Finite Group Databasebeta

← #30603866

Subgroups — #30603866

Order 15616.

450 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 102 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#21462047C212yesmaximal
2#21460756C212yesmaximal, complemented
3#21460755C212yesmaximal, complemented
4C2×C4⋊C8×D61C211yesmaximal, characteristic
5C2×#14519852—22no—
6#16840657—22no—
7C22⋊#11758187C2214yes—
8C22×C8×D61C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×C42×D61C411yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519706C411yescharacteristic
13C2×#14519706C2211yescharacteristic
14C4⋊C8×D61—22no—
15C4⋊C8×D61—22no—
16C2×C4⋊C8×C61C411yescharacteristic
17#14519852—44no—
18C2×#11758187—24no—
19C22×C4×D61C811yescharacteristic
20C22×C4×D61C811yescharacteristic
21C22×C4×D61C2×C411yescharacteristic
22C22×#92418C2×C411yescharacteristic
23C22×#92418C2311yescharacteristic
24C2×C8×D61—21no—
25C2×C8×D61—21no—
26C2×C8×D61—42no—
27C2×C8×D61—42no—
28C2×C8×D61D412yes—
29C2×C8×D61D412yes—
30C2×C4×Dic61C811yescharacteristic
31C2×C4×Dic61C811yescharacteristic
32C2×C4×Dic61C2×C411yescharacteristic
33C42×D61—21no—
34C42×D61—21no—
35C42×D61—21no—
36C42×D61—21no—
37C4⋊#92418—22no—
38#14519706—22no—
39#14519706—22no—
40C22×C8×C61C2×C411yescharacteristic
41C22×C8×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C4⋊C8×C61—22no—
44C23×D61C2×C811yescharacteristic
45C22×C4×C61C2×C811yescharacteristic
46C22×C4×C61C2×C811yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61C2×C811yescharacteristic
49C22×Dic61C2×C811yescharacteristic
50C22×Dic61C2×C811yescharacteristic
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—42no—
60C2×C4×D61C22⋊C411yescharacteristic
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61M1611yescharacteristic
63C2×C4×D61M1611yescharacteristic
64C2×C8×C61—21no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61C22⋊C412yes—
68C42×C61—21no—
69C42×C61—21no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C2×#92418—21no—
77C2×#92418—41no—
78C2×#92418—41no—
79C2×#92418C2×D412yes—
80C8×D61—24no—
81C8×D61—42no—
82C8×D61—42no—
83C8×D61—42no—
84#11758187—44no—
85C23×C61C22×C811yescharacteristic
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61C22⋊C811yescharacteristic
91C22×D61C22⋊C811yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61M3212yescomplemented
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61C22⋊C811yescharacteristic
107C2×Dic61C22⋊C811yescharacteristic
108C2×Dic61M3212yescomplemented
109C4×D61—24no—
110C4×D61—24no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—22no—
115C4×D61—42no—
116C4×D61—42no—
117C4×D61#9912yes—
118C4×D61#10112yes—
119C8×C61—22no—
120C8×C61—41no—
121#92418—22no—
122#92418—41no—
123#11440—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61C2×C22⋊C811yescharacteristic
127C22×C61C2×M3211yescharacteristic
128C22×C61C2×M3211yescharacteristic
129C2×D61—24no—
130C2×D61—24no—
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61#32412yes—
136C2×D61#34912yes—
137C4×C61—22no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61C2×#9911yescharacteristic
141C4×C61C2×#10111yescharacteristic
142Dic61—22no—
143Dic61—21no—
144Dic61—41no—
145Dic61#32412yes—
146C22×C4⋊C8—611no—
147#2112—612no—
148#1322—612no—
149#1322—612no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61C2×#32411yescharacteristic
153C2×C61#211211yescharacteristic
154C2×C61C2×#34911yescharacteristic
155D61—22no—
156D61—22no—
157C23×C8—611no—
158C23×C8—611no—
159C22×C42—611no—
160C2×M32—1222no—
161C2×C4⋊C8—611no—
162C2×C4⋊C8—611no—
163C2×C4⋊C8—611no—
164C2×C4⋊C8—1222no—
165C2×C4⋊C8—1222no—
166C2×C4⋊C8#692311yescharacteristic
167C22⋊C16—614no—
168C22⋊C16—1222no—
169C61#1144011yescharacteristic, complemented, Sylow
170C23×C4—611no—
171C23×C4—611no—
172C23×C4—611no—
173C22×C8—611no—
174C22×C8—612no—
175C22×C8—612no—
176C22×C8—611no—
177C22×C8—1221no—
178C22×C8—1221no—
179C22×C8—2442no—
180C22×C8—2442no—
181C22×C8C2×#692311yescharacteristic
182C22×C8C2×#692311yescharacteristic
183C2×C42—611no—
184C2×C42—611no—
185C2×C42—611no—
186C2×C42—1221no—
187C2×C42—1221no—
188C2×C42—1221no—
189C2×C42—1221no—
190C2×C42C2×#692311yescharacteristic
191M32—2444no—
192C2×C16—1224no—
193C4⋊C8—22no—
194C4⋊C8—1222no—
195C4⋊C8—1222no—
196C4⋊C8—1222no—
197C24—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1222no—
213C22×C4—2442no—
214C22×C4D61⋊C811yescharacteristic
215C22×C4D61⋊C811yescharacteristic
216C22×C4C22×#692311yescharacteristic
217C2×C8—21no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—612no—
221C2×C8—1224no—
222C2×C8—1221no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2441no—
227C2×C8—2441no—
228C2×C8C22⋊#692312yes—
229C42—21no—
230C42—21no—
231C42—1221no—
232C42—1221no—
233C42—1221no—
234C42—1221no—
235C42—1221no—
236C42—1221no—
237C16—2444no—
238C23—611no—
239C23—611no—
240C23—1222no—
241C23—1222no—
242C23—1221no—
243C23—1221no—
244C23C2×D61⋊C811yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—611no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—611no—
255C2×C4—612no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1224no—
259C2×C4—1224no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2441no—
269C2×C4#1451985212yescomplemented
270C2×C4C2×C22⋊#692311yescharacteristic
271C2×C4D61⋊M1611yescharacteristic
272C8—22no—
273C8—41no—
274C8—1222no—
275C8—2441no—
276C22—21no—
277C22—21no—
278C22—612no—
279C22—612no—
280C22—1224no—
281C22—1224no—
282C22—1221no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22D61⋊(C22⋊C8)11yescharacteristic
287C22D61⋊M3211yescharacteristic
288C22C2×#1451985211yescharacteristic
289C4—22no—
290C4—21no—
291C4—41no—
292C4—612no—
293C4—1222no—
294C4—1221no—
295C4—2441no—
296C4D61⋊#9911yescharacteristic
297C4D61⋊#10111yescharacteristic
298C2—21no—
299C2—21no—
300C2—1222no—
301C2—1222no—
302C2D61⋊#32411yescharacteristic
303C2#2146204711yescharacteristic
304C2D61⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×#92418C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#11440
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21460756C2semidirect
3. #21460755C2semidirect
98. C2×C4×C61M32semidirect
108. C2×Dic61M32semidirect
169. C61#11440semidirect
269. C2×C4#14519852semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214607562
#214607552
C2×C4⋊C8×D612
#1144061