Finite Group Databasebeta

← #29583152

Subgroups — #29583152

Order 15616.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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#21449124C211yesmaximal, characteristic, complemented
2#21446651C211yesmaximal, characteristic
3#21444315C212yesmaximal
4#21443721C212yesmaximal, complemented
5C61×#1274C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839786C2211yescharacteristic
8C2×#14519705—22no—
9#16839704—22no—
10#16839696—22no—
11C4×#11758196—22no—
12C4×C4⋊Dic61C2212yes—
13#16839497—22no—
14#16839497—22no—
15C61×#431C2212yes—
16C61×#376C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758194—21no—
19#14519777Q811yescharacteristic
20#14519774Q811yescharacteristic
21#14519765—21no—
22#14519751—22no—
23C4×D244—22no—
24C2×C4⋊Dic61—22no—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×C4×Dic61—22no—
28C4⋊#92418—22no—
29#14519705—44no—
30#14519684—22no—
31#14519684—22no—
32#14519684D412yes—
33#14519684D412yes—
34C2×C42×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38C4×C8×C61—22no—
39#95×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61C2×D411yescharacteristic
43C2×C22⋊D61—41no—
44C22×Dic61—22no—
45C22×Dic61—22no—
46#11758222—42no—
47#11758222—42no—
48C2×D244—21no—
49C2×D244—22no—
50C2×C4×D61—41no—
51C2×Dic122—21no—
52C2×C8×C61—42no—
53C42×C61—22no—
54C42×C61—22no—
55C42×C61C2×Q811yescharacteristic
56C42×C61#4112yes—
57C42×C61#4111yescharacteristic
58#11758198—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—44no—
61#11758196—44no—
62#11758196—44no—
63C4×Dic61—42no—
64C4×Dic61—42no—
65#11758194—42no—
66C2×#92418—41no—
67C23×C61#12011yescharacteristic
68C22×D61—41no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61C22⋊Q812yes—
74C2×C4×C61C22⋊Q811yescharacteristic
75C2×C4×C61#12412yes—
76C2×C4×C61#12411yescharacteristic
77C2×C4×C61#13512yes—
78C2×C4×C61AGL(1,ℤ/8)12yes—
79C22⋊D61—82no—
80C2×Dic61—24no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—41no—
86C2×Dic61—42no—
87D244—42no—
88D244—82no—
89C4×D61—81no—
90C4×D61—81no—
91Dic122—42no—
92C8×C61—82no—
93#92418—81no—
94#10372—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61#39311yescharacteristic
97C22×C61#44912yes—
98C2×D61—81no—
99C2×D61—82no—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—82no—
103C4×C61#47812yes—
104C4×C61#48811yescharacteristic
105C4×C61#49011yescharacteristic
106Dic61—44no—
107Dic61—82no—
108Dic61—81no—
109#2402—611no—
110#1963—611no—
111#1502—612no—
112#1303—612no—
113#1274D6111yescharacteristic, complemented
114C2×C61—22no—
115C2×C61#202511yescharacteristic
116C2×C61#203112yes—
117D61—161no—
118#532—611no—
119#431C2×D6112yes—
120#423—611no—
121C2×#104—1222no—
122#400—1222no—
123#398—1222no—
124C4×C4⋊C4—612no—
125C4×C4⋊C4—1222no—
126#376C2×D6111yescharacteristic
127#327—1222no—
128#327—1222no—
129C61#1037211yescharacteristic, complemented, Sylow
130C2×#41—1221no—
131C2×M16—1221no—
132C4⋊Q8—611no—
133#127—611no—
134#124—1221no—
135#121—1222no—
136C4×D4—1222no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4—1222no—
140C2×C42—1222no—
141C2×C42D24412yes—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—1222no—
145#104—2444no—
146C22⋊C8—22no—
147C4×C8—22no—
148#95—22no—
149#95—612no—
150#95—612no—
151#95—1222no—
152#95—1222no—
153#41—2442no—
154#41—2442no—
155C2×Q8—1221no—
156C2×D4—1222no—
157C2×D4—1221no—
158C2×D4—2441no—
159C22×C4—22no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4—2441no—
163C22×C4C2×D24411yescharacteristic
164C22×C4D4×D6112yes—
165M16—2442no—
166C2×C8—42no—
167C2×C8—2441no—
168C4⋊C4—1222no—
169C4⋊C4—2444no—
170C4⋊C4—2444no—
171C4⋊C4—2444no—
172C22⋊C4—2442no—
173C42—22no—
174C42—22no—
175C42—2442no—
176C42—2442no—
177C42#1175822212yes—
178C42#1175822411yescharacteristic
179C42Q8×D6111yescharacteristic
180C23—2441no—
181C23#1451974711yescharacteristic
182Q8—2442no—
183D4—4882no—
184D4—4882no—
185D4—2442no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—1224no—
191C2×C4—4881no—
192C2×C4—4881no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2441no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4#1451975512yes—
200C2×C4#1451975711yescharacteristic
201C2×C4#1451976312yes—
202C2×C4#1451976511yescharacteristic
203C2×C4#1451979912yes—
204C2×C4#1451980512yes—
205C8—82no—
206C8—4881no—
207C22—22no—
208C22—4881no—
209C22—4882no—
210C22#1683967511yescharacteristic
211C22#1683990912yes—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—4882no—
216C4—4881no—
217C4—2444no—
218C4#1684006312yes—
219C4#1684011711yescharacteristic
220C4#1684012711yescharacteristic
221C2—22no—
222C2—9761no—
223C2#2144696611yescharacteristic
224C2#2144699012yes—
subgroupG/H
centerC2×C4#14519765
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#1274D61
hypocenterC61#10372
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
1. #21449124C2semidirect
4. #21443721C2semidirect
5. C61×#1274C2semidirect
113. #1274D61semidirect
129. C61#10372semidirect

Maximal subgroups

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

subgroupindex
#214491242
#214466512
#214443152
#214437212
C61×#12742
#1037261