Finite Group Databasebeta

← #30594767

Subgroups — #30594767

Order 15616.

244 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 48 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#21461712C211yesmaximal, characteristic
2#21461071C211yesmaximal, characteristic
3#21444150C211yesmaximal, characteristic
4#16840783—21no—
5C2×C22⋊#92420C411yescharacteristic
6C2×C22⋊#92420C411yescharacteristic
7#16840628—21no—
8#16840628—21no—
9#16840608—21no—
10#16840605C412yes—
11C2×#14519733C2211yescharacteristic
12#16839816—21no—
13#16839487—21no—
14#16839486C411yescharacteristic
15C61×#323C411yescharacteristic
16C22×#92420—21no—
17C22×#92420—21no—
18C4⋊#92420—41no—
19C22⋊#92420—22no—
20C22⋊#92420—41no—
21C22⋊#92420—41no—
22#14519832—41no—
23C23×Dic61C2×C411yescharacteristic
24#14519733—41no—
25#14519733—41no—
26C2×#11758196D411yescharacteristic
27C2×#11758196Q811yescharacteristic
28C2×C22⋊Dic61C2×C411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31#14519706—41no—
32C22⋊#92418—21no—
33#14519687—41no—
34C2×C22⋊C4×C61C2×C411yescharacteristic
35C22⋊C8×C61—21no—
36C24×C61C4211yescharacteristic
37C22×C4×C61C22⋊C411yescharacteristic
38C22×C4×C61C4⋊C411yescharacteristic
39C22×Dic61—21no—
40C22×Dic61—21no—
41C22×Dic61—41no—
42C22×Dic61—41no—
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C4⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C2×#92420—42no—
48C2×#92420—41no—
49C2×#92420—41no—
50C2×#92420—41no—
51C2×#92420—41no—
52C2×#92420—41no—
53C2×#92420—41no—
54C2×C8×C61—41no—
55C22⋊C4×C61—41no—
56C22⋊Dic61—41no—
57#11758196—41no—
58#11758196—41no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C2×#92418—41no—
64C23×C61—21no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61#9511yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61#9911yescharacteristic
86C2×Dic61#9911yescharacteristic
87#92420—81no—
88#92420—81no—
89#92420—82no—
90C8×C61—81no—
91#92418—81no—
92#7325—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—81no—
99C22×C61—81no—
100C22×C61#34211yescharacteristic
101C22×C61#34411yescharacteristic
102C22×C61#34411yescharacteristic
103C4×C61—41no—
104C4×C61—41no—
105Dic61—21no—
106Dic61—21no—
107Dic61—41no—
108Dic61—41no—
109Dic61—41no—
110#1818—611no—
111#1464—611no—
112#1464—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—81no—
116C2×C61#130611yescharacteristic
117C2×C61#139111yescharacteristic
118C2×C61#139211yescharacteristic
119C2×#117—611no—
120#432—1221no—
121#432—1221no—
122C2×C22⋊C8—611no—
123C2×C22⋊C8—611no—
124#336—1221no—
125#336—1221no—
126#324—1221no—
127#324—1221no—
128#323—612no—
129#323—611no—
130#323#692311yescharacteristic
131C61#732511yescharacteristic, complemented, Sylow
132C23×C4—611no—
133C22×C8—1221no—
134C22×C8—1221no—
135#117—2441no—
136#117—2441no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—611no—
139C2×C22⋊C4—611no—
140C2×C22⋊C4C2×#692311yescharacteristic
141C2×C42—611no—
142C2×C42—611no—
143C4⋊C8—2441no—
144C4⋊C8—2441no—
145C22⋊C8—21no—
146C22⋊C8—1222no—
147C22⋊C8—1221no—
148C22⋊C8—2441no—
149C22⋊C8—2441no—
150#97—2441no—
151#97—2441no—
152C24C4×#692311yescharacteristic
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1221no—
158C22×C4—1221no—
159C22×C4—2441no—
160C22×C4—2441no—
161C22×C4C4⋊#692311yescharacteristic
162C22×C4C22⋊#692311yescharacteristic
163C2×C8—41no—
164C2×C8—2441no—
165C2×C8—2441no—
166C2×C8—2441no—
167C2×C8—2442no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8—2441no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C22⋊C4—41no—
175C22⋊C4—2441no—
176C42—1221no—
177C42—1221no—
178C42—1221no—
179C42—1221no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23(C2×#6923)⋊C411yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2441no—
202C2×C4—2441no—
203C8—81no—
204C8—4881no—
205C8—4881no—
206C8—4881no—
207C8—4882no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—41no—
213C22—81no—
214C22—81no—
215C22#1684063911yescharacteristic
216C22#1684064411yescharacteristic
217C22#1684064511yescharacteristic
218C4—41no—
219C4—41no—
220C4—1221no—
221C4—1221no—
222C4—2441no—
223C4—2441no—
224C4—2441no—
225C2—21no—
226C2—21no—
227C2—81no—
228C2#2146072311yescharacteristic
229C2#2146090611yescharacteristic
230C2#2146090911yescharacteristic
subgroupG/H
centerC22#16840639
commutator, prime radicalC24×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
cosocleC2×#14519733C22
hypercenter#323#6923
hypocenterC61#7325
LCSG ▷ C24×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
131. C61#7325semidirect

Maximal subgroups

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

subgroupindex
#214617122
#214610712
#214441502
#732561