Finite Group Databasebeta

← #29592943

Subgroups — #29592943

Order 15616.

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

normal subgroups only

This group has 334 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#21453581C211yesmaximal, characteristic
2#21447166C211yesmaximal, characteristic
3#21444827C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443826C211yesmaximal, characteristic
6#21443762C211yesmaximal, characteristic
7C61×#1605C211yesmaximal, characteristic
8#16840090—21no—
9#16839805—21no—
10C61⋊#401—21no—
11#16839701—21no—
12#16839692C2211yescharacteristic
13#16839669—21no—
14#16839649—21no—
15#16839648—21no—
16#16839647—21no—
17#16839627C2211yescharacteristic
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#451—21no—
24C61×#395C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61D411yescharacteristic
34#14519710—41no—
35#14519708—41no—
36#14519708—41no—
37#14519701—41no—
38C22⋊#92418—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#14519684—21no—
48#14519684D411yescharacteristic
49C22×Q8×C61D411yescharacteristic
50C2×Q16×C61—41no—
51C4⋊Q8×C61—41no—
52#125×C61—41no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55#117×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2311yescharacteristic
58#103×C61—41no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61—42no—
65C2×Q8×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75Q16×C61—82no—
76C2×C8×C61—41no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61—41no—
87C4⋊Dic61—42no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—81no—
95#11758194—22no—
96#11758194—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61#12011yescharacteristic
100Q8×C61—42no—
101Q8×C61—81no—
102Q8×C61—81no—
103Q8×C61—81no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
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—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#13511yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C8×C61—81no—
132#92418—42no—
133#92418—81no—
134#12237—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61#45211yescharacteristic
138C22×C61#45611yescharacteristic
139C22×C61B(4,𝔽2)11yescharacteristic
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—42no—
145C4×C61—81no—
146C4×C61—81no—
147C4×C61—81no—
148Dic61—81no—
149Dic61—81no—
150Dic61—81no—
151Dic61—81no—
152#2789—611no—
153#2061—611no—
154#1611—611no—
155#1605D6111yescharacteristic
156#1354—611no—
157#1346—611no—
158#1324—611no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61#160311yescharacteristic
162C2×C61#219711yescharacteristic
163C2×C61#220311yescharacteristic
164#544C2×D6111yescharacteristic
165#483—1221no—
166#451—21no—
167#428—1221no—
168#401—1221no—
169#400—1221no—
170#398—611no—
171#395C2×D6111yescharacteristic
172#391—1221no—
173#387—1221no—
174#387—1221no—
175#387—1221no—
176#382—611no—
177#343—611no—
178#339—1221no—
179#328—21no—
180#328—1221no—
181#324—611no—
182#324C2×D6111yescharacteristic
183C61#1223711yescharacteristic, complemented, Sylow
184C22×Q8C22⋊D6111yescharacteristic
185C2×Q16—41no—
186C2×M16—1221no—
187C4⋊Q8—41no—
188#125—41no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191#117—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4C22×D6111yescharacteristic
198C2×C42—611no—
199C2×C42—1221no—
200#107—2441no—
201#106—2441no—
202#106—2441no—
203#103—41no—
204#103—2441no—
205C22⋊C8—21no—
206C22⋊C8—1221no—
207#95—21no—
208#95—611no—
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—
218#95C22⋊D6111yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—42no—
222C2×Q8—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4D4×D6111yescharacteristic
230C22×C4D4×D6111yescharacteristic
231C22×C4C2×C22⋊D6111yescharacteristic
232Q16—82no—
233M16—1222no—
234M16—2441no—
235C2×C8—41no—
236C2×C8—2441no—
237C2×C8—2441no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C4⋊C4—2442no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C22⋊C4—41no—
252C42—41no—
253C42—1221no—
254C42—1221no—
255C42—4881no—
256C23#1451974511yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—81no—
260Q8—81no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
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—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2442no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4#1451980011yescharacteristic
287C2×C4#1451980911yescharacteristic
288C8—81no—
289C8—4881no—
290C8—2442no—
291C22—21no—
292C22—21no—
293C22#1683992311yescharacteristic
294C22#1683994311yescharacteristic
295C22#1683994811yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—4881no—
305C4—4881no—
306C4—4881no—
307C4—4881no—
308C2—21no—
309C2—21no—
310C2#2144478111yescharacteristic
311C2#2144780711yescharacteristic
312C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1605C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1605D61
hypocenterC61#12237
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1605

Complements

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

NH ≅ G/Ntype
183. C61#12237semidirect

Maximal subgroups

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

subgroupindex
#214535812
#214471662
#214448272
#214438492
#214438262
#214437622
C61×#16052
#1223761