Finite Group Databasebeta

← #29589376

Subgroups — #29589376

Order 15616.

662 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 77 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#21448199C211yesmaximal, characteristic
2#21444150C212yesmaximal, complemented
3#21443749C211yesmaximal, characteristic, complemented
4#21443746C212yesmaximal
5C61×#1317C211yesmaximal, characteristic, complemented
6C23×C4×D61C411yescharacteristic
7C2×#14519733C411yescharacteristic
8C2×#14519733C2211yescharacteristic
9#16839816—22no—
10#16839625C411yescharacteristic
11#16839621—22no—
12#16839617C411yescharacteristic
13#16839617C2211yescharacteristic
14#16839609—22no—
15#16839487—22no—
16#16839486C2212yes—
17C61×#381C2211yescharacteristic
18C61×#323C2212yes—
19C24×D61C2×C411yescharacteristic
20C23×Dic61C2×C411yescharacteristic
21C22×C4×D61—22no—
22C22×C4×D61—22no—
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—42no—
26C22×C4×D61—42no—
27#14519733—42no—
28#14519733—42no—
29C2×#11758196—21no—
30C2×#11758196D412yes—
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×C22⋊Dic61C2×C411yescharacteristic
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61D412yes—
37#14519706—42no—
38C22⋊#92418—22no—
39#14519687—42no—
40#14519684—22no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C411yescharacteristic
43C2×C22⋊C4×C61C2311yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C24×C61C22×C411yescharacteristic
47C23×D61—21no—
48C23×D61—21no—
49C23×D61—44no—
50C23×D61—41no—
51C23×D61—41no—
52C23×D61M1612yes—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61M1612yes—
59C22×C4×C61C2×D412yes—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C412yes—
68C2×C4×D61—24no—
69C2×C4×D61—24no—
70C2×C4×D61—48no—
71C2×C4×D61—48no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×C4×D61—42no—
75C2×C4×D61—42no—
76C2×C8×C61—42no—
77C22⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊Dic61—41no—
80C22⋊Dic61—41no—
81#11758198—44no—
82#11758198—44no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—42no—
88C2×#92418—42no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—42no—
92C23×C61C2×C22⋊C411yescharacteristic
93C23×C61C2×M1611yescharacteristic
94C23×C61C2×M1611yescharacteristic
95C22×D61—24no—
96C22×D61—22no—
97C22×D61—44no—
98C22×D61—44no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—48no—
102C22×D61—44no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—42no—
106C22×D61—44no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×Dic61—24no—
117C2×Dic61—24no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61#9912yes—
127C2×Dic61#10012yes—
128C4×D61—48no—
129C4×D61—48no—
130C8×C61—82no—
131#92418—82no—
132#11501—611nomaximal, Sylow
133C22×C61—22no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—42no—
139C22×C61—42no—
140C22×C61#40711yescharacteristic
141C22×C61C2×#9911yescharacteristic
142C22×C61C2×#10011yescharacteristic
143C2×D61—24no—
144C2×D61—44no—
145C2×D61—42no—
146C2×D61—48no—
147C2×D61—44no—
148C2×D61—44no—
149C2×D61—42no—
150C2×D61—44no—
151C4×C61—42no—
152C4×C61—42no—
153C4×C61—81no—
154Dic61—22no—
155Dic61—22no—
156Dic61—42no—
157Dic61—81no—
158#2280—611no—
159#1464—612no—
160#1317—611no—
161#1317D6111yescharacteristic, complemented
162#1316—612no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—41no—
166C2×C61—41no—
167C2×C61#146211yescharacteristic
168C2×C61#212012yes—
169D61—44no—
170C24×C4—611no—
171C2×#117—611no—
172C2×#117—611no—
173#432—1222no—
174#381—611no—
175#381C2×D6111yescharacteristic
176#380—1222no—
177#379—611no—
178#379—611no—
179C4×C22⋊C4—1222no—
180#324—1222no—
181#323—612no—
182#323C2×D6112yes—
183C61#1150111yescharacteristic, complemented, Sylow
184C25—611no—
185C23×C4—611no—
186C23×C4—1221no—
187C23×C4—1221no—
188C23×C4—1222no—
189C23×C4—1222no—
190C23×C4—2442no—
191C23×C4—2442no—
192C23×C4C4×D6111yescharacteristic
193#117—2442no—
194#117—2442no—
195C2×C4⋊C4—612no—
196C2×C4⋊C4—1221no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—1222no—
200C2×C22⋊C4—1222no—
201C2×C22⋊C4C4×D6111yescharacteristic
202C2×C22⋊C4C22×D6111yescharacteristic
203C2×C42—612no—
204C2×C42—1221no—
205C4⋊C8—2442no—
206C22⋊C8—22no—
207C22⋊C8—1222no—
208#97—2442no—
209#95—22no—
210#95—1222no—
211C24—612no—
212C24—1221no—
213C24—1221no—
214C24—2441no—
215C24—2441no—
216C24—2444no—
217C24C2×C4×D6111yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—612no—
226C22×C4—1224no—
227C22×C4—1224no—
228C22×C4—1222no—
229C22×C4—1222no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—2442no—
234C22×C4—2442no—
235C22×C4—2448no—
236C22×C4—2442no—
237C22×C4—2442no—
238C22×C4—2448no—
239C22×C4#1175818912yes—
240C22×C4D4×D6112yes—
241C2×C8—42no—
242C2×C8—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—2444no—
248C22⋊C4—2444no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C42—1222no—
252C42—1222no—
253C42—2442no—
254C23—21no—
255C23—21no—
256C23—42no—
257C23—1224no—
258C23—1222no—
259C23—2442no—
260C23—2442no—
261C23—2442no—
262C23—2444no—
263C23—2444no—
264C23—2444no—
265C23—2448no—
266C23—2444no—
267C23—2441no—
268C23—2441no—
269C23C22⋊C4×D6111yescharacteristic
270C23M16×D6111yescharacteristic
271C23C2×#1175818911yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—612no—
282C2×C4—612no—
283C2×C4—1224no—
284C2×C4—1224no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1222no—
290C2×C4—2448no—
291C2×C4—2448no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2442no—
295C8—82no—
296C8—4882no—
297C22—22no—
298C22—21no—
299C22—21no—
300C22—41no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—1224no—
305C22—2444no—
306C22—2442no—
307C22—2444no—
308C22—2444no—
309C22—2448no—
310C22—2444no—
311C22—2442no—
312C22#1683972411yescharacteristic
313C22#99×D6111yescharacteristic
314C22#100×D6111yescharacteristic
315C4—42no—
316C4—42no—
317C4—81no—
318C4—1222no—
319C4—1222no—
320C4—4881no—
321C4—2442no—
322C2—21no—
323C2—21no—
324C2—41no—
325C2—41no—
326C2—2444no—
327C2#2144414411yescharacteristic
328C2#2144745912yes—
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61C2×#99
prime radicalC24×D61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1317D61
hypocenterC61#11501
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #21444150C2semidirect
3. #21443749C2semidirect
5. C61×#1317C2semidirect
161. #1317D61semidirect
183. C61#11501semidirect

Maximal subgroups

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

subgroupindex
#214481992
#214441502
#214437492
#214437462
C61×#13172
#1150161