Finite Group Databasebeta

← #30597793

Subgroups — #30597793

Order 15616.

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

normal subgroups only

This group has 488 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#21461536C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3C2×#16840619C212yesmaximal
4#21460695C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×#14519832—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840619C418yescomplemented
13C2×#14519768C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839647—21no—
16#16839643—21no—
17#16839627C2211yescharacteristic
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519832—24no—
27#14519832—22no—
28#14519832—22no—
29#14519832C2×C414yes—
30#14519832C2×C414yes—
31C4×#92420—24no—
32#14519768—22no—
33#14519768C2×C414yes—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
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×#92420—24no—
69C2×#92420—24no—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61C4212yes—
78C42×C61—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—24no—
81C4⋊Dic61—41no—
82C4⋊Dic61C4212yes—
83#11758196—24no—
84#11758196—42no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—42no—
91C4×Dic61—42no—
92C4×Dic61C22×C412yes—
93C4×Dic61#4112yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#10412yes—
109C2×C4×C61C2×C4211yescharacteristic
110C2×C4×C61#11711yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#10112yes—
126C2×Dic61#10412yes—
127C2×Dic61C4×D412yes—
128C2×Dic61C4×D412yes—
129#92420—28no—
130#92420—44no—
131#8227—611nomaximal, Sylow
132C22×C61C4×C22⋊C411yescharacteristic
133C22×C61C2×#10111yescharacteristic
134C22×C61#41311yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61C2×#10411yescharacteristic
137C22×C61#42111yescharacteristic
138C22×C61#42111yescharacteristic
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—42no—
143C4×C61—41no—
144C4×C61—81no—
145Dic61—22no—
146Dic61—22no—
147Dic61—22no—
148Dic61—22no—
149Dic61—42no—
150Dic61—81no—
151C4×#125—611no—
152#1745—611no—
153C4×#97—611no—
154C2×#330—612no—
155#1295—612no—
156C2×C61#152811yescharacteristic
157C2×C61#152911yescharacteristic
158C2×C61#153111yescharacteristic
159C2×C61#153211yescharacteristic
160C2×C61C4×#10111yescharacteristic
161C2×C61C4×#10411yescharacteristic
162C2×C61#175911yescharacteristic
163C2×#125—611no—
164C2×#97—612no—
165C2×#97—612no—
166C2×#97—1221no—
167C2×C4×C8—1221no—
168#389—611no—
169#389#692311yescharacteristic
170#387—1221no—
171#387—1221no—
172#382—611no—
173C4×C4⋊C4—611no—
174C4×C4⋊C4—611no—
175C4×C4⋊C4—1221no—
176C4×C4⋊C4—1221no—
177C43—611no—
178#336—1221no—
179#336—1221no—
180#330—618no—
181C61#822711yescharacteristic, complemented, Sylow
182C22×C8—1222no—
183C22×C8—1222no—
184#125—614no—
185#125—1222no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C4⋊C4C2×#692311yescharacteristic
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—1221no—
201C2×C42—1221no—
202C2×C42C2×#692311yescharacteristic
203#97—614no—
204#97—614no—
205#97—1222no—
206#97—1222no—
207#97—1224no—
208C4×C8—1224no—
209#95—21no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4C22⋊#692311yescharacteristic
224C22×C4C22⋊#692311yescharacteristic
225C22×C4C22×#692311yescharacteristic
226C2×C8—1224no—
227C2×C8—1224no—
228C2×C8—1224no—
229C2×C8—1224no—
230C2×C8—2442no—
231C2×C8—2442no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—612no—
236C4⋊C4—1224no—
237C4⋊C4—1224no—
238C4⋊C4—1221no—
239C4⋊C4—2441no—
240C4⋊C4—2442no—
241C4⋊C4C4×#692312yes—
242C42—41no—
243C42—612no—
244C42—612no—
245C42—1222no—
246C42—1222no—
247C42—1222no—
248C42—2441no—
249C42—2441no—
250C42—2442no—
251C42—2442no—
252C23C2×C22⋊#692311yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—612no—
267C2×C4—612no—
268C2×C4—612no—
269C2×C4—612no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1222no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4#1451984212yes—
285C2×C4C2×C4×#692311yescharacteristic
286C2×C4#1451985611yescharacteristic
287C8—1228no—
288C8—2444no—
289C22C4×C22⋊#692311yescharacteristic
290C22D61⋊#10111yescharacteristic
291C22#1684074911yescharacteristic
292C22D61⋊#10411yescharacteristic
293C22C2×#1451984211yescharacteristic
294C22#1684075911yescharacteristic
295C22#1684076011yescharacteristic
296C4—22no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—42no—
301C4—81no—
302C4—1222no—
303C4—1222no—
304C4—1222no—
305C4—1222no—
306C4—4881no—
307C4—2442no—
308C2#2146128211yescharacteristic
309C2#2146128511yescharacteristic
310C2#2146129311yescharacteristic
311C2#2146129711yescharacteristic
312C2#2146157211yescharacteristic
313C2C4×#1451984211yescharacteristic
314C2#2146158211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8227
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. #16840619C4semidirect
181. C61#8227semidirect

Maximal subgroups

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

subgroupindex
#214615362
C4×#145198322
C2×#168406192
#214606952
#214483782
#822761