149311yescharacteristic
135C2×C61#150211yescharacteristic
136C2×C61#151811yescharacteristic
137C2×C61#152811yescharacteristic
138C2×C61C2×#33211yescharacteristic
139C2×#125—1221no—
140C2×C4⋊C8—1221no—
141C2×C4⋊C8—1221no—
142C2×C4×C8—1221no—
143#389—612no—
144#389—612no—
145#389—1221no—
146#389—1221no—
147#384—611no—
148#384#692311yescharacteristic
149#382—1221no—
150C43—611no—
151#336—612no—
152#336—612no—
153#336—1221no—
154C61#766311yescharacteristic, complemented, Sylow
155C22×C8—1222no—
156C22×C8—1222no—
157#125—2442no—
158#125—2442no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4C2×#692312yes—
167C2×C42—611no—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42C2×#692311yescharacteristic
174C4⋊C8—1224no—
175C4⋊C8—2442no—
176C4×C8—2442no—
177#95—1222no—
178#95—1222no—
179C22×C4—22no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1222no—
185C22×C4C22⋊#692311yescharacteristic
186C22×C4C22⋊#692311yescharacteristic
187C22×C4C22×#692311yescharacteristic
188C2×C8—1224no—
189C2×C8—2442no—
190C2×C8—2442no—
191C2×C8—2442no—
192C2×C8—2442no—
193C2×C8—2442no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—1224no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C4⋊C4—2444no—
202C4⋊C4—2442no—
203C42—22no—
204C42—612no—
205C42—612no—
206C42—612no—
207C42—612no—
208C42—1222no—
209C42—1222no—
210C42—2441no—
211C42—2441no—
212C23C2×C22⋊#692311yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—612no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—612no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4#1451983812yes—
238C2×C4#1451983912yes—
239C2×C4#1451984012yes—
240C2×C4#1451984112yes—
241C2×C4#1451986512yes—
242C8—4882no—
243C8—2444no—
244C22#1684073711yescharacteristic
245C22#1684074211yescharacteristic
246C22C2×#1451983811yescharacteristic
247C22C2×#1451983911yescharacteristic
248C22C2×#1451984011yescharacteristic
249C22C2×#1451984111yescharacteristic
250C22#1684076111yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—1221no—
255C4—1221no—
256C4—1222no—
257C4—1222no—
258C4—1221no—
259C4—1221no—
260C4—4882no—
261C4#1684062114yes—
262C2#2146109311yescharacteristic
263C2#2146112611yescharacteristic
264C2#2146116911yescharacteristic
265C2#2146119911yescharacteristic
266C2#2146125311yescharacteristic
267C2#2146128111yescharacteristic
268C2C2×#1684062111yescharacteristic
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#7663
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#7663semidirect

Maximal subgroups

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

subgroupindex
#214617362
C4×#145198442
#214606382
#214541802
#766361