Finite Group Databasebeta

← #30598196

Subgroups — #30598196

Order 15616.

930 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 144 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#21461123C214yesmaximal, complemented
2#21461050C212yesmaximal
3C2×#16840239C211yesmaximal, characteristic
4#16840778C2214yes—
5#16840612—28no—
6#16840607—22no—
7#16840605—22no—
8C23×Dic122C411yescharacteristic
9#16840239—28no—
10C2×C4×Dic122—22no—
11C2×#14519742C412yes—
12C2×#14519742C2212yes—
13C2×#14519736C2211yescharacteristic
14C2×#14519733—22no—
15C2×#117×C61C411yescharacteristic
16C4⋊#92420—24no—
17C22⋊#92420—24no—
18C4×#92420—24no—
19C22×Dic122—21no—
20C22×Dic122—22no—
21C22×Dic122—24no—
22C22×Dic122—24no—
23C22×Dic122C814yescomplemented
24C22×Dic122C2×C412yes—
25C23×Dic61—21no—
26C4×Dic122—216no—
27#14519742—24no—
28#14519742—24no—
29#14519742—24no—
30#14519742D418yes—
31#14519736—24no—
32#14519733—216no—
33C2×C4⋊Dic61D412yes—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×C22⋊Dic61D412yes—
37C2×C4×Dic61—22no—
38C2×C4×Dic61—22no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41C23×C4×C61C2×C411yescharacteristic
42#117×C61—24no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C22⋊C4×C61—21no—
45C2×C42×C61—21no—
46C24×C61C22⋊C411yescharacteristic
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C2×C812yes—
52C22×C4×C61M1612yes—
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—24no—
55C22×Dic61—24no—
56C22×Dic61—24no—
57C22×Dic61—22no—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C2×D412yes—
60C2×Dic122—24no—
61C2×Dic122—216no—
62C2×Dic122—24no—
63C2×Dic122—24no—
64C2×Dic122—22no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—216no—
68C2×Dic122C22⋊C414yes—
69C2×Dic122C2×C814yes—
70C2×Dic122M1614yes—
71C2×#92420—44no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61C22⋊C414yes—
74C22⋊C4×C61—24no—
75C42×C61—24no—
76C22⋊Dic61—24no—
77C4⋊Dic61—24no—
78#11758196—28no—
79#11758196—28no—
80C4×Dic61—28no—
81C4×Dic61—22no—
82C4×Dic61—28no—
83C4×Dic61C2×D414yes—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—42no—
87C23×C61C22⋊C812yes—
88C23×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—24no—
92C2×C4×C61—24no—
93C2×C4×C61—24no—
94C2×C4×C61—44no—
95C2×C4×C61C22⋊C812yes—
96C2×C4×C61C2×C22⋊C412yes—
97C2×C4×C61C22×C811yescharacteristic
98C2×C4×C61C2×M1612yes—
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—216no—
101C2×Dic61—24no—
102C2×Dic61—24no—
103C2×Dic61—24no—
104C2×Dic61—22no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61#12014yes—
108Dic122—216no—
109Dic122—24no—
110Dic122—24no—
111Dic122—24no—
112Dic122C22⋊C818yes—
113#92420—84no—
114#8323—611nomaximal, Sylow
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61#37911yescharacteristic
121C22×C61C2×C22⋊C811yescharacteristic
122C22×C61#40711yescharacteristic
123C4×C61—22no—
124C4×C61—44no—
125C4×C61C2×C22⋊C812yes—
126C4×C61#40712yes—
127Dic61—24no—
128Dic61—28no—
129Dic61—42no—
130C2×#519—611no—
131#1479—614no—
132#1458—612no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61—42no—
136C2×C61#177911yescharacteristic
137C2×C61#179612yes—
138C23×Q8—611no—
139#519—1228no—
140C2×C4×Q8—612no—
141C2×C4×Q8—612no—
142C2×C4×Q8—1222no—
143C2×#117—611no—
144C2×#117—1222no—
145C2×#117#692311yescharacteristic
146#431—614no—
147Q8⋊C8—1228no—
148#324—1222no—
149#323—1222no—
150C61#832311yescharacteristic, complemented, Sylow
151C22×Q8—614no—
152C22×Q8—612no—
153C22×Q8—1224no—
154C22×Q8—1224no—
155C22×Q8—1222no—
156C22×Q8—1221no—
157C23×C4—1221no—
158C23×C4C2×#692311yescharacteristic
159C4×Q8—618no—
160C4×Q8—12216no—
161C4×Q8—1224no—
162C4×Q8—1224no—
163C4×Q8—1224no—
164#117—24no—
165#117—1224no—
166#117—12216no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4C2×#692312yes—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—612no—
173C2×C42—21no—
174C2×C42—611no—
175C2×C42—611no—
176C2×C42—1222no—
177C2×C42—1222no—
178C4⋊C8—1224no—
179C22⋊C8—1224no—
180C4×C8—1224no—
181C24C22⋊#692311yescharacteristic
182C2×Q8—614no—
183C2×Q8—614no—
184C2×Q8—614no—
185C2×Q8—12216no—
186C2×Q8—1224no—
187C2×Q8—1224no—
188C2×Q8—12216no—
189C2×Q8—1224no—
190C2×Q8—1222no—
191C2×Q8—1222no—
192C2×Q8—1222no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—612no—
197C22×C4—612no—
198C22×C4—1224no—
199C22×C4—1224no—
200C22×C4—1224no—
201C22×C4—1222no—
202C22×C4D61⋊C812yes—
203C22×C4#1175821312yes—
204C22×C4C22⋊#692311yescharacteristic
205C22×C4C22×#692311yescharacteristic
206C2×C8—2444no—
207C4⋊C4—22no—
208C4⋊C4—1224no—
209C4⋊C4—1228no—
210C4⋊C4—1228no—
211C4⋊C4C22⋊#692314yes—
212C22⋊C4—24no—
213C22⋊C4—1224no—
214C42—24no—
215C42—614no—
216C42—1228no—
217C42—1228no—
218C42—1222no—
219C23—21no—
220C23—21no—
221C23—42no—
222C23#1451983412yes—
223C23C2×C22⋊#692311yescharacteristic
224Q8—618no—
225Q8—12216no—
226Q8—1224no—
227Q8—1224no—
228Q8—1224no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—24no—
232C2×C4—24no—
233C2×C4—24no—
234C2×C4—44no—
235C2×C4—614no—
236C2×C4—12216no—
237C2×C4—1224no—
238C2×C4—1224no—
239C2×C4—1224no—
240C2×C4—1222no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4#1451983412yes—
244C2×C4C2×C22⋊#692312yes—
245C2×C4C2×D61⋊C811yescharacteristic
246C2×C4D61⋊M1612yes—
247C2×C4C2×#1175821311yescharacteristic
248C8—4884no—
249C22—22no—
250C22—22no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22#1684070311yescharacteristic
255C22C2×#1451983411yescharacteristic
256C22#1684073411yescharacteristic
257C4—22no—
258C4—44no—
259C4—1228no—
260C4—1224no—
261C4—2442no—
262C4D61⋊(C22⋊C8)12yes—
263C4#1684073312yes—
264C2—21no—
265C2—21no—
266C2—42no—
267C2#2146164211yescharacteristic
268C2#2146167212yes—
subgroupG/H
centerC22#16840703
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61#379
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461123C2semidirect
23. C22×Dic122C8semidirect
150. C61#8323semidirect

Maximal subgroups

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

subgroupindex
#214611232
#214610502
C2×#168402392
#832361