Finite Group Databasebeta

← #30604110

Subgroups — #30604110

Order 15616.

510 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461073C212yesmaximal
2#21460750C212yesmaximal, complemented
3#21460749C212yesmaximal, complemented
4#21448402C211yesmaximal, characteristic
5#16840783—22no—
6#16840607C2214yes—
7#16840606—22no—
8C22×Q8×D61C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10C2×#14519734C411yescharacteristic
11#16839669C2211yescharacteristic
12#16839668C2211yescharacteristic
13#16839667C411yescharacteristic
14#16839666—22no—
15#16839624—22no—
16C61×#391C411yescharacteristic
17C4⋊#92420—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C22×Dic122—21no—
21C22×Dic122C2×C411yescharacteristic
22C2×Q8×D61—22no—
23C2×Q8×D61—22no—
24C2×Q8×D61—42no—
25C2×Q8×D61—42no—
26C22×C4×D61—21no—
27C22×C4×D61C2×C411yescharacteristic
28#14519735—42no—
29#14519734—42no—
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758196—21no—
32C2×#11758198—21no—
33C2×#11758198D412yes—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D412yes—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C22×Q8×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#95×C61—22no—
43C23×D61C22⋊C411yescharacteristic
44C2×Q8×C61—21no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61M1612yes—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C412yes—
51C22×C4×C61C22×C411yescharacteristic
52C22×Dic61—21no—
53C22×Dic61—21no—
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C2×D412yes—
56Q8×D61—48no—
57Q8×D61—48no—
58C2×C4×D61—22no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—22no—
62C2×C4×D61—24no—
63C2×C4×D61—42no—
64C2×C4×D61—42no—
65C2×Dic122—24no—
66C2×Dic122—21no—
67C2×Dic122—42no—
68C2×Dic122—42no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122M1612yes—
72C2×#92420—44no—
73C4⋊C4×C61—41no—
74C42×C61—41no—
75#11758198—42no—
76#11758198—42no—
77C4⋊Dic61—41no—
78#11758196—42no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—41no—
82C23×C61C2×C22⋊C411yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61#10012yes—
88Q8×C61—42no—
89Q8×C61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61C2×M1611yescharacteristic
101C2×C4×C61C2×M1611yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61#9912yes—
113C4×D61—24no—
114C4×D61—24no—
115C4×D61—48no—
116Dic122—48no—
117Dic122—42no—
118Dic122—42no—
119#92420—84no—
120#11510—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#40711yescharacteristic
124C22×C61C2×#9911yescharacteristic
125C22×C61C2×#10011yescharacteristic
126C2×D61—22no—
127C2×D61—42no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—42no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61—42no—
135C4×C61—81no—
136Dic61—22no—
137Dic61—42no—
138Dic61—42no—
139Dic61—81no—
140#2310—611no—
141#1464—612no—
142#1319—612no—
143#1319—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#146211yescharacteristic
147C2×C61#212911yescharacteristic
148C2×C61#213511yescharacteristic
149D61—42no—
150C23×Q8—611no—
151C2×#117—611no—
152C2×#117—611no—
153#432—1222no—
154#391—611no—
155#391—611no—
156#391—611no—
157#391—1222no—
158#391#692311yescharacteristic
159#381—1222no—
160#324—614no—
161#323—1222no—
162C61#1151011yescharacteristic, complemented, Sylow
163C22×Q8—611no—
164C22×Q8—1221no—
165C22×Q8—1222no—
166C22×Q8—1222no—
167C22×Q8—2442no—
168C22×Q8—2442no—
169C22×Q8C2×#692311yescharacteristic
170C23×C4—611no—
171C23×C4—1221no—
172#117—2442no—
173#117—2442no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4C2×#692311yescharacteristic
177C2×C22⋊C4—612no—
178C2×C22⋊C4—1221no—
179C2×C42—612no—
180C2×C42—611no—
181C2×C42C2×#692311yescharacteristic
182C4⋊C8—2442no—
183C22⋊C8—1224no—
184#97—2442no—
185#95—22no—
186#95—1222no—
187#95—1222no—
188#95—1222no—
189C24—611no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—612no—
194C2×Q8—1224no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C2×Q8—2441no—
198C2×Q8—2442no—
199C2×Q8—2442no—
200C2×Q8—2448no—
201C2×Q8—2448no—
202C2×Q8#1175821312yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—612no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4—1224no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—2442no—
215C22×C4—2442no—
216C22×C4C22⋊#692312yes—
217C22×C4C22×#692311yescharacteristic
218C2×C8—2444no—
219C4⋊C4—41no—
220C4⋊C4—2441no—
221C4⋊C4—2442no—
222C22⋊C4—2442no—
223C22⋊C4—2442no—
224C42—41no—
225C42—1222no—
226C42—1222no—
227C42—2441no—
228C23—612no—
229C23—1221no—
230C23—1221no—
231C23—2441no—
232C23—2441no—
233C23C2×C22⋊#692311yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—2442no—
237Q8—2442no—
238Q8—2448no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—612no—
250C2×C4—1224no—
251C2×C4—1224no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—2448no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2442no—
263C2×C4D61⋊M1611yescharacteristic
264C2×C4C2×#1175821311yescharacteristic
265C8—4884no—
266C22—21no—
267C22—21no—
268C22—1222no—
269C22—2442no—
270C22—2442no—
271C22—2441no—
272C22—2441no—
273C22#1684073311yescharacteristic
274C22D61⋊#9911yescharacteristic
275C22D61⋊#10011yescharacteristic
276C4—21no—
277C4—21no—
278C4—42no—
279C4—42no—
280C4—81no—
281C4—1222no—
282C4—4881no—
283C4—2442no—
284C4—2442no—
285C2—21no—
286C2—21no—
287C2—2442no—
288C2#2146106511yescharacteristic
289C2#2146210211yescharacteristic
290C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#391#6923
hypocenterC61#11510
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #21460750C2semidirect
3. #21460749C2semidirect
162. C61#11510semidirect

Maximal subgroups

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

subgroupindex
#214610732
#214607502
#214607492
#214484022
#1151061