Finite Group Databasebeta

← #30595654

Subgroups — #30595654

Order 15616.

624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 114 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#21460636C214yesmaximal, complemented
3#21448381C211yesmaximal, characteristic
4C2×#14519844—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—
15#14519844—44no—
16C22×D244—22no—
17C22×D244C2×C412yes—
18C22×C4×D61—22no—
19#14519774—24no—
20#14519739—44no—
21#14519739—44no—
22#14519739—44no—
23C2×#11758198—22no—
24C2×#11758198—24no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D412yes—
27C2×C4×Dic61D412yes—
28C2×C4×Dic61C2311yescharacteristic
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61C2×C412yes—
31C2×C42×C61C2×C411yescharacteristic
32C23×D61—22no—
33C22×C4×C61—22no—
34C22×C4×C61C22⋊C412yes—
35C22×C4×C61C22×C411yescharacteristic
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C22⋊C411yescharacteristic
38C22×Dic61C2×D412yes—
39C2×D244—28no—
40C2×D244—22no—
41C2×D244—44no—
42C2×D244—42no—
43C2×D244—42no—
44C2×D244—44no—
45C2×D244M1614yes—
46C2×C4×D61—44no—
47C2×C4×D61—48no—
48C2×#92420—44no—
49C2×#92420—44no—
50C2×#92420—44no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—44no—
53C42×C61—22no—
54#11758198—44no—
55#11758198—44no—
56#11758198—44no—
57C4×Dic61—22no—
58C4×Dic61—42no—
59C4×Dic61—41no—
60C4×Dic61D814yes—
61C4×Dic61SD1614yes—
62C23×C61C2×C22⋊C411yescharacteristic
63C22×D61—24no—
64C22×D61—42no—
65C22×D61—42no—
66C22×D61—44no—
67C22×D61—44no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—44no—
74C2×C4×C61#10214yes—
75C2×C4×C61C2×M1612yes—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61#10012yes—
81C2×Dic61#10214yes—
82C2×Dic61C2×D812yes—
83C2×Dic61C2×SD1612yes—
84D244—44no—
85D244—44no—
86D244—416no—
87C4×D61—88no—
88#92420—84no—
89#7651—611nomaximal, Sylow
90C22×C61#40711yescharacteristic
91C22×C61#41011yescharacteristic
92C22×C61C2×#10011yescharacteristic
93C22×C61C2×#10212yes—
94C22×C61#42112yes—
95C2×D61—44no—
96C2×D61—48no—
97C2×D61—82no—
98C2×D61—82no—
99C2×D61—84no—
100C4×C61—22no—
101C4×C61—24no—
102C4×C61—82no—
103Dic61—22no—
104Dic61—22no—
105Dic61—41no—
106Dic61#33114yes—
107C4×#127—611no—
108#1831—612no—
109#1270—614no—
110C2×C61#146611yescharacteristic
111C2×C61#148612yes—
112C2×C61#151712yes—
113C2×C61#153611yescharacteristic
114C2×C61C2×#33111yescharacteristic
115D61—84no—
116C2×#127—611no—
117C2×C4×D4—612no—
118C2×C4×D4—1222no—
119C2×C4⋊C8—1222no—
120#390—612no—
121#390—1222no—
122#384#692311yescharacteristic
123C43—611no—
124#336—614no—
125#336—1222no—
126C61#765111yescharacteristic, complemented, Sylow
127C22×D4—612no—
128C22×D4—1222no—
129C23×C4—1222no—
130C22×C8—1224no—
131#127—1224no—
132C4×D4—2444no—
133C4×D4—2444no—
134C4×D4—2444no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C2×#692312yes—
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—1222no—
146C2×D4—614no—
147C2×D4—1228no—
148C2×D4—1222no—
149C2×D4—2442no—
150C2×D4—2442no—
151C2×D4—2444no—
152C2×D4—2444no—
153C22×C4—22no—
154C22×C4—611no—
155C22×C4—612no—
156C22×C4—611no—
157C22×C4—2448no—
158C22×C4—2444no—
159C22×C4C22⋊#692312yes—
160C22×C4C22×#692311yescharacteristic
161C2×C8—2444no—
162C2×C8—2444no—
163C2×C8—2444no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C22⋊C4—2444no—
167C22⋊C4—2444no—
168C22⋊C4—2444no—
169C42—22no—
170C42—614no—
171C42—614no—
172C42—1222no—
173C42—2441no—
174C42—2442no—
175C23—1224no—
176C23—2442no—
177C23—2442no—
178C23—2444no—
179C23—2444no—
180C23C2×C22⋊#692311yescharacteristic
181D4—2444no—
182D4—2444no—
183D4—24416no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—612no—
191C2×C4—614no—
192C2×C4—612no—
193C2×C4—612no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—1222no—
198C2×C4—4888no—
199C2×C4#1451983914yes—
200C2×C4D61⋊M1612yes—
201C8—4884no—
202C22—4884no—
203C22—4882no—
204C22—4882no—
205C22—2444no—
206C22—2448no—
207C22#1684073411yescharacteristic
208C22#1684074311yescharacteristic
209C22D61⋊#10011yescharacteristic
210C22C2×#1451983912yes—
211C22#1684076112yes—
212C4—22no—
213C4—24no—
214C4—82no—
215C4—614no—
216C4—1222no—
217C4—1222no—
218C4—2441no—
219C2—4884no—
220C2#2146108011yescharacteristic
221C2#2146114612yes—
222C2#2146125012yes—
223C2#2146130911yescharacteristic
224C2D61⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7651
LCSG ▷ C22×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. #21461735C2semidirect
2. #21460636C2semidirect
126. C61#7651semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606362
#214483812
#765161