Finite Group Databasebeta

← #30604088

Subgroups — #30604088

Order 15616.

670 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461070C212yesmaximal, complemented
2#21460744C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4#16840782—22no—
5#16840607—22no—
6#16840605C2214yes—
7C23×D244C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839664—22no—
10#16839663—22no—
11#16839617C412yes—
12#16839617C2212yes—
13C2×#117×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17C24×D61C2×C412yes—
18C22×D244—24no—
19C22×D244—21no—
20C22×D244—21no—
21C22×D244—41no—
22C22×D244—41no—
23C22×D244—42no—
24#14519736—41no—
25#14519736—41no—
26C2×C4⋊Dic61D412yes—
27C2×C22⋊Dic61C2×C411yescharacteristic
28C2×C22⋊Dic61C2311yescharacteristic
29C2×#11758198—24no—
30C2×#11758198—24no—
31C2×C4×Dic61D412yes—
32C23×C4×C61C2×C411yescharacteristic
33#117×C61—42no—
34C2×C4⋊C4×C61—21no—
35C2×C22⋊C4×C61C2×C412yes—
36C2×C42×C61—21no—
37C24×C61C22×C411yescharacteristic
38C23×D61—22no—
39C23×D61—22no—
40C23×D61—42no—
41C23×D61—42no—
42C23×D61—84no—
43C23×D61M1614yes—
44C22×C4×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×Dic61C22⋊C412yes—
52C22×Dic61C2×D412yes—
53C2×D244—24no—
54C2×D244—24no—
55C2×D244—48no—
56C2×D244—48no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244—42no—
62C2×#92420—44no—
63C4⋊C4×C61—42no—
64C22⋊C4×C61—42no—
65C42×C61—42no—
66C22⋊Dic61—41no—
67C22⋊Dic61—41no—
68#11758198—84no—
69#11758198—84no—
70C4⋊Dic61—42no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—42no—
76C23×C61C2×C22⋊C411yescharacteristic
77C23×C61C2×M1612yes—
78C22×D61—24no—
79C22×D61—44no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—42no—
83C22×D61—42no—
84C22×D61—44no—
85C22×D61—84no—
86C22×D61—84no—
87C22×D61—88no—
88C22×D61—88no—
89C2×C4×C61—24no—
90C2×C4×C61—24no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—44no—
96C2×C4×C61—42no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#10012yes—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104D244—44no—
105D244—44no—
106D244—48no—
107#92420—84no—
108#11503—611nomaximal, Sylow
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61#40711yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10011yescharacteristic
117C2×D61—44no—
118C2×D61—44no—
119C2×D61—44no—
120C2×D61—84no—
121C2×D61—88no—
122C2×D61—84no—
123C2×D61—88no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—22no—
127C4×C61—82no—
128Dic61—42no—
129Dic61—42no—
130#2309—611no—
131#1464—612no—
132#1316—614no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61—42no—
136C2×C61#146211yescharacteristic
137C2×C61#212212yes—
138D61—84no—
139C23×D4—611no—
140C2×#117—611no—
141C2×#117#692311yescharacteristic
142#432—1222no—
143#390—1222no—
144#390—1222no—
145#379—612no—
146#379—612no—
147#324—1222no—
148#323—614no—
149C61#1150311yescharacteristic, complemented, Sylow
150C25—612no—
151C22×D4—1224no—
152C22×D4—1221no—
153C22×D4—1221no—
154C22×D4—2441no—
155C22×D4—2441no—
156C22×D4—2442no—
157C23×C4C2×#692311yescharacteristic
158#117—42no—
159#117—2441no—
160#117—2441no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—612no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—1224no—
166C2×C22⋊C4—1224no—
167C2×C22⋊C4C2×#692312yes—
168C2×C42—21no—
169C2×C42—612no—
170C4⋊C8—2442no—
171C22⋊C8—1224no—
172#97—2442no—
173C24—614no—
174C24—1222no—
175C24—1222no—
176C24—4884no—
177C24—2442no—
178C24—2442no—
179C24C22×#692311yescharacteristic
180C2×D4—1224no—
181C2×D4—1224no—
182C2×D4—2448no—
183C2×D4—2448no—
184C2×D4—2442no—
185C2×D4—2442no—
186C2×D4—2441no—
187C2×D4—2441no—
188C2×D4—2442no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—612no—
195C22×C4—612no—
196C22×C4C22⋊#692311yescharacteristic
197C22×C4C22⋊#692311yescharacteristic
198C2×C8—2444no—
199C4⋊C4—42no—
200C4⋊C4—2442no—
201C22⋊C4—42no—
202C22⋊C4—4884no—
203C22⋊C4—4884no—
204C22⋊C4—2441no—
205C22⋊C4—2441no—
206C42—42no—
207C42—1222no—
208C42—1222no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—1224no—
213C23—4888no—
214C23—4888no—
215C23—4884no—
216C23—4884no—
217C23—2444no—
218C23—2444no—
219C23—2444no—
220C23—2444no—
221C23—2442no—
222C23—2442no—
223C23C2×C22⋊#692311yescharacteristic
224C23D61⋊M1612yes—
225D4—2444no—
226D4—2444no—
227D4—2448no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—44no—
235C2×C4—42no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4#1451983611yescharacteristic
241C2×C4#1451983611yescharacteristic
242C2×C4#1451983712yes—
243C8—4884no—
244C22—22no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—4884no—
250C22—4888no—
251C22—4888no—
252C22—4884no—
253C22—2444no—
254C22—2444no—
255C22—2444no—
256C22#1684073411yescharacteristic
257C22C2×#1451983611yescharacteristic
258C22C2×#1451983711yescharacteristic
259C4—21no—
260C4—21no—
261C4—22no—
262C4—82no—
263C4—2442no—
264C4—2442no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—4884no—
269C2#2146106611yescharacteristic
270C2#2146208012yes—
subgroupG/H
centerC22C2×#14519836
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C22⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11503
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21460744C2semidirect
149. C61#11503semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607442
#214483992
#1150361