Finite Group Databasebeta

← #29592935

Subgroups — #29592935

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#21453639C211yesmaximal, characteristic
2#21444861C211yesmaximal, characteristic
3#21444827C211yesmaximal, characteristic
4#21443845C211yesmaximal, characteristic
5#21443824C211yesmaximal, characteristic
6#21443765C211yesmaximal, characteristic
7C61×#2060C211yesmaximal, characteristic
8#16840095—21no—
9#16840090—21no—
10#16839701C2211yescharacteristic
11#16839700—21no—
12#16839700—21no—
13#16839692C2211yescharacteristic
14#16839648—21no—
15#16839648—21no—
16#16839646—21no—
17#16839643—21no—
18#16839499—21no—
19#16839499—21no—
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#428—21no—
24C61×#384C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#339—21no—
27C2×C4⋊Dic61D411yescharacteristic
28C2×C4⋊Dic61D411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32#14519710—41no—
33#14519708—41no—
34#14519701—41no—
35#14519701—41no—
36C22⋊#92418—21no—
37C22⋊#92418—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—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C2×M16×C61—21no—
50C4⋊Q8×C61—41no—
51#125×C61—41no—
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54#117×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61D411yescharacteristic
60#107×C61—41no—
61#106×C61—41no—
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—
73M16×C61—22no—
74M16×C61—41no—
75C2×C8×C61—41no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—81no—
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—22no—
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×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#13511yescharacteristic
116C2×C4×C61#13711yescharacteristic
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—42no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C8×C61—42no—
129#92418—81no—
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—42no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—81no—
143C4×C61—81no—
144C4×C61—81no—
145Dic61—81no—
146Dic61—81no—
147Dic61—81no—
148Dic61—81no—
149#2794—611no—
150#2060D6111yescharacteristic
151#1617—611no—
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—1221no—
163#483—1221no—
164#428—21no—
165#400—611no—
166#400—1221no—
167#400—1221no—
168#398—611no—
169#387—1221no—
170#387—1221no—
171#387—1221no—
172#387—1221no—
173#384C2×D6111yescharacteristic
174#343C2×D6111yescharacteristic
175#339—21no—
176#328—1221no—
177#328—1221no—
178#324—611no—
179#324—611no—
180C61#1223611yescharacteristic, complemented, Sylow
181C2×M16—21no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4C22⋊D6111yescharacteristic
194C2×C4⋊C4C22×D6111yescharacteristic
195C2×C42—1221no—
196C2×C42C22⋊D6111yescharacteristic
197#107—41no—
198#107—2441no—
199#106—41no—
200#106—2441no—
201#103—2441no—
202#103—2441no—
203C22⋊C8—1221no—
204C22⋊C8—1221no—
205#95—611no—
206#95—611no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
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—22no—
228M16—41no—
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—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—4881no—
252C23#1451974511yescharacteristic
253Q8—81no—
254Q8—81no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2442no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4#1451979711yescharacteristic
281C2×C4#1451980811yescharacteristic
282C8—42no—
283C8—4881no—
284C8—4881no—
285C22—21no—
286C22—21no—
287C22#1683992211yescharacteristic
288C22#1683994411yescharacteristic
289C22#1683994811yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—4881no—
299C4—4881no—
300C4—4881no—
301C4—4881no—
302C2—21no—
303C2—21no—
304C2#2144478011yescharacteristic
305C2#2144781411yescharacteristic
306C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2060C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2060D61
hypocenterC61#12236
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

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
#214536392
#214448612
#214448272
#214438452
#214438242
#214437652
C61×#20602
#1223661