Finite Group Databasebeta

← #29583146

Subgroups — #29583146

Order 15616.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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#21449112C211yesmaximal, characteristic
2#21444318C212yesmaximal
3#21443720C212yesmaximal
4#21443648C211yesmaximal, characteristic
5C61×#1995C211yesmaximal, characteristic
6C2×C4×Dic122—21no—
7#16839815C2212yes—
8#16839694—22no—
9#16839683—22no—
10C4×C4⋊Dic61—21no—
11C4×C4⋊Dic61C2212yes—
12#16839499—22no—
13#16839499—22no—
14C61×#533C2211yescharacteristic
15C61×#423C2211yescharacteristic
16C61×#376C2211yescharacteristic
17C61×#339—21no—
18C61×#339—21no—
19C22×Dic122—21no—
20C4×Dic122—42no—
21C4×Dic122—42no—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—22no—
25C2×#11758196—22no—
26C2×C4×Dic61—22no—
27C4⋊#92418—22no—
28C22⋊#92418—22no—
29C4×#92418—22no—
30#14519684—21no—
31#14519684—21no—
32#14519684D412yes—
33#14519684D412yes—
34C2×M16×C61—21no—
35C4⋊Q8×C61Q812yescomplemented
36#125×C61—21no—
37C22⋊Q8×C61—22no—
38C4×Q8×C61—22no—
39#117×C61—21no—
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—22no—
44#95×C61—22no—
45C2×Q8×C61—22no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52C2×Dic122—44no—
53C2×Dic122—42no—
54M16×C61—41no—
55M16×C61—41no—
56C2×C8×C61—41no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—42no—
60C22⋊C4×C61—41no—
61C42×C61—21no—
62C42×C61—21no—
63C42×C61—41no—
64C42×C61SD1612yes—
65C42×C61Q1612yes—
66C42×C61C2×Q811yescharacteristic
67C42×C61#4111yescharacteristic
68C42×C61#4112yes—
69C4⋊Dic61—44no—
70C4⋊Dic61—44no—
71C4⋊Dic61—42no—
72#11758196—44no—
73C4×Dic61—42no—
74C4×Dic61—42no—
75C2×#92418—42no—
76C23×C61#12011yescharacteristic
77Q8×C61—82no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61C22⋊Q812yes—
85C2×C4×C61C22⋊Q811yescharacteristic
86C2×C4×C61#12412yes—
87C2×C4×C61#12411yescharacteristic
88C2×C4×C61C2×SD1611yescharacteristic
89C2×C4×C61C2×Q1611yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C61#13711yescharacteristic
92C2×Dic61—24no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98Dic122—48no—
99C8×C61—81no—
100#92418—82no—
101#10371—611nomaximal, Sylow
102C22×C61—22no—
103C22×C61#39311yescharacteristic
104C22×C61#45011yescharacteristic
105C22×C61#45111yescharacteristic
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—42no—
109C4×C61—42no—
110C4×C61—82no—
111C4×C61#47511yescharacteristic
112C4×C61#47711yescharacteristic
113C4×C61#48711yescharacteristic
114C4×C61#48911yescharacteristic
115Dic61—44no—
116Dic61—82no—
117#2399—611no—
118#1995D6111yescharacteristic
119#1503—612no—
120#1303—612no—
121#1274—611no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#202411yescharacteristic
125C2×C61#203112yes—
126#533C2×D6111yescharacteristic
127C2×C4×Q8—1221no—
128#431—612no—
129#423C2×D6111yescharacteristic
130#398—1222no—
131#395—1222no—
132C4×C4⋊C4—612no—
133C4×C4⋊C4—1221no—
134#376C2×D6111yescharacteristic
135#339—21no—
136#339—21no—
137#328—1222no—
138#328—1222no—
139C61#1037111yescharacteristic, complemented, Sylow
140C22×Q8—1221no—
141C2×M16—21no—
142C4⋊Q8Dic12212yescomplemented
143#125—21no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146C4×Q8—2442no—
147C4×Q8—2442no—
148#117—21no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1222no—
153C2×C42—1222no—
154C2×C42C22⋊D6111yescharacteristic
155C2×C42C22⋊D6111yescharacteristic
156C2×C42C22×D6111yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—1222no—
159C22⋊C8—1222no—
160C4×C8—1222no—
161#95—22no—
162#95—612no—
163#95—612no—
164#95—1221no—
165#95—1221no—
166C2×Q8—22no—
167C2×Q8—2442no—
168C2×Q8—2444no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4D4×D6112yes—
174C22×C4C2×C22⋊D6111yescharacteristic
175M16—41no—
176M16—41no—
177C2×C8—41no—
178C2×C8—2442no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—2444no—
183C4⋊C4—2442no—
184C4⋊C4—2444no—
185C4⋊C4—2444no—
186C22⋊C4—41no—
187C42—21no—
188C42—21no—
189C42—41no—
190C42—2442no—
191C42—2442no—
192C42#1175820112yes—
193C42#1175820212yes—
194C42C2×Dic12211yescharacteristic
195C42#1175822211yescharacteristic
196C42#1175822412yes—
197C23#1451974511yescharacteristic
198Q8—82no—
199Q8—2448no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—1224no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451975412yes—
213C2×C4#1451975611yescharacteristic
214C2×C4#1451976312yes—
215C2×C4#1451976411yescharacteristic
216C2×C4C2×#1175820111yescharacteristic
217C2×C4C2×#1175820211yescharacteristic
218C2×C4#1451980211yescharacteristic
219C2×C4#1451980711yescharacteristic
220C8—81no—
221C8—4882no—
222C22—22no—
223C22#1683967411yescharacteristic
224C22#1683991211yescharacteristic
225C22#1683991711yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—82no—
231C4—4882no—
232C4—2444no—
233C4#1684004711yescharacteristic
234C4#1684005711yescharacteristic
235C4#1684011211yescharacteristic
236C4#1684012111yescharacteristic
237C2—21no—
238C2—21no—
239C2#2144696011yescharacteristic
240C2#2144698912yes—
subgroupG/H
centerC2×C4#14519764
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1995C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1995D61
hypocenterC61#10371
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
35. C4⋊Q8×C61Q8semidirect
139. C61#10371semidirect
142. C4⋊Q8Dic122semidirect

Maximal subgroups

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

subgroupindex
#214491122
#214443182
#214437202
#214436482
C61×#19952
#1037161