Finite Group Databasebeta

← #30604130

Subgroups — #30604130

Order 15616.

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

normal subgroups only

This group has 418 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#21460762C212yesmaximal, complemented
3#21460761C212yesmaximal, complemented
4#21448444C211yesmaximal, characteristic
5#16840783—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519735C2211yescharacteristic
9C2×#14519734C411yescharacteristic
10C2×C4⋊C4×D61C411yescharacteristic
11#16839659—22no—
12#16839636—22no—
13#16839632C2211yescharacteristic
14#16839631C2211yescharacteristic
15#16839627C411yescharacteristic
16C61×#382C411yescharacteristic
17C4⋊#92420—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22#14519735—42no—
23#14519734—22no—
24#14519734—22no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2311yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—22no—
31C4⋊C4×D61—42no—
32C2×#11758198—21no—
33C2×#11758198D412yes—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D412yes—
36#14519684—22no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40#95×C61—22no—
41C23×D61C22⋊C411yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C412yes—
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C2×D412yes—
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61—42no—
55C2×C4×D61—82no—
56C2×#92420—44no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C42×C61—21no—
60C42×C61M1612yes—
61#11758198—24no—
62#11758198—42no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4⋊Dic61—82no—
66#11758196—24no—
67#11758196—42no—
68#11758196—82no—
69C4×Dic61—21no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61M1612yes—
73C23×C61C2×C22⋊C411yescharacteristic
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61#10112yes—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61C2×M1611yescharacteristic
89C2×C4×C61C2×M1611yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—41no—
99C2×Dic61#9912yes—
100C4×D61—24no—
101C4×D61—24no—
102C4×D61—84no—
103#92420—84no—
104#11516—611nomaximal, Sylow
105C22×C61—21no—
106C22×C61—21no—
107C22×C61#40711yescharacteristic
108C22×C61C2×#9911yescharacteristic
109C22×C61C2×#10111yescharacteristic
110C2×D61—22no—
111C2×D61—42no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—42no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—42no—
118C4×C61—42no—
119C4×C61—81no—
120Dic61—22no—
121Dic61—42no—
122Dic61—42no—
123Dic61—81no—
124#2317—611no—
125#1464—612no—
126#1325—612no—
127#1325—612no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61#146311yescharacteristic
131C2×C61#212811yescharacteristic
132C2×C61#213511yescharacteristic
133D61—42no—
134C2×#117—611no—
135C2×#117—611no—
136C22×C4⋊C4—611no—
137#432—1222no—
138#389—1222no—
139#385—1222no—
140#384—611no—
141#384—611no—
142#382—611no—
143#382#692311yescharacteristic
144#324—614no—
145#323—1222no—
146C61#1151611yescharacteristic, complemented, Sylow
147C23×C4—611no—
148C23×C4—1221no—
149#117—1222no—
150#117—1222no—
151#117—2442no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—2442no—
159C2×C4⋊C4C2×#692311yescharacteristic
160C2×C4⋊C4C2×#692311yescharacteristic
161C2×C22⋊C4—612no—
162C2×C22⋊C4—1221no—
163C2×C42—611no—
164C2×C42—612no—
165C2×C42C2×#692311yescharacteristic
166C4⋊C8—2442no—
167C22⋊C8—1224no—
168#97—2442no—
169#95—22no—
170#95—1222no—
171C24—611no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—1222no—
177C22×C4—1222no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4—4882no—
183C22×C4—2442no—
184C22×C4C22⋊#692312yes—
185C22×C4C22×#692311yescharacteristic
186C2×C8—2444no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—1224no—
190C4⋊C4—4882no—
191C4⋊C4—4882no—
192C4⋊C4—2441no—
193C4⋊C4—2441no—
194C4⋊C4—2442no—
195C22⋊C4—1224no—
196C22⋊C4—2442no—
197C42—21no—
198C42—612no—
199C42—1222no—
200C42—1222no—
201C42—1221no—
202C42#1175821312yes—
203C23—612no—
204C23—1221no—
205C23—1221no—
206C23—2441no—
207C23—2441no—
208C23C2×C22⋊#692311yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—612no—
219C2×C4—1224no—
220C2×C4—1224no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—4884no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4—2442no—
231C2×C4D61⋊M1611yescharacteristic
232C2×C4C2×#1175821311yescharacteristic
233C8—4884no—
234C22—21no—
235C22—21no—
236C22—1222no—
237C22—2442no—
238C22—2442no—
239C22—2441no—
240C22—2441no—
241C22#1684073311yescharacteristic
242C22D61⋊#9911yescharacteristic
243C22D61⋊#10111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—81no—
249C4—1222no—
250C4—4881no—
251C4—2442no—
252C4—2442no—
253C2—21no—
254C2—21no—
255C2—2442no—
256C2#2146106811yescharacteristic
257C2#2146209911yescharacteristic
258C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#382#6923
hypocenterC61#11516
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460762C2semidirect
3. #21460761C2semidirect
146. C61#11516semidirect

Maximal subgroups

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

subgroupindex
#214610732
#214607622
#214607612
#214484442
#1151661