Finite Group Databasebeta

← #29569218

Subgroups — #29569218

Order 15616.

350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453804C211yesmaximal, characteristic
2#21447378C211yesmaximal, characteristic
3#21447295C211yesmaximal, characteristic
4#21447229C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519708—21no—
9C2×#14519702—21no—
10#16839704—21no—
11#16839693—21no—
12#16839692—21no—
13#16839668C2211yescharacteristic
14#16839666—21no—
15#16839660C2211yescharacteristic
16#16839648—21no—
17#16839643—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39#14519708—42no—
40#14519702—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C22×C8×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—41no—
66C2×Dic122—21no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×Dic122SD1612yes—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C42×C61—41no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—42no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—81no—
94#11758196—81no—
95C4×Dic61—81no—
96C2×#92418—22no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61#12011yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61C2×SD1611yescharacteristic
113C2×C4×C61#13511yescharacteristic
114C2×C4×C61#13511yescharacteristic
115C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C61#13711yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×Dic61—22no—
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—81no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133Dic122—42no—
134Dic122—81no—
135C8×C61—81no—
136C8×C61—81no—
137#92418—42no—
138#7813—611nomaximal, Sylow
139C22×C61#44811yescharacteristic
140C22×C61#44911yescharacteristic
141C22×C61#45211yescharacteristic
142C22×C61#45411yescharacteristic
143C22×C61#45511yescharacteristic
144C22×C61#45611yescharacteristic
145C22×C61#45811yescharacteristic
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—81no—
153C4×C61—81no—
154Dic61—42no—
155Dic61—81no—
156Dic61—81no—
157Dic61—81no—
158Dic61—161no—
159#2809—611no—
160#2099—611no—
161#2084—611no—
162#2072—611no—
163#1272—611no—
164#1271—611no—
165#1271D6111yescharacteristic
166C2×C61#160811yescharacteristic
167C2×C61#160911yescharacteristic
168C2×C61#161511yescharacteristic
169C2×C61#162611yescharacteristic
170C2×C61#164611yescharacteristic
171C2×C61#165311yescharacteristic
172C2×C61#166411yescharacteristic
173C2×#106—1221no—
174C2×#103—1221no—
175#400—1221no—
176#398—1221no—
177#398—1221no—
178#391—611no—
179#391—1221no—
180#389—611no—
181#389C2×D6111yescharacteristic
182#387—1221no—
183#387—1221no—
184#384—611no—
185#340—1221no—
186#340—1221no—
187#340—1221no—
188#340—1221no—
189#336—611no—
190#336C2×D6111yescharacteristic
191#336C2×D6111yescharacteristic
192C61#781311yescharacteristic, complemented, Sylow
193C22×Q8—611no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—1221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4D24411yescharacteristic
208C2×C4⋊C4D24411yescharacteristic
209C2×C42—1221no—
210C2×C42C22×D6111yescharacteristic
211#106—2442no—
212#103—2442no—
213#95—21no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222C2×Q8—612no—
223C2×Q8—1221no—
224C2×Q8—2441no—
225C2×Q8—2441no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—2441no—
233C22×C4C2×D24411yescharacteristic
234C22×C4D4×D6111yescharacteristic
235C22×C4D4×D6111yescharacteristic
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—1222no—
243C2×C8—2441no—
244C2×C8—2441no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—4881no—
253C4⋊C4—4881no—
254C4⋊C4—2442no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C42—41no—
264C42—4881no—
265C23#1451974711yescharacteristic
266Q8—4881no—
267Q8—2442no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—1222no—
281C2×C4—4881no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4SD16×D6111yescharacteristic
296C2×C4#1451979611yescharacteristic
297C2×C4#1451979911yescharacteristic
298C2×C4#1451980511yescharacteristic
299C2×C4#1451980611yescharacteristic
300C2×C4#1451980911yescharacteristic
301C8—81no—
302C8—81no—
303C8—2442no—
304C22#1683990211yescharacteristic
305C22#1683990911yescharacteristic
306C22#1683992511yescharacteristic
307C22#1683993611yescharacteristic
308C22#1683994111yescharacteristic
309C22#1683994711yescharacteristic
310C22#1683995311yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—9761no—
320C4—4881no—
321C4—4881no—
322C4—4881no—
323C4—2442no—
324C2#2144481111yescharacteristic
325C2#2144481811yescharacteristic
326C2#2144485111yescharacteristic
327C2#2144491711yescharacteristic
328C2#2144504911yescharacteristic
329C2#2144509711yescharacteristic
330C2#2144515511yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7813
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
192. C61#7813semidirect

Maximal subgroups

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

subgroupindex
#214538042
#214473782
#214472952
#214472292
#214436442
#214436412
C61×#12712
#781361