Finite Group Databasebeta

← #30605352

Subgroups — #30605352

Order 15616.

344 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462182C211yesmaximal, characteristic, complemented
2#21461744C211yesmaximal, characteristic, complemented
3#21460809C214yesmaximal, complemented
4#21456396C211yesmaximal, characteristic
5#16840767—21no—
6#16840683—21no—
7#16840657C2212yes—
8#16840650—21no—
9#16840638—21no—
10#16840638C2212yes—
11#16840310—21no—
12#16840167C411yescharacteristic
13#16840108—21no—
14#16839995—21no—
15#16839995C2212yes—
16D8×Dic61—21no—
17D8×Dic61C412yes—
18C4×C8×D61C2211yescharacteristic
19C61×#493C411yescharacteristic
20C2×#11758213—22no—
21C2×#11758187—22no—
22#14519844—41no—
23#14519844—41no—
24C2×#11758224—41no—
25C2×C8×D61D411yescharacteristic
26C2×C8×D61C2311yescharacteristic
27#14519777—21no—
28#14519764—41no—
29#14519748—22no—
30#14519748—41no—
31D4×Dic61—22no—
32D4×Dic61—41no—
33C42×D61D411yescharacteristic
34#14519711—21no—
35#14519711C2×C412yes—
36#14519698—22no—
37#14519698—22no—
38C4×#92418D411yescharacteristic
39C8×Dic61C2×C411yescharacteristic
40C8×Dic61D411yescharacteristic
41C2×D8×C61—21no—
42C2×D8×C61C2×C412yes—
43#127×C61—21no—
44C4×C8×C61C2×C411yescharacteristic
45C2×D4×C61—22no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×C22⋊D61—42no—
49C22×Dic61—42no—
50#11758224—84no—
51C2×C4×D61SD1611yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53C2×C4×D61C2×D411yescharacteristic
54C2×Dic122—41no—
55C2×#92420—42no—
56#11758213—42no—
57#11758213—42no—
58D8×C61—42no—
59D8×C61—42no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22×C411yescharacteristic
62C42×C61C22⋊C411yescharacteristic
63C22⋊Dic61—42no—
64C22⋊Dic61—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—41no—
67C4×Dic61C22⋊C411yescharacteristic
68C4×Dic61D811yescharacteristic
69C4×Dic61D811yescharacteristic
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C2×D411yescharacteristic
72C8×D61—41no—
73C8×D61—41no—
74#11758187—42no—
75C23×C61—42no—
76C22×D61C2×SD1611yescharacteristic
77D4×C61—42no—
78D4×C61—42no—
79D4×C61—82no—
80D4×C61—82no—
81C2×C4×C61#10211yescharacteristic
82C2×C4×C61#10211yescharacteristic
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C22⋊D61—84no—
85C2×Dic61—42no—
86C2×Dic61—84no—
87C2×Dic61#10211yescharacteristic
88C2×Dic61#10211yescharacteristic
89C2×Dic61C2×D811yescharacteristic
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—22no—
93C4×D61—41no—
94Dic122—82no—
95#92420—82no—
96C8×C61—21no—
97C8×C61—21no—
98#92418—21no—
99#92418—21no—
100#11864—611nomaximal, Sylow
101C22×C61—82no—
102C22×C61—82no—
103C22×C61—82no—
104C22×C61C2×#10211yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61#41011yescharacteristic
111C4×C61#42111yescharacteristic
112Dic61—21no—
113Dic61—21no—
114Dic61—82no—
115Dic61#36112yes—
116#3169—611no—
117#2163—611no—
118#1837—611no—
119#1349—614no—
120C2×C61—162no—
121C2×C61#151711yescharacteristic
122C2×C61#214311yescharacteristic
123C2×C61C2×#36111yescharacteristic
124D61—41no—
125#532—1221no—
126#500—611no—
127#493#692311yescharacteristic
128#486—1221no—
129#466—612no—
130#466—1221no—
131C4×D8—612no—
132C4×D8—1221no—
133#423—1221no—
134C2×C4×C8—611no—
135C4⋊C16—1221no—
136C22⋊C16—612no—
137#346—1221no—
138#341—612no—
139#341—1221no—
140C61#1186411yescharacteristic, complemented, Sylow
141C2×#41—2441no—
142C2×D8—21no—
143C2×D8C2×#692312yes—
144C2×M16—1222no—
145C22×C8—611no—
146C22×C8—611no—
147C4⋊Q8—1221no—
148#127—21no—
149#124—2441no—
150#121—1222no—
151#121—2441no—
152C4×D4—1222no—
153C4×D4—2441no—
154C2×C42—611no—
155C2×C16—1222no—
156#107—612no—
157#107—1221no—
158C4⋊C8—2441no—
159C4⋊C8—2441no—
160#102—1222no—
161#102—1222no—
162C4×C8—611no—
163C4×C8—611no—
164C4×C8—611no—
165C4×C8C2×#692311yescharacteristic
166#41—4884no—
167C2×Q8—2441no—
168C2×D4—22no—
169C2×D4—41no—
170C2×D4—41no—
171C2×D4—2442no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—2442no—
176D8—42no—
177D8—42no—
178M16—2442no—
179M16—2442no—
180C2×C8—611no—
181C2×C8—611no—
182C2×C8—2441no—
183C2×C8—2441no—
184C2×C8—2442no—
185C2×C8C22⋊#692311yescharacteristic
186C2×C8C22×#692311yescharacteristic
187C4⋊C4—1222no—
188C4⋊C4—2441no—
189C22⋊C4—2442no—
190C22⋊C4—2442no—
191C42—611no—
192C42—611no—
193C42—611no—
194C42C22⋊#692311yescharacteristic
195C16—2442no—
196C23—42no—
197C23—611no—
198Q8—4882no—
199D4—42no—
200D4—42no—
201D4—82no—
202D4—82no—
203D4—4884no—
204C2×C4—611no—
205C2×C4—611no—
206C2×C4—611no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—4884no—
211C2×C4—2441no—
212C2×C4—2442no—
213C2×C4#1451983911yescharacteristic
214C2×C4#1451983911yescharacteristic
215C2×C4C2×C22⋊#692311yescharacteristic
216C8—21no—
217C8—21no—
218C8—1221no—
219C8—1221no—
220C8—4882no—
221C22—82no—
222C22—82no—
223C22—82no—
224C22—1221no—
225C22—1221no—
226C22—1221no—
227C22C2×#1451983911yescharacteristic
228C4—21no—
229C4—21no—
230C4—612no—
231C4—1221no—
232C4—1221no—
233C4—4882no—
234C4#1684074211yescharacteristic
235C4#1684076011yescharacteristic
236C2—162no—
237C2—2441no—
238C2#2146124811yescharacteristic
239C2#2146213411yescharacteristic
240C2D61⋊#36111yescharacteristic
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#11864
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. #21462182C2semidirect
2. #21461744C2semidirect
3. #21460809C2semidirect
140. C61#11864semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214617442
#214608092
#214563962
#1186461