Finite Group Databasebeta

← #29569326

Subgroups — #29569326

Order 15616.

322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453810C211yesmaximal, characteristic
2#21447381C211yesmaximal, characteristic
3#21447381C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#2100C211yesmaximal, characteristic
8#16839702—21no—
9#16839701—21no—
10#16839700—21no—
11#16839660C2211yescharacteristic
12#16839660C2211yescharacteristic
13#16839649—21no—
14#16839648—21no—
15#16839643—21no—
16#16839524—21no—
17#16839524—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C61×#389C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#340—21no—
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C22×C8×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61C2311yescharacteristic
53#95×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—41no—
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—81no—
87C2×#92418—41no—
88C2×#92418—41no—
89C2×#92418—41no—
90C2×#92418—41no—
91C2×#92418—41no—
92C2×#92418—41no—
93C23×C61#12011yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61#13511yescharacteristic
110C2×C4×C61#13511yescharacteristic
111C2×C4×C61#13511yescharacteristic
112C2×C4×C61#13711yescharacteristic
113C2×C4×C61#13711yescharacteristic
114C2×C4×C61#13711yescharacteristic
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C8×C61—81no—
128#92418—81no—
129#92418—81no—
130#7832—611nomaximal, Sylow
131C22×C61#45211yescharacteristic
132C22×C61#45211yescharacteristic
133C22×C61#45211yescharacteristic
134C22×C61#45411yescharacteristic
135C22×C61#45411yescharacteristic
136C22×C61#45411yescharacteristic
137C22×C61#45811yescharacteristic
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—81no—
145C4×C61—81no—
146C4×C61—161no—
147Dic61—81no—
148Dic61—81no—
149Dic61—81no—
150Dic61—81no—
151#2810—611no—
152#2100—611no—
153#2100—611no—
154#2100D6111yescharacteristic
155#1271—611no—
156#1271—611no—
157#1271—611no—
158C2×C61#161511yescharacteristic
159C2×C61#161511yescharacteristic
160C2×C61#161511yescharacteristic
161C2×C61#163811yescharacteristic
162C2×C61#163811yescharacteristic
163C2×C61#163811yescharacteristic
164C2×C61#165811yescharacteristic
165#400—1221no—
166#400—1221no—
167#400—1221no—
168#389—611no—
169#389—611no—
170#389C2×D6111yescharacteristic
171#387—1221no—
172#387—1221no—
173#387—1221no—
174#384C2×D6111yescharacteristic
175#340—21no—
176#340—21no—
177#340—1221no—
178#340—1221no—
179#340—1221no—
180#340—1221no—
181#336—611no—
182#336—611no—
183#336C2×D6111yescharacteristic
184C61#783211yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—1221no—
187C22×C8—1221no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C22⋊D6111yescharacteristic
199C2×C4⋊C4C22⋊D6111yescharacteristic
200C2×C42—1221no—
201C2×C42C22×D6111yescharacteristic
202#95—21no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4D4×D6111yescharacteristic
220C22×C4D4×D6111yescharacteristic
221C22×C4C2×C22⋊D6111yescharacteristic
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—2441no—
226C2×C8—2441no—
227C2×C8—2441no—
228C2×C8—2441no—
229C2×C8—2441no—
230C2×C8—2441no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C42—41no—
250C42—4881no—
251C23#1451974511yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4#1451979711yescharacteristic
280C2×C4#1451979811yescharacteristic
281C2×C4#1451980011yescharacteristic
282C2×C4#1451980611yescharacteristic
283C2×C4#1451980811yescharacteristic
284C2×C4#1451980911yescharacteristic
285C8—81no—
286C8—4881no—
287C8—4881no—
288C22#1683992111yescharacteristic
289C22#1683992211yescharacteristic
290C22#1683992311yescharacteristic
291C22#1683993311yescharacteristic
292C22#1683993311yescharacteristic
293C22#1683993411yescharacteristic
294C22#1683995111yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4—4881no—
305C4—4881no—
306C4—4881no—
307C4—4881no—
308C2#2144484711yescharacteristic
309C2#2144484811yescharacteristic
310C2#2144484911yescharacteristic
311C2#2144498811yescharacteristic
312C2#2144498911yescharacteristic
313C2#2144499011yescharacteristic
314C2#2144512011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2100C2
socle, prime radicalC23×C61#120
hypercenter#2100D61
hypocenterC61#7832
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
184. C61#7832semidirect

Maximal subgroups

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

subgroupindex
#214538102
#214473812
#214436432
#214436422
#214436412
C61×#21002
#783261