Finite Group Databasebeta

← #29589418

Subgroups — #29589418

Order 15616.

434 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 77 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#21448444C211yesmaximal, characteristic
2#21444147C212yesmaximal
3#21443764C212yesmaximal, complemented
4#21443763C211yesmaximal, characteristic, complemented
5C61×#1324C211yesmaximal, characteristic, complemented
6C2×#14519735C411yescharacteristic
7C2×#14519734C411yescharacteristic
8C2×C4⋊C4×D61C2211yescharacteristic
9#16839724—22no—
10#16839659—22no—
11#16839636—22no—
12#16839632C411yescharacteristic
13#16839631C2211yescharacteristic
14#16839627C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×C4×D61C2×C411yescharacteristic
20C22×C4×D61D412yes—
21C2×#11758189—42no—
22#14519735—42no—
23#14519734—22no—
24#14519734—22no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×#11758196D412yes—
31C4⋊C4×D61—42no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C22⋊#92418—22no—
37#14519689—42no—
38#14519684—22no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C22⋊C8×C61—22no—
43#95×C61—22no—
44C23×D61C22⋊C411yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22×C411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C412yes—
53C2×C4×D61—22no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—82no—
60C2×C8×C61—42no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C42×C61—21no—
64C42×C61M1612yescomplemented
65#11758198—24no—
66#11758198—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—82no—
70#11758196—24no—
71#11758196—42no—
72#11758196—82no—
73C4×Dic61—21no—
74C4×Dic61—42no—
75C4×Dic61M1612yescomplemented
76C2×#92418—42no—
77#11758189—84no—
78C23×C61C2×C22⋊C411yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61#9912yes—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61C2×M1611yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—41no—
104C2×Dic61#10112yes—
105C4×D61—24no—
106C4×D61—24no—
107C4×D61—44no—
108C4×D61—82no—
109C8×C61—82no—
110#92418—82no—
111#11514—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61#40711yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10111yescharacteristic
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—42no—
121C2×D61—42no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—42no—
125C4×C61—42no—
126C4×C61—81no—
127Dic61—22no—
128Dic61—42no—
129Dic61—42no—
130Dic61—81no—
131#2317—611no—
132#1463—612no—
133#1325—612no—
134#1324—611no—
135#1324D6111yescharacteristic, complemented
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#146311yescharacteristic
139C2×C61#212711yescharacteristic
140C2×C61#213311yescharacteristic
141D61—42no—
142C2×#117—611no—
143C2×#117—611no—
144C22×C4⋊C4—611no—
145#407—1222no—
146#389—1222no—
147#385—1222no—
148#384—611no—
149#384—611no—
150#382—611no—
151#382C2×D6111yescharacteristic
152#324—612no—
153#324—1222no—
154#324C2×D6112yes—
155C61#1151411yescharacteristic, complemented, Sylow
156C23×C4—611no—
157C23×C4—612no—
158C2×M16—2442no—
159#117—1222no—
160#117—1222no—
161#117—2442no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4—1222no—
167C2×C4⋊C4—1222no—
168C2×C4⋊C4—2442no—
169C2×C4⋊C4C4×D6111yescharacteristic
170C2×C4⋊C4C22×D6111yescharacteristic
171C2×C22⋊C4—1221no—
172C2×C22⋊C4—1221no—
173C2×C42—611no—
174C2×C42—1221no—
175C2×C42C4×D6111yescharacteristic
176C22⋊C8—22no—
177C22⋊C8—1222no—
178C22⋊C8—2442no—
179#95—22no—
180#95—1222no—
181C24—611no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—611no—
185C22×C4—612no—
186C22×C4—1222no—
187C22×C4—1222no—
188C22×C4—1222no—
189C22×C4—1222no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—4882no—
195C22×C4C2×C4×D6111yescharacteristic
196C22×C4D4×D6112yes—
197M16—4884no—
198C2×C8—42no—
199C2×C8—2442no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—1224no—
203C4⋊C4—4882no—
204C4⋊C4—4882no—
205C4⋊C4—2442no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C22⋊C4—1224no—
209C22⋊C4—2442no—
210C42—21no—
211C42—612no—
212C42—1221no—
213C42—2442no—
214C42#1175818912yescomplemented
215C23—612no—
216C23—1221no—
217C23—1221no—
218C23—2441no—
219C23—2441no—
220C23C22⋊C4×D6111yescharacteristic
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—612no—
231C2×C4—1224no—
232C2×C4—1224no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—4882no—
238C2×C4—2444no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2442no—
244C2×C4M16×D6111yescharacteristic
245C2×C4C2×#1175818911yescharacteristic
246C8—82no—
247C8—4882no—
248C22—21no—
249C22—21no—
250C22—1222no—
251C22—1222no—
252C22—1222no—
253C22—2442no—
254C22—2442no—
255C22#1683972411yescharacteristic
256C22#99×D6111yescharacteristic
257C22#101×D6111yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—81no—
263C4—1222no—
264C4—4881no—
265C4—2442no—
266C4—2442no—
267C2—21no—
268C2—21no—
269C2—2442no—
270C2#2144414711yescharacteristic
271C2#2144748711yescharacteristic
272C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11514
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #21443764C2semidirect
4. #21443763C2semidirect
5. C61×#1324C2semidirect
64. C42×C61M16semidirect
75. C4×Dic61M16semidirect
135. #1324D61semidirect
155. C61#11514semidirect
214. C42#11758189semidirect

Maximal subgroups

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

subgroupindex
#214484442
#214441472
#214437642
#214437632
C61×#13242
#1151461