Finite Group Databasebeta

← #30599187

Subgroups — #30599187

Order 15616.

358 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 84 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×#14519848C211yesmaximal, characteristic, complemented
2#21461382C211yesmaximal, characteristic, complemented
3#21461284C212yesmaximal
4#21460685C212yesmaximal, complemented
5#21454791C211yesmaximal, characteristic
6#16840784C2212yes—
7C2×#14519848—21no—
8C4×#11758213C2212yes—
9#16840638—21no—
10#16840626—21no—
11#16840624—21no—
12#16840619—22no—
13#16840617—22no—
14#16840294C2211yescharacteristic
15#16839889C411yescharacteristic
16C8×Dic122C411yescharacteristic
17#16839840C411yescharacteristic
18#16839836—21no—
19C8×C22⋊D61—21no—
20#16839820—21no—
21#16839818C2211yescharacteristic
22#16839717—21no—
23C4×C8×D61C2211yescharacteristic
24C8×D4×C61C411yescharacteristic
25C2×#11758213—22no—
26#14519848—24no—
27C4⋊#92420—22no—
28#14519834—22no—
29#14519832—22no—
30#14519832—22no—
31C4×#92420—22no—
32C2×#11758194—21no—
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35#14519770—21no—
36#14519768D411yescharacteristic
37#14519764D411yescharacteristic
38#14519759—21no—
39#14519757Q811yescharacteristic
40#14519748Q811yescharacteristic
41C4×Dic122C2×C411yescharacteristic
42C4×C22⋊D61—21no—
43#14519736—21no—
44C42×D61C2311yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47#14519706—21no—
48C22⋊#92418—21no—
49#14519689—21no—
50#14519687—21no—
51#14519687—21no—
52C4×#92418C2×C411yescharacteristic
53C8×Dic61—21no—
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C22×C8×C61—21no—
57C4×D4×C61C2×C411yescharacteristic
58C4⋊C8×C61C2×C411yescharacteristic
59C22⋊C8×C61—21no—
60C4×C8×C61C2×C411yescharacteristic
61C2×D4×C61C4⋊C411yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C4×D61C2×D411yescharacteristic
65C2×C4×D61C2×Q811yescharacteristic
66C2×C4×D61#4111yescharacteristic
67C2×Dic122C4⋊C411yescharacteristic
68C2×#92420—42no—
69C2×#92420—42no—
70#11758213—24no—
71#11758213—42no—
72C2×C8×C61—21no—
73C2×C8×C61—42no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22⋊C411yescharacteristic
76C4⋊C4×C61C4⋊C411yescharacteristic
77C22⋊C4×C61—21no—
78C42×C61C22×C411yescharacteristic
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61C4⋊C411yescharacteristic
86#11758196—21no—
87#11758196—21no—
88C4×Dic61—21no—
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61C2×D411yescharacteristic
91C4×Dic61#4111yescharacteristic
92#11758194—42no—
93C2×#92418—21no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C22⋊C411yescharacteristic
96C8×D61—22no—
97C8×D61—41no—
98C23×C61—21no—
99C22×D61C22⋊Q811yescharacteristic
100D4×C61—41no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61C2×C4⋊C411yescharacteristic
106C2×C4×C61#11711yescharacteristic
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61#12111yescharacteristic
111C2×Dic61#12111yescharacteristic
112C2×Dic61C22⋊Q811yescharacteristic
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—41no—
116C4×D61—41no—
117Dic122—41no—
118#92420—44no—
119#92420—82no—
120C8×C61—21no—
121C8×C61—21no—
122C8×C61—41no—
123#92418—21no—
124#92418—41no—
125#92418#10412yes—
126#8693—611nomaximal, Sylow
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61#38011yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61C2×#10411yescharacteristic
138C4×C61#42111yescharacteristic
139Dic61—21no—
140Dic61—21no—
141Dic61—21no—
142Dic61—41no—
143Dic61—41no—
144#2966—611no—
145C4×#108—611no—
146#1568—611no—
147#1529—612no—
148#1291—612no—
149C2×C61—81no—
150C2×C61#180611yescharacteristic
151C2×C61#181311yescharacteristic
152C2×C61#181411yescharacteristic
153D61—41no—
154#529—611no—
155#446—611no—
156C8×Q8—611no—
157#436—611no—
158#435—1221no—
159C8×D4—1221no—
160C8×D4#692311yescharacteristic
161#433—1221no—
162#432—611no—
163#432—612no—
164C2×#108—1221no—
165#405—1221no—
166C4×M16—612no—
167C2×C4×C8—611no—
168#341—1221no—
169#335—1221no—
170#334—1221no—
171#330—1222no—
172#329—1222no—
173C61#869311yescharacteristic, complemented, Sylow
174C2×M16—1221no—
175C2×M16—1222no—
176C22×C8—21no—
177C22×C8—611no—
178C22×C8—611no—
179#126—1221no—
180#125—611no—
181#124—611no—
182#123—1221no—
183C22⋊Q8—611no—
184#121—611no—
185C4×Q8—611no—
186C4×D4—1221no—
187C4×D4C2×#692311yescharacteristic
188#117—1221no—
189C2×C42—611no—
190#108—1224no—
191C4⋊C8—611no—
192C4⋊C8—1222no—
193C4⋊C8—1221no—
194C4⋊C8—1221no—
195C4⋊C8C2×#692311yescharacteristic
196C22⋊C8—21no—
197C22⋊C8—1221no—
198C22⋊C8—1221no—
199C22⋊C8—1222no—
200#97—1221no—
201#97—1222no—
202#97—1222no—
203#97—1221no—
204C4×C8—611no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8—1222no—
208C4×C8—1221no—
209C4×C8C2×#692311yescharacteristic
210C2×Q8—611no—
211C2×D4—1221no—
212C2×D4C4⋊#692311yescharacteristic
213C22×C4—21no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217M16—1224no—
218M16—2442no—
219M16—2442no—
220C2×C8—21no—
221C2×C8—42no—
222C2×C8—611no—
223C2×C8—611no—
224C2×C8—1222no—
225C2×C8—1221no—
226C2×C8—2441no—
227C2×C8—2442no—
228C2×C8—2442no—
229C2×C8C22⋊#692311yescharacteristic
230C2×C8C22⋊#692311yescharacteristic
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C4⋊C4C4⋊#692311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—1221no—
239C22⋊C4—1221no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C42—611no—
243C42—611no—
244C42—611no—
245C42—1221no—
246C42C22×#692311yescharacteristic
247C23—21no—
248C23—611no—
249Q8—2441no—
250D4—41no—
251D4—2442no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4C2×C22⋊#692311yescharacteristic
265C2×C4C2×C4⋊#692311yescharacteristic
266C2×C4#1451985611yescharacteristic
267C8—21no—
268C8—21no—
269C8—41no—
270C8—612no—
271C8—1221no—
272C8—4882no—
273C8—2444no—
274C8—2441no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—1221no—
279C22—1221no—
280C22—1221no—
281C22#1684070411yescharacteristic
282C4—21no—
283C4—21no—
284C4—41no—
285C4—1221no—
286C4—1221no—
287C4—1221no—
288C4—2441no—
289C4—2441no—
290C4D61⋊#10411yescharacteristic
291C4#1684076011yescharacteristic
292C2—81no—
293C2—2441no—
294C2#2146169311yescharacteristic
295C2#2146170311yescharacteristic
296C2#2146170611yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61#380
prime radical#14519748Q8
cosocleC42×D61C23
hypercenterC8×D4#6923
hypocenterC61#8693
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14519848C2semidirect
2. #21461382C2semidirect
4. #21460685C2semidirect
173. C61#8693semidirect

Maximal subgroups

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

subgroupindex
C4×#145198482
#214613822
#214612842
#214606852
#214547912
#869361