Finite Group Databasebeta

← #30604703

Subgroups — #30604703

Order 15616.

322 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 80 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×#14519852C211yesmaximal, characteristic, complemented
2#21461380C211yesmaximal, characteristic, complemented
3#21460779C212yesmaximal, complemented
4#21460777C212yesmaximal, complemented
5#21456386C211yesmaximal, characteristic
6C2×#14519852—21no—
7#16840784—21no—
8#16840651C2212yes—
9C4×#11758187—21no—
10#16840625—21no—
11#16840623C2212yes—
12#16840291—21no—
13#16840164C411yescharacteristic
14#16840116—21no—
15#16840000C411yescharacteristic
16#16839995C411yescharacteristic
17#16839988—21no—
18Q16×Dic61C2211yescharacteristic
19SD16×Dic61—21no—
20D8×Dic61C2211yescharacteristic
21C4×C8×D61C2211yescharacteristic
22C61×#495C411yescharacteristic
23#14519852—24no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26#14519834—41no—
27#14519832—41no—
28C2×C8×D61C2×C411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519770—41no—
31#14519769—21no—
32#14519759—41no—
33#14519753—21no—
34#14519748—21no—
35Q8×Dic61—21no—
36D4×Dic61—21no—
37#14519737—41no—
38#14519733—41no—
39C42×D61D411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519709—21no—
43#14519701—21no—
44#14519701—21no—
45#14519698—21no—
46#14519698—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×Q16×C61C2×C411yescharacteristic
51C2×SD16×C61—21no—
52C2×D8×C61C2×C411yescharacteristic
53#124×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61—21no—
56C2×D4×C61—21no—
57C2×C22⋊D61—41no—
58C22×Dic61—41no—
59C2×C4×D61C22⋊C411yescharacteristic
60C2×C4×D61D811yescharacteristic
61C2×C4×D61SD1611yescharacteristic
62C2×#92420—42no—
63Q16×C61—22no—
64SD16×C61—42no—
65D8×C61—22no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22×C411yescharacteristic
68C22⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70C42×C61C22⋊C411yescharacteristic
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73#11758198—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80C4×Dic61—41no—
81C4×Dic61D811yescharacteristic
82C4×Dic61SD1611yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86C8×D61—22no—
87C8×D61—22no—
88#11758187—24no—
89C23×C61—41no—
90C22×D61#10211yescharacteristic
91Q8×C61—41no—
92Q8×C61—41no—
93D4×C61—41no—
94D4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C22⋊D61—82no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—82no—
103C2×Dic61#10211yescharacteristic
104C2×Dic61C2×D811yescharacteristic
105C2×Dic61C2×SD1611yescharacteristic
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—41no—
109C4×D61—41no—
110#92420—82no—
111C8×C61#10412yes—
112C8×C61#13112yes—
113#92418—21no—
114#92418—21no—
115#11682—611nomaximal, Sylow
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61C2×#10211yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—81no—
126C4×C61#40811yescharacteristic
127C4×C61C2×#10411yescharacteristic
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—81no—
132Dic61—81no—
133#3168—611no—
134C4×M32—611no—
135#1568—611no—
136#1334—612no—
137#1333—612no—
138C2×C61—161no—
139C2×C61#149211yescharacteristic
140C2×C61#214511yescharacteristic
141C2×C61#214811yescharacteristic
142D61—41no—
143#529—1221no—
144C2×M32—1221no—
145#499—611no—
146#495#692311yescharacteristic
147#488—1221no—
148#467—611no—
149#466—611no—
150#465—1221no—
151C4×Q16—611no—
152C4×SD16—1221no—
153C4×D8—611no—
154#432—1221no—
155C2×C4×C8—611no—
156#346—612no—
157C4×C16—1221no—
158#335—1221no—
159#334—612no—
160C61#1168211yescharacteristic, complemented, Sylow
161C2×Q16C2×#692311yescharacteristic
162C2×SD16—21no—
163C2×D8C2×#692311yescharacteristic
164C22×C8—611no—
165C22×C8—611no—
166#126—2441no—
167#125—1221no—
168#124—21no—
169#123—2441no—
170C22⋊Q8—1221no—
171#121—1221no—
172C4×Q8—1221no—
173C4×D4—1221no—
174C4×D4—2441no—
175#117—2441no—
176C2×C42—611no—
177M32—1224no—
178C2×C16—1222no—
179#107—611no—
180#107—611no—
181#106—1221no—
182C4⋊C8—1222no—
183#103—1221no—
184#103—1221no—
185#102—1221no—
186#102—1221no—
187C22⋊C8—2441no—
188#97—2441no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8C2×#692311yescharacteristic
193C2×Q8—21no—
194C2×D4—21no—
195C2×D4—2441no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—2441no—
200Q16—22no—
201SD16—42no—
202D8—22no—
203C2×C8—611no—
204C2×C8—611no—
205C2×C8—1222no—
206C2×C8—1222no—
207C2×C8—2442no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22×#692311yescharacteristic
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C42—611no—
222C42—611no—
223C42—611no—
224C42—2441no—
225C42C22⋊#692311yescharacteristic
226C16—1224no—
227C23—41no—
228C23—611no—
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—41no—
233D4—4882no—
234C2×C4—41no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—4882no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983911yescharacteristic
246C2×C4#1451983911yescharacteristic
247C2×C4C2×C22⋊#692311yescharacteristic
248C8—1221no—
249C8—1221no—
250C8—4882no—
251C8#1451984112yes—
252C8#1451986412yes—
253C22—81no—
254C22—81no—
255C22—81no—
256C22—1221no—
257C22—1221no—
258C22—1221no—
259C22C2×#1451983911yescharacteristic
260C4—21no—
261C4—21no—
262C4—81no—
263C4—1221no—
264C4—1221no—
265C4—1221no—
266C4—4881no—
267C4—4881no—
268C4#1684073611yescharacteristic
269C4C2×#1451984111yescharacteristic
270C2—161no—
271C2—2441no—
272C2#2146116511yescharacteristic
273C2#2146213911yescharacteristic
274C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#495C4
socleC22×C61C2×#102
prime radical#16839995C4
cosocleC8×Dic61C23
hypercenter#495#6923
hypocenterC61#11682
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C4×#14519852C2semidirect
2. #21461380C2semidirect
3. #21460779C2semidirect
4. #21460777C2semidirect
160. C61#11682semidirect

Maximal subgroups

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

subgroupindex
C4×#145198522
#214613802
#214607792
#214607772
#214563862
#1168261