Finite Group Databasebeta

← #29589128

Subgroups — #29589128

Order 15616.

526 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 115 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#21448403C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic
3#21443752C214yesmaximal, complemented
4C61×#1458C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic
6C2×#14519736C411yescharacteristic
7#16839815—21no—
8#16839668—21no—
9#16839668—21no—
10#16839667C412yes—
11#16839667C2212yes—
12#16839623—21no—
13#16839623—21no—
14#16839488C2212yes—
15#16839486—21no—
16C2×#117×C61C2211yescharacteristic
17C61×#431—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×Dic122—21no—
21C22×Dic122—22no—
22C22×Dic122—41no—
23C22×Dic122—41no—
24C22×Dic122—42no—
25C22×Dic122C814yescomplemented
26C22×Dic122C2×C412yes—
27C23×Dic61—21no—
28#14519736—42no—
29C2×C4⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61C2×C412yes—
32C4⋊#92418—41no—
33C22⋊#92418—22no—
34C4×#92418—41no—
35#14519684—22no—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C23×C4×C61C2×C411yescharacteristic
40#117×C61—41no—
41#117×C61—41no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C22⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C4⋊C8×C61—41no—
49C22⋊C8×C61—22no—
50C4×C8×C61—41no—
51C24×C61C22⋊C411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C2×C812yes—
59C22×C4×C61M1612yes—
60C22×C4×C61C22×C411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—24no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68C2×Dic122—24no—
69C2×Dic122—22no—
70C2×Dic122—44no—
71C2×Dic122—44no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—42no—
75C2×Dic122—42no—
76C2×Dic122—42no—
77C2×Dic122—44no—
78C2×Dic122—44no—
79C2×Dic122C2×C814yes—
80C2×C8×C61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—42no—
90C4⋊Dic61—42no—
91C4×Dic61—42no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61C22⋊C812yes—
98C23×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61C22⋊C812yes—
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#10012yes—
117C2×C4×C61C22×C811yescharacteristic
118C2×C4×C61C2×M1611yescharacteristic
119C2×Dic61—24no—
120C2×Dic61—48no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126Dic122—44no—
127Dic122—44no—
128Dic122—44no—
129Dic122—44no—
130C8×C61—82no—
131#92418—82no—
132#11434—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—22no—
136C22×C61—42no—
137C22×C61—42no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61C2×C22⋊C811yescharacteristic
141C22×C61C2×#9911yescharacteristic
142C22×C61C2×#10011yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61#32312yes—
150C4×C61#32312yes—
151Dic61—44no—
152Dic61—82no—
153#2310—611no—
154#1458—611no—
155#1458D6111yescharacteristic
156#1319—614no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—42no—
160C2×C61C2×#32311yescharacteristic
161C2×C61#212911yescharacteristic
162C2×C61#213511yescharacteristic
163C23×Q8—611no—
164C2×#117—611no—
165C2×#117C2×D6111yescharacteristic
166#431—21no—
167#431—1221no—
168#391—612no—
169#391—612no—
170#391—1221no—
171#391—1221no—
172#381—1221no—
173#381—1221no—
174#324—612no—
175#324C2×D6112yes—
176#323—21no—
177#323—1221no—
178C61#1143411yescharacteristic, complemented, Sylow
179C22×Q8—614no—
180C22×Q8—612no—
181C22×Q8—1222no—
182C22×Q8—1221no—
183C22×Q8—2441no—
184C22×Q8—2441no—
185C22×Q8—2442no—
186C23×C4—1221no—
187C23×C4C4×D6111yescharacteristic
188#117—41no—
189#117—41no—
190#117—2442no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C4×D6111yescharacteristic
193C2×C4⋊C4C22×D6111yescharacteristic
194C2×C22⋊C4—1221no—
195C2×C22⋊C4D24411yescharacteristic
196C2×C22⋊C4C22⋊D6111yescharacteristic
197C2×C42—612no—
198C2×C42D24411yescharacteristic
199C2×C42C22⋊D6111yescharacteristic
200C4⋊C8—41no—
201C4⋊C8—2441no—
202C22⋊C8—22no—
203C22⋊C8—1222no—
204C4×C8—41no—
205C4×C8—2441no—
206#95—1222no—
207#95—1222no—
208#95—1222no—
209#95—1222no—
210C24#1175819811yescharacteristic
211C2×Q8—614no—
212C2×Q8—1224no—
213C2×Q8—1222no—
214C2×Q8—2444no—
215C2×Q8—2444no—
216C2×Q8—2444no—
217C2×Q8—2444no—
218C2×Q8—2442no—
219C2×Q8—2442no—
220C2×Q8—2441no—
221C2×Q8—2441no—
222C2×Q8—2442no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—1224no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—2442no—
230C22×C4—2442no—
231C22×C4C8×D6112yes—
232C22×C4#1175818912yes—
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4#1175819811yescharacteristic
236C22×C4C2×C4×D6111yescharacteristic
237C22×C4C2×D24411yescharacteristic
238C22×C4C2×C22⋊D6111yescharacteristic
239C2×C8—42no—
240C2×C8—2442no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—2442no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—2442no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—2442no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23#1451968912yes—
257C23C2×#1175819811yescharacteristic
258Q8—2444no—
259Q8—2444no—
260Q8—2444no—
261Q8—2444no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—1224no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2448no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4#1451968912yes—
284C2×C4#1451969111yescharacteristic
285C2×C4#1451969111yescharacteristic
286C2×C4#1451969312yes—
287C2×C4C2×C8×D6111yescharacteristic
288C2×C4C2×#1175818911yescharacteristic
289C8—82no—
290C8—4882no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22C2×#1451968911yescharacteristic
299C22C2×#1451969111yescharacteristic
300C22C2×#1451969311yescharacteristic
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—4882no—
308C4—2444no—
309C4#1683948512yes—
310C4#1683948512yes—
311C2—21no—
312C2—21no—
313C2—42no—
314C2C2×#1683948511yescharacteristic
315C2#2144749311yescharacteristic
316C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1458C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1458D61
hypocenterC61#11434
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21443752C2semidirect
25. C22×Dic122C8semidirect
178. C61#11434semidirect

Maximal subgroups

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

subgroupindex
#214484032
#214441332
#214437522
C61×#14582
#1143461