Finite Group Databasebeta

← #30595542

Subgroups — #30595542

Order 15616.

410 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461536C211yesmaximal, characteristic
3#21460637C212yesmaximal
4#21460637C212yesmaximal
5#125×Dic61C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839661C2211yescharacteristic
13#16839661C2211yescharacteristic
14#16839648—21no—
15#16839648—21no—
16#16839628C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C2×#125×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519832—24no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#125×C61—22no—
46#125×C61—22no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×#92420—24no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C4⋊C4×C61—24no—
70C4⋊C4×C61—24no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61M1612yes—
74C4⋊C4×C61M1612yes—
75C42×C61—21no—
76C42×C61—21no—
77C4⋊Dic61—42no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61—42no—
90C4×Dic61—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C2×M1611yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61#10112yes—
123C2×Dic61#10412yes—
124C2×Dic61#13512yes—
125C2×Dic61AGL(1,ℤ/8)11yescharacteristic
126C2×Dic61#13711yescharacteristic
127#92420—44no—
128#92420—82no—
129#7619—611nomaximal, Sylow
130C22×C61#40711yescharacteristic
131C22×C61#41011yescharacteristic
132C22×C61C2×#10111yescharacteristic
133C22×C61#41611yescharacteristic
134C22×C61#41711yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—42no—
141C4×C61—41no—
142C4×C61—42no—
143Dic61—22no—
144Dic61—22no—
145Dic61—21no—
146Dic61—21no—
147Dic61—22no—
148Dic61—81no—
149Dic61—81no—
150C4×#125—611no—
151#1831—611no—
152#1745—611no—
153#1271—612no—
154#1271—612no—
155C2×C61#146711yescharacteristic
156C2×C61#148811yescharacteristic
157C2×C61#148911yescharacteristic
158C2×C61#150011yescharacteristic
159C2×C61#151211yescharacteristic
160C2×C61#152811yescharacteristic
161C2×C61#155211yescharacteristic
162C2×#125#692311yescharacteristic
163C2×C4⋊C8—1221no—
164C2×#97—1221no—
165#389—611no—
166#389—611no—
167#387—1221no—
168#387—1221no—
169#382—611no—
170C4×C4⋊C4—611no—
171C4×C4⋊C4—611no—
172C4×C4⋊C4—1221no—
173C4×C4⋊C4—1221no—
174C43—611no—
175#336—612no—
176#336—612no—
177#336—1221no—
178#336—1221no—
179C61#761911yescharacteristic, complemented, Sylow
180C22×C8—1222no—
181C22×C8—1222no—
182#125—22no—
183#125—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4C2×#692311yescharacteristic
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—1221no—
199C2×C42—1221no—
200C2×C42C2×#692311yescharacteristic
201C4⋊C8—2442no—
202#97—1224no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4C22⋊#692311yescharacteristic
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22×#692311yescharacteristic
220C2×C8—1224no—
221C2×C8—2442no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2442no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4#1175821712yes—
236C4⋊C4#1175821712yes—
237C42—21no—
238C42—21no—
239C42—1222no—
240C42—1221no—
241C42—1222no—
242C42—1222no—
243C42—1221no—
244C42—2441no—
245C42—2441no—
246C42—2442no—
247C42—2442no—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—612no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4C2×#1175821711yescharacteristic
283C2×C4C2×#1175821711yescharacteristic
284C8—4882no—
285C8—2444no—
286C22#1684073211yescharacteristic
287C22#1684074311yescharacteristic
288C22D61⋊#10111yescharacteristic
289C22#1684075211yescharacteristic
290C22#1684075311yescharacteristic
291C22D61⋊#10411yescharacteristic
292C22#1684075911yescharacteristic
293C4—21no—
294C4—21no—
295C4—41no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—1222no—
300C4—1222no—
301C4—1222no—
302C4—1221no—
303C4—1221no—
304C4—4881no—
305C4—4881no—
306C2#2146108211yescharacteristic
307C2#2146115011yescharacteristic
308C2#2146115411yescharacteristic
309C2#2146119311yescharacteristic
310C2#2146123311yescharacteristic
311C2#2146128211yescharacteristic
312C2#2146134111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#7619
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
179. C61#7619semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615362
#214606372
#125×Dic612
#761961