Finite Group Databasebeta

← #30595649

Subgroups — #30595649

Order 15616.

384 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461747C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519768C211yesmaximal, characteristic
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519768C411yescharacteristic
13#16839661C2211yescharacteristic
14#16839658C2211yescharacteristic
15#16839649—21no—
16#16839645—21no—
17#16839627C411yescharacteristic
18C4×#11758196—21no—
19C4×C4⋊Dic61—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519768—22no—
26#14519768—22no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C42×C61—21no—
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—21no—
56C22×Dic61—21no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×#92420—42no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61M1612yes—
70C42×C61—22no—
71C42×C61—42no—
72C4⋊Dic61—24no—
73C4⋊Dic61—21no—
74C4⋊Dic61—42no—
75C4⋊Dic61—41no—
76C4⋊Dic61M1612yes—
77#11758196—24no—
78#11758196—42no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61—42no—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#10112yes—
102C2×C4×C61C2×M1611yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#13512yes—
121C2×Dic61#13512yes—
122#92420—82no—
123#92420—82no—
124#7650—611nomaximal, Sylow
125C22×C61#40711yescharacteristic
126C22×C61#41011yescharacteristic
127C22×C61C2×#10111yescharacteristic
128C22×C61#41611yescharacteristic
129C22×C61#41611yescharacteristic
130C22×C61#42111yescharacteristic
131C22×C61#42111yescharacteristic
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—22no—
135C4×C61—41no—
136C4×C61—42no—
137C4×C61—81no—
138Dic61—22no—
139Dic61—22no—
140Dic61—41no—
141Dic61—41no—
142Dic61—42no—
143Dic61—81no—
144C4×#125—611no—
145#1839—611no—
146#1839—611no—
147#1271—612no—
148#1271—612no—
149C2×C61#146711yescharacteristic
150C2×C61#148811yescharacteristic
151C2×C61#148811yescharacteristic
152C2×C61#152111yescharacteristic
153C2×C61#152111yescharacteristic
154C2×C61#153411yescharacteristic
155C2×C61#154411yescharacteristic
156C2×#125—611no—
157#389—611no—
158#389—611no—
159#387—1221no—
160#387—1221no—
161#382—611no—
162C4×C4⋊C4—611no—
163C4×C4⋊C4—1221no—
164C4×C4⋊C4—1221no—
165C4×C4⋊C4#692311yescharacteristic
166C43—611no—
167#336—612no—
168#336—612no—
169#336—1221no—
170#336—1221no—
171#336—1221no—
172#336—1221no—
173C61#765011yescharacteristic, complemented, Sylow
174C22×C8—1222no—
175C22×C8—1222no—
176#125—1222no—
177#125—1222no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4C2×#692311yescharacteristic
185C2×C4⋊C4C2×#692311yescharacteristic
186C2×C42—21no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—1221no—
194C2×C42C2×#692311yescharacteristic
195#95—21no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212C2×C8—2442no—
213C2×C8—2442no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—612no—
221C4⋊C4—1224no—
222C4⋊C4—1224no—
223C4⋊C4—1221no—
224C4⋊C4—2441no—
225C4⋊C4—2442no—
226C4⋊C4—2442no—
227C4⋊C4#1175821312yes—
228C42—22no—
229C42—42no—
230C42—1222no—
231C42—1222no—
232C42—1221no—
233C42—1221no—
234C42—2441no—
235C42—2441no—
236C42—2441no—
237C42—2442no—
238C23C2×C22⋊#692311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451983812yes—
271C2×C4D61⋊M1611yescharacteristic
272C2×C4C2×#1175821311yescharacteristic
273C8—4882no—
274C8—4882no—
275C22#1684073311yescharacteristic
276C22#1684074111yescharacteristic
277C22C2×#1451983811yescharacteristic
278C22#1684075211yescharacteristic
279C22#1684075211yescharacteristic
280C22#1684076011yescharacteristic
281C22#1684076111yescharacteristic
282C4—22no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—42no—
287C4—81no—
288C4—1222no—
289C4—1222no—
290C4—4881no—
291C4—2441no—
292C4—2441no—
293C4—2442no—
294C2#2146108111yescharacteristic
295C2#2146115111yescharacteristic
296C2#2146115311yescharacteristic
297C2#2146126111yescharacteristic
298C2#2146126311yescharacteristic
299C2#2146130111yescharacteristic
300C2#2146132411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7650
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
173. C61#7650semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606382
#214606372
C4×#145197682
#765061