Finite Group Databasebeta

← #30595361

Subgroups — #30595361

Order 15616.

444 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461534C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519768C211yesmaximal, characteristic
6C2×C4×#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519768C411yescharacteristic
13#16839661C2211yescharacteristic
14#16839658C2211yescharacteristic
15#16839649—21no—
16#16839645—21no—
17#16839627C411yescharacteristic
18C4×#11758196—21no—
19C4×C4⋊Dic61—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4×#92420—24no—
26C4×#92420—24no—
27#14519768—22no—
28#14519768C814yescomplemented
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×#92420—24no—
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61C2×C812yes—
72C42×C61—22no—
73C42×C61—42no—
74C4⋊Dic61—21no—
75C4⋊Dic61—24no—
76C4⋊Dic61—42no—
77C4⋊Dic61—41no—
78C4⋊Dic61C2×C812yes—
79#11758196—24no—
80#11758196—42no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—42no—
87C4×Dic61C2×C812yes—
88C4×Dic61M1612yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#10112yes—
102C2×C4×C61#10412yes—
103C2×C4×C61#10412yes—
104C2×C4×C61C22×C811yescharacteristic
105C2×C4×C61C2×M1611yescharacteristic
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61C22⋊C812yes—
121C2×Dic61C22⋊C812yes—
122C2×Dic61#13512yes—
123C2×Dic61#13512yes—
124#92420—44no—
125#92420—44no—
126#7568—611nomaximal, Sylow
127C22×C61C2×C22⋊C811yescharacteristic
128C22×C61#41011yescharacteristic
129C22×C61C2×#10111yescharacteristic
130C22×C61#41611yescharacteristic
131C22×C61#41611yescharacteristic
132C22×C61C2×#10411yescharacteristic
133C22×C61C2×#10411yescharacteristic
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61—81no—
139C4×C61#33014yes—
140Dic61—22no—
141Dic61—22no—
142Dic61—22no—
143Dic61—22no—
144Dic61—42no—
145Dic61—81no—
146C4×#125—611no—
147#1744—611no—
148#1744—611no—
149#1271—612no—
150#1271—612no—
151C2×C61#146111yescharacteristic
152C2×C61#147611yescharacteristic
153C2×C61#147611yescharacteristic
154C2×C61#150011yescharacteristic
155C2×C61#150011yescharacteristic
156C2×C61C2×#33011yescharacteristic
157C2×C61#154411yescharacteristic
158C2×#125—611no—
159C2×C4×C8—1221no—
160C2×C4×C8—1221no—
161#389—611no—
162#389—611no—
163#387—1221no—
164#387—1221no—
165#382—611no—
166C4×C4⋊C4—611no—
167C4×C4⋊C4—1221no—
168C4×C4⋊C4—1221no—
169C4×C4⋊C4#692311yescharacteristic
170C43—611no—
171#336—612no—
172#336—612no—
173#336—1221no—
174#336—1221no—
175C61#756811yescharacteristic, complemented, Sylow
176C22×C8—1222no—
177C22×C8—1222no—
178#125—614no—
179#125—1222no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4C2×#692311yescharacteristic
187C2×C4⋊C4C2×#692311yescharacteristic
188C2×C42—21no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—1221no—
196C2×C42C2×#692311yescharacteristic
197C4×C8—1224no—
198C4×C8—1224no—
199#95—21no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4C22⋊#692311yescharacteristic
214C22×C4C22⋊#692311yescharacteristic
215C22×C4C22×#692311yescharacteristic
216C2×C8—1224no—
217C2×C8—1224no—
218C2×C8—2442no—
219C2×C8—2442no—
220C2×C8—2442no—
221C2×C8—2442no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—612no—
225C4⋊C4—1224no—
226C4⋊C4—1224no—
227C4⋊C4—1221no—
228C4⋊C4—2441no—
229C4⋊C4—2442no—
230C4⋊C4—2442no—
231C4⋊C4D61⋊C812yes—
232C42—22no—
233C42—42no—
234C42—612no—
235C42—612no—
236C42—1222no—
237C42—1222no—
238C42—1222no—
239C42—1222no—
240C42—2441no—
241C42—2442no—
242C23C2×C22⋊#692311yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—612no—
255C2×C4—612no—
256C2×C4—612no—
257C2×C4—612no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4#1451983812yes—
273C2×C4#1451984112yes—
274C2×C4#1451984212yes—
275C2×C4C2×D61⋊C811yescharacteristic
276C2×C4D61⋊M1611yescharacteristic
277C8—2444no—
278C8—2444no—
279C22D61⋊(C22⋊C8)11yescharacteristic
280C22#1684074111yescharacteristic
281C22C2×#1451983811yescharacteristic
282C22#1684075211yescharacteristic
283C22#1684075211yescharacteristic
284C22C2×#1451984111yescharacteristic
285C22C2×#1451984211yescharacteristic
286C4—21no—
287C4—21no—
288C4—41no—
289C4—42no—
290C4—81no—
291C4—1222no—
292C4—1222no—
293C4—1222no—
294C4—1222no—
295C4—4881no—
296C4—2442no—
297C4#1684061914yes—
298C2#2146106111yescharacteristic
299C2#2146111111yescharacteristic
300C2#2146111311yescharacteristic
301C2#2146119011yescharacteristic
302C2#2146119211yescharacteristic
303C2C2×#1684061911yescharacteristic
304C2#2146132411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7568
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
28. #14519768C8semidirect
175. C61#7568semidirect

Maximal subgroups

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

subgroupindex
#214615342
#214606382
#214606372
C4×#145197682
#756861