Finite Group Databasebeta

← #29685451

Subgroups — #29685451

Order 15616.

668 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 227 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#21448316C211yesmaximal, characteristic
2#21446432C214yesmaximal
3#21446383C214yesmaximal, complemented
4#21445677C212yesmaximal, complemented
5#21445586C212yesmaximal
6#21445568C211yesmaximal, characteristic, complemented
7C4×#97×C61C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9C2×#14519706C2214yes—
10C2×#14519689C2214yes—
11C2×#14519688C2212yes—
12#16839653C414yes—
13#16839646C414yes—
14C4×#11758196C2212yes—
15C4×#11758198C2212yes—
16#16839608C2211yescharacteristic
17#16839517C2214yes—
18#16839516C2214yes—
19#16839516C2214yes—
20C2×#97×C61C2214yes—
21C2×C4×C8×C61C2212yes—
22C43×C61C2211yescharacteristic
23C22×C4×D61C2311yescharacteristic
24C22×#92418C2314yes—
25#14519734—24no—
26C2×#11758196C2×C412yes—
27C2×#11758196C2×C414yes—
28C2×#11758198C2×C412yes—
29C2×#11758198C2×C414yes—
30C2×C4×Dic61C2311yescharacteristic
31C2×C4×Dic61C2312yes—
32#14519706—28no—
33#14519689—28no—
34#14519688—24no—
35#14519684C2×C414yes—
36#14519684C2×C414yes—
37#14519684C2×C414yes—
38C22×C8×C61C2314yes—
39C2×C42×C61C2×C414yes—
40C2×C42×C61C2312yes—
41C2×C42×C61C2311yescharacteristic
42#97×C61—28no—
43C4×C8×C61—24no—
44C23×D61C22×C411yescharacteristic
45C22×C4×C61C22×C414yes—
46C22×C4×C61C22×C412yes—
47C22×C4×C61C2411yescharacteristic
48C22×Dic61C22×C411yescharacteristic
49C22×Dic61C22×C414yes—
50C22×Dic61C22×C412yes—
51C2×C4×D61—24no—
52C2×C4×D61—22no—
53C2×C8×C61—24no—
54C2×C8×C61—24no—
55C2×C8×C61#4118yes—
56C42×C61—24no—
57C42×C61—44no—
58C42×C61#4114yes—
59#11758198—24no—
60#11758198—44no—
61#11758196—24no—
62#11758196—44no—
63C4×Dic61—24no—
64C4×Dic61—22no—
65C2×#92418—24no—
66C2×#92418—24no—
67C2×#92418—24no—
68C23×C61C23×C411yescharacteristic
69C22×D61—21no—
70C22×D61—22no—
71C22×D61—24no—
72C2×C4×C61—24no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—24no—
76C2×C4×C61#11714yes—
77C2×C4×C61C2×#4112yes—
78C2×C4×C61C2×#4114yes—
79C2×Dic61—22no—
80C2×Dic61—21no—
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C4×D61—44no—
87C8×C61—28no—
88#92418—44no—
89#21433—611nomaximal, Sylow
90C22×C61C2×#11711yescharacteristic
91C22×C61C4×#4112yes—
92C22×C61#56814yes—
93C2×D61—42no—
94C2×D61—44no—
95C2×D61—41no—
96C4×C61—24no—
97C4×C61—44no—
98C4×C61#52914yes—
99Dic61—42no—
100Dic61—44no—
101Dic61—41no—
102#2298—611no—
103#1924—614no—
104#1917—614no—
105#1768—612no—
106#1750—612no—
107#1745—611no—
108C4×#97D6111yescharacteristic, complemented
109C2×C61#229811yescharacteristic
110C2×C61#292312yes—
111C2×C61#296714yes—
112D61—81no—
113C2×#117—611no—
114C2×C4⋊C8—614no—
115C2×C22⋊C8—614no—
116C2×#97—612no—
117C2×#97C2×D6114yes—
118C2×C4×C8C2×D6112yes—
119#388—614no—
120#387—614no—
121C4×C4⋊C4—612no—
122C4×C22⋊C4—612no—
123#376—611no—
124C43C2×D6111yescharacteristic
125#336—614no—
126#336—614no—
127#336—614no—
128C61#2143311yescharacteristic, complemented, Sylow
129C23×C4—611no—
130C22×C8—614no—
131C22×C8C22×D6114yes—
132#117—1224no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—614no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4—614no—
137C2×C42—611no—
138C2×C42—612no—
139C2×C42C4×D6114yes—
140C2×C42C22×D6112yes—
141C2×C42C22×D6111yescharacteristic
142C4⋊C8—1228no—
143C22⋊C8—1228no—
144#97—28no—
145#97—1224no—
146C4×C8—24no—
147#95—614no—
148#95—614no—
149#95—614no—
150C24—611no—
151C22×C4—614no—
152C22×C4—611no—
153C22×C4—612no—
154C22×C4—1224no—
155C22×C4—1222no—
156C22×C4C2×C4×D6114yes—
157C22×C4C2×C4×D6112yes—
158C22×C4C23×D6111yescharacteristic
159C2×C8—24no—
160C2×C8—24no—
161C2×C8—1224no—
162C2×C8—1224no—
163C2×C8—1224no—
164C2×C8#1175822218yes—
165C4⋊C4—1224no—
166C4⋊C4—2444no—
167C22⋊C4—1224no—
168C22⋊C4—2444no—
169C42—24no—
170C42—44no—
171C42—1224no—
172C42—1222no—
173C42#1175822214yes—
174C23—1221no—
175C23—1222no—
176C23—1224no—
177C23C22×C4×D6111yescharacteristic
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—1222no—
183C2×C4—1221no—
184C2×C4—1224no—
185C2×C4—1222no—
186C2×C4—1224no—
187C2×C4—1224no—
188C2×C4—1224no—
189C2×C4—2444no—
190C2×C4#1451973414yes—
191C2×C4C2×#1175822212yes—
192C2×C4C2×#1175822214yes—
193C8—28no—
194C8—2444no—
195C22—2441no—
196C22—2442no—
197C22—2444no—
198C22C2×#1451973411yescharacteristic
199C22C4×#1175822212yes—
200C22#1684052814yes—
201C4—24no—
202C4—44no—
203C4—2441no—
204C4—2442no—
205C4—2444no—
206C4#1684029614yes—
207C2—4881no—
208C2#2144831611yescharacteristic
209C2#2145446812yes—
210C2#2145480414yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC4×#97×C61C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC4×#97D61
hypocenterC61#21433
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
3. #21446383C2semidirect
4. #21445677C2semidirect
6. #21445568C2semidirect
7. C4×#97×C61C2semidirect
108. C4×#97D61semidirect
128. C61#21433semidirect

Maximal subgroups

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

subgroupindex
#214483162
#214464322
#214463832
#214456772
#214455862
#214455682
C4×#97×C612
#2143361