Finite Group Databasebeta

← #30595445

Subgroups — #30595445

Order 15616.

846 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 132 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#21461709C212yesmaximal, complemented
2#21460635C214yesmaximal, complemented
3C2×#16839665C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840628—22no—
6#16840628C2214yescomplemented
7C22×C4⋊Dic61C411yescharacteristic
8C22×C22⋊Dic61—22no—
9C22×C4×Dic61C2211yescharacteristic
10#16839665—22no—
11#16839665C412yes—
12#16839665C2212yes—
13C23×D4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—44no—
16C23×Dic61—21no—
17C23×Dic61D412yes—
18C2×C4⋊Dic61—21no—
19C2×C4⋊Dic61—42no—
20C2×C4⋊Dic61C2×C412yes—
21C2×C22⋊Dic61—24no—
22C2×C22⋊Dic61—24no—
23C2×C22⋊Dic61—48no—
24C2×C4×Dic61—42no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28C25×C61—21no—
29C22×D4×C61—21no—
30C22×D4×C61—22no—
31C22×D4×C61—42no—
32C22×D4×C61—42no—
33C22×D4×C61C814yescomplemented
34C22×D4×C61C2×C412yes—
35C23×C4×C61C2×C411yescharacteristic
36C24×C61—24no—
37C24×C61—22no—
38C24×C61—44no—
39C24×C61—44no—
40C24×C61—42no—
41C24×C61—42no—
42C24×C61C22⋊C411yescharacteristic
43C2×D4×C61—24no—
44C2×D4×C61—22no—
45C2×D4×C61—48no—
46C2×D4×C61—42no—
47C2×D4×C61—42no—
48C2×D4×C61—48no—
49C2×D4×C61—42no—
50C2×D4×C61—42no—
51C2×D4×C61C2×C814yes—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C2×C812yes—
56C22×C4×C61M1612yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—24no—
59C22×Dic61—24no—
60C22×Dic61—22no—
61C22×Dic61—42no—
62C22×Dic61—44no—
63C22×Dic61—42no—
64C22×Dic61C22⋊C412yes—
65C22×Dic61C2×D412yes—
66C2×#92420—44no—
67C2×#92420—44no—
68C2×#92420—44no—
69C22⋊Dic61—48no—
70C22⋊Dic61—48no—
71C4⋊Dic61—42no—
72C4⋊Dic61—42no—
73C4×Dic61—41no—
74C4×Dic61—42no—
75C4×Dic61—41no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—24no—
79C23×C61—416no—
80C23×C61—48no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61—44no—
84C23×C61—44no—
85C23×C61—84no—
86C23×C61—88no—
87C23×C61—84no—
88C23×C61C22⋊C812yes—
89C23×C61#9912yes—
90C23×C61#10012yes—
91C23×C61C2×C22⋊C411yescharacteristic
92D4×C61—44no—
93D4×C61—48no—
94D4×C61—44no—
95C2×C4×C61—24no—
96C2×C4×C61—24no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61C22⋊C812yes—
102C2×C4×C61C22×C811yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—48no—
110C2×Dic61—42no—
111C2×Dic61—44no—
112C2×Dic61—84no—
113C2×Dic61AGL(1,ℤ/8)14yes—
114#92420—84no—
115#7592—611nomaximal, Sylow
116C22×C61—22no—
117C22×C61—24no—
118C22×C61—24no—
119C22×C61—22no—
120C22×C61—44no—
121C22×C61—48no—
122C22×C61—816no—
123C22×C61—82no—
124C22×C61—84no—
125C22×C61—82no—
126C22×C61#32314yes—
127C22×C61C2×C22⋊C811yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#10011yescharacteristic
130C22×C61#41812yes—
131C22×C61#42112yes—
132C4×C61—22no—
133C4×C61—21no—
134C4×C61—21no—
135Dic61—24no—
136Dic61—42no—
137Dic61—82no—
138C2×#390—611no—
139#1817—612no—
140#1270—614no—
141C2×C61—24no—
142C2×C61—84no—
143C2×C61C2×#32311yescharacteristic
144C2×C61#147812yes—
145C2×C61#151012yes—
146C2×C61#153311yescharacteristic
147C2×C61#155511yescharacteristic
148C23×D4#692311yescharacteristic
149C22×C4⋊C4—611no—
150C22×C22⋊C4—1222no—
151C22×C42—611no—
152C2×C22⋊C8—1222no—
153#390—612no—
154#390—612no—
155#390—1222no—
156#336—614no—
157#336—1222no—
158C61#759211yescharacteristic, complemented, Sylow
159C25—21no—
160C22×D4—22no—
161C22×D4—21no—
162C22×D4—42no—
163C22×D4—42no—
164C22×D4#9242014yescomplemented
165C22×D4C2×#692312yes—
166C23×C4—612no—
167C23×C4—1221no—
168C23×C4C2×#692311yescharacteristic
169C22×C8—1224no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—2442no—
173C2×C22⋊C4—1224no—
174C2×C22⋊C4—1224no—
175C2×C22⋊C4—2448no—
176C2×C42—612no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—2442no—
180C22⋊C8—2444no—
181C24—24no—
182C24—22no—
183C24—44no—
184C24—44no—
185C24—42no—
186C24—42no—
187C24C22⋊#692311yescharacteristic
188C2×D4—24no—
189C2×D4—22no—
190C2×D4—48no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—48no—
196C2×D4C2×#9242014yes—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—612no—
200C22×C4—612no—
201C22×C4—1224no—
202C22×C4—1224no—
203C22×C4—1222no—
204C22×C4—2442no—
205C22×C4—2444no—
206C22×C4—2442no—
207C22×C4C2×#9242012yes—
208C22×C4#1175821712yes—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22×#692311yescharacteristic
211C2×C8—2444no—
212C2×C8—2444no—
213C2×C8—2444no—
214C4⋊C4—2442no—
215C4⋊C4—2442no—
216C22⋊C4—2448no—
217C22⋊C4—2448no—
218C42—2442no—
219C42—2441no—
220C42—2441no—
221C23—22no—
222C23—22no—
223C23—24no—
224C23—416no—
225C23—42no—
226C23—42no—
227C23—44no—
228C23—44no—
229C23—48no—
230C23—84no—
231C23—84no—
232C23—88no—
233C23C22⋊#9242012yes—
234C23#1451983512yes—
235C23#1451983712yes—
236C23C2×C22⋊#692311yescharacteristic
237D4—44no—
238D4—48no—
239D4—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—614no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—4884no—
253C2×C4—2448no—
254C2×C4—2442no—
255C2×C4—2444no—
256C2×C4C22⋊#9242012yes—
257C2×C4C22×#9242011yescharacteristic
258C2×C4C2×#1175821711yescharacteristic
259C8—4884no—
260C22—22no—
261C22—22no—
262C22—24no—
263C22—24no—
264C22—44no—
265C22—48no—
266C22—816no—
267C22—82no—
268C22—82no—
269C22—84no—
270C22#1684060514yes—
271C22C2×C22⋊#9242011yescharacteristic
272C22C2×#1451983511yescharacteristic
273C22C2×#1451983711yescharacteristic
274C22#1684075412yes—
275C22#1684076012yes—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—1224no—
280C4—4882no—
281C4—2442no—
282C2—24no—
283C2—84no—
284C2C2×#1684060511yescharacteristic
285C2#2146111812yes—
286C2#2146122412yes—
287C2#2146129811yescharacteristic
288C2#2146134611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
Fitting, prime radicalC23×D4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC23×D4#6923
hypocenterC61#7592
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21461709C2semidirect
2. #21460635C2semidirect
6. #16840628C22semidirect
33. C22×D4×C61C8semidirect
158. C61#7592semidirect
164. C22×D4#92420semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214606352
C2×#168396652
#759261