Finite Group Databasebeta

← #30604921

Subgroups — #30604921

Order 15616.

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

normal subgroups only

This group has 390 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#21462183C211yesmaximal, characteristic, complemented
2C4×#14519845C211yesmaximal, characteristic, complemented
3#21460805C214yesmaximal, complemented
4#21456396C211yesmaximal, characteristic
5C2×#14519845—21no—
6C4×C4⋊#6923—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840651—21no—
10#16840636C2212yes—
11#16840310—21no—
12#16840167C411yescharacteristic, complemented
13#16840108—21no—
14#16839995—21no—
15#16839995C2212yes—
16D8×Dic61—21no—
17D8×Dic61C412yescomplemented
18C4×C8×D61C2211yescharacteristic
19C61×#493C411yescharacteristic, complemented
20C2×C4⋊#6923—22no—
21C2×C4×#6923—41no—
22C2×#11758187—22no—
23#14519845—24no—
24(C2×#6923)⋊C4—41no—
25C2×#11758224—41no—
26C2×C8×D61D411yescharacteristic
27C2×C8×D61C2311yescharacteristic
28#14519777—21no—
29#14519764—41no—
30#14519748—22no—
31#14519748—41no—
32D4×Dic61—22no—
33D4×Dic61—41no—
34C42×D61D411yescharacteristic
35#14519711—21no—
36#14519711C2×C412yes—
37#14519698—22no—
38#14519698—22no—
39C4×#92418D411yescharacteristic
40C8×Dic61C2×C411yescharacteristic
41C8×Dic61D411yescharacteristic
42C2×D8×C61—21no—
43C2×D8×C61C2×C412yes—
44#127×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C22×#6923—42no—
47C2×D4×C61—22no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×C22⋊D61—42no—
51C22×Dic61—42no—
52#11758224—84no—
53C2×C4×D61D811yescharacteristic
54C2×C4×D61D811yescharacteristic
55C2×C4×D61C2×D411yescharacteristic
56C2×Dic122—41no—
57C4⋊#6923—24no—
58C4⋊#6923—42no—
59C4×#6923—82no—
60D8×C61—42no—
61D8×C61—42no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22×C411yescharacteristic
64C42×C61C22⋊C411yescharacteristic
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67C4⋊Dic61—22no—
68C4⋊Dic61—41no—
69C4×Dic61C22⋊C411yescharacteristic
70C4×Dic61SD1611yescharacteristic
71C4×Dic61SD1611yescharacteristic
72C2×#92418C22⋊C411yescharacteristic
73C2×#92418C2×D411yescharacteristic
74C8×D61—22no—
75C8×D61—41no—
76#11758187—42no—
77C23×C61—42no—
78C22×D61C2×D811yescharacteristic
79C2×#6923—44no—
80C2×#6923—82no—
81C2×#6923—82no—
82D4×C61—42no—
83D4×C61—42no—
84D4×C61—82no—
85D4×C61—82no—
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61#10211yescharacteristic
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C22⋊D61—84no—
90C2×Dic61—42no—
91C2×Dic61—84no—
92C2×Dic61#10211yescharacteristic
93C2×Dic61#10211yescharacteristic
94C2×Dic61C2×SD1611yescharacteristic
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—21no—
98C4×D61—21no—
99Dic122—82no—
100C8×C61—21no—
101C8×C61#10412yes—
102#92418—21no—
103#92418—21no—
104#11744—611nomaximal, Sylow
105C22×C61—82no—
106C22×C61—82no—
107C22×C61—82no—
108C22×C61C2×#10211yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61#50912yes—
112#6923—84no—
113C4×C61—21no—
114C4×C61#36012yes—
115C4×C61#41011yescharacteristic
116C4×C61C2×#10411yescharacteristic
117Dic61—21no—
118Dic61—21no—
119Dic61—21no—
120Dic61—82no—
121#3169—611no—
122#2163—611no—
123C4×#106—611no—
124#1347—614no—
125C2×C61—162no—
126C2×C61#150211yescharacteristic
127C2×C61#214011yescharacteristic
128C2×C61C2×#36011yescharacteristic
129D61—22no—
130#532—1221no—
131#500—611no—
132#493#692311yescharacteristic, complemented
133#486—1221no—
134#466—612no—
135#466—1221no—
136C4×D8—612no—
137C4×D8—1221no—
138C2×#106—1221no—
139C2×C4×C8—611no—
140C4×C4⋊C4—1221no—
141C4⋊C16—1221no—
142C22⋊C16—612no—
143#346—1221no—
144#340—612no—
145C61#1174411yescharacteristic, complemented, Sylow
146C2×#41—2441no—
147C2×D8—21no—
148C2×D8C2×#692312yes—
149C22×C8—611no—
150C22×C8—611no—
151C4⋊Q8—1221no—
152#127—21no—
153#124—2441no—
154#121—1222no—
155#121—2441no—
156C4×D4—1222no—
157C4×D4—2441no—
158C2×C4⋊C4—1222no—
159C2×C42—611no—
160C2×C42—2441no—
161C2×C16—1222no—
162#107—612no—
163#107—1221no—
164#106—1224no—
165#102—1222no—
166#102—1222no—
167C4×C8—611no—
168C4×C8—611no—
169C4×C8—611no—
170C4×C8C2×#692311yescharacteristic
171#95—2441no—
172#41—4884no—
173C2×Q8—2441no—
174C2×D4—22no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—2442no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—2442no—
182C22×C4—2442no—
183D8—42no—
184D8—42no—
185C2×C8—611no—
186C2×C8—611no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8C22⋊#692311yescharacteristic
190C2×C8C22×#692311yescharacteristic
191C4⋊C4—1224no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2441no—
195C22⋊C4—2442no—
196C22⋊C4—2442no—
197C42—611no—
198C42—611no—
199C42—611no—
200C42—4882no—
201C42C22⋊#692311yescharacteristic
202C16—2442no—
203C23—42no—
204C23—611no—
205Q8—4882no—
206D4—42no—
207D4—42no—
208D4—82no—
209D4—82no—
210D4—4884no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—4884no—
219C2×C4—4882no—
220C2×C4—4882no—
221C2×C4—2444no—
222C2×C4—2442no—
223C2×C4#1451983911yescharacteristic
224C2×C4#1451983911yescharacteristic
225C2×C4C2×C22⋊#692311yescharacteristic
226C8—21no—
227C8—1221no—
228C8—1221no—
229C8#1451984112yes—
230C22—82no—
231C22—82no—
232C22—82no—
233C22—612no—
234C22—1221no—
235C22—1221no—
236C22C2×#1451983911yescharacteristic
237C4—21no—
238C4—1221no—
239C4—1221no—
240C4—1221no—
241C4—4884no—
242C4—4882no—
243C4#1684067812yes—
244C4#1684074211yescharacteristic
245C4C2×#1451984111yescharacteristic
246C2—162no—
247C2—1222no—
248C2#2146119911yescharacteristic
249C2#2146212811yescharacteristic
250C2C2×#1684067811yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#493C4
socleC22×C61C2×#102
prime radical#21456396C2
cosocleC2×C8×D61C23
hypercenter#493#6923
hypocenterC61#11744
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21462183C2semidirect
2. C4×#14519845C2semidirect
3. #21460805C2semidirect
12. #16840167C4semidirect
17. D8×Dic61C4semidirect
19. C61×#493C4semidirect
132. #493#6923semidirect
145. C61#11744semidirect

Maximal subgroups

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

subgroupindex
#214621832
C4×#145198452
#214608052
#214563962
#1174461