Finite Group Databasebeta

← #29590601

Subgroups — #29590601

Order 15616.

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

normal subgroups only

This group has 464 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#21450127C211yesmaximal, characteristic
2C4×#14519694C211yesmaximal, characteristic
3#21443826C214yesmaximal, complemented
4C61×#1465C211yesmaximal, characteristic
5C2×#14519758—21no—
6C22×C4⋊Dic61C411yescharacteristic
7C2×#14519694—21no—
8C4×#11758194—21no—
9#16839692C2212yes—
10#16839687C412yes—
11#16839660—21no—
12#16839623—21no—
13#16839622—21no—
14#16839622C411yescharacteristic
15#16839531C2212yes—
16C2×C4×D4×C61C2211yescharacteristic
17C61×#407—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C23×Dic61—21no—
21C2×#11758194—22no—
22#14519758—44no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—41no—
26C2×C4⋊Dic61—41no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C22⋊Dic61—22no—
30C2×C22⋊Dic61—21no—
31#14519694—24no—
32#14519688—41no—
33C4×#92418—41no—
34#14519684—22no—
35#14519684—22no—
36#14519684C2×C412yes—
37C22×D4×C61D411yescharacteristic
38C23×C4×C61C2×C411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C2×M16×C61—41no—
41C4×D4×C61—41no—
42C4×D4×C61—41no—
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C22⋊C4×C61C2×C411yescharacteristic
45C2×C22⋊C4×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C22⋊C8×C61—22no—
48C22⋊C8×C61—41no—
49C24×C61C22⋊C411yescharacteristic
50C24×C61C22⋊C411yescharacteristic
51C2×D4×C61—22no—
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—42no—
59C22×C4×C61—42no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61—42no—
70M16×C61—82no—
71C2×C8×C61—42no—
72C4⋊C4×C61—41no—
73C22⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C42×C61—21no—
76C42×C61—21no—
77C22⋊Dic61—42no—
78C22⋊Dic61—44no—
79C4⋊Dic61—42no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—42no—
83#11758196—44no—
84#11758194—24no—
85#11758194—42no—
86C2×#92418—42no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—41no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61—41no—
96C23×C61#10412yes—
97C23×C61C2×C22⋊C411yescharacteristic
98D4×C61—44no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—81no—
112C2×C4×C61#9911yescharacteristic
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61AGL(1,ℤ/8)12yes—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—84no—
122C8×C61—82no—
123#92418—44no—
124#11780—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—22no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61C2×#9911yescharacteristic
138C22×C61#41811yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61#35212yes—
146Dic61—82no—
147Dic61—82no—
148#2486—611no—
149C4×#100—611no—
150#1465D6111yescharacteristic
151#1346—614no—
152C2×C61—21no—
153C2×C61—21no—
154C2×C61—42no—
155C2×C61—81no—
156C2×C61#150711yescharacteristic
157C2×C61C2×#35211yescharacteristic
158C2×C61#213511yescharacteristic
159C2×#123—1221no—
160C2×C4×D4C2×D6111yescharacteristic
161C22×C4⋊C4—611no—
162C2×#100—1221no—
163#407—21no—
164C4×M16—1221no—
165#398—612no—
166#397—612no—
167#389—1221no—
168#381—1221no—
169#380—611no—
170#380—1221no—
171#343—612no—
172#324C2×D6112yes—
173#323—21no—
174C61#1178011yescharacteristic, complemented, Sylow
175C22×D4D24411yescharacteristic
176C23×C4—1221no—
177C23×C4C4×D6111yescharacteristic
178C23×C4C22⋊D6111yescharacteristic
179C2×M16—41no—
180C2×M16—1222no—
181#123—2444no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—612no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1222no—
188C2×C4⋊C4—2441no—
189C2×C4⋊C4—2441no—
190C2×C4⋊C4C22×D6111yescharacteristic
191C2×C22⋊C4—1221no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4C4×D6111yescharacteristic
194C2×C22⋊C4C22⋊D6111yescharacteristic
195C2×C42D24411yescharacteristic
196#100—1224no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199#97—2441no—
200C4×C8—2441no—
201#95—612no—
202#95—1222no—
203#95—1222no—
204C24#1175819811yescharacteristic
205C24#1175819811yescharacteristic
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—1222no—
216C22×C4—1222no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4—2442no—
220C22×C4#1175819811yescharacteristic
221C22×C4#1175819811yescharacteristic
222C22×C4C2×C4×D6111yescharacteristic
223C22×C4C2×D24411yescharacteristic
224C22×C4C2×C22⋊D6111yescharacteristic
225M16—82no—
226M16—1224no—
227M16—2442no—
228C2×C8—42no—
229C2×C8—2442no—
230C4⋊C4—41no—
231C4⋊C4—2442no—
232C4⋊C4—2442no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2444no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—2442no—
239C22⋊C4—2444no—
240C42—21no—
241C42—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#1451970312yes—
252C23C2×#1175819811yescharacteristic
253D4—44no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—4884no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4#1451969111yescharacteristic
275C2×C4#1451969111yescharacteristic
276C2×C4#1451980512yes—
277C8—82no—
278C8—2444no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22C2×#1451969111yescharacteristic
292C22#1683976811yescharacteristic
293C22C2×#1451970311yescharacteristic
294C4—21no—
295C4—22no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—4882no—
300C4—4882no—
301C4#1683955112yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2#2144433611yescharacteristic
307C2C2×#1683955111yescharacteristic
308C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1465C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1465D61
hypocenterC61#11780
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21443826C2semidirect
174. C61#11780semidirect

Maximal subgroups

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

subgroupindex
#214501272
C4×#145196942
#214438262
C61×#14652
#1178061