Finite Group Databasebeta

← #29592812

Subgroups — #29592812

Order 15616.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#21451484C211yesmaximal, characteristic
2#21446986C211yesmaximal, characteristic
3#21444846C212yesmaximal
4#21443844C212yesmaximal
5C61×#1317C211yesmaximal, characteristic
6#16840388C2211yescharacteristic
7#16840098—22no—
8#16839698C2212yes—
9#16839674—21no—
10#16839666—22no—
11#16839649—22no—
12#16839625—21no—
13C4×C22⋊Dic61—21no—
14#16839529C2211yescharacteristic
15#16839528—21no—
16#16839500—22no—
17C61×#381C2211yescharacteristic
18C61×#323C2212yes—
19C22×Dic122—21no—
20#14519756—22no—
21#14519754—42no—
22C2×C4⋊Dic61D412yes—
23C2×#11758196—22no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—21no—
26C2×C22⋊Dic61—21no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61—21no—
29#14519711—42no—
30#14519702—42no—
31#14519684—22no—
32#14519684—21no—
33#14519684—22no—
34#14519684—42no—
35#14519684D412yes—
36C23×C4×C61D411yescharacteristic
37C2×C22⋊C4×C61D411yescharacteristic
38C2×C22⋊C4×C61C2311yescharacteristic
39C22⋊C8×C61—22no—
40#95×C61—22no—
41C24×C61C2×D411yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61Q1612yes—
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—41no—
53C2×Dic122—22no—
54C2×Dic122—44no—
55C2×Dic122—81no—
56C2×C8×C61—42no—
57C22⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59C22⋊Dic61—44no—
60C22⋊Dic61—41no—
61C22⋊Dic61—41no—
62C22⋊Dic61—41no—
63C22⋊Dic61—41no—
64C4⋊Dic61—22no—
65C4⋊Dic61—42no—
66#11758196—44no—
67#11758196—42no—
68C4×Dic61—81no—
69C4×Dic61—81no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—42no—
73C23×C61#12011yescharacteristic
74C23×C61C2×Q1611yescharacteristic
75C23×C61#13711yescharacteristic
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—41no—
84C2×C4×C61—81no—
85C2×Dic61—24no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—82no—
93C2×Dic61—81no—
94C2×Dic61—82no—
95Dic122—84no—
96Dic122—82no—
97C8×C61—82no—
98#12216—611nomaximal, Sylow
99C22×C61—22no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61—81no—
106C22×C61#45111yescharacteristic
107C22×C61#45511yescharacteristic
108C22×C61B(4,𝔽2)11yescharacteristic
109C4×C61—42no—
110C4×C61—42no—
111C4×C61—81no—
112Dic61—44no—
113Dic61—82no—
114Dic61—82no—
115Dic61—161no—
116#2607—611no—
117#2030—611no—
118#1614—612no—
119#1352—612no—
120#1317D6111yescharacteristic
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—41no—
124C2×C61—41no—
125C2×C61#160211yescharacteristic
126C2×C61#219812yes—
127#543—611no—
128#484—1222no—
129#399—612no—
130#393—1221no—
131#391—1222no—
132#387—1222no—
133#381—1221no—
134#381C2×D6111yescharacteristic
135C4×C22⋊C4—1221no—
136#342—611no—
137#342—1221no—
138#328—1222no—
139#323C2×D6112yes—
140C61#1221611yescharacteristic, complemented, Sylow
141C22×Q8—1221no—
142C23×C4D24411yescharacteristic
143C22⋊Q8—1222no—
144C22⋊Q8—2442no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—1222no—
147C2×C22⋊C4—1221no—
148C2×C22⋊C4—1222no—
149C2×C22⋊C4—1221no—
150C2×C22⋊C4D24411yescharacteristic
151C2×C22⋊C4C22×D6111yescharacteristic
152C2×C42—1221no—
153C2×C42—1221no—
154#107—2442no—
155#103—2442no—
156C22⋊C8—22no—
157#95—22no—
158#95—612no—
159#95—1222no—
160#95—1221no—
161#95—1222no—
162#95—2442no—
163C24C2×D24411yescharacteristic
164C2×Q8—1222no—
165C2×Q8—4881no—
166C2×Q8—2444no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—2441no—
176C22×C4Dic24412yes—
177C22×C4D4×D6112yes—
178C2×C8—42no—
179C4⋊C4—1222no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C4⋊C4—2444no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—2444no—
186C22⋊C4—2441no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C42—4881no—
191C42—4881no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23#1451974711yescharacteristic
196C23C2×Dic24411yescharacteristic
197C23#1451981011yescharacteristic
198Q8—4882no—
199Q8—4884no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—1224no—
210C2×C4—4881no—
211C2×C4—4882no—
212C2×C4—4882no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4—2442no—
219C8—82no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22#1683992011yescharacteristic
228C22#1683994211yescharacteristic
229C22#1683995011yescharacteristic
230C4—42no—
231C4—42no—
232C4—81no—
233C4—9761no—
234C4—4882no—
235C4—4882no—
236C4—2444no—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2#2144477811yescharacteristic
242C2#2144781612yes—
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#1317D61
hypocenterC61#12216
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
140. C61#12216semidirect

Maximal subgroups

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

subgroupindex
#214514842
#214469862
#214448462
#214438442
C61×#13172
#1221661