Finite Group Databasebeta

← #30598150

Subgroups — #30598150

Order 15616.

1174 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 136 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#21461642C212yesmaximal
2C2×#16840608C214yesmaximal, complemented
3C22×#14519753C211yesmaximal, characteristic
4C2×#14519834—24no—
5C2×C22⋊#92420C2214yes—
6#16840608—28no—
7C23×C4×D61C2211yescharacteristic
8C2×#14519753—28no—
9C2×#14519753—24no—
10C22×C4⋊Dic61C411yescharacteristic
11C22×#11758196C2212yes—
12C22×#11758198C412yes—
13C23×Q8×C61C411yescharacteristic
14C22×#92420—24no—
15#14519834—48no—
16C22⋊#92420—28no—
17C24×D61C2×C411yescharacteristic
18C23×Dic61C2×C412yes—
19C23×Dic61C2311yescharacteristic
20C22×C4×D61—24no—
21C22×C4×D61—44no—
22C22×C4×D61D414yes—
23#14519753—232no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—24no—
26C2×#11758196—24no—
27C2×#11758196—24no—
28C2×#11758196D418yes—
29C2×#11758198—24no—
30C2×#11758198—24no—
31C2×#11758198—24no—
32C22×Q8×C61—24no—
33C22×Q8×C61—22no—
34C22×Q8×C61—44no—
35C23×C4×C61C2×C412yes—
36C23×C4×C61C2×C411yescharacteristic
37C24×C61C22×C411yescharacteristic
38C23×D61—22no—
39C23×D61—24no—
40C23×D61—24no—
41C23×D61—42no—
42C23×D61C22⋊C412yes—
43C2×Q8×C61—28no—
44C2×Q8×C61—416no—
45C2×Q8×C61—44no—
46C2×Q8×C61—44no—
47C22×C4×C61—22no—
48C22×C4×C61—24no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—44no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22⋊C414yes—
54C22×Dic61—22no—
55C22×Dic61—22no—
56C22×Dic61—28no—
57C22×Dic61—42no—
58C22×Dic61C22⋊C414yes—
59C22×Dic61C2×D412yes—
60C22×Dic61C2×D414yes—
61C2×C4×D61—28no—
62C2×C4×D61—28no—
63C2×C4×D61—44no—
64C2×C4×D61—416no—
65C2×#92420—48no—
66C2×#92420—44no—
67#11758198—216no—
68C4⋊Dic61—28no—
69#11758196—216no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2×C22⋊C412yes—
73C23×C61C2×C22⋊C411yescharacteristic
74C23×C61#13114yes—
75C22×D61—28no—
76C22×D61—22no—
77C22×D61—24no—
78C22×D61—24no—
79C22×D61—22no—
80C22×D61—416no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61#10114yes—
84Q8×C61—416no—
85C2×C4×C61—28no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—24no—
89C2×C4×C61—44no—
90C2×C4×C61—44no—
91C2×C4×C61—44no—
92C2×C4×C61#9914yes—
93C2×Dic61—24no—
94C2×Dic61—24no—
95C2×Dic61—28no—
96C2×Dic61—44no—
97C2×Dic61—44no—
98C2×Dic61—44no—
99C2×Dic61#12014yes—
100C4×D61—416no—
101#92420—84no—
102#8308—611nomaximal, Sylow
103C22×C61—28no—
104C22×C61—22no—
105C22×C61—22no—
106C22×C61#37911yescharacteristic
107C22×C61#40814yes—
108C22×C61#40812yes—
109C22×C61C2×#9912yes—
110C22×C61C2×#10112yes—
111C2×D61—28no—
112C2×D61—24no—
113C2×D61—416no—
114C2×D61—44no—
115C2×D61—42no—
116C2×D61—42no—
117C4×C61—24no—
118C4×C61—44no—
119Dic61—24no—
120Dic61—44no—
121C22×C22⋊Q8—611no—
122#1779—612no—
123C2×#324—614no—
124C2×C61—24no—
125C2×C61#147214yes—
126C2×C61#178011yescharacteristic
127C2×C61#178111yescharacteristic
128C2×C61#178411yescharacteristic
129D61—44no—
130C23×Q8#692311yescharacteristic
131C24×C4—611no—
132C2×C22⋊Q8—1228no—
133C2×C22⋊Q8—1224no—
134C22×C4⋊C4—612no—
135C22×C4⋊C4—611no—
136C22×C22⋊C4—612no—
137C2×C22⋊C8—614no—
138C2×C22⋊C8—1224no—
139#324—1228no—
140C61#830811yescharacteristic, complemented, Sylow
141C25—611no—
142C22×Q8—24no—
143C22×Q8—22no—
144C22×Q8—44no—
145C23×C4—611no—
146C23×C4—612no—
147C23×C4—614no—
148C23×C4—1224no—
149C23×C4—2444no—
150C23×C4C2×#692312yes—
151C23×C4C2×#692311yescharacteristic
152C22×C8—1224no—
153C22⋊Q8—12232no—
154C2×C4⋊C4—618no—
155C2×C4⋊C4—1224no—
156C2×C4⋊C4—1224no—
157C2×C4⋊C4—1224no—
158C2×C4⋊C4—1222no—
159C2×C22⋊C4—1224no—
160C2×C22⋊C4—1224no—
161C2×C22⋊C4—1224no—
162C22⋊C8—1228no—
163C22⋊C8—2448no—
164C24—612no—
165C24—1224no—
166C24—1222no—
167C24—1224no—
168C24—2442no—
169C24C22×#692311yescharacteristic
170C2×Q8—28no—
171C2×Q8—416no—
172C2×Q8—44no—
173C2×Q8—44no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—44no—
179C22×C4—612no—
180C22×C4—614no—
181C22×C4—614no—
182C22×C4—1228no—
183C22×C4—1222no—
184C22×C4—1222no—
185C22×C4—1228no—
186C22×C4—1228no—
187C22×C4—2444no—
188C22×C4—24416no—
189C22×C4—2442no—
190C22×C4C22⋊#692312yes—
191C22×C4C22⋊#692314yes—
192C2×C8—2444no—
193C2×C8—2448no—
194C4⋊C4—12216no—
195C4⋊C4—1228no—
196C22⋊C4—12216no—
197C23—22no—
198C23—22no—
199C23—614no—
200C23—1228no—
201C23—1224no—
202C23—1224no—
203C23—1222no—
204C23—1222no—
205C23—24416no—
206C23—2444no—
207C23—2444no—
208C23C2×C22⋊#692312yes—
209C23C2×C22⋊#692311yescharacteristic
210C23#1451986514yes—
211Q8—416no—
212C2×C4—28no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—44no—
219C2×C4—614no—
220C2×C4—1224no—
221C2×C4—1228no—
222C2×C4—1224no—
223C2×C4—24416no—
224C2×C4—2444no—
225C2×C4—2444no—
226C2×C4—2444no—
227C2×C4#1451983514yes—
228C8—4884no—
229C22—28no—
230C22—22no—
231C22—22no—
232C22—1228no—
233C22—1224no—
234C22—24416no—
235C22—2444no—
236C22—2442no—
237C22—2442no—
238C22#1684070311yescharacteristic
239C22#1684073714yes—
240C22#1684073712yes—
241C22C2×#1451983512yes—
242C22D61⋊#10112yes—
243C4—24no—
244C4—44no—
245C4—1224no—
246C4—2444no—
247C2—24no—
248C2—2444no—
249C2#2146109914yes—
250C2#2146164411yescharacteristic
251C2#2146164511yescharacteristic
252C2#2146165411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC23×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC23×Q8#6923
hypocenterC61#8308
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16840608C2semidirect
140. C61#8308semidirect

Maximal subgroups

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

subgroupindex
#214616422
C2×#168406082
C22×#145197532
#830861