Finite Group Databasebeta

← #30604689

Subgroups — #30604689

Order 15616.

332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462020C211yesmaximal, characteristic, complemented
2#21461374C211yesmaximal, characteristic, complemented
3#21460780C212yesmaximal, complemented
4#21460778C212yesmaximal, complemented
5#21456391C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840766—21no—
8#16840651C2212yes—
9#16840650—21no—
10#16840623—21no—
11#16840623C2212yes—
12#16840297—21no—
13#16840146C411yescharacteristic
14#16840119—21no—
15#16840004C411yescharacteristic
16#16839999C411yescharacteristic
17#16839992—21no—
18#16839856C2211yescharacteristic
19#16839849—21no—
20#16839844C2211yescharacteristic
21C4×C8×D61C2211yescharacteristic
22C61×#499C411yescharacteristic
23C2×#11758213—41no—
24D61⋊C16—24no—
25C2×#11758187—22no—
26C4⋊#92420—22no—
27C4⋊#92420—41no—
28C2×Dic244C2×C411yescharacteristic
29C2×#11758190—21no—
30C2×D488C2×C411yescharacteristic
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519772—41no—
34#14519765—21no—
35#14519762—41no—
36#14519757—21no—
37#14519752—21no—
38#14519742—21no—
39#14519739—21no—
40#14519739—41no—
41#14519735—41no—
42C42×D61D411yescharacteristic
43#14519700—21no—
44#14519700—21no—
45#14519697—21no—
46#14519697—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50#125×C61—21no—
51#107×C61C2×C411yescharacteristic
52#107×C61C2×C411yescharacteristic
53#106×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D244—21no—
56C2×D244—41no—
57C2×C4×D61—41no—
58C2×C4×D61C22⋊C411yescharacteristic
59C2×C4×D61D811yescharacteristic
60C2×C4×D61SD1611yescharacteristic
61C2×Dic122—21no—
62C2×#92420—42no—
63#11758213—82no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61C22⋊C411yescharacteristic
71#11758198—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61D811yescharacteristic
80C4×Dic61SD1611yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—22no—
85D488—22no—
86#11758190—42no—
87C8×D61—22no—
88C8×D61—22no—
89#11758187—24no—
90C22×D61—41no—
91C22×D61#10211yescharacteristic
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×Dic61—41no—
98C2×Dic61#10211yescharacteristic
99C2×Dic61C2×D811yescharacteristic
100C2×Dic61C2×SD1611yescharacteristic
101D244—41no—
102D244—41no—
103D244—82no—
104C4×D61—22no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—41no—
108C4×D61—82no—
109Dic122—41no—
110Dic122—41no—
111#92420—82no—
112C8×C61#10412yes—
113C8×C61#13112yes—
114#92418—21no—
115#92418—21no—
116#11677—611nomaximal, Sylow
117C22×C61C2×#10211yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—81no—
121C2×D61—81no—
122C2×D61—81no—
123C2×D61#36012yes—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61—81no—
128C4×C61#40811yescharacteristic
129C4×C61C2×#10411yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—81no—
134#3168—611no—
135C2×#346—611no—
136#1566—611no—
137#1334—612no—
138#1333—612no—
139C2×C61#149211yescharacteristic
140C2×C61C2×#36011yescharacteristic
141C2×C61#214811yescharacteristic
142D61—22no—
143D61—161no—
144#529—1221no—
145C22×C16—1221no—
146#499#692311yescharacteristic
147#495—611no—
148#488—1221no—
149#467—611no—
150#466—611no—
151#465—1221no—
152C4×Q16—611no—
153C4×SD16—1221no—
154C4×D8—611no—
155#423—1221no—
156C2×C4×C8—611no—
157#346—612no—
158#346—1221no—
159#334—612no—
160#334—1221no—
161C61#1167711yescharacteristic, complemented, Sylow
162C2×Q16—611no—
163C2×SD16—1221no—
164C2×D8—611no—
165C2×M16—2441no—
166C22×C8—611no—
167C22×C8—611no—
168#126—2441no—
169#125—21no—
170#124—1221no—
171#123—2441no—
172C22⋊Q8—1221no—
173#121—1221no—
174C4×Q8—1221no—
175C4×D4—1221no—
176C4×D4—2441no—
177#117—2441no—
178C2×C42—611no—
179C2×C16—1222no—
180C2×C16—1224no—
181#107C2×#692311yescharacteristic
182#107C2×#692311yescharacteristic
183#106—21no—
184C4⋊C8—1222no—
185C4⋊C8—2441no—
186#103—1221no—
187#103—1221no—
188#102—1221no—
189#102—1221no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8—611no—
193C4×C8C2×#692311yescharacteristic
194C2×Q8—1221no—
195C2×D4—1221no—
196C2×D4—2441no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—2441no—
201Q16—1222no—
202SD16—2442no—
203D8—1222no—
204M16—4882no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—1222no—
208C2×C8—1222no—
209C2×C8—2442no—
210C2×C8C22⋊#692311yescharacteristic
211C2×C8C22×#692311yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—2441no—
227C42C22⋊#692311yescharacteristic
228C16—1224no—
229C23—611no—
230C23—2441no—
231Q8—2441no—
232Q8—2441no—
233D4—4882no—
234D4—2441no—
235D4—2441no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—4882no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451983911yescharacteristic
248C2×C4#1451983911yescharacteristic
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—1221no—
251C8—1221no—
252C8—4882no—
253C8#1451984212yes—
254C8#1451986512yes—
255C22—612no—
256C22—1221no—
257C22—1221no—
258C22—4881no—
259C22—4881no—
260C22—4881no—
261C22C2×#1451983911yescharacteristic
262C4—21no—
263C4—21no—
264C4—81no—
265C4—81no—
266C4—1221no—
267C4—1221no—
268C4—1221no—
269C4—4881no—
270C4#1684073711yescharacteristic
271C4C2×#1451984211yescharacteristic
272C2—1222no—
273C2—9761no—
274C2#2146116611yescharacteristic
275C2D61⋊#36011yescharacteristic
276C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#499C4
socleC22×C61C2×#102
prime radical#16839999C4
cosocleC8×Dic61C23
hypercenter#499#6923
hypocenterC61#11677
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #21462020C2semidirect
2. #21461374C2semidirect
3. #21460780C2semidirect
4. #21460778C2semidirect
161. C61#11677semidirect

Maximal subgroups

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

subgroupindex
#214620202
#214613742
#214607802
#214607782
#214563912
#1167761