Finite Group Databasebeta

← #30595490

Subgroups — #30595490

Order 15616.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461747C212yesmaximal
2#21460640C212yesmaximal
3#21460639C212yesmaximal
4C4×#14519775C211yesmaximal, characteristic
5#16840628—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×#14519775C411yescharacteristic
9C2×C4×Dic122C411yescharacteristic
10#16839669C2211yescharacteristic
11#16839667C2211yescharacteristic
12#16839657—22no—
13#16839631C411yescharacteristic
14C4×#11758196—22no—
15C42×Dic61C2211yescharacteristic
16C2×C4×Q8×C61C411yescharacteristic
17C22×#92420—24no—
18C22×Dic122C2×C411yescharacteristic
19#14519775—22no—
20#14519775C814yescomplemented
21C4×Dic122—42no—
22C2×C4⋊Dic61C2×C411yescharacteristic
23C2×#11758196—22no—
24C2×#11758196—21no—
25C2×#11758196—22no—
26C2×C4×Dic61—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D412yes—
29C2×C4×Dic61D412yes—
30C2×C4×Dic61C2311yescharacteristic
31#14519684—22no—
32#14519684—22no—
33C22×Q8×C61C2×C411yescharacteristic
34C4×Q8×C61—42no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C2×C42×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C2×Q8×C61—21no—
40C2×Q8×C61—41no—
41C2×Q8×C61—41no—
42C2×Q8×C61C2×C812yes—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61C22⋊C412yes—
51C22×Dic61C2×D412yes—
52C2×Dic122—21no—
53C2×Dic122—41no—
54C2×Dic122—41no—
55C2×Dic122C2×C812yes—
56C2×#92420—44no—
57C2×#92420—44no—
58C2×#92420—44no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—41no—
61C42×C61—22no—
62C42×C61—42no—
63C4⋊Dic61—41no—
64#11758196—28no—
65#11758196—44no—
66#11758196—42no—
67C4×Dic61—24no—
68C4×Dic61—42no—
69C4×Dic61—41no—
70C4×Dic61—42no—
71C4×Dic61C2×C812yes—
72C4×Dic61M1612yes—
73C23×C61C2×C22⋊C411yescharacteristic
74Q8×C61—42no—
75Q8×C61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—42no—
86C2×C4×C61#10012yes—
87C2×C4×C61C22×C811yescharacteristic
88C2×C4×C61C2×M1611yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98C2×Dic61C22⋊C814yes—
99C2×Dic61#13714yes—
100Dic122—42no—
101Dic122—42no—
102#92420—84no—
103#7605—611nomaximal, Sylow
104C22×C61C2×C22⋊C811yescharacteristic
105C22×C61#41011yescharacteristic
106C22×C61C2×#10011yescharacteristic
107C22×C61#41912yes—
108C22×C61#42112yes—
109C4×C61—22no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61—81no—
115Dic61—24no—
116Dic61—24no—
117Dic61—42no—
118Dic61—81no—
119C4×C4⋊Q8—611no—
120#1839—612no—
121#1272—612no—
122#1272—612no—
123C2×C61#146011yescharacteristic
124C2×C61#147912yes—
125C2×C61#151512yes—
126C2×C61#153611yescharacteristic
127C2×C61#155811yescharacteristic
128C2×C4⋊Q8—611no—
129C2×C4×Q8—611no—
130C2×C4×Q8#692311yescharacteristic
131#391—611no—
132#391—611no—
133#389—1222no—
134#384—611no—
135C4×C4⋊C4—1222no—
136C43—611no—
137#336—614no—
138#336—1222no—
139#336—1222no—
140C61#760511yescharacteristic, complemented, Sylow
141C22×Q8—611no—
142C22×Q8C2×#692311yescharacteristic
143C22×C8—1224no—
144C4⋊Q8—614no—
145C4⋊Q8—1222no—
146C4×Q8—42no—
147C4×Q8—2442no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1221no—
153C2×C4⋊C4C2×#692311yescharacteristic
154C2×C42—21no—
155C2×C42—611no—
156C2×C42—612no—
157C2×C42—612no—
158C2×C42—611no—
159C2×C42—1221no—
160C2×C42C2×#692311yescharacteristic
161#95—1222no—
162#95—1222no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—612no—
167C2×Q8—1221no—
168C2×Q8—2441no—
169C2×Q8—2441no—
170C2×Q8D61⋊C812yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22⋊#692311yescharacteristic
178C22×C4C22⋊#692311yescharacteristic
179C22×C4C22×#692311yescharacteristic
180C2×C8—2444no—
181C2×C8—2444no—
182C2×C8—2444no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—1228no—
186C4⋊C4—2441no—
187C4⋊C4—2442no—
188C4⋊C4—2444no—
189C42—22no—
190C42—42no—
191C42—612no—
192C42—612no—
193C42—1224no—
194C42—2441no—
195C42—2442no—
196C42—2442no—
197C23C2×C22⋊#692311yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—2442no—
201Q8—2442no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—614no—
213C2×C4—614no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—2441no—
220C2×C4—2442no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4#1451983712yes—
224C2×C4C2×D61⋊C811yescharacteristic
225C2×C4D61⋊M1611yescharacteristic
226C8—4884no—
227C22D61⋊(C22⋊C8)11yescharacteristic
228C22#1684074111yescharacteristic
229C22C2×#1451983711yescharacteristic
230C22#1684075512yes—
231C22#1684075912yes—
232C4—21no—
233C4—21no—
234C4—22no—
235C4—41no—
236C4—42no—
237C4—81no—
238C4—1224no—
239C4—1224no—
240C4—4881no—
241C4—2442no—
242C2#2146105811yescharacteristic
243C2#2146112212yes—
244C2#2146124112yes—
245C2#2146130711yescharacteristic
246C2#2146135211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7605
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
20. #14519775C8semidirect
140. C61#7605semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606402
#214606392
C4×#145197752
#760561