Finite Group Databasebeta

← #29582307

Subgroups — #29582307

Order 15616.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#21456965C212yesmaximal
2#21456343C211yesmaximal, characteristic
3#21446639C211yesmaximal, characteristic
4#21444384C212yesmaximal
5C61×#1281C211yesmaximal, characteristic
6#16840319C2212yes—
7C2×#14519777C2211yescharacteristic
8#16840171—22no—
9#16840171—22no—
10#16840160—22no—
11#16840113—22no—
12#16840093—24no—
13#16840048—24no—
14#16839800—22no—
15C2×#14519702—22no—
16#16839628C2211yescharacteristic
17#16839500—24no—
18C61×#431C2212yes—
19C2×#97×C61C2211yescharacteristic
20C22×Dic122—21no—
21#14519777—22no—
22#14519777—21no—
23#14519777D412yes—
24#14519777D412yes—
25#14519777D412yes—
26#14519769—22no—
27#14519756—22no—
28#14519756—22no—
29C4×Dic122—22no—
30C4×Dic122—22no—
31#14519736—22no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61—21no—
34#14519711—24no—
35#14519709—28no—
36#14519709—22no—
37#14519709—22no—
38#14519702—28no—
39#14519702—44no—
40#14519684—22no—
41C22×C8×C61D412yes—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—22no—
44C22⋊C8×C61D414yes—
45#97×C61—22no—
46C4×C8×C61—22no—
47C22×C4×C61C2×D412yes—
48C22×C4×C61C2×D411yescharacteristic
49C22×Dic61—41no—
50C22×Dic61—41no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122—41no—
57C2×C8×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61—24no—
60C2×C8×C61SD1614yes—
61C42×C61C2×D412yes—
62C42×C61C2×D411yescharacteristic
63C42×C61#4111yescharacteristic
64C22⋊Dic61—42no—
65C4⋊Dic61—24no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72#11758196—42no—
73#11758196—42no—
74C4×Dic61—42no—
75C23×C61#12711yescharacteristic
76C2×C4×C61—42no—
77C2×C4×C61#12012yes—
78C2×C4×C61#12011yescharacteristic
79C2×C4×C61#12112yes—
80C2×C4×C61#12111yescharacteristic
81C2×C4×C61C2×SD1612yes—
82C2×C4×C61#13712yes—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—81no—
87C2×Dic61—81no—
88C2×Dic61—82no—
89C2×Dic61—81no—
90Dic122—44no—
91Dic122—44no—
92Dic122—82no—
93Dic122—82no—
94C8×C61—24no—
95C8×C61—44no—
96#10227—611nomaximal, Sylow
97C22×C61—22no—
98C22×C61#39211yescharacteristic
99C22×C61#49211yescharacteristic
100C22×C61#49711yescharacteristic
101C4×C61—22no—
102C4×C61—22no—
103C4×C61#44812yes—
104C4×C61#46112yes—
105Dic61—82no—
106Dic61—82no—
107Dic61—82no—
108Dic61—161no—
109#3229—612no—
110#3162—611no—
111#1960—611no—
112#1518—612no—
113#1281D6111yescharacteristic
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#200912yes—
117C2×C61#201311yescharacteristic
118#533—612no—
119C2×C4⋊Q8—611no—
120#501—1222no—
121#501—1222no—
122#498—1222no—
123#487—1222no—
124#483—1224no—
125#475—1224no—
126#431C2×D6112yes—
127#427—1222no—
128C2×#103—1222no—
129C2×#97C2×D6111yescharacteristic
130#382—611no—
131#328—1224no—
132C61#1022711yescharacteristic, complemented, Sylow
133C22×Q8—1221no—
134C22×C8D24412yes—
135C4⋊Q8—612no—
136C4⋊Q8—612no—
137C4⋊Q8—612no—
138C4⋊Q8—1222no—
139C4⋊Q8—1221no—
140#125—1222no—
141C22⋊Q8—1222no—
142C22⋊Q8—1222no—
143C4×Q8—1222no—
144C4×Q8—1222no—
145#117—1222no—
146C2×C4⋊C4—1222no—
147C2×C4⋊C4—1221no—
148C2×C42C22×D6111yescharacteristic
149#107—1224no—
150#106—1222no—
151#106—1222no—
152#106—1228no—
153C4⋊C8—22no—
154#103—1228no—
155#103—2444no—
156C22⋊C8D24414yes—
157#97—22no—
158C4×C8—22no—
159#95—1222no—
160C2×Q8—1222no—
161C2×Q8—1222no—
162C2×Q8—1222no—
163C2×Q8—2442no—
164C2×Q8—2442no—
165C2×Q8—2441no—
166C22×C4—2441no—
167C22×C4—2441no—
168C22×C4C2×D24412yes—
169C22×C4C2×D24411yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—24no—
173C2×C8#1175819014yes—
174C4⋊C4—1224no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C22⋊C4—2442no—
184C42—2442no—
185C42D4×D6112yes—
186C42D4×D6111yescharacteristic
187C42#1175822611yescharacteristic
188C23#1451977411yescharacteristic
189Q8—4882no—
190Q8—4882no—
191Q8—2444no—
192Q8—2444no—
193C2×C4—42no—
194C2×C4—4882no—
195C2×C4—4881no—
196C2×C4—4881no—
197C2×C4—4881no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4#1451974712yes—
202C2×C4#1451974711yescharacteristic
203C2×C4#1451975212yes—
204C2×C4#1451975211yescharacteristic
205C2×C4C2×#1175819012yes—
206C2×C4#1451981012yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22#1683967211yescharacteristic
211C22#1684013511yescharacteristic
212C22#1684015611yescharacteristic
213C4—22no—
214C4—22no—
215C4—9761no—
216C4—4882no—
217C4—4882no—
218C4—4882no—
219C4#1683990312yes—
220C4#1683996812yes—
221C2—21no—
222C2—21no—
223C2#2144688212yes—
224C2#2144690411yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1281C2
socleC22×C61#392
prime radicalC23×C61#127
hypercenter#1281D61
hypocenterC61#10227
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
132. C61#10227semidirect

Maximal subgroups

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

subgroupindex
#214569652
#214563432
#214466392
#214443842
C61×#12812
#1022761