Finite Group Databasebeta

← #29580885

Subgroups — #29580885

Order 15616.

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

normal subgroups only

This group has 528 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#21455859C212yesmaximal
2#21449112C211yesmaximal, characteristic
3#21446800C211yesmaximal, characteristic
4#21444249C212yesmaximal
5C61×#1274C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7C2×C4×Dic122C2212yes—
8#16840098—22no—
9#16840058—22no—
10#16839973—22no—
11#16839920—22no—
12C4×Dic244—24no—
13#16839786C2211yescharacteristic
14#16839694—22no—
15#16839683—22no—
16C4×C4⋊Dic61—22no—
17#16839522—22no—
18#16839494—24no—
19C61×#431C2212yes—
20C61×#376C2211yescharacteristic
21C22×Dic122D412yes—
22C2×Dic244—24no—
23C2×#11758194—21no—
24#14519777D412yes—
25#14519769—21no—
26#14519756—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C4×Dic122—22no—
30C4×Dic122—22no—
31C4×Dic122—22no—
32#14519736—21no—
33C2×C4⋊Dic61—24no—
34C2×C4⋊Dic61D412yes—
35C2×#11758196—22no—
36C2×C4×Dic61—22no—
37#14519711—24no—
38C4⋊#92418—22no—
39#14519702—24no—
40#14519702—24no—
41#14519684—22no—
42#14519684—22no—
43C2×C42×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45C4⋊C8×C61—22no—
46C22⋊C8×C61—22no—
47C4×C8×C61D414yes—
48#95×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61C2×D412yes—
51C22×C4×C61C2×D411yescharacteristic
52C22×Dic61—22no—
53C22×Dic61—22no—
54C2×Dic122—22no—
55C2×Dic122—22no—
56C2×Dic122—22no—
57C2×Dic122—44no—
58C2×C8×C61—24no—
59C42×C61—22no—
60C42×C61Q1614yescomplemented
61C42×C61C2×D411yescharacteristic
62C42×C61C2×D412yes—
63C42×C61#4111yescharacteristic
64C22⋊Dic61—41no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—48no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73C4×Dic61—42no—
74C4×Dic61—42no—
75C4×Dic61—41no—
76#11758194—42no—
77C2×#92418—41no—
78Dic244—48no—
79C23×C61#12011yescharacteristic
80C2×C4×C61—24no—
81C2×C4×C61—42no—
82C2×C4×C61—44no—
83C2×C4×C61#12012yes—
84C2×C4×C61#12112yes—
85C2×C4×C61#12111yescharacteristic
86C2×C4×C61#12711yescharacteristic
87C2×C4×C61C2×Q1612yes—
88C2×C4×C61#13712yes—
89C2×Dic61—24no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—44no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95Dic122—24no—
96Dic122—24no—
97Dic122—42no—
98Dic122—42no—
99Dic122—44no—
100C8×C61—44no—
101#92418—81no—
102#10017—611nomaximal, Sylow
103C22×C61—22no—
104C22×C61#39211yescharacteristic
105C22×C61#45112yes—
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—44no—
109C4×C61#46212yes—
110C4×C61#49411yescharacteristic
111C4×C61#49711yescharacteristic
112Dic61—44no—
113Dic61—82no—
114Dic61—82no—
115#3104—612no—
116#2399—611no—
117#1995—611no—
118#1487—612no—
119#1274D6111yescharacteristic
120C2×C61—22no—
121C2×C61#201012yes—
122C2×C61#201611yescharacteristic
123#533—611no—
124C2×C4×Q8—612no—
125#484—1222no—
126#477—1222no—
127#462—1222no—
128#451—1222no—
129C4×Q16—1224no—
130#431C2×D6112yes—
131#423—611no—
132#398—1222no—
133#395—1222no—
134C4×C4⋊C4—1222no—
135#376C2×D6111yescharacteristic
136#339—1222no—
137Q8⋊C8—1224no—
138C61#1001711yescharacteristic, complemented, Sylow
139C22×Q8—612no—
140C2×Q16—1224no—
141C2×M16—1221no—
142C4⋊Q8—612no—
143#125—1221no—
144C22⋊Q8—1222no—
145C4×Q8—1222no—
146C4×Q8—1222no—
147C4×Q8—1222no—
148C4×Q8—1222no—
149C4×Q8—1222no—
150#117—1221no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—1224no—
153C2×C4⋊C4—1222no—
154C2×C42—1222no—
155C2×C42D24412yes—
156C2×C42C22×D6111yescharacteristic
157#107—1224no—
158C4⋊C8—22no—
159C4⋊C8—1222no—
160#103—1224no—
161#103—1224no—
162C22⋊C8—22no—
163C4×C8D24414yes—
164#95—22no—
165#95—1222no—
166#95—1222no—
167C2×Q8—1222no—
168C2×Q8—1222no—
169C2×Q8—1222no—
170C2×Q8—2444no—
171C22×C4—22no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4C2×D24411yescharacteristic
175C22×C4D4×D6112yes—
176Q16—2448no—
177M16—2442no—
178C2×C8—24no—
179C2×C8—2441no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—2448no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C22⋊C4—2441no—
189C42—22no—
190C42—2442no—
191C42—2442no—
192C42—2441no—
193C42Dic24414yescomplemented
194C42C2×D24412yes—
195C42D4×D6111yescharacteristic
196C42#1175822611yescharacteristic
197C23#1451974711yescharacteristic
198Q8—1224no—
199Q8—1224no—
200Q8—2444no—
201Q8—2442no—
202Q8—2442no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—1224no—
207C2×C4—2444no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451974712yes—
213C2×C4#1451975212yes—
214C2×C4#1451975211yescharacteristic
215C2×C4#1451977411yescharacteristic
216C2×C4C2×Dic24412yes—
217C2×C4#1451981012yes—
218C8—44no—
219C8—4881no—
220C22—22no—
221C22#1683967211yescharacteristic
222C22#1683992012yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—4882no—
227C4—4882no—
228C4—2444no—
229C4#1683997312yes—
230C4#1684014211yescharacteristic
231C4#1684015611yescharacteristic
232C2—22no—
233C2#2144688712yes—
234C2#2144692111yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#1274D61
hypocenterC61#10017
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
60. C42×C61Q16semidirect
138. C61#10017semidirect
193. C42Dic244semidirect

Maximal subgroups

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

subgroupindex
#214558592
#214491122
#214468002
#214442492
C61×#12742
#1001761