Finite Group Databasebeta

← #29592969

Subgroups — #29592969

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#21453315C211yesmaximal, characteristic
2#21447166C211yesmaximal, characteristic
3#21444861C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic
5#21443825C211yesmaximal, characteristic
6#21443762C211yesmaximal, characteristic
7C61×#1611C211yesmaximal, characteristic
8#16840095—21no—
9#16839805—21no—
10#16839701—21no—
11#16839701C2211yescharacteristic
12#16839694—21no—
13#16839661—21no—
14#16839647—21no—
15#16839643—21no—
16#16839629—21no—
17#16839627C2211yescharacteristic
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#483—21no—
24C61×#398C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61D411yescharacteristic
35#14519710—41no—
36#14519710—41no—
37#14519708—41no—
38#14519701—41no—
39C22⋊#92418—21no—
40#14519684—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×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57#106×C61—41no—
58#103×C61—41no—
59C22⋊C8×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—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—41no—
86C4⋊Dic61—42no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—81no—
90#11758196—42no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—42no—
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—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—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C8×C61—81no—
130#92418—42no—
131#92418—81no—
132#12241—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#45211yescharacteristic
136C22×C61#45611yescharacteristic
137C22×C61B(4,𝔽2)11yescharacteristic
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—42no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—81no—
144C4×C61—81no—
145C4×C61—81no—
146Dic61—81no—
147Dic61—81no—
148Dic61—81no—
149Dic61—81no—
150#2769—611no—
151#2061—611no—
152#1617—611no—
153#1611D6111yescharacteristic
154#1353—611no—
155#1346—611no—
156#1324—611no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61#160311yescharacteristic
160C2×C61#220111yescharacteristic
161C2×C61#220411yescharacteristic
162#544C2×D6111yescharacteristic
163#484—1221no—
164#483—21no—
165#428—1221no—
166#400—611no—
167#400—1221no—
168#398—1221no—
169#398C2×D6111yescharacteristic
170#389—1221no—
171#387—1221no—
172#387—1221no—
173#383—1221no—
174#382—611no—
175#343—611no—
176#339—1221no—
177#328—21no—
178#328—1221no—
179#324—611no—
180#324C2×D6111yescharacteristic
181C61#1224111yescharacteristic, complemented, Sylow
182C2×M16—1221no—
183C4⋊Q8—41no—
184#125—41no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#117—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4C22⋊D6111yescharacteristic
195C2×C4⋊C4C22×D6111yescharacteristic
196C2×C42—611no—
197C2×C42—1221no—
198#107—2441no—
199#107—2441no—
200#106—41no—
201#106—2441no—
202#103—41no—
203#103—2441no—
204C22⋊C8—21no—
205C22⋊C8—1221no—
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#95—1221no—
216#95C22⋊D6111yescharacteristic
217C2×Q8—21no—
218C2×Q8—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4D4×D6111yescharacteristic
226C22×C4D4×D6111yescharacteristic
227C22×C4C2×C22⋊D6111yescharacteristic
228M16—1222no—
229M16—2441no—
230C2×C8—41no—
231C2×C8—2441no—
232C2×C8—2441no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—4881no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2442no—
247C4⋊C4—2442no—
248C22⋊C4—41no—
249C42—41no—
250C42—1221no—
251C42—1221no—
252C42—2442no—
253C23#1451974511yescharacteristic
254Q8—81no—
255Q8—81no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
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—41no—
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—2441no—
281C2×C4—2441no—
282C2×C4#1451979811yescharacteristic
283C2×C4#1451980611yescharacteristic
284C8—81no—
285C8—4881no—
286C8—2442no—
287C22—21no—
288C22—21no—
289C22#1683992111yescharacteristic
290C22#1683994311yescharacteristic
291C22#1683994811yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—4881no—
301C4—4881no—
302C4—4881no—
303C4—4881no—
304C2—21no—
305C2—21no—
306C2#2144477911yescharacteristic
307C2#2144783011yescharacteristic
308C2#2144784411yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1611C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1611D61
hypocenterC61#12241
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
181. C61#12241semidirect

Maximal subgroups

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

subgroupindex
#214533152
#214471662
#214448612
#214438472
#214438252
#214437622
C61×#16112
#1224161