Finite Group Databasebeta

← #30603908

Subgroups — #30603908

Order 15616.

562 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#16840605C212yesmaximal
2#21460764C214yesmaximal, complemented
3#21448431C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840605—22no—
6#16840605C2214yes—
7C22×C22⋊Dic61C411yescharacteristic
8C22×C22⋊Dic61C2211yescharacteristic
9#16839635C412yes—
10#16839635C2212yes—
11#16839634—22no—
12#16839620—22no—
13C22×C22⋊C4×C61C411yescharacteristic
14C22×#92420—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×#11758196—22no—
20C2×#11758196—22no—
21C2×C22⋊Dic61—21no—
22C2×C22⋊Dic61—22no—
23C2×C22⋊Dic61—42no—
24C2×C22⋊Dic61C814yescomplemented
25C2×C22⋊Dic61C2×C412yes—
26C2×C22⋊Dic61C2×C411yescharacteristic
27C2×C22⋊Dic61D412yes—
28C2×C22⋊Dic61C2311yescharacteristic
29#14519684—22no—
30#14519684—22no—
31C25×C61C2×C411yescharacteristic
32C23×C4×C61C2×C412yes—
33C2×C22⋊C4×C61—21no—
34C2×C22⋊C4×C61—21no—
35C2×C22⋊C4×C61—42no—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—82no—
39C24×C61C22⋊C411yescharacteristic
40C24×C61C22⋊C411yescharacteristic
41C24×C61C2×C812yes—
42C24×C61M1612yes—
43C24×C61C22×C411yescharacteristic
44C22×C4×C61—22no—
45C22×C4×C61—42no—
46C22×C4×C61—82no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—24no—
50C22×Dic61—22no—
51C22×Dic61—82no—
52C22×Dic61—82no—
53C22×Dic61C22⋊C412yes—
54C22×Dic61C2×D412yes—
55C2×#92420—44no—
56C2×#92420—84no—
57C22⋊C4×C61—42no—
58C22⋊C4×C61—42no—
59C22⋊Dic61—24no—
60C22⋊Dic61—22no—
61C22⋊Dic61—41no—
62C22⋊Dic61—42no—
63C22⋊Dic61—41no—
64C22⋊Dic61C2×C814yescomplemented
65#11758196—82no—
66#11758196—82no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—24no—
72C23×C61—24no—
73C23×C61—42no—
74C23×C61—42no—
75C23×C61—42no—
76C23×C61—82no—
77C23×C61—82no—
78C23×C61—84no—
79C23×C61—82no—
80C23×C61—82no—
81C23×C61C22⋊C812yes—
82C23×C61C22⋊C812yes—
83C23×C61#9912yes—
84C23×C61#10112yes—
85C23×C61C2×C22⋊C411yescharacteristic
86C23×C61C22×C811yescharacteristic
87C23×C61C2×M1611yescharacteristic
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—84no—
92C2×Dic61—24no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—44no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—82no—
101C2×Dic61—84no—
102#92420—84no—
103#11453—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—42no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—84no—
120C22×C61—84no—
121C22×C61#32414yes—
122C22×C61C2×C22⋊C811yescharacteristic
123C22×C61C2×#9911yescharacteristic
124C22×C61C2×#10111yescharacteristic
125C4×C61—82no—
126Dic61—44no—
127Dic61—42no—
128Dic61—42no—
129#2315—611no—
130C2×#323—612no—
131#1326—614no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—24no—
135C2×C61—42no—
136C2×C61—41no—
137C2×C61—41no—
138C2×C61C2×#32411yescharacteristic
139C2×C61#212112yes—
140C22×C22⋊C4—611no—
141C22×C22⋊C4—611no—
142C22×C22⋊C4#692311yescharacteristic
143C2×C22⋊C8—1222no—
144#385—612no—
145#385—612no—
146#385—1222no—
147#380—1222no—
148#323—614no—
149#323—1222no—
150C61#1145311yescharacteristic, complemented, Sylow
151C25C2×#692311yescharacteristic
152C23×C4—612no—
153C23×C4—1221no—
154C23×C4C2×#692312yes—
155C22×C8—2442no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1222no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—42no—
161C2×C22⋊C4—614no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—611no—
166C2×C22⋊C4—1222no—
167C2×C22⋊C4—1221no—
168C2×C22⋊C4—2442no—
169C22⋊C8—1224no—
170C22⋊C8—2442no—
171#95—1222no—
172#95—1222no—
173C24—22no—
174C24—22no—
175C24—82no—
176C24D61⋊C812yes—
177C24#1175821312yes—
178C24C22⋊#692311yescharacteristic
179C24C22⋊#692311yescharacteristic
180C24C22×#692311yescharacteristic
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—82no—
184C22×C4—612no—
185C22×C4—612no—
186C22×C4—1224no—
187C22×C4—1222no—
188C22×C4—1222no—
189C22×C4—1222no—
190C22×C4—4882no—
191C22×C4—4882no—
192C2×C8—4884no—
193C2×C8—2444no—
194C4⋊C4—4882no—
195C4⋊C4—4882no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—614no—
199C22⋊C4—1224no—
200C22⋊C4—1222no—
201C22⋊C4—2441no—
202C22⋊C4—2442no—
203C22⋊C4—2441no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—24no—
209C23—24no—
210C23—42no—
211C23—42no—
212C23—42no—
213C23—82no—
214C23—82no—
215C23—82no—
216C23—82no—
217C23—84no—
218C23#1451983412yes—
219C23#1451983412yes—
220C23#1451983512yes—
221C23#1451983812yes—
222C23C2×C22⋊#692311yescharacteristic
223C23C2×D61⋊C811yescharacteristic
224C23C2×#1175821311yescharacteristic
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—1224no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—4882no—
233C2×C4—4884no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2444no—
237C2×C4—2442no—
238C2×C4—2442no—
239C8—4884no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—84no—
257C22#1684060814yes—
258C22C2×#1451983411yescharacteristic
259C22C2×#1451983511yescharacteristic
260C22C2×#1451983811yescharacteristic
261C4—82no—
262C4—2444no—
263C4—2442no—
264C4—2442no—
265C2—21no—
266C2—21no—
267C2—24no—
268C2—42no—
269C2—41no—
270C2—41no—
271C2C2×#1684060811yescharacteristic
272C2#2146207412yes—
subgroupG/H
centerC22C2×#14519835
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#11453
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460764C2semidirect
24. C2×C22⋊Dic61C8semidirect
64. C22⋊Dic61C2×C8semidirect
150. C61#11453semidirect

Maximal subgroups

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

subgroupindex
C2×#168406052
#214607642
#214484312
#1145361