Finite Group Databasebeta

← #30594773

Subgroups — #30594773

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#21461713C211yesmaximal, characteristic
2#21461073C211yesmaximal, characteristic
3#21444152C211yesmaximal, characteristic
4#16840783—21no—
5C2×#14519834C411yescharacteristic
6C2×#14519834C411yescharacteristic
7#16840628—21no—
8#16840628—21no—
9#16840607C412yes—
10#16840606—21no—
11C2×#14519735C2211yescharacteristic
12#16839816—21no—
13#16839488C411yescharacteristic
14#16839485—21no—
15C61×#324C411yescharacteristic
16C22×#92420—21no—
17C22×#92420—21no—
18C4⋊#92420—41no—
19#14519834—41no—
20#14519834—41no—
21C22⋊#92420—22no—
22#14519832—41no—
23C22×C4×D61C2×C411yescharacteristic
24#14519735—41no—
25#14519735—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758198D411yescharacteristic
28C2×#11758198Q811yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31#14519706—41no—
32C22⋊#92418—21no—
33#14519687—41no—
34C2×C4⋊C4×C61C2×C411yescharacteristic
35C22⋊C8×C61—21no—
36C23×D61C4⋊C411yescharacteristic
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
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—
55C4⋊C4×C61—41no—
56#11758198—41no—
57#11758198—41no—
58C4⋊Dic61—41no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C2×#92418—41no—
64C23×C61#9511yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—41no—
69C22×D61—41no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61#9911yescharacteristic
84C2×Dic61#9911yescharacteristic
85C4×D61—42no—
86C4×D61—42no—
87#92420—81no—
88#92420—81no—
89#92420—82no—
90C8×C61—81no—
91#92418—81no—
92#7327—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#34211yescharacteristic
96C22×C61#34411yescharacteristic
97C22×C61#34411yescharacteristic
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—81no—
102C2×D61—81no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61—41no—
106Dic61—21no—
107Dic61—21no—
108Dic61—41no—
109Dic61—41no—
110#1818—611no—
111#1464—611no—
112#1464—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#130611yescharacteristic
116C2×C61#139511yescharacteristic
117C2×C61#139511yescharacteristic
118D61—81no—
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—612no—
127#324—611no—
128#324#692311yescharacteristic
129#323—1221no—
130#323—1221no—
131C61#732711yescharacteristic, complemented, Sylow
132C23×C4—611no—
133C22×C8—1221no—
134C22×C8—1221no—
135#117—2441no—
136#117—2441no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4C2×#692311yescharacteristic
139C2×C22⋊C4—611no—
140C2×C22⋊C4—611no—
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—
152C24—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4—2441no—
159C22×C4—2441no—
160C22×C4C4×#692311yescharacteristic
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—41no—
173C4⋊C4—2441no—
174C22⋊C4—2441no—
175C22⋊C4—2441no—
176C42—1221no—
177C42—1221no—
178C42—1221no—
179C42—1221no—
180C23—1221no—
181C23—1221no—
182C23—1221no—
183C23—2441no—
184C23—2441no—
185C23(C2×#6923)⋊C411yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—611no—
194C2×C4—611no—
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—4881no—
211C22—4881no—
212C22—2441no—
213C22—2441no—
214C22—2441no—
215C22#1684063911yescharacteristic
216C22#1684064411yescharacteristic
217C22#1684064511yescharacteristic
218C4—41no—
219C4—41no—
220C4—41no—
221C4—1221no—
222C4—1221no—
223C4—2441no—
224C4—2441no—
225C2—21no—
226C2—21no—
227C2—4881no—
228C2#2146072311yescharacteristic
229C2#2146091811yescharacteristic
230C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×D61C4⋊C4
cosocleC2×#14519735C22
hypercenter#324#6923
hypocenterC61#7327
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
131. C61#7327semidirect

Maximal subgroups

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

subgroupindex
#214617132
#214610732
#214441522
#732761