Finite Group Databasebeta

← #29569148

Subgroups — #29569148

Order 15616.

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

normal subgroups only

This group has 338 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#21447376C211yesmaximal, characteristic
3#21447296C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#2083C211yesmaximal, characteristic
8C2×#14519708—21no—
9#16839702—21no—
10#16839701—21no—
11#16839700—21no—
12#16839660C2211yescharacteristic
13#16839660C2211yescharacteristic
14#16839649—21no—
15#16839648—21no—
16#16839643—21no—
17#16839524—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#107×C61—21no—
23C61×#389C2211yescharacteristic
24C61×#384C2211yescharacteristic
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#14519708—42no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×C8×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C42×C61C2311yescharacteristic
54#107×C61—42no—
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C2×C8×C61—22no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—81no—
91C2×#92418—22no—
92C2×#92418—41no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C23×C61#12011yescharacteristic
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—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—81no—
111C2×C4×C61—81no—
112C2×C4×C61—81no—
113C2×C4×C61#13511yescharacteristic
114C2×C4×C61#13511yescharacteristic
115C2×C4×C61#13511yescharacteristic
116C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C8×C61—42no—
132#92418—42no—
133#92418—81no—
134#7803—611nomaximal, Sylow
135C22×C61#44911yescharacteristic
136C22×C61#44911yescharacteristic
137C22×C61#45211yescharacteristic
138C22×C61#45411yescharacteristic
139C22×C61#45611yescharacteristic
140C22×C61#45611yescharacteristic
141C22×C61#45811yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—81no—
149C4×C61—81no—
150C4×C61—161no—
151Dic61—81no—
152Dic61—81no—
153Dic61—81no—
154Dic61—81no—
155#2810—611no—
156#2099—611no—
157#2084—611no—
158#2083D6111yescharacteristic
159#1271—611no—
160#1271—611no—
161#1271—611no—
162C2×C61#160911yescharacteristic
163C2×C61#160911yescharacteristic
164C2×C61#161511yescharacteristic
165C2×C61#162811yescharacteristic
166C2×C61#165011yescharacteristic
167C2×C61#165211yescharacteristic
168C2×C61#166311yescharacteristic
169C2×#107—21no—
170C2×#106—1221no—
171#400—1221no—
172#400—1221no—
173#400—1221no—
174#389—611no—
175#389—611no—
176#389C2×D6111yescharacteristic
177#387—1221no—
178#387—1221no—
179#387—1221no—
180#384C2×D6111yescharacteristic
181#340—21no—
182#340—1221no—
183#340—1221no—
184#340—1221no—
185#336—611no—
186#336—611no—
187#336C2×D6111yescharacteristic
188C61#780311yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—1221no—
191C22×C8—1221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C22⋊D6111yescharacteristic
203C2×C4⋊C4C22⋊D6111yescharacteristic
204C2×C42—1221no—
205C2×C42C22×D6111yescharacteristic
206#107—42no—
207#106—2442no—
208#95—21no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4D4×D6111yescharacteristic
226C22×C4D4×D6111yescharacteristic
227C22×C4C2×C22⋊D6111yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—1222no—
232C2×C8—2441no—
233C2×C8—2441no—
234C2×C8—2441no—
235C2×C8—2441no—
236C2×C8—2441no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C42—41no—
258C42—4881no—
259C23#1451974511yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4#1451979611yescharacteristic
288C2×C4#1451979711yescharacteristic
289C2×C4#1451980011yescharacteristic
290C2×C4#1451980111yescharacteristic
291C2×C4#1451980311yescharacteristic
292C2×C4#1451980911yescharacteristic
293C8—42no—
294C8—4881no—
295C8—2442no—
296C22#1683990411yescharacteristic
297C22#1683990511yescharacteristic
298C22#1683992311yescharacteristic
299C22#1683993311yescharacteristic
300C22#1683994311yescharacteristic
301C22#1683994411yescharacteristic
302C22#1683995111yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—4881no—
313C4—4881no—
314C4—4881no—
315C4—4881no—
316C2#2144481311yescharacteristic
317C2#2144481411yescharacteristic
318C2#2144484911yescharacteristic
319C2#2144492711yescharacteristic
320C2#2144507211yescharacteristic
321C2#2144508711yescharacteristic
322C2#2144514611yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2083C2
socle, prime radicalC23×C61#120
hypercenter#2083D61
hypocenterC61#7803
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
188. C61#7803semidirect

Maximal subgroups

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

subgroupindex
#214538102
#214473762
#214472962
#214436432
#214436422
#214436412
C61×#20832
#780361