Finite Group Databasebeta

← #29593033

Subgroups — #29593033

Order 15616.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#21453885C211yesmaximal, characteristic
2#21447166C211yesmaximal, characteristic
3#21444827C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic
5#21443825C211yesmaximal, characteristic
6#21443762C211yesmaximal, characteristic
7C61×#1611C211yesmaximal, characteristic
8C2×#14519767—21no—
9#16840090—21no—
10#16839805—21no—
11#16839704—21no—
12#16839703—21no—
13#16839696—21no—
14#16839695—21no—
15#16839695—21no—
16#16839692C2211yescharacteristic
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—
28#14519767—42no—
29#14519767—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61D411yescharacteristic
39#14519710—41no—
40#14519708—41no—
41#14519708—41no—
42#14519701—41no—
43C22⋊#92418—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684D411yescharacteristic
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×C61D411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59#106×C61—41no—
60#103×C61—41no—
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
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—
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—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—42no—
92#11758196—42no—
93#11758196—42no—
94#11758196—41no—
95#11758196—41no—
96#11758196—81no—
97C4×Dic61—21no—
98C4×Dic61SD1612yes—
99#11758194—22no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12011yescharacteristic
104Q8×C61—81no—
105Q8×C61—81no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
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—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×SD1611yescharacteristic
121C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—42no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C8×C61—81no—
134#92418—42no—
135#92418—81no—
136#12251—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#45011yescharacteristic
140C22×C61#45611yescharacteristic
141C22×C61B(4,𝔽2)11yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61—81no—
148C4×C61—81no—
149C4×C61—81no—
150Dic61—42no—
151Dic61—81no—
152Dic61—81no—
153Dic61—81no—
154#2822—611no—
155#2061—611no—
156#1611—611no—
157#1611D6111yescharacteristic
158#1346—611no—
159#1346—611no—
160#1324—611no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#160411yescharacteristic
164C2×C61#220111yescharacteristic
165C2×C61#220311yescharacteristic
166#544C2×D6111yescharacteristic
167C2×#125—1221no—
168#483—21no—
169#483—1221no—
170#428—1221no—
171#400—1221no—
172#400—1221no—
173#398—611no—
174#398—1221no—
175#398—1221no—
176#398—1221no—
177#398C2×D6111yescharacteristic
178#382—611no—
179#343—611no—
180#339—1221no—
181#328—21no—
182#328—1221no—
183#324—611no—
184#324C2×D6111yescharacteristic
185C61#1225111yescharacteristic, complemented, Sylow
186C2×M16—1221no—
187C4⋊Q8—41no—
188#125—41no—
189#125—2442no—
190#125—2442no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193#117—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4C22⋊D6111yescharacteristic
204C2×C4⋊C4C22×D6111yescharacteristic
205C2×C42—611no—
206#107—2441no—
207#106—41no—
208#106—2441no—
209#106—2441no—
210#103—41no—
211#103—2441no—
212C22⋊C8—21no—
213C22⋊C8—1221no—
214#95—21no—
215#95—611no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95C22⋊D6111yescharacteristic
223C2×Q8—21no—
224C2×Q8—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4D4×D6111yescharacteristic
232C22×C4D4×D6111yescharacteristic
233C22×C4C2×C22⋊D6111yescharacteristic
234M16—1222no—
235M16—2441no—
236C2×C8—41no—
237C2×C8—2441no—
238C2×C8—2441no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—4881no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C22⋊C4—41no—
259C42—41no—
260C42—612no—
261C42—1221no—
262C23#1451974511yescharacteristic
263Q8—81no—
264Q8—81no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—1222no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4SD16×D6111yescharacteristic
291C2×C4#1451980411yescharacteristic
292C8—81no—
293C8—4881no—
294C8—2442no—
295C22—21no—
296C22—21no—
297C22#1683991111yescharacteristic
298C22#1683994311yescharacteristic
299C22#1683994811yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—4881no—
309C4—4881no—
310C4—4881no—
311C4—2442no—
312C2—21no—
313C2—21no—
314C2#2144478611yescharacteristic
315C2#2144783011yescharacteristic
316C2#2144783811yescharacteristic
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#12251
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
185. C61#12251semidirect

Maximal subgroups

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

subgroupindex
#214538852
#214471662
#214448272
#214438262
#214438252
#214437622
C61×#16112
#1225161