Finite Group Databasebeta

← #30605416

Subgroups — #30605416

Order 15616.

408 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461685C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460803C214yesmaximal
4#21450808C211yesmaximal, characteristic
5#16840779—21no—
6#16840765—21no—
7C2×#14519838—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840607—21no—
11C2×#14519775—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839693C412yes—
14#16839693C2212yes—
15#16839669—21no—
16#16839658—21no—
17#16839658—21no—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758217—22no—
21#14519844—41no—
22#14519844—41no—
23C4⋊#92420—41no—
24#14519838—42no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27C22×Dic122D411yescharacteristic
28#14519775—42no—
29#14519775—42no—
30C4×Dic122—41no—
31C4×Dic122—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196C2311yescharacteristic
38C2×C4×Dic61—21no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519684—22no—
42#14519684—22no—
43#14519684C2×C412yes—
44C22×Q8×C61—21no—
45C4⋊Q8×C61—41no—
46C4⋊Q8×C61—41no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C412yes—
49C2×C42×C61C2×C411yescharacteristic
50C2×Q8×C61—42no—
51C2×Q8×C61—42no—
52C2×Q8×C61—42no—
53C22×C4×C61—22no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—22no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×Dic122D812yes—
65C2×Dic122SD1612yes—
66#11758217—42no—
67#11758217—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C42×C61—21no—
74C42×C61—21no—
75C4⋊Dic61—24no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—44no—
80#11758196—42no—
81#11758196—42no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61—42no—
87C23×C61C2×C22⋊C411yescharacteristic
88Q8×C61—84no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#10212yes—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—24no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61#10212yes—
112C2×Dic61C2×D811yescharacteristic
113C2×Dic61C2×SD1611yescharacteristic
114Dic122—42no—
115Dic122—42no—
116#92420—82no—
117#92420—82no—
118#11883—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61C2×#9911yescharacteristic
122C22×C61C2×#10211yescharacteristic
123C22×C61#42111yescharacteristic
124C4×C61—21no—
125C4×C61—22no—
126C4×C61—41no—
127C4×C61—82no—
128C4×C61#35612yes—
129Dic61—21no—
130Dic61—22no—
131Dic61—21no—
132Dic61—44no—
133Dic61—41no—
134Dic61—41no—
135#2546—611no—
136#1801—611no—
137#1461—611no—
138#1346—614no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#151911yescharacteristic
142C2×C61#212311yescharacteristic
143C2×C61C2×#35611yescharacteristic
144C2×C4⋊Q8—1221no—
145C2×C4⋊Q8#692311yescharacteristic
146C2×C4×Q8—611no—
147#431—1221no—
148#423—1221no—
149C2×#101—1221no—
150#398—612no—
151#398—612no—
152#391—1221no—
153#389—1221no—
154#389—1221no—
155C4×C4⋊C4—611no—
156#343—612no—
157#324—612no—
158#324—1221no—
159C61#1188311yescharacteristic, complemented, Sylow
160C22×Q8—21no—
161C22×Q8—611no—
162C2×M16—1222no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4⋊Q8—2442no—
166C4⋊Q8—2442no—
167C4×Q8—2441no—
168C4×Q8—2441no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—1221no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—1222no—
176C2×C4⋊C4C2×#692312yes—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—1221no—
180C2×C42C2×#692311yescharacteristic
181C4⋊C8—2441no—
182C4⋊C8—2441no—
183C4⋊C8—2441no—
184#101—2442no—
185C22⋊C8—1222no—
186C4×C8—2441no—
187#95—612no—
188#95—1222no—
189#95—1222no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—612no—
194C2×Q8—612no—
195C2×Q8—2441no—
196C2×Q8—2441no—
197C22×C4—22no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1222no—
203C22×C4C22⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205C22×C4C22×#692311yescharacteristic
206M16—2442no—
207M16—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—1224no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2444no—
218C4⋊C4—2442no—
219C4⋊C4—2442no—
220C42—21no—
221C42—21no—
222C42—1221no—
223C42—1221no—
224C42—1221no—
225C42—1221no—
226C42—2442no—
227C23C2×C22⋊#692311yescharacteristic
228Q8—84no—
229Q8—2442no—
230Q8—2442no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—612no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1224no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—2442no—
250C2×C4—2442no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451983511yescharacteristic
254C2×C4#1451983511yescharacteristic
255C2×C4#1451983912yes—
256C8—4882no—
257C8—4882no—
258C22—21no—
259C22—21no—
260C22C2×#1451983511yescharacteristic
261C22C2×#1451983911yescharacteristic
262C22#1684076011yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—82no—
267C4—1221no—
268C4—1222no—
269C4—1221no—
270C4—2444no—
271C4—2441no—
272C4—2441no—
273C4#1684067212yes—
274C2—21no—
275C2—21no—
276C2#2146125511yescharacteristic
277C2#2146208111yescharacteristic
278C2C2×#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×#11758196C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11883
LCSG ▷ C22×C4×C61 ▷ C23×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
159. C61#11883semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214608032
#214508082
#1188361