Finite Group Databasebeta

← #30595486

Subgroups — #30595486

Order 15616.

608 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461746C212yesmaximal, complemented
2#21460636C214yesmaximal, complemented
3#21448381C211yesmaximal, characteristic
4#16840628—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×#14519774C411yescharacteristic
8C2×#14519739—22no—
9C2×#14519739C412yes—
10#16839663—22no—
11#16839663C2212yes—
12C42×Dic61C2211yescharacteristic
13C61×#384C411yescharacteristic
14C22×#92420—24no—
15C22×D244—22no—
16C22×D244C2×C412yes—
17C22×C4×D61—22no—
18#14519774—22no—
19#14519774C814yescomplemented
20#14519739—48no—
21#14519739—44no—
22C2×#11758198—22no—
23C2×#11758198—24no—
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61C2×C412yes—
30C2×C42×C61C2×C411yescharacteristic
31C23×D61—22no—
32C22×C4×C61—22no—
33C22×C4×C61C22⋊C412yes—
34C22×C4×C61C22×C411yescharacteristic
35C22×Dic61C22⋊C411yescharacteristic
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×D244—28no—
39C2×D244—22no—
40C2×D244—44no—
41C2×D244—44no—
42C2×D244—42no—
43C2×D244—42no—
44C2×D244C2×C814yes—
45C2×C4×D61—48no—
46C2×C4×D61—44no—
47C2×#92420—44no—
48C2×#92420—44no—
49C2×#92420—44no—
50C4⋊C4×C61—44no—
51C4⋊C4×C61—42no—
52C42×C61C2×C812yes—
53C42×C61M1612yes—
54#11758198—44no—
55#11758198—48no—
56C4×Dic61—22no—
57C4×Dic61—24no—
58C4×Dic61—42no—
59C4×Dic61—41no—
60C23×C61C2×C22⋊C411yescharacteristic
61C22×D61—24no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61—44no—
65C22×D61—44no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—42no—
71C2×C4×C61—44no—
72C2×C4×C61C22⋊C814yes—
73C2×C4×C61C22×C811yescharacteristic
74C2×C4×C61C2×M1611yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61#10012yes—
81C2×Dic61AGL(1,ℤ/8)14yes—
82D244—44no—
83D244—44no—
84D244—416no—
85C4×D61—88no—
86#92420—84no—
87#7603—611nomaximal, Sylow
88C22×C61C2×C22⋊C811yescharacteristic
89C22×C61#41011yescharacteristic
90C22×C61C2×#10011yescharacteristic
91C22×C61#41812yes—
92C22×C61#42112yes—
93C2×D61—44no—
94C2×D61—48no—
95C2×D61—82no—
96C2×D61—82no—
97C2×D61—84no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—24no—
101C4×C61—82no—
102Dic61—22no—
103Dic61—24no—
104Dic61—41no—
105C4×#127—611no—
106#1839—612no—
107#1270—614no—
108C2×C61#146011yescharacteristic
109C2×C61#147812yes—
110C2×C61#151412yes—
111C2×C61#153611yescharacteristic
112C2×C61#155511yescharacteristic
113D61—84no—
114C2×#127—611no—
115C2×C4×D4—612no—
116C2×C4×D4—1222no—
117#390—612no—
118#390—1222no—
119#384#692311yescharacteristic
120C43—611no—
121#336—614no—
122#336—1222no—
123#336—1222no—
124C61#760311yescharacteristic, complemented, Sylow
125C22×D4—612no—
126C22×D4—1222no—
127C23×C4—1222no—
128C22×C8—1224no—
129#127—614no—
130#127—1222no—
131C4×D4—2448no—
132C4×D4—2444no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4C2×#692312yes—
135C2×C22⋊C4—1222no—
136C2×C22⋊C4—1224no—
137C2×C42—612no—
138C2×C42—611no—
139C2×C42—612no—
140C2×C42—611no—
141C2×C42C2×#692311yescharacteristic
142C24—1222no—
143C2×D4—614no—
144C2×D4—1228no—
145C2×D4—1222no—
146C2×D4—2442no—
147C2×D4—2442no—
148C2×D4—2444no—
149C2×D4—2444no—
150C22×C4—22no—
151C22×C4—612no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—2444no—
155C22×C4—2448no—
156C22×C4C22⋊#692312yes—
157C22×C4C22×#692311yescharacteristic
158C2×C8—2444no—
159C2×C8—2444no—
160C2×C8—2444no—
161C4⋊C4—42no—
162C4⋊C4—44no—
163C22⋊C4—2448no—
164C22⋊C4—2444no—
165C42—1222no—
166C42—1224no—
167C42—2441no—
168C42—2442no—
169C42D61⋊C812yes—
170C42#1175821312yes—
171C23—1224no—
172C23—2442no—
173C23—2442no—
174C23—2444no—
175C23—2444no—
176C23C2×C22⋊#692311yescharacteristic
177D4—2444no—
178D4—2444no—
179D4—24416no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—44no—
186C2×C4—612no—
187C2×C4—614no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1221no—
192C2×C4—1222no—
193C2×C4—4888no—
194C2×C4#1451983414yes—
195C2×C4C2×D61⋊C811yescharacteristic
196C2×C4C2×#1175821311yescharacteristic
197C8—4884no—
198C22—4882no—
199C22—4882no—
200C22—4884no—
201C22—2444no—
202C22—2448no—
203C22C2×#1451983411yescharacteristic
204C22#1684074311yescharacteristic
205C22D61⋊#10011yescharacteristic
206C22#1684075412yes—
207C22#1684076112yes—
208C4—21no—
209C4—21no—
210C4—24no—
211C4—82no—
212C4—1222no—
213C4—1224no—
214C4—2441no—
215C2—4884no—
216C2#2146106011yescharacteristic
217C2#2146112012yes—
218C2#2146124012yes—
219C2#2146130911yescharacteristic
220C2#2146134711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #21461746C2semidirect
2. #21460636C2semidirect
19. #14519774C8semidirect
124. C61#7603semidirect

Maximal subgroups

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

subgroupindex
#214617462
#214606362
#214483812
#760361