Finite Group Databasebeta

← #29589406

Subgroups — #29589406

Order 15616.

510 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 87 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#21444153C211yesmaximal, characteristic
3#21443752C214yesmaximal, complemented
4C61×#1464C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic
6C2×#14519736C411yescharacteristic
7#16839819—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×#432—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×Dic122—21no—
21C22×Dic122—24no—
22C22×Dic122—42no—
23C22×Dic122—41no—
24C22×Dic122—41no—
25C22×Dic122C2×C412yes—
26C23×Dic61—21no—
27#14519736—42no—
28C2×C4⋊Dic61—21no—
29C2×C22⋊Dic61—21no—
30C2×C4×Dic61C2×C412yes—
31C4⋊#92418—41no—
32C22⋊#92418—22no—
33#14519688—41no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684—22no—
38C23×C4×C61C2×C411yescharacteristic
39#117×C61—41no—
40#117×C61—41no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C22⋊C4×C61D411yescharacteristic
44C2×C22⋊C4×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C4⋊C8×C61—41no—
48C22⋊C8×C61—22no—
49#97×C61—41no—
50C24×C61C22⋊C411yescharacteristic
51C22×C4×C61—22no—
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×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—24no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—42no—
65C22×Dic61—42no—
66C2×Dic122—24no—
67C2×Dic122—22no—
68C2×Dic122—42no—
69C2×Dic122—48no—
70C2×Dic122—48no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—42no—
74C2×Dic122—42no—
75C2×Dic122M1614yes—
76C2×C8×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—42no—
86C4⋊Dic61—42no—
87C4×Dic61—42no—
88C2×#92418—42no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61#10012yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—24no—
96C2×C4×C61—24no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61#9911yescharacteristic
111C2×C4×C61C2×M1612yes—
112C2×Dic61—24no—
113C2×Dic61—48no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119Dic122—44no—
120Dic122—44no—
121Dic122—44no—
122Dic122—44no—
123C8×C61—82no—
124#92418—82no—
125#11510—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—22no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61#40711yescharacteristic
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10011yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—22no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—41no—
143Dic61—44no—
144Dic61—82no—
145#2310—611no—
146#1464—611no—
147#1464D6111yescharacteristic
148#1319—614no—
149C2×C61—21no—
150C2×C61—21no—
151C2×C61—42no—
152C2×C61#146211yescharacteristic
153C2×C61#212911yescharacteristic
154C2×C61#213511yescharacteristic
155C23×Q8—611no—
156C2×#117—611no—
157C2×#117C2×D6111yescharacteristic
158#432—21no—
159#432—1221no—
160#391—612no—
161#391—612no—
162#391—1221no—
163#391—1221no—
164#381—1221no—
165#381—1221no—
166#324—612no—
167#324C2×D6112yes—
168#323—21no—
169#323—1221no—
170C61#1151011yescharacteristic, complemented, Sylow
171C22×Q8—612no—
172C22×Q8—1224no—
173C22×Q8—1221no—
174C22×Q8—2441no—
175C22×Q8—2441no—
176C22×Q8—2442no—
177C23×C4—1221no—
178C23×C4C4×D6111yescharacteristic
179#117—41no—
180#117—41no—
181#117—2442no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4C4×D6111yescharacteristic
184C2×C4⋊C4C22×D6111yescharacteristic
185C2×C22⋊C4—1221no—
186C2×C22⋊C4D24411yescharacteristic
187C2×C22⋊C4C22⋊D6111yescharacteristic
188C2×C42—612no—
189C2×C42D24411yescharacteristic
190C2×C42C22⋊D6111yescharacteristic
191C4⋊C8—41no—
192C4⋊C8—2441no—
193C22⋊C8—22no—
194C22⋊C8—1222no—
195#97—41no—
196#97—2441no—
197#95—1222no—
198#95—1222no—
199#95—1222no—
200#95—1222no—
201C24#1175819811yescharacteristic
202C2×Q8—614no—
203C2×Q8—1224no—
204C2×Q8—1222no—
205C2×Q8—2448no—
206C2×Q8—2448no—
207C2×Q8—2442no—
208C2×Q8—2442no—
209C2×Q8—2442no—
210C2×Q8—2441no—
211C2×Q8—2441no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—1224no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—2442no—
220C22×C4—2442no—
221C22×C4#1175819811yescharacteristic
222C22×C4#1175819811yescharacteristic
223C22×C4#1175819811yescharacteristic
224C22×C4C2×C4×D6111yescharacteristic
225C22×C4C2×D24411yescharacteristic
226C22×C4C2×C22⋊D6111yescharacteristic
227C2×C8—42no—
228C2×C8—2442no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—2442no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—2442no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—2442no—
240C23—21no—
241C23—21no—
242C23—41no—
243C23—41no—
244C23#1451969312yes—
245C23C2×#1175819811yescharacteristic
246Q8—2444no—
247Q8—2444no—
248Q8—2444no—
249Q8—2444no—
250C2×C4—24no—
251C2×C4—24no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—1224no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2448no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4#1451969111yescharacteristic
272C2×C4#1451969111yescharacteristic
273C2×C4M16×D6112yes—
274C8—82no—
275C8—4882no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22#1683972511yescharacteristic
284C22C2×#1451969111yescharacteristic
285C22C2×#1451969311yescharacteristic
286C4—21no—
287C4—21no—
288C4—22no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—4882no—
294C4—2444no—
295C2—21no—
296C2—21no—
297C2—42no—
298C2#2144414511yescharacteristic
299C2#2144749311yescharacteristic
300C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11510
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #21443752C2semidirect
170. C61#11510semidirect

Maximal subgroups

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

subgroupindex
#214484032
#214441532
#214437522
C61×#14642
#1151061