Finite Group Databasebeta

← #30604704

Subgroups — #30604704

Order 15616.

322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462025C211yesmaximal, characteristic, complemented
2#21461379C211yesmaximal, characteristic, complemented
3#21460779C212yesmaximal, complemented
4#21460778C212yesmaximal, complemented
5#21456390C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840783—21no—
8#16840651C2212yes—
9#16840648—21no—
10#16840626—21no—
11#16840623C2212yes—
12#16840298—21no—
13#16840163C411yescharacteristic
14#16840147C411yescharacteristic
15#16840118—21no—
16#16839998C411yescharacteristic
17#16839993—21no—
18Q16×Dic61C2211yescharacteristic
19#16839847—21no—
20#16839844C2211yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#467C411yescharacteristic
23#14519851—24no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26C22⋊#92420—41no—
27#14519832—41no—
28C2×#11758201—21no—
29C2×D488C2×C411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519772—41no—
32#14519768—21no—
33#14519766—21no—
34#14519761—41no—
35#14519751—21no—
36Q8×Dic61—21no—
37#14519739—21no—
38#14519737—41no—
39#14519735—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519701—21no—
44#14519699—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×Q16×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52C22⋊Q8×C61—21no—
53#107×C61C2×C411yescharacteristic
54#103×C61—21no—
55C2×Q8×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—41no—
58C22×Dic61D811yescharacteristic
59C22×Dic61SD1611yescharacteristic
60C2×D244—21no—
61C2×C4×D61—41no—
62C2×#92420—42no—
63Q16×C61—22no—
64C2×C8×C61—22no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22×C411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70#11758201—42no—
71#11758198—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—41no—
79C4×Dic61—41no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61D811yescharacteristic
82C4×Dic61SD1611yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C2×#92418—22no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87D488—22no—
88#11758187—24no—
89C23×C61#10211yescharacteristic
90C22×D61—41no—
91Q8×C61—41no—
92Q8×C61—41no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C22⋊D61—82no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61#10211yescharacteristic
104C2×Dic61#10211yescharacteristic
105C2×Dic61C2×D811yescharacteristic
106C2×Dic61C2×SD1611yescharacteristic
107D244—41no—
108D244—41no—
109C4×D61—82no—
110#92420—82no—
111C8×C61—21no—
112C8×C61#13112yes—
113#92418—21no—
114#92418#10412yes—
115#11682—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61C2×#10211yescharacteristic
120C2×D61—81no—
121C2×D61—81no—
122C2×D61—81no—
123C4×C61—21no—
124C4×C61—81no—
125C4×C61—81no—
126C4×C61#40811yescharacteristic
127C4×C61C2×#10411yescharacteristic
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—81no—
133#3168—611no—
134C4×M32—611no—
135#1568—611no—
136#1334—612no—
137#1333—612no—
138C2×C61—41no—
139C2×C61#149211yescharacteristic
140C2×C61#214511yescharacteristic
141C2×C61#214811yescharacteristic
142D61—161no—
143#529—1221no—
144C2×M32—1221no—
145#499—611no—
146#495—611no—
147#488—1221no—
148#467#692311yescharacteristic
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—1221no—
163C2×D8—611no—
164C22×C8—611no—
165C22×C8C2×#692311yescharacteristic
166#126—2441no—
167#125—1221no—
168#124—1221no—
169#123—2441no—
170C22⋊Q8—21no—
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#107C2×#692311yescharacteristic
181#106—1221no—
182C4⋊C8—1222no—
183#103—21no—
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×C8—611no—
193C2×Q8—21no—
194C2×D4—1221no—
195C2×D4—2441no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—2441no—
199C22×C4C22⋊#692311yescharacteristic
200Q16—22no—
201SD16—2442no—
202D8—1222no—
203C2×C8—22no—
204C2×C8—611no—
205C2×C8—611no—
206C2×C8—1222no—
207C2×C8—2442no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22×#692311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—1221no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—41no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C42—611no—
222C42—611no—
223C42—611no—
224C42—611no—
225C42—2441no—
226C16—1224no—
227C23—2441no—
228C23#1451983911yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—4882no—
232D4—2441no—
233D4—2441no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—4882no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4#1451983911yescharacteristic
247C2×C4C2×C22⋊#692311yescharacteristic
248C8—21no—
249C8—612no—
250C8—1221no—
251C8—4882no—
252C8#1451986412yes—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—4881no—
257C22—4881no—
258C22—4881no—
259C22C2×#1451983911yescharacteristic
260C4—21no—
261C4—81no—
262C4—81no—
263C4—1221no—
264C4—1221no—
265C4—1221no—
266C4—1221no—
267C4—4881no—
268C4#1684073511yescharacteristic
269C4D61⋊#10411yescharacteristic
270C2—41no—
271C2—9761no—
272C2#2146116411yescharacteristic
273C2#2146214111yescharacteristic
274C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#467C4
socleC22×C61C2×#102
prime radical#16839998C4
cosocleC8×Dic61C23
hypercenter#467#6923
hypocenterC61#11682
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #21462025C2semidirect
2. #21461379C2semidirect
3. #21460779C2semidirect
4. #21460778C2semidirect
160. C61#11682semidirect

Maximal subgroups

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

subgroupindex
#214620252
#214613792
#214607792
#214607782
#214563902
#1168261