Finite Group Databasebeta

← #30595646

Subgroups — #30595646

Order 15616.

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

normal subgroups only

This group has 468 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#21461747C212yesmaximal, complemented
2#21460639C212yesmaximal, complemented
3#21460635C212yesmaximal
4#124×Dic61C211yesmaximal, characteristic
5#16840628—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×Q8×Dic61C411yescharacteristic
9C2×D4×Dic61C411yescharacteristic
10#16839669C2211yescharacteristic
11#16839665C2211yescharacteristic
12#16839655—22no—
13#16839628C411yescharacteristic
14C22⋊C4×Dic61—22no—
15C42×Dic61C2211yescharacteristic
16C2×#124×C61C411yescharacteristic
17C22×#92420—24no—
18C23×Dic61—21no—
19Q8×Dic61—42no—
20D4×Dic61—42no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61C2×C411yescharacteristic
23C2×C4⋊Dic61C2×C411yescharacteristic
24C2×C22⋊Dic61—21no—
25C2×C22⋊Dic61—22no—
26C2×C4×Dic61—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D412yes—
29C2×C4×Dic61D412yes—
30C2×C4×Dic61C2311yescharacteristic
31#14519684—22no—
32#14519684—22no—
33C22×Q8×C61C2×C411yescharacteristic
34C22×D4×C61C2×C411yescharacteristic
35#124×C61—22no—
36#124×C61—22no—
37C2×C22⋊C4×C61—22no—
38C2×C42×C61C2×C411yescharacteristic
39C24×C61—21no—
40C2×Q8×C61—21no—
41C2×Q8×C61—41no—
42C2×Q8×C61—41no—
43C2×Q8×C61M1612yes—
44C2×D4×C61—21no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61M1612yes—
48C22×C4×C61—21no—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61—44no—
54C22×Dic61—42no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D412yes—
58C2×#92420—44no—
59C2×#92420—44no—
60C2×#92420—44no—
61C22⋊C4×C61—28no—
62C42×C61—21no—
63C42×C61—21no—
64C22⋊Dic61—42no—
65C22⋊Dic61—44no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4×Dic61—22no—
70C4×Dic61—24no—
71C4×Dic61—42no—
72C4×Dic61—41no—
73C4×Dic61—42no—
74C23×C61—22no—
75C23×C61—41no—
76C23×C61—41no—
77C23×C61—42no—
78C23×C61—42no—
79C23×C61C2×C22⋊C411yescharacteristic
80Q8×C61—42no—
81Q8×C61—42no—
82D4×C61—42no—
83D4×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61C2×M1611yescharacteristic
93C2×C4×C61C2×M1611yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—84no—
104C2×Dic61#10012yes—
105C2×Dic61#13514yes—
106#92420—84no—
107#7649—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—44no—
110C22×C61—81no—
111C22×C61—82no—
112C22×C61—81no—
113C22×C61#40711yescharacteristic
114C22×C61#41011yescharacteristic
115C22×C61C2×#10011yescharacteristic
116C22×C61#41612yes—
117C22×C61#42112yes—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—42no—
122Dic61—24no—
123Dic61—22no—
124Dic61—41no—
125Dic61—81no—
126Dic61—81no—
127C4×#124—611no—
128#1839—612no—
129#1272—612no—
130#1270—612no—
131C2×C61—82no—
132C2×C61#146611yescharacteristic
133C2×C61#148812yes—
134C2×C61#152112yes—
135C2×C61#153311yescharacteristic
136C2×C61#154311yescharacteristic
137C2×#124#692311yescharacteristic
138C2×C4×Q8—611no—
139C2×C4×D4—611no—
140#391—611no—
141#390—611no—
142#388—1222no—
143#382—611no—
144C4×C22⋊C4—1222no—
145C43—611no—
146#336—614no—
147#336—1222no—
148#336—1222no—
149C61#764911yescharacteristic, complemented, Sylow
150C22×Q8C2×#692311yescharacteristic
151C22×D4C2×#692311yescharacteristic
152C23×C4—1221no—
153C22×C8—1224no—
154#124—22no—
155#124—22no—
156C4×Q8—2442no—
157C4×D4—2442no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—1221no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—1221no—
163C2×C22⋊C4—1222no—
164C2×C42—612no—
165C2×C42—611no—
166C2×C42—612no—
167C2×C42—611no—
168C2×C42—1221no—
169C2×C42C2×#692311yescharacteristic
170#95—1222no—
171#95—1222no—
172C24—21no—
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8#1175821712yes—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#1175821712yes—
181C22×C4—21no—
182C22×C4—612no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—2442no—
188C22×C4—2444no—
189C22×C4C22⋊#692312yes—
190C22×C4C22×#692311yescharacteristic
191C2×C8—2444no—
192C2×C8—2444no—
193C2×C8—2444no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4—2442no—
197C22⋊C4—28no—
198C22⋊C4—2444no—
199C22⋊C4—2442no—
200C42—21no—
201C42—21no—
202C42—1224no—
203C42—1222no—
204C42—2441no—
205C42—2442no—
206C42—2442no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—42no—
211C23—42no—
212C23C2×C22⋊#692311yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—612no—
226C2×C4—614no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—4884no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4C2×#1175821711yescharacteristic
238C2×C4C2×#1175821711yescharacteristic
239C8—4884no—
240C22—42no—
241C22—44no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22#1684073211yescharacteristic
246C22#1684074211yescharacteristic
247C22D61⋊#10011yescharacteristic
248C22#1684075212yes—
249C22#1684075912yes—
250C4—21no—
251C4—21no—
252C4—42no—
253C4—42no—
254C4—1224no—
255C4—1222no—
256C4—4881no—
257C4—4881no—
258C4—2441no—
259C2—82no—
260C2#2146107911yescharacteristic
261C2#2146115012yes—
262C2#2146126012yes—
263C2#2146129911yescharacteristic
264C2#2146132311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#7649
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21460639C2semidirect
149. C61#7649semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606392
#214606352
#124×Dic612
#764961