Finite Group Databasebeta

← #29593013

Subgroups — #29593013

Order 15616.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#21451192C211yesmaximal, characteristic
2#21447164C211yesmaximal, characteristic
3#21444829C212yesmaximal
4#21443826C212yesmaximal
5C61×#1325C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7C2×C4×Dic122—21no—
8#16840093—22no—
9#16839802—21no—
10#16839692—21no—
11#16839692C2212yes—
12#16839667—22no—
13#16839661—22no—
14#16839531C2211yescharacteristic
15#16839522—21no—
16#16839500—22no—
17C61×#384C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122—21no—
20C2×#11758194—21no—
21#14519776—41no—
22#14519768—41no—
23#14519756—22no—
24C4×Dic122—42no—
25C4×Dic122—42no—
26#14519736—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D412yes—
30C2×#11758196—22no—
31C2×C4×Dic61—22no—
32#14519710—41no—
33#14519709—42no—
34#14519708—41no—
35#14519702—42no—
36#14519684—22no—
37#14519684—21no—
38#14519684—22no—
39#14519684D412yes—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61D411yescharacteristic
44C22⋊C8×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C2×Dic122—24no—
52C2×Dic122—22no—
53C2×Dic122—42no—
54C2×Dic122—42no—
55C2×C8×C61—42no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—44no—
58C4⋊C4×C61—41no—
59C42×C61—21no—
60C42×C61SD1612yes—
61C22⋊Dic61—41no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—81no—
68#11758196—42no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—44no—
72C4×Dic61—41no—
73#11758194—22no—
74#11758194—41no—
75C2×#92418—41no—
76C23×C61#12011yescharacteristic
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—41no—
86C2×C4×C61C2×SD1611yescharacteristic
87C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
88C2×Dic61—24no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61—42no—
96Dic122—48no—
97Dic122—82no—
98C8×C61—82no—
99#92418—42no—
100#12247—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#45011yescharacteristic
104C22×C61#45611yescharacteristic
105C22×C61B(4,𝔽2)11yescharacteristic
106C4×C61—24no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61—81no—
111Dic61—44no—
112Dic61—82no—
113Dic61—81no—
114Dic61—81no—
115#2582—611no—
116#2060—611no—
117#1611—612no—
118#1346—612no—
119#1325D6111yescharacteristic
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#160411yescharacteristic
123C2×C61#219811yescharacteristic
124C2×C61#220511yescharacteristic
125#544—611no—
126C2×C4×Q8—1221no—
127#483—1222no—
128#428—1221no—
129#398—612no—
130#398—1221no—
131#391—1222no—
132#389—1222no—
133#384C2×D6111yescharacteristic
134#343—611no—
135#339—1221no—
136#328—1222no—
137#324C2×D6112yes—
138C61#1224711yescharacteristic, complemented, Sylow
139C22×Q8—1221no—
140C2×M16—1221no—
141C4⋊Q8—2441no—
142#125—2441no—
143C22⋊Q8—1222no—
144C4×Q8—2442no—
145C4×Q8—2442no—
146#117—1221no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4D24411yescharacteristic
153C2×C4⋊C4C22×D6111yescharacteristic
154C2×C42—1222no—
155C2×C42D24411yescharacteristic
156#107—2441no—
157#106—2441no—
158#106—2442no—
159#103—2442no—
160C22⋊C8—22no—
161#95—612no—
162#95—1222no—
163#95—1221no—
164#95—1222no—
165C2×Q8—1224no—
166C2×Q8—1222no—
167C2×Q8—2442no—
168C2×Q8—2442no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4C2×D24411yescharacteristic
174C22×C4D4×D6112yes—
175M16—1222no—
176M16—2441no—
177C2×C8—42no—
178C2×C8—2441no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—44no—
182C4⋊C4—1221no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—4881no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C4⋊C4—2442no—
191C22⋊C4—2441no—
192C42—21no—
193C42—2444no—
194C42—2441no—
195C42#1175819012yes—
196C23#1451974711yescharacteristic
197Q8—4882no—
198Q8—2448no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—1224no—
209C2×C4—2442no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4C2×#1175819011yescharacteristic
217C2×C4#1451980511yescharacteristic
218C8—82no—
219C8—2442no—
220C22—21no—
221C22—21no—
222C22#1683991511yescharacteristic
223C22#1683994711yescharacteristic
224C22#1683995011yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4—4881no—
231C4—4881no—
232C4—4882no—
233C4—2444no—
234C2—21no—
235C2—21no—
236C2#2144479011yescharacteristic
237C2#2144781711yescharacteristic
238C2#2144785011yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1325D61
hypocenterC61#12247
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
138. C61#12247semidirect

Maximal subgroups

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

subgroupindex
#214511922
#214471642
#214448292
#214438262
C61×#13252
#1224761