Finite Group Databasebeta

← #30593947

Subgroups — #30593947

Order 15616.

442 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×#14519834C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21445576C211yesmaximal, characteristic
4C22×#11758213C412yes—
5C2×#14519834—21no—
6C2×C4×#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C412yes—
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12C2×C8×Dic61—21no—
13#16839517C411yescharacteristic
14C61×#336C411yescharacteristic
15C2×#11758213—22no—
16C2×#11758213—42no—
17C2×#11758213—42no—
18C2×#11758213C814yescomplemented
19C22×#92420—22no—
20C22×#92420—22no—
21#14519834—22no—
22#14519834—22no—
23C4×#92420—42no—
24C22×C4×D61C2×C411yescharacteristic
25C22×C4×D61D411yescharacteristic
26C22×C4×D61Q811yescharacteristic
27C22×#92418—21no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C42×D61—42no—
32#14519689—24no—
33C8×Dic61—42no—
34C22×C8×C61—21no—
35C2×C42×C61C2×C411yescharacteristic
36C23×D61C4⋊C411yescharacteristic
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×C4×D61C2×C812yes—
55C2×C4×D61M1612yes—
56C2×#92420—24no—
57C2×#92420—24no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C2×#92420—42no—
62#11758213—44no—
63#11758213—44no—
64C2×C8×C61—22no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C42×C61—41no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61—41no—
71C2×#92418—22no—
72C2×#92418—41no—
73C2×#92418—41no—
74C23×C61#9511yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61C4⋊C812yes—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61C4×C811yescharacteristic
89C2×C4×C61#9711yescharacteristic
90C2×C4×C61#10411yescharacteristic
91C2×C4×C61#10411yescharacteristic
92C2×C4×C61#10811yescharacteristic
93C2×C4×C61#10811yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61C22⋊C812yes—
99C2×Dic61#9912yes—
100C2×Dic61#10011yescharacteristic
101C2×Dic61#10111yescharacteristic
102C2×Dic61#10412yes—
103C2×Dic61#10812yes—
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—42no—
109C4×D61—42no—
110C4×D61—42no—
111C4×D61—42no—
112#92420—44no—
113#92420—44no—
114C8×C61—42no—
115#92418—42no—
116#7026—611nomaximal, Sylow
117C22×C61#33611yescharacteristic
118C22×C61#33911yescharacteristic
119C22×C61#33911yescharacteristic
120C22×C61#34111yescharacteristic
121C22×C61#34111yescharacteristic
122C22×C61#34211yescharacteristic
123C22×C61#34311yescharacteristic
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—21no—
137Dic61—22no—
138Dic61—22no—
139Dic61#32312yes—
140Dic61#32412yes—
141C4×C22⋊C8—611no—
142C4×C22⋊C8—611no—
143#1728—611no—
144C2×C61#127811yescharacteristic
145C2×C61#127811yescharacteristic
146C2×C61#128011yescharacteristic
147C2×C61#129711yescharacteristic
148C2×C61#129811yescharacteristic
149C2×C61#129911yescharacteristic
150C2×C61#129911yescharacteristic
151D61—42no—
152C22×M16—612no—
153C22×C42—611no—
154C2×C22⋊C8—1221no—
155C2×C22⋊C8—1221no—
156C2×C4×C8—1221no—
157C2×C4×C8—1221no—
158#336—612no—
159#336—611no—
160#336—1221no—
161#336—1221no—
162#336#692311yescharacteristic
163C61#702611yescharacteristic, complemented, Sylow
164C23×C4—611no—
165C23×C4—611no—
166C23×C4—611no—
167C2×M16—614no—
168C2×M16—1222no—
169C2×M16—2442no—
170C2×M16—2442no—
171C22×C8—21no—
172C22×C8—1222no—
173C22×C8—1222no—
174C22×C8—1221no—
175C2×C42—611no—
176C2×C42—611no—
177C2×C42—611no—
178C2×C42—2442no—
179C2×C42C2×#692311yescharacteristic
180C22⋊C8—1224no—
181C22⋊C8—1222no—
182C22⋊C8—1222no—
183C4×C8—2442no—
184C4×C8—2442no—
185C24—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—612no—
190C22×C4—612no—
191C22×C4—1222no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—1221no—
200C22×C4—2441no—
201C22×C4—2441no—
202C22×C4C4×#692311yescharacteristic
203C22×C4C4⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205M16—2444no—
206M16—2444no—
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—1222no—
211C2×C8—1224no—
212C2×C8—1224no—
213C2×C8—2441no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C2×C8—2441no—
219C42—41no—
220C42—1222no—
221C42—1222no—
222C42—2441no—
223C23—612no—
224C23—1221no—
225C23—1221no—
226C23—1221no—
227C23—1221no—
228C23—1221no—
229C23—1221no—
230C23(C2×#6923)⋊C411yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—612no—
238C2×C4—612no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—612no—
242C2×C4—612no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4—2442no—
255C2×C4C8×#692311yescharacteristic
256C2×C4#1451983111yescharacteristic
257C2×C4#1451984111yescharacteristic
258C2×C4#1451984211yescharacteristic
259C2×C4#1451984711yescharacteristic
260C2×C4#1451984811yescharacteristic
261C8—42no—
262C8—2442no—
263C8—2444no—
264C8—2444no—
265C22—1222no—
266C22—1222no—
267C22—1222no—
268C22—2441no—
269C22—2441no—
270C22—2441no—
271C22—2441no—
272C22(C2×#6923)⋊C811yescharacteristic
273C22#1684063211yescharacteristic
274C22#1684063311yescharacteristic
275C22#1684063711yescharacteristic
276C22#1684063811yescharacteristic
277C22#1684063911yescharacteristic
278C22#1684064111yescharacteristic
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—612no—
286C4—612no—
287C4—1222no—
288C4—1222no—
289C2—2442no—
290C2#2146065011yescharacteristic
291C2#2146065111yescharacteristic
292C2#2146065611yescharacteristic
293C2#2146070011yescharacteristic
294C2#2146070211yescharacteristic
295C2#2146070411yescharacteristic
296C2#2146070511yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C4×C8
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenter#336#6923
hypocenterC61#7026
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
18. C2×#11758213C8semidirect
163. C61#7026semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614832
#214455762
#702661