Finite Group Databasebeta

← #30604194

Subgroups — #30604194

Order 15616.

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

normal subgroups only

This group has 504 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#21461076C212yesmaximal, complemented
2#21460759C212yesmaximal, complemented
3#21460748C212yesmaximal, complemented
4#21448544C211yesmaximal, characteristic
5#16840733—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519774C411yescharacteristic
9C2×C4×D244C411yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839664C411yescharacteristic
12#16839664C2211yescharacteristic
13#16839640—22no—
14#16839640—22no—
15#16839628C2211yescharacteristic
16C61×#376C411yescharacteristic
17C2×#11758213—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C22×D244—22no—
21C22×D244C2×C411yescharacteristic
22C22×D244C2×C411yescharacteristic
23C22×C4×D61—21no—
24C22×C4×D61D412yes—
25#14519774—22no—
26#14519774—22no—
27C4×D244—42no—
28C4×D244—42no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758198—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198D412yes—
35#14519684—22no—
36C2×C42×C61C2×C411yescharacteristic
37C2×C42×C61C2×C411yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39#95×C61—21no—
40#95×C61—21no—
41C23×D61—21no—
42C23×D61C22⋊C412yes—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—21no—
49C22×Dic61C2×D412yes—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244—28no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244—41no—
58C2×D244—82no—
59C2×D244—82no—
60C2×D244M1612yescomplemented
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—42no—
64C2×C4×D61—82no—
65C2×C4×D61—82no—
66C2×#92420—44no—
67#11758213—84no—
68C42×C61—22no—
69C42×C61—21no—
70C42×C61—41no—
71C42×C61M1612yescomplemented
72#11758198—42no—
73#11758198—42no—
74#11758198—82no—
75#11758198—82no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C23×C61C2×C22⋊C411yescharacteristic
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—42no—
84C22×D61—42no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61—41no—
88C22×D61—41no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61#9912yes—
101C2×C4×C61C2×M1611yescharacteristic
102C2×C4×C61C2×M1611yescharacteristic
103C2×Dic61—22no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—41no—
107D244—42no—
108D244—42no—
109D244—42no—
110D244—42no—
111D244—88no—
112C4×D61—44no—
113C4×D61—82no—
114C4×D61—84no—
115#92420—84no—
116#11533—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61#40711yescharacteristic
120C22×C61C2×#9911yescharacteristic
121C22×C61#41311yescharacteristic
122C2×D61—44no—
123C2×D61—44no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—82no—
129C2×D61—81no—
130C2×D61—81no—
131C2×D61—82no—
132C4×C61—22no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—42no—
136C4×C61—41no—
137C4×C61—81no—
138Dic61—42no—
139Dic61—81no—
140#2328—611no—
141#1465—612no—
142#1324—612no—
143#1318—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#146511yescharacteristic
147C2×C61#212711yescharacteristic
148C2×C61#213411yescharacteristic
149D61—82no—
150D61—82no—
151C2×#127—611no—
152C2×C4×D4—611no—
153C2×C4×D4—611no—
154#407—1222no—
155#390—611no—
156#390—611no—
157#386—1222no—
158#386—1222no—
159#382—611no—
160#376#692311yescharacteristic
161#324—614no—
162#323—1222no—
163C61#1153311yescharacteristic, complemented, Sylow
164C22×D4—611no—
165C22×D4—611no—
166C22×D4—1222no—
167C23×C4—612no—
168C23×C4—1221no—
169C2×M16—2442no—
170#127—1222no—
171#127—1222no—
172C4×D4—2442no—
173C4×D4—2442no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—611no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—1222no—
178C2×C22⋊C4—1222no—
179C2×C22⋊C4—1221no—
180C2×C42C2×#692311yescharacteristic
181C2×C42C2×#692311yescharacteristic
182C2×C42C2×#692311yescharacteristic
183C22⋊C8—1224no—
184C22⋊C8—2442no—
185#95—21no—
186#95—21no—
187#95—1222no—
188C24—612no—
189C24—1221no—
190C2×D4—612no—
191C2×D4—1228no—
192C2×D4—1221no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4—4882no—
196C2×D4—4882no—
197C2×D4—2441no—
198C2×D4—2441no—
199C2×D4—2441no—
200C2×D4—2441no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—612no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1221no—
207C22×C4—4882no—
208C22×C4—4882no—
209C22×C4—2442no—
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22⋊#692311yescharacteristic
212C22×C4C22×#692311yescharacteristic
213M16—4884no—
214C2×C8—2444no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C22⋊C4—4882no—
218C22⋊C4—4882no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C42—22no—
222C42—21no—
223C42—41no—
224C42#1175821312yescomplemented
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23—1222no—
229C23—2442no—
230C23—2442no—
231C23—2442no—
232C23—2442no—
233C23—2441no—
234C23—2441no—
235C23C2×C22⋊#692311yescharacteristic
236D4—4888no—
237D4—2442no—
238D4—2442no—
239D4—2442no—
240D4—2442no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—1222no—
253C2×C4—4882no—
254C2×C4—4884no—
255C2×C4—2444no—
256C2×C4—2442no—
257C2×C4—2441no—
258C2×C4—2442no—
259C2×C4#1451983612yes—
260C2×C4D61⋊M1611yescharacteristic
261C2×C4C2×#1175821311yescharacteristic
262C8—4884no—
263C22—21no—
264C22—21no—
265C22—4882no—
266C22—4882no—
267C22—4881no—
268C22—4881no—
269C22—2444no—
270C22—2444no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22—2442no—
275C22#1684073311yescharacteristic
276C22C2×#1451983611yescharacteristic
277C22#1684074811yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—42no—
282C4—41no—
283C4—81no—
284C4—4881no—
285C4—2442no—
286C2—21no—
287C2—21no—
288C2—4882no—
289C2—4882no—
290C2#2146107611yescharacteristic
291C2#2146209611yescharacteristic
292C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#376C4
socleC22×C61C2×#99
prime radicalC2×#14519774C4
cosocleC2×C4⋊Dic61C23
hypercenter#376#6923
hypocenterC61#11533
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #21461076C2semidirect
2. #21460759C2semidirect
3. #21460748C2semidirect
60. C2×D244M16semidirect
71. C42×C61M16semidirect
163. C61#11533semidirect
224. C42#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214607592
#214607482
#214485442
#1153361