Finite Group Databasebeta

← #30595485

Subgroups — #30595485

Order 15616.

608 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 118 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#21460635C214yesmaximal, complemented
3#127×Dic61C211yesmaximal, characteristic
4#16840628—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×D4×Dic61—22no—
8C2×D4×Dic61C412yes—
9#16839665—22no—
10#16839665C2212yes—
11#16839632C411yescharacteristic
12C42×Dic61C2211yescharacteristic
13C2×#127×C61C411yescharacteristic
14C22×#92420—24no—
15C23×Dic61—22no—
16D4×Dic61—48no—
17D4×Dic61—44no—
18C2×C4⋊Dic61—22no—
19C2×C4⋊Dic61C2×C412yes—
20C2×C22⋊Dic61—22no—
21C2×C22⋊Dic61—24no—
22C2×C4×Dic61C2×C411yescharacteristic
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26C22×D4×C61—22no—
27C22×D4×C61C2×C412yes—
28#127×C61—22no—
29#127×C61C814yescomplemented
30C2×C42×C61C2×C411yescharacteristic
31C24×C61—22no—
32C2×D4×C61—28no—
33C2×D4×C61—22no—
34C2×D4×C61—44no—
35C2×D4×C61—44no—
36C2×D4×C61—42no—
37C2×D4×C61—42no—
38C2×D4×C61C2×C814yes—
39C22×C4×C61C22⋊C412yes—
40C22×C4×C61C22×C411yescharacteristic
41C22×Dic61—22no—
42C22×Dic61—48no—
43C22×Dic61—44no—
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C2×D412yes—
47C2×#92420—44no—
48C2×#92420—44no—
49C2×#92420—44no—
50C42×C61C2×C812yes—
51C42×C61M1612yes—
52C22⋊Dic61—44no—
53C22⋊Dic61—48no—
54C4⋊Dic61—44no—
55C4⋊Dic61—42no—
56C4×Dic61—22no—
57C4×Dic61—24no—
58C4×Dic61—42no—
59C4×Dic61—41no—
60C23×C61—24no—
61C23×C61—42no—
62C23×C61—42no—
63C23×C61—44no—
64C23×C61—44no—
65C23×C61C2×C22⋊C411yescharacteristic
66D4×C61—44no—
67D4×C61—44no—
68D4×C61—416no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C22⋊C814yes—
74C2×C4×C61C22×C811yescharacteristic
75C2×C4×C61C2×M1611yescharacteristic
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—44no—
83C2×Dic61—88no—
84C2×Dic61#10012yes—
85C2×Dic61AGL(1,ℤ/8)14yes—
86#92420—84no—
87#7603—611nomaximal, Sylow
88C22×C61—44no—
89C22×C61—48no—
90C22×C61—82no—
91C22×C61—82no—
92C22×C61—84no—
93C22×C61C2×C22⋊C811yescharacteristic
94C22×C61#41011yescharacteristic
95C22×C61C2×#10011yescharacteristic
96C22×C61#41812yes—
97C22×C61#42112yes—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—24no—
101Dic61—22no—
102Dic61—24no—
103Dic61—41no—
104Dic61—82no—
105C4×#127—611no—
106#1839—612no—
107#1270—614no—
108C2×C61—84no—
109C2×C61#146011yescharacteristic
110C2×C61#147812yes—
111C2×C61#151412yes—
112C2×C61#153611yescharacteristic
113C2×C61#155511yescharacteristic
114C2×#127#692311yescharacteristic
115C2×C4×D4—612no—
116C2×C4×D4—1222no—
117#390—612no—
118#390—1222no—
119#384—611no—
120C43—611no—
121#336—614no—
122#336—1222no—
123#336—1222no—
124C61#760311yescharacteristic, complemented, Sylow
125C22×D4—22no—
126C22×D4C2×#692312yes—
127C23×C4—1222no—
128C22×C8—1224no—
129#127—22no—
130#127#9242014yescomplemented
131C4×D4—2448no—
132C4×D4—2444no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—1222no—
135C2×C22⋊C4—1222no—
136C2×C22⋊C4—1224no—
137C2×C42—612no—
138C2×C42—611no—
139C2×C42—612no—
140C2×C42—611no—
141C2×C42C2×#692311yescharacteristic
142C24—22no—
143C2×D4—28no—
144C2×D4—22no—
145C2×D4—42no—
146C2×D4—42no—
147C2×D4—44no—
148C2×D4—44no—
149C2×D4C2×#9242014yes—
150C22×C4—612no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—1222no—
154C22×C4—2444no—
155C22×C4—2448no—
156C22×C4C22⋊#692312yes—
157C22×C4C22×#692311yescharacteristic
158C2×C8—2444no—
159C2×C8—2444no—
160C2×C8—2444no—
161C4⋊C4—2442no—
162C4⋊C4—2444no—
163C22⋊C4—2448no—
164C22⋊C4—2444no—
165C42—1222no—
166C42—1224no—
167C42—2441no—
168C42—2442no—
169C42C2×#9242012yes—
170C42#1175821712yes—
171C23—24no—
172C23—42no—
173C23—42no—
174C23—44no—
175C23—44no—
176C23C2×C22⋊#692311yescharacteristic
177D4—44no—
178D4—44no—
179D4—416no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—612no—
185C2×C4—614no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1221no—
190C2×C4—1222no—
191C2×C4—4888no—
192C2×C4—2442no—
193C2×C4—2444no—
194C2×C4C22⋊#9242014yes—
195C2×C4C22×#9242011yescharacteristic
196C2×C4C2×#1175821711yescharacteristic
197C8—4884no—
198C22—44no—
199C22—48no—
200C22—82no—
201C22—82no—
202C22—84no—
203C22C2×C22⋊#9242011yescharacteristic
204C22#1684074211yescharacteristic
205C22D61⋊#10011yescharacteristic
206C22#1684075412yes—
207C22#1684076012yes—
208C4—21no—
209C4—21no—
210C4—24no—
211C4—1222no—
212C4—1224no—
213C4—4882no—
214C4—2441no—
215C2—84no—
216C2#2146105911yescharacteristic
217C2#2146111812yes—
218C2#2146123912yes—
219C2#2146130811yescharacteristic
220C2#2146134711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#127#6923
hypocenterC61#7603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21461746C2semidirect
2. #21460635C2semidirect
29. #127×C61C8semidirect
124. C61#7603semidirect
130. #127#92420semidirect

Maximal subgroups

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

subgroupindex
#214617462
#214606352
#127×Dic612
#760361