Finite Group Databasebeta

← #30595653

Subgroups — #30595653

Order 15616.

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

normal subgroups only

This group has 624 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#21461735C212yesmaximal, complemented
2#21460635C214yesmaximal, complemented
3#127×Dic61C211yesmaximal, characteristic
4C2×#14519844—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—
15#14519844—44no—
16C23×Dic61—22no—
17D4×Dic61—44no—
18D4×Dic61—44no—
19D4×Dic61—44no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×C22⋊Dic61—22no—
23C2×C22⋊Dic61—24no—
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28C22×D4×C61—22no—
29C22×D4×C61C2×C412yes—
30#127×C61—24no—
31C2×C42×C61C2×C411yescharacteristic
32C24×C61—22no—
33C2×D4×C61—28no—
34C2×D4×C61—22no—
35C2×D4×C61—44no—
36C2×D4×C61—42no—
37C2×D4×C61—42no—
38C2×D4×C61—44no—
39C2×D4×C61M1614yes—
40C22×C4×C61C22⋊C412yes—
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—44no—
44C22×Dic61—48no—
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C2×D412yes—
48C2×#92420—44no—
49C2×#92420—44no—
50C2×#92420—44no—
51C42×C61—22no—
52C22⋊Dic61—44no—
53C22⋊Dic61—44no—
54C22⋊Dic61—44no—
55C4⋊Dic61—44no—
56C4⋊Dic61—42no—
57C4×Dic61—22no—
58C4×Dic61—42no—
59C4×Dic61—41no—
60C4×Dic61D814yes—
61C4×Dic61SD1614yes—
62C23×C61—24no—
63C23×C61—42no—
64C23×C61—42no—
65C23×C61—44no—
66C23×C61—44no—
67C23×C61C2×C22⋊C411yescharacteristic
68D4×C61—44no—
69D4×C61—44no—
70D4×C61—416no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61#10214yes—
76C2×C4×C61C2×M1612yes—
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×Dic61#10214yes—
86C2×Dic61C2×D812yes—
87C2×Dic61C2×SD1612yes—
88#92420—84no—
89#7651—611nomaximal, Sylow
90C22×C61—44no—
91C22×C61—48no—
92C22×C61—82no—
93C22×C61—82no—
94C22×C61—84no—
95C22×C61#40711yescharacteristic
96C22×C61#41011yescharacteristic
97C22×C61C2×#10011yescharacteristic
98C22×C61C2×#10212yes—
99C22×C61#42112yes—
100C4×C61—22no—
101C4×C61—24no—
102Dic61—22no—
103Dic61—22no—
104Dic61—41no—
105Dic61—82no—
106Dic61#33114yes—
107C4×#127—611no—
108#1831—612no—
109#1270—614no—
110C2×C61—84no—
111C2×C61#146611yescharacteristic
112C2×C61#148612yes—
113C2×C61#151712yes—
114C2×C61#153611yescharacteristic
115C2×C61C2×#33111yescharacteristic
116C2×#127#692311yescharacteristic
117C2×C4×D4—612no—
118C2×C4×D4—1222no—
119C2×C4⋊C8—1222no—
120#390—612no—
121#390—1222no—
122#384—611no—
123C43—611no—
124#336—614no—
125#336—1222no—
126C61#765111yescharacteristic, complemented, Sylow
127C22×D4—22no—
128C22×D4C2×#692312yes—
129C23×C4—1222no—
130C22×C8—1224no—
131#127—24no—
132C4×D4—2444no—
133C4×D4—2444no—
134C4×D4—2444no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1222no—
137C2×C22⋊C4—1222no—
138C2×C22⋊C4—1224no—
139C2×C42—612no—
140C2×C42—611no—
141C2×C42—612no—
142C2×C42—611no—
143C2×C42C2×#692311yescharacteristic
144C4⋊C8—2444no—
145C24—22no—
146C2×D4—28no—
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—42no—
150C2×D4—44no—
151C2×D4—44no—
152C2×D4#1175821714yes—
153C22×C4—611no—
154C22×C4—612no—
155C22×C4—611no—
156C22×C4—1222no—
157C22×C4—2448no—
158C22×C4—2444no—
159C22×C4C22⋊#692312yes—
160C22×C4C22×#692311yescharacteristic
161C2×C8—2444no—
162C2×C8—2444no—
163C2×C8—2444no—
164C4⋊C4—2442no—
165C4⋊C4—2444no—
166C22⋊C4—2444no—
167C22⋊C4—2444no—
168C22⋊C4—2444no—
169C42—22no—
170C42—614no—
171C42—614no—
172C42—1222no—
173C42—2441no—
174C42—2442no—
175C23—24no—
176C23—42no—
177C23—42no—
178C23—44no—
179C23—44no—
180C23C2×C22⋊#692311yescharacteristic
181D4—44no—
182D4—44no—
183D4—416no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—612no—
189C2×C4—614no—
190C2×C4—612no—
191C2×C4—612no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1221no—
195C2×C4—1222no—
196C2×C4—4888no—
197C2×C4—2442no—
198C2×C4—2444no—
199C2×C4#1451983914yes—
200C2×C4C2×#1175821712yes—
201C8—4884no—
202C22—44no—
203C22—48no—
204C22—84no—
205C22—82no—
206C22—82no—
207C22#1684073211yescharacteristic
208C22#1684074211yescharacteristic
209C22D61⋊#10011yescharacteristic
210C22C2×#1451983912yes—
211C22#1684076012yes—
212C4—22no—
213C4—24no—
214C4—614no—
215C4—1222no—
216C4—1222no—
217C4—4882no—
218C4—2441no—
219C2—84no—
220C2#2146107911yescharacteristic
221C2#2146114412yes—
222C2#2146124812yes—
223C2#2146130811yescharacteristic
224C2D61⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#127#6923
hypocenterC61#7651
LCSG ▷ C22×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. #21461735C2semidirect
2. #21460635C2semidirect
126. C61#7651semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606352
#127×Dic612
#765161