Finite Group Databasebeta

← #30605244

Subgroups — #30605244

Order 15616.

340 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461081C211yesmaximal, characteristic
3#21460818C212yesmaximal
4#21460803C212yesmaximal
5#21451696C211yesmaximal, characteristic
6#16840783—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839701—21no—
14#16839700C411yescharacteristic
15#16839700C2211yescharacteristic
16#16839693C411yescharacteristic
17#16839693C2211yescharacteristic
18#16839682—21no—
19#16839643—21no—
20#16839643—21no—
21#16839630C411yescharacteristic
22C2×#125×C61C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29#14519832—41no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—41no—
32C4×Dic122—41no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196C2311yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50#125×C61—41no—
51#125×C61—41no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72#11758217—42no—
73#11758217—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C42×C61—21no—
82C42×C61—21no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C23×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#9911yescharacteristic
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61AGL(1,ℤ/8)11yescharacteristic
123C2×Dic61#13711yescharacteristic
124Dic122—42no—
125Dic122—42no—
126#92420—82no—
127#92420—82no—
128#11835—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61C2×#9911yescharacteristic
132C22×C61#41711yescharacteristic
133C22×C61#42111yescharacteristic
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—81no—
139C4×C61—81no—
140Dic61—21no—
141Dic61—21no—
142Dic61—41no—
143Dic61—41no—
144Dic61—41no—
145Dic61—81no—
146Dic61—81no—
147#2634—611no—
148#1801—611no—
149#1467—611no—
150#1353—612no—
151#1346—612no—
152C2×C61—21no—
153C2×C61—21no—
154C2×C61#151311yescharacteristic
155C2×C61#212311yescharacteristic
156C2×C61#213311yescharacteristic
157C2×#125#692311yescharacteristic
158C2×C4×Q8—611no—
159#432—1221no—
160#423—1221no—
161C2×#101—1221no—
162#400—611no—
163#400—611no—
164#400—1221no—
165#398—611no—
166#398—611no—
167#395—1221no—
168#387—1221no—
169#387—1221no—
170#383—611no—
171#343—612no—
172#324—612no—
173#324—1221no—
174C61#1183511yescharacteristic, complemented, Sylow
175C22×Q8—611no—
176C2×M16—1222no—
177#125—41no—
178#125—41no—
179C4×Q8—2441no—
180C4×Q8—2441no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C4⋊C4C2×#692311yescharacteristic
190C2×C42—611no—
191C2×C42—611no—
192C2×C42C2×#692311yescharacteristic
193C4⋊C8—2441no—
194C4⋊C8—2441no—
195C4⋊C8—2441no—
196#101—2442no—
197C22⋊C8—1222no—
198#97—2441no—
199#95—611no—
200#95—611no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209C2×Q8—1221no—
210C2×Q8—1221no—
211C2×Q8—2441no—
212C2×Q8—2441no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22⋊#692311yescharacteristic
223C22×C4C22×#692311yescharacteristic
224M16—2442no—
225M16—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2442no—
239C42—21no—
240C42—21no—
241C42—1221no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C23C2×C22⋊#692311yescharacteristic
246Q8—2442no—
247Q8—2442no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4#1451983511yescharacteristic
277C2×C4#1451983511yescharacteristic
278C8—4882no—
279C8—4882no—
280C22—21no—
281C22—21no—
282C22C2×#1451983511yescharacteristic
283C22#1684075311yescharacteristic
284C22#1684075911yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—41no—
289C4—81no—
290C4—81no—
291C4—1221no—
292C4—1221no—
293C4—4881no—
294C4—4881no—
295C4—2441no—
296C4—2441no—
297C4—2441no—
298C2—21no—
299C2—21no—
300C2#2146123411yescharacteristic
301C2#2146208111yescharacteristic
302C2#2146211411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×#125#6923
hypocenterC61#11835
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
174. C61#11835semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610812
#214608182
#214608032
#214516962
#1183561