Finite Group Databasebeta

← #30595479

Subgroups — #30595479

Order 15616.

492 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 106 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#21460639C212yesmaximal, complemented
3#21460636C212yesmaximal
4C4×#14519766C211yesmaximal, characteristic
5C2×#14519844—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×#14519766C411yescharacteristic
9C2×C4×D244C411yescharacteristic
10#16839669C2211yescharacteristic
11#16839663C2211yescharacteristic
12#16839652—22no—
13#16839627C411yescharacteristic
14C4×#11758198—22no—
15C42×Dic61C2211yescharacteristic
16C2×C4×Q8×C61C411yescharacteristic
17C22×#92420—24no—
18#14519844—44no—
19C22×D244C2×C411yescharacteristic
20C22×C4×D61—21no—
21#14519766—22no—
22#14519766C814yescomplemented
23C4×D244—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×#11758198—22no—
26C2×#11758198—21no—
27C2×#11758198—22no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—22no—
33#14519684—22no—
34C22×Q8×C61C2×C411yescharacteristic
35C4×Q8×C61—42no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C42×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40C23×D61—21no—
41C2×Q8×C61—21no—
42C2×Q8×C61—41no—
43C2×Q8×C61—41no—
44C2×Q8×C61C2×C812yes—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—21no—
51C22×Dic61C22⋊C412yes—
52C22×Dic61C2×D412yes—
53C2×D244—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244C2×C812yes—
57C2×C4×D61—44no—
58C2×C4×D61—42no—
59C2×#92420—44no—
60C2×#92420—44no—
61C2×#92420—44no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—41no—
64C42×C61—22no—
65C42×C61—42no—
66#11758198—28no—
67#11758198—42no—
68#11758198—42no—
69#11758198—42no—
70C4⋊Dic61—41no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C4×Dic61C2×C812yes—
76C4×Dic61M1612yes—
77C23×C61C2×C22⋊C411yescharacteristic
78C22×D61—22no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61—42no—
82C22×D61—42no—
83Q8×C61—42no—
84Q8×C61—42no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61#10012yes—
96C2×C4×C61C22×C811yescharacteristic
97C2×C4×C61C2×M1611yescharacteristic
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61C22⋊C814yes—
105C2×Dic61AGL(1,ℤ/8)12yes—
106C2×Dic61#13712yes—
107D244—42no—
108D244—42no—
109C4×D61—84no—
110#92420—84no—
111#7601—611nomaximal, Sylow
112C22×C61C2×C22⋊C811yescharacteristic
113C22×C61#41011yescharacteristic
114C22×C61C2×#10011yescharacteristic
115C22×C61#41712yes—
116C22×C61#42112yes—
117C2×D61—42no—
118C2×D61—44no—
119C2×D61—81no—
120C2×D61—82no—
121C2×D61—81no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—41no—
126C4×C61—42no—
127C4×C61—81no—
128Dic61—24no—
129Dic61—22no—
130Dic61—22no—
131Dic61—81no—
132C4×#124—611no—
133#1831—612no—
134#1272—612no—
135#1270—612no—
136C2×C61#146011yescharacteristic
137C2×C61#147712yes—
138C2×C61#151212yes—
139C2×C61#153311yescharacteristic
140C2×C61#156011yescharacteristic
141D61—82no—
142C2×#124—611no—
143C2×C4×Q8#692311yescharacteristic
144C2×C4×D4—611no—
145C2×C4⋊C8—1222no—
146#391—611no—
147#390—611no—
148#388—1222no—
149#382—611no—
150C4×C22⋊C4—1222no—
151C43—611no—
152#336—614no—
153#336—1222no—
154C61#760111yescharacteristic, complemented, Sylow
155C22×Q8C2×#692311yescharacteristic
156C22×D4—611no—
157C23×C4—1221no—
158C22×C8—1224no—
159#124—614no—
160#124—1222no—
161C4×Q8—42no—
162C4×D4—2442no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4C2×#692311yescharacteristic
166C2×C22⋊C4—1222no—
167C2×C22⋊C4—1222no—
168C2×C22⋊C4—1221no—
169C2×C42—21no—
170C2×C42—611no—
171C2×C42—612no—
172C2×C42—612no—
173C2×C42—611no—
174C2×C42C2×#692311yescharacteristic
175C4⋊C8—2444no—
176#95—1222no—
177#95—1222no—
178C24—1221no—
179C2×Q8—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8D61⋊C812yes—
183C2×D4—612no—
184C2×D4—1221no—
185C2×D4—2441no—
186C2×D4—2441no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—612no—
190C22×C4—612no—
191C22×C4—1221no—
192C22×C4—2444no—
193C22×C4—2442no—
194C22×C4C22⋊#692311yescharacteristic
195C22×C4C22⋊#692311yescharacteristic
196C22×C4C22×#692311yescharacteristic
197C2×C8—2444no—
198C2×C8—2444no—
199C2×C8—2444no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—2441no—
203C22⋊C4—1228no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C42—22no—
208C42—42no—
209C42—612no—
210C42—612no—
211C42—1222no—
212C42—1222no—
213C42—2441no—
214C42—2442no—
215C23—1222no—
216C23—2441no—
217C23—2441no—
218C23—2442no—
219C23—2442no—
220C23C2×C22⋊#692311yescharacteristic
221Q8—42no—
222Q8—42no—
223D4—2442no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—614no—
236C2×C4—612no—
237C2×C4—612no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—4884no—
243C2×C4—2441no—
244C2×C4—2442no—
245C2×C4#1451983712yes—
246C2×C4C2×D61⋊C811yescharacteristic
247C2×C4D61⋊M1611yescharacteristic
248C8—4884no—
249C22—4881no—
250C22—4881no—
251C22—4882no—
252C22—2442no—
253C22—2444no—
254C22D61⋊(C22⋊C8)11yescharacteristic
255C22#1684074111yescharacteristic
256C22C2×#1451983711yescharacteristic
257C22#1684075312yes—
258C22#1684076112yes—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—42no—
263C4—41no—
264C4—81no—
265C4—1224no—
266C4—1222no—
267C4—1222no—
268C4—4881no—
269C2—4882no—
270C2#2146105811yescharacteristic
271C2#2146111712yes—
272C2#2146123212yes—
273C2#2146130011yescharacteristic
274C2#2146135611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7601
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21461735C2semidirect
2. #21460639C2semidirect
22. #14519766C8semidirect
154. C61#7601semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606392
#214606362
C4×#145197662
#760161