Finite Group Databasebeta

← #29592936

Subgroups — #29592936

Order 15616.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#21453644C211yesmaximal, characteristic
2#21447161C211yesmaximal, characteristic
3#21444827C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic
5#21443826C211yesmaximal, characteristic
6#21443764C211yesmaximal, characteristic
7C61×#1617C211yesmaximal, characteristic
8#16840090—21no—
9#16839805—21no—
10#16839704—21no—
11#16839704—21no—
12#16839692C2211yescharacteristic
13#16839649—21no—
14#16839649—21no—
15#16839647—21no—
16#16839643—21no—
17#16839631C2211yescharacteristic
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#484—21no—
24C61×#400C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61D411yescharacteristic
36#14519710—41no—
37#14519708—41no—
38#14519708—41no—
39#14519701—41no—
40C22⋊#92418—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684D411yescharacteristic
49C4⋊Q8×C61—41no—
50#125×C61—41no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—21no—
53#117×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56#107×C61—41no—
57#103×C61—41no—
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C2×C8×C61—41no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—41no—
84C4⋊Dic61—42no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—42no—
88#11758196—42no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—81no—
94#11758194—22no—
95#11758194—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C23×C61#12011yescharacteristic
99Q8×C61—81no—
100Q8×C61—81no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#13511yescharacteristic
115C2×C4×C61#13711yescharacteristic
116C2×Dic61—22no—
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—
127C2×Dic61—41no—
128C8×C61—81no—
129#92418—42no—
130#92418—81no—
131#12236—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61#45211yescharacteristic
135C22×C61#45611yescharacteristic
136C22×C61B(4,𝔽2)11yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—81no—
142C4×C61—81no—
143C4×C61—81no—
144C4×C61—81no—
145Dic61—42no—
146Dic61—81no—
147Dic61—81no—
148Dic61—81no—
149#2794—611no—
150#2060—611no—
151#1617D6111yescharacteristic
152#1611—611no—
153#1353—611no—
154#1346—611no—
155#1325—611no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61#160311yescharacteristic
159C2×C61#219811yescharacteristic
160C2×C61#220311yescharacteristic
161#544C2×D6111yescharacteristic
162#484—21no—
163#483—1221no—
164#428—1221no—
165#400—1221no—
166#400—1221no—
167#400C2×D6111yescharacteristic
168#398—611no—
169#387—1221no—
170#387—1221no—
171#387—1221no—
172#387—1221no—
173#384—611no—
174#343—611no—
175#339—1221no—
176#328—21no—
177#328—1221no—
178#324—611no—
179#324C2×D6111yescharacteristic
180C61#1223611yescharacteristic, complemented, Sylow
181C2×M16—1221no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4C22⋊D6111yescharacteristic
194C2×C4⋊C4C22×D6111yescharacteristic
195C2×C42—611no—
196C2×C42—1221no—
197#107—41no—
198#107—2441no—
199#106—2441no—
200#106—2441no—
201#103—41no—
202#103—2441no—
203C22⋊C8—21no—
204C22⋊C8—1221no—
205#95—21no—
206#95—21no—
207#95—611no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95C22⋊D6111yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4D4×D6111yescharacteristic
225C22×C4D4×D6111yescharacteristic
226C22×C4C2×C22⋊D6111yescharacteristic
227M16—1222no—
228M16—2441no—
229C2×C8—41no—
230C2×C8—2441no—
231C2×C8—2441no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—41no—
248C42—41no—
249C42—1221no—
250C42—1221no—
251C42—4881no—
252C23#1451974511yescharacteristic
253Q8—81no—
254Q8—81no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—1222no—
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—2441no—
280C2×C4#1451980011yescharacteristic
281C2×C4#1451980911yescharacteristic
282C8—81no—
283C8—4881no—
284C8—2442no—
285C22—21no—
286C22—21no—
287C22#1683992311yescharacteristic
288C22#1683994311yescharacteristic
289C22#1683994811yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—4881no—
299C4—4881no—
300C4—4881no—
301C4—2442no—
302C2—21no—
303C2—21no—
304C2#2144478111yescharacteristic
305C2#2144781311yescharacteristic
306C2#2144783911yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1617C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1617D61
hypocenterC61#12236
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1617

Complements

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

NH ≅ G/Ntype
180. C61#12236semidirect

Maximal subgroups

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

subgroupindex
#214536442
#214471612
#214448272
#214438462
#214438262
#214437642
C61×#16172
#1223661