Finite Group Databasebeta

← #29583143

Subgroups — #29583143

Order 15616.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446800C211yesmaximal, characteristic
2#21444317C212yesmaximal
3#21443722C212yesmaximal
4#21443648C211yesmaximal, characteristic
5C61×#2399C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9#16839522—21no—
10#16839522—21no—
11#16839498—22no—
12#16839498—22no—
13C2×C4×Q8×C61—21no—
14C61×#398—22no—
15C61×#395—22no—
16C4×C4⋊C4×C61—21no—
17C4×C4⋊C4×C61C2212yes—
18C61×#376C2211yescharacteristic
19C2×#11758194—21no—
20#14519777Q812yescomplemented
21#14519769—21no—
22#14519756—22no—
23C4×Dic122—22no—
24#14519736—21no—
25C4⋊#92418—22no—
26C4⋊#92418—22no—
27C22⋊#92418—22no—
28C4×#92418—22no—
29C22×Q8×C61—21no—
30C4×Q8×C61—42no—
31C4×Q8×C61—42no—
32C2×C4⋊C4×C61—22no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—22no—
36C2×C42×C61—22no—
37C2×C42×C61D411yescharacteristic
38C2×C42×C61D411yescharacteristic
39C2×C42×C61C2311yescharacteristic
40#95×C61—21no—
41#95×C61—21no—
42#95×C61—22no—
43#95×C61D412yes—
44#95×C61D412yes—
45C2×Q8×C61—42no—
46C2×Q8×C61—44no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61C2×D412yes—
52C22×C4×C61C2×D411yescharacteristic
53C2×Dic122—22no—
54C4⋊C4×C61—44no—
55C4⋊C4×C61—44no—
56C4⋊C4×C61—44no—
57C4⋊C4×C61—42no—
58C42×C61—21no—
59C42×C61—21no—
60C42×C61—42no—
61C42×C61—42no—
62C42×C61SD1612yes—
63C42×C61Q1612yes—
64C42×C61C2×Q811yescharacteristic
65C42×C61#4112yes—
66C42×C61#4111yescharacteristic
67C22⋊Dic61—41no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70#11758196—42no—
71C4×Dic61—41no—
72#11758194—41no—
73#11758194—41no—
74C2×#92418—42no—
75C2×#92418—41no—
76C23×C61#12011yescharacteristic
77Q8×C61—48no—
78C2×C4×C61—24no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61C22⋊Q812yes—
90C2×C4×C61C22⋊Q811yescharacteristic
91C2×C4×C61#12412yes—
92C2×C4×C61#12411yescharacteristic
93C2×C4×C61C2×SD1611yescharacteristic
94C2×C4×C61C2×Q1611yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C61#13711yescharacteristic
97C2×Dic61—42no—
98Dic122—82no—
99#92418—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—44no—
110C4×C61—42no—
111C4×C61—82no—
112C4×C61#47511yescharacteristic
113C4×C61#47711yescharacteristic
114C4×C61#48711yescharacteristic
115C4×C61#48911yescharacteristic
116Dic61—82no—
117#2399D6111yescharacteristic
118#1995—611no—
119#1503—612no—
120#1303—612no—
121#1274—611no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#202411yescharacteristic
125C2×C61#203112yes—
126#533—611no—
127C2×C4×Q8—21no—
128#431—612no—
129#423—611no—
130#398—22no—
131#395—22no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4C2×D6112yes—
134#376C2×D6111yescharacteristic
135#339—1221no—
136#339—1221no—
137#328—1222no—
138#328—1222no—
139C61#1037111yescharacteristic, complemented, Sylow
140C22×Q8—21no—
141C2×M16—1221no—
142C4⋊Q8—612no—
143#125—1221no—
144C22⋊Q8—1222no—
145C4×Q8—42no—
146C4×Q8—42no—
147C4×Q8—1222no—
148#117—1221no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C42—22no—
154C2×C42C22⋊D6111yescharacteristic
155C2×C42C22⋊D6111yescharacteristic
156C2×C42C22×D6111yescharacteristic
157C4⋊C8—1222no—
158C4⋊C8—1222no—
159C22⋊C8—1222no—
160C4×C8—1222no—
161#95—21no—
162#95—21no—
163#95—22no—
164#95C22⋊D6112yes—
165#95C22⋊D6112yes—
166C2×Q8—42no—
167C2×Q8—44no—
168C2×Q8—1222no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4C2×C22⋊D6112yes—
174C22×C4C2×C22⋊D6111yescharacteristic
175M16—2441no—
176M16—2441no—
177C2×C8—2442no—
178C2×C8—2441no—
179C4⋊C4—44no—
180C4⋊C4—42no—
181C4⋊C4—44no—
182C4⋊C4—44no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—2442no—
186C22⋊C4—2441no—
187C42—21no—
188C42—21no—
189C42—42no—
190C42—42no—
191C42—2441no—
192C42#1175820012yes—
193C42#1175820212yes—
194C42Q8×D6111yescharacteristic
195C42#1175822611yescharacteristic
196C42#1175822612yes—
197C23#1451974611yescharacteristic
198Q8—48no—
199Q8—4882no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—2442no—
212C2×C4#1451975312yes—
213C2×C4#1451975311yescharacteristic
214C2×C4#1451976612yes—
215C2×C4#1451976611yescharacteristic
216C2×C4C2×#1175820011yescharacteristic
217C2×C4C2×#1175820211yescharacteristic
218C2×C4#1451980311yescharacteristic
219C2×C4#1451980811yescharacteristic
220C8—4882no—
221C8—4881no—
222C22—22no—
223C22#1683967311yescharacteristic
224C22#1683991311yescharacteristic
225C22#1683991811yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—44no—
230C4—42no—
231C4—82no—
232C4—4882no—
233C4#1684004411yescharacteristic
234C4#1684005411yescharacteristic
235C4#1684011411yescharacteristic
236C4#1684012411yescharacteristic
237C2—21no—
238C2—21no—
239C2#2144695711yescharacteristic
240C2#2144698812yes—
subgroupG/H
centerC2×C4#14519766
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2399C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#2399D61
hypocenterC61#10371
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
20. #14519777Q8semidirect
139. C61#10371semidirect

Maximal subgroups

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

subgroupindex
#214468002
#214443172
#214437222
#214436482
C61×#23992
#1037161