Finite Group Databasebeta

← #30604325

Subgroups — #30604325

Order 15616.

394 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461081C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460749C214yesmaximal
4#21450808C211yesmaximal, characteristic
5#16840783—21no—
6#16840779—21no—
7#16840608—21no—
8#16840608—21no—
9#16840607C2212yes—
10#16840607C2212yes—
11C2×#14519775C412yes—
12C2×C4×Dic122C2211yescharacteristic
13#16839693—21no—
14#16839693—21no—
15#16839669C2212yes—
16#16839658—21no—
17#16839658—21no—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20#14519844—41no—
21C4⋊#92420—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24#14519832—41no—
25C4×#92420—41no—
26C22×Dic122C2×C411yescharacteristic
27#14519775—44no—
28C4×Dic122—41no—
29C4×Dic122—41no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2311yescharacteristic
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196D411yescharacteristic
35C2×#11758196D411yescharacteristic
36C2×C4×Dic61C2×C412yes—
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39#14519684—21no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61C2×C412yes—
43C4⋊Q8×C61—41no—
44C4⋊Q8×C61—41no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C42×C61C2×C411yescharacteristic
48C2×Q8×C61—24no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C22×C4×C61—22no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—41no—
63C2×#92420—42no—
64C2×#92420—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C42×C61—21no—
69C42×C61—21no—
70C4⋊Dic61—24no—
71C4⋊Dic61—41no—
72#11758196—41no—
73#11758196—41no—
74#11758196—44no—
75#11758196—44no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—42no—
81C23×C61C2×C22⋊C411yescharacteristic
82Q8×C61—84no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61#9911yescharacteristic
92C2×C4×C61#9911yescharacteristic
93C2×C4×C61#13112yes—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—24no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61#10012yes—
107Dic122—44no—
108#92420—82no—
109#92420—82no—
110#11568—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—21no—
113C22×C61#40811yescharacteristic
114C22×C61C2×#9911yescharacteristic
115C22×C61C2×#10011yescharacteristic
116C4×C61—21no—
117C4×C61—22no—
118C4×C61—41no—
119C4×C61—82no—
120C4×C61#35612yes—
121Dic61—22no—
122Dic61—44no—
123Dic61—41no—
124Dic61—41no—
125Dic61—41no—
126#2546—611no—
127#1467—611no—
128#1461—611no—
129#1319—614no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61#147111yescharacteristic
133C2×C61#212911yescharacteristic
134C2×C61C2×#35611yescharacteristic
135C2×C4⋊Q8—612no—
136C2×C4⋊Q8#692311yescharacteristic
137C2×C4×Q8—611no—
138#432—1221no—
139#431—1221no—
140#398—1221no—
141#398—1221no—
142#391—612no—
143#389—1221no—
144#389—1221no—
145C4×C4⋊C4—611no—
146#324—612no—
147#324—612no—
148#324—1221no—
149#324—1221no—
150C61#1156811yescharacteristic, complemented, Sylow
151C22×Q8—611no—
152C22×Q8C2×#692312yes—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4⋊Q8—2444no—
156C4×Q8—2441no—
157C4×Q8—2441no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4—1222no—
166C2×C42—611no—
167C2×C42—611no—
168C2×C42—612no—
169C2×C42C2×#692311yescharacteristic
170C4⋊C8—2441no—
171C4⋊C8—2441no—
172C22⋊C8—1222no—
173C22⋊C8—1222no—
174#97—2441no—
175C4×C8—2441no—
176#95—1222no—
177#95—1222no—
178#95—1221no—
179C2×Q8—24no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—1222no—
183C2×Q8—1222no—
184C2×Q8—2441no—
185C22×C4—22no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1222no—
191C22×C4C22⋊#692311yescharacteristic
192C22×C4C22⋊#692311yescharacteristic
193C22×C4C22×#692311yescharacteristic
194C2×C8—2442no—
195C2×C8—2442no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—1224no—
200C4⋊C4—2441no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C4⋊C4—2444no—
204C4⋊C4—2444no—
205C42—21no—
206C42—21no—
207C42—1221no—
208C42—1221no—
209C42—1221no—
210C42—1221no—
211C42—2442no—
212C23C2×C22⋊#692311yescharacteristic
213Q8—84no—
214Q8—2444no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—612no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1224no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4#1451983511yescharacteristic
237C2×C4#1451983511yescharacteristic
238C2×C4#1451986412yes—
239C8—4882no—
240C8—4882no—
241C22—21no—
242C22—21no—
243C22#1684073611yescharacteristic
244C22C2×#1451983511yescharacteristic
245C22D61⋊#10011yescharacteristic
246C4—21no—
247C4—22no—
248C4—41no—
249C4—82no—
250C4—1222no—
251C4—2444no—
252C4—2441no—
253C4—2441no—
254C4—2441no—
255C4#1684067212yes—
256C2—21no—
257C2—21no—
258C2#2146109411yescharacteristic
259C2#2146210111yescharacteristic
260C2C2×#1684067211yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11568
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
150. C61#11568semidirect

Maximal subgroups

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

subgroupindex
#214610812
#214610612
#214607492
#214508082
#1156861