Finite Group Databasebeta

← #29583147

Subgroups — #29583147

Order 15616.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#21446800C211yesmaximal, characteristic
3#21444319C212yesmaximal
4#21443721C212yesmaximal
5C61×#1274C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7C2×C4×Dic122—21no—
8#16839786C2211yescharacteristic
9#16839694—22no—
10#16839683—22no—
11C4×C4⋊Dic61—21no—
12C4×C4⋊Dic61C2212yes—
13#16839522—21no—
14#16839522—21no—
15#16839500—22no—
16#16839500—22no—
17C61×#431C2212yes—
18C61×#376C2211yescharacteristic
19C22×Dic122—21no—
20C2×#11758194—21no—
21#14519777Q812yescomplemented
22#14519769—21no—
23#14519756—22no—
24C4×Dic122—22no—
25C4×Dic122—42no—
26C4×Dic122—42no—
27#14519736—21no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×#11758196—22no—
32C2×C4×Dic61—22no—
33C4⋊#92418—22no—
34#14519684—21no—
35#14519684—21no—
36#14519684D412yes—
37#14519684D412yes—
38C2×C42×C61D411yescharacteristic
39C2×C42×C61D411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—22no—
42C22⋊C8×C61—22no—
43C4×C8×C61—22no—
44#95×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2×D412yes—
48C22×C4×C61C2×D411yescharacteristic
49C22×Dic61—22no—
50C22×Dic61—22no—
51C2×Dic122—22no—
52C2×Dic122—44no—
53C2×Dic122—42no—
54C2×C8×C61—42no—
55C42×C61—21no—
56C42×C61—21no—
57C42×C61SD1612yes—
58C42×C61Q1612yes—
59C42×C61C2×Q811yescharacteristic
60C42×C61#4112yes—
61C42×C61#4111yescharacteristic
62C22⋊Dic61—41no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—44no—
66C4⋊Dic61—44no—
67C4⋊Dic61—42no—
68#11758196—44no—
69#11758196—42no—
70C4×Dic61—41no—
71C4×Dic61—42no—
72C4×Dic61—42no—
73#11758194—41no—
74#11758194—41no—
75C2×#92418—41no—
76C23×C61#12011yescharacteristic
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61C22⋊Q812yes—
83C2×C4×C61C22⋊Q811yescharacteristic
84C2×C4×C61#12412yes—
85C2×C4×C61#12411yescharacteristic
86C2×C4×C61C2×SD1611yescharacteristic
87C2×C4×C61C2×Q1611yescharacteristic
88C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C61#13711yescharacteristic
90C2×Dic61—24no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97Dic122—48no—
98Dic122—82no—
99C8×C61—82no—
100#92418—81no—
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#47511yescharacteristic
111C4×C61#47711yescharacteristic
112C4×C61#48711yescharacteristic
113C4×C61#48911yescharacteristic
114Dic61—44no—
115Dic61—82no—
116Dic61—82no—
117#2399—611no—
118#1995—611no—
119#1503—612no—
120#1303—612no—
121#1274D6111yescharacteristic
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#202411yescharacteristic
125C2×C61#203112yes—
126#533—611no—
127C2×C4×Q8—1221no—
128#431C2×D6112yes—
129#423—611no—
130#398—1222no—
131#395—1222no—
132C4×C4⋊C4—612no—
133C4×C4⋊C4—1221no—
134#376C2×D6111yescharacteristic
135#339—1221no—
136#339—1221no—
137#328—1222no—
138#328—1222no—
139C61#1037111yescharacteristic, complemented, Sylow
140C22×Q8—1221no—
141C2×M16—1221no—
142C4⋊Q8—612no—
143#125—1221no—
144C22⋊Q8—1222no—
145C4×Q8—1222no—
146C4×Q8—2442no—
147C4×Q8—2442no—
148#117—1221no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1222no—
153C2×C42—1222no—
154C2×C42D24411yescharacteristic
155C2×C42D24411yescharacteristic
156C2×C42C22×D6111yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—1222no—
159C22⋊C8—22no—
160C4×C8—22no—
161#95—22no—
162#95—612no—
163#95—612no—
164#95—1221no—
165#95—1221no—
166C2×Q8—1222no—
167C2×Q8—2442no—
168C2×Q8—2444no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4C2×D24411yescharacteristic
174C22×C4D4×D6112yes—
175M16—2441no—
176M16—2441no—
177C2×C8—42no—
178C2×C8—2441no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—2444no—
182C4⋊C4—2442no—
183C4⋊C4—2444no—
184C4⋊C4—2444no—
185C4⋊C4—2442no—
186C22⋊C4—2441no—
187C42—21no—
188C42—21no—
189C42—2441no—
190C42—2442no—
191C42—2442no—
192C42#1175819012yes—
193C42Dic24412yes—
194C42#1175822212yes—
195C42#1175822411yescharacteristic
196C42Q8×D6111yescharacteristic
197C23#1451974711yescharacteristic
198Q8—4882no—
199Q8—2448no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—1224no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451975512yes—
213C2×C4#1451975711yescharacteristic
214C2×C4#1451976312yes—
215C2×C4#1451976511yescharacteristic
216C2×C4C2×#1175819011yescharacteristic
217C2×C4C2×Dic24411yescharacteristic
218C2×C4#1451980511yescharacteristic
219C2×C4#1451981011yescharacteristic
220C8—82no—
221C8—4881no—
222C22—22no—
223C22#1683967511yescharacteristic
224C22#1683991511yescharacteristic
225C22#1683992011yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—4882no—
231C4—4882no—
232C4—2444no—
233C4#1684004811yescharacteristic
234C4#1684005811yescharacteristic
235C4#1684011311yescharacteristic
236C4#1684012211yescharacteristic
237C2—21no—
238C2—21no—
239C2#2144696111yescharacteristic
240C2#2144699012yes—
subgroupG/H
centerC2×C4#14519765
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1274D61
hypocenterC61#10371
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
21. #14519777Q8semidirect
139. C61#10371semidirect

Maximal subgroups

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

subgroupindex
#214491122
#214468002
#214443192
#214437212
C61×#12742
#1037161