Finite Group Databasebeta

← #30594445

Subgroups — #30594445

Order 15616.

276 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461721C211yesmaximal, characteristic
2#21461549C211yesmaximal, characteristic
3#21444150C211yesmaximal, characteristic
4#16840732—21no—
5C2×C22⋊#92420—21no—
6C2×#14519832C411yescharacteristic
7C2×C4×#92420C411yescharacteristic
8#16840642—21no—
9#16840642C412yes—
10#16840628—21no—
11C2×#14519733C2211yescharacteristic
12#16839816—21no—
13#16839487—21no—
14#16839486C411yescharacteristic
15C61×#323C411yescharacteristic
16C2×#11758217—22no—
17C22×#92420—21no—
18C22×#92420—21no—
19C22⋊#92420—24no—
20C22⋊#92420—41no—
21C22⋊#92420—41no—
22#14519832—41no—
23C4×#92420—41no—
24C23×Dic61D411yescharacteristic
25#14519733—41no—
26#14519733—41no—
27C2×#11758196C2×C411yescharacteristic
28C2×#11758196D411yescharacteristic
29C2×C22⋊Dic61Q811yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32#14519706—41no—
33C22⋊#92418—21no—
34#14519687—41no—
35C2×C22⋊C4×C61C2×C411yescharacteristic
36C22⋊C8×C61—21no—
37C24×C61C4⋊C411yescharacteristic
38C22×C4×C61C4211yescharacteristic
39C22×C4×C61C22⋊C411yescharacteristic
40C22×Dic61—21no—
41C22×Dic61—21no—
42C22×Dic61—22no—
43C22×Dic61—41no—
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C22×Dic61C4⋊C411yescharacteristic
48#11758217—42no—
49#11758217—42no—
50C2×#92420—22no—
51C2×#92420—22no—
52C2×#92420—41no—
53C2×#92420—41no—
54C2×#92420—41no—
55C2×#92420—41no—
56C2×#92420—42no—
57C2×C8×C61—41no—
58C22⋊C4×C61—41no—
59C22⋊Dic61—41no—
60#11758196—41no—
61#11758196—41no—
62C4×Dic61—21no—
63C4×Dic61—21no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C2×#92418—41no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—41no—
71C23×C61—41no—
72C23×C61#9511yescharacteristic
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—21no—
82C2×Dic61—21no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61#9911yescharacteristic
88C2×Dic61#9911yescharacteristic
89C2×Dic61#10412yes—
90#92420—42no—
91#92420—42no—
92#92420—82no—
93C8×C61—81no—
94#92418—81no—
95#7216—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—42no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61H(3,ℤ/4)11yescharacteristic
104C22×C61#33911yescharacteristic
105C22×C61#34211yescharacteristic
106C4×C61—41no—
107C4×C61—41no—
108Dic61—21no—
109Dic61—21no—
110Dic61—22no—
111Dic61—41no—
112Dic61—41no—
113#1822—611no—
114#1750—611no—
115#1464—611no—
116C2×C61—21no—
117C2×C61—21no—
118C2×C61—81no—
119C2×C61#128411yescharacteristic
120C2×C61#139211yescharacteristic
121C2×C61#139511yescharacteristic
122C2×#117—611no—
123#432—1221no—
124#407—1221no—
125C2×C22⋊C8—1221no—
126C2×#97—611no—
127C2×C4×C8—611no—
128#343—612no—
129#343—1221no—
130#336—1221no—
131#324—1221no—
132#323—611no—
133#323#692311yescharacteristic
134C61#721611yescharacteristic, complemented, Sylow
135C23×C4—611no—
136C2×M16—1222no—
137C22×C8—1221no—
138C22×C8—1221no—
139#117—2441no—
140#117—2441no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C22⋊C4—611no—
144C2×C22⋊C4C2×#692311yescharacteristic
145C2×C42—611no—
146C2×C42—611no—
147C4⋊C8—2441no—
148C22⋊C8—21no—
149C22⋊C8—1224no—
150C22⋊C8—1221no—
151C22⋊C8—2441no—
152C22⋊C8—2441no—
153#97—2441no—
154#97—2441no—
155C4×C8—2441no—
156C24C4⋊#692311yescharacteristic
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—1222no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4—2441no—
165C22×C4C4×#692311yescharacteristic
166C22×C4C22⋊#692311yescharacteristic
167M16—2442no—
168M16—2442no—
169C2×C8—41no—
170C2×C8—1222no—
171C2×C8—1222no—
172C2×C8—2441no—
173C2×C8—2442no—
174C2×C8—2441no—
175C2×C8—2441no—
176C2×C8—2441no—
177C2×C8—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—41no—
181C22⋊C4—2441no—
182C42—1221no—
183C42—1221no—
184C42—1221no—
185C42—1221no—
186C23—21no—
187C23—21no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23(C2×#6923)⋊C411yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—612no—
197C2×C4—611no—
198C2×C4—611no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2441no—
208C2×C4—2441no—
209C8—81no—
210C8—4881no—
211C8—4882no—
212C8—2442no—
213C8—2442no—
214C22—21no—
215C22—21no—
216C22—42no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22#1684063011yescharacteristic
222C22#1684063411yescharacteristic
223C22#1684063911yescharacteristic
224C4—41no—
225C4—41no—
226C4—1222no—
227C4—1221no—
228C4—1221no—
229C4—2441no—
230C4—2441no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#2146066811yescharacteristic
235C2#2146090911yescharacteristic
236C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC24×C61C4⋊C4
cosocleC2×#14519733C22
hypercenter#323#6923
hypocenterC61#7216
LCSG ▷ C22×C4×C61 ▷ C22×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
134. C61#7216semidirect

Maximal subgroups

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

subgroupindex
#214617212
#214615492
#214441502
#721661