Finite Group Databasebeta

← #30605672

Subgroups — #30605672

Order 15616.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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
2#21461382C211yesmaximal, characteristic
3#21460836C214yesmaximal, complemented
4#21456330C211yesmaximal, characteristic
5#16840784—21no—
6#16840683C2212yes—
7#16840657—21no—
8#16840650—21no—
9#16840626—21no—
10#16840624C2212yes—
11#16840317—21no—
12#16840167C411yescharacteristic
13#16840163—21no—
14#16840163C2212yes—
15#16840158—21no—
16#16839799—21no—
17#16839799C412yes—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic
20C2×#11758187—22no—
21C4⋊#92420—22no—
22#14519834—41no—
23#14519832—41no—
24C2×C8×D61C2×C411yescharacteristic
25C2×C8×D61D411yescharacteristic
26#14519777—21no—
27#14519768—22no—
28#14519757—41no—
29#14519753—41no—
30Q8×Dic61—41no—
31#14519742—41no—
32#14519735—22no—
33C42×D61D411yescharacteristic
34#14519711—21no—
35#14519711C2×C412yes—
36#14519708—22no—
37#14519708—22no—
38C4×#92418D411yescharacteristic
39C8×Dic61D411yescharacteristic
40C8×Dic61C2311yescharacteristic
41C4⋊Q8×C61—21no—
42#107×C61—21no—
43#107×C61C2×C412yes—
44C4×C8×C61C2×C411yescharacteristic
45C2×Q8×C61—41no—
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61D811yescharacteristic
48C2×C4×D61SD1611yescharacteristic
49C2×Dic122—41no—
50C2×#92420—42no—
51C2×C8×C61C22⋊C411yescharacteristic
52C2×C8×C61C22×C411yescharacteristic
53C4⋊C4×C61—22no—
54C4⋊C4×C61—41no—
55C42×C61C22⋊C411yescharacteristic
56#11758198—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—41no—
59C4⋊Dic61—42no—
60#11758196—42no—
61C4×Dic61—42no—
62C4×Dic61D811yescharacteristic
63C4×Dic61SD1611yescharacteristic
64C4×Dic61C2×D411yescharacteristic
65C2×#92418C22⋊C411yescharacteristic
66C2×#92418C2×D411yescharacteristic
67C8×D61—22no—
68C8×D61—22no—
69#11758187—42no—
70C22×D61#10211yescharacteristic
71Q8×C61—82no—
72C2×C4×C61—42no—
73C2×C4×C61#10211yescharacteristic
74C2×C4×C61#10211yescharacteristic
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C2×Dic61—42no—
77C2×Dic61#10211yescharacteristic
78C2×Dic61C2×D811yescharacteristic
79C2×Dic61C2×SD1611yescharacteristic
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—82no—
85#92420—82no—
86C8×C61—21no—
87C8×C61—21no—
88#92418#10112yes—
89#92418#13712yes—
90#11970—611nomaximal, Sylow
91C22×C61C2×#10211yescharacteristic
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—82no—
98C4×C61C2×#10111yescharacteristic
99C4×C61#41911yescharacteristic
100Dic61—21no—
101Dic61—21no—
102Dic61—21no—
103Dic61—82no—
104#3160—611no—
105#2163—611no—
106#1568—611no—
107#1363—614no—
108C2×C61#154611yescharacteristic
109C2×C61#214311yescharacteristic
110C2×C61#214511yescharacteristic
111D61—41no—
112#533—1221no—
113#500—611no—
114#500#692311yescharacteristic
115#499—612no—
116#499—1221no—
117#498—1221no—
118#432—1221no—
119#427—612no—
120#427—1221no—
121C2×C4×C8—611no—
122C4⋊C16—612no—
123C22⋊C16—1221no—
124#346—1221no—
125#335—1221no—
126#334—612no—
127C61#1197011yescharacteristic, complemented, Sylow
128C22×C8—611no—
129C22×C8—611no—
130C4⋊Q8—21no—
131C4⋊Q8—1221no—
132#125—1222no—
133C22⋊Q8—2441no—
134C22⋊Q8—2441no—
135C4×Q8—2441no—
136C4×Q8—2441no—
137#117—1222no—
138C2×C42—611no—
139C2×C16—1222no—
140#107—21no—
141#107—612no—
142#107—1221no—
143#107C2×#692312yes—
144#106—1222no—
145#106—1222no—
146C4⋊C8—1222no—
147C22⋊C8—2441no—
148#97—2441no—
149C4×C8—611no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8C2×#692311yescharacteristic
153C2×Q8—41no—
154C2×Q8—2441no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—1222no—
161C2×C8—1222no—
162C2×C8—2442no—
163C2×C8C22⋊#692311yescharacteristic
164C2×C8C22×#692311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—41no—
167C4⋊C4—1222no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4—2441no—
171C22⋊C4—2442no—
172C42—611no—
173C42—611no—
174C42—611no—
175C42—2442no—
176C42C22⋊#692311yescharacteristic
177C16—2442no—
178C23—611no—
179Q8—82no—
180Q8—4882no—
181C2×C4—42no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2442no—
190C2×C4#1451983911yescharacteristic
191C2×C4#1451983911yescharacteristic
192C2×C4C2×C22⋊#692311yescharacteristic
193C8—21no—
194C8—21no—
195C8—612no—
196C8—612no—
197C8—4882no—
198C22—1221no—
199C22—1221no—
200C22—1221no—
201C22C2×#1451983911yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—1221no—
206C4—1221no—
207C4—1221no—
208C4—4882no—
209C4D61⋊#10111yescharacteristic
210C4#1684075511yescharacteristic
211C2—2441no—
212C2#2146132911yescharacteristic
213C2#2146213511yescharacteristic
214C2#2146214011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#500C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenter#500#6923
hypocenterC61#11970
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #21460836C2semidirect
127. C61#11970semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214613822
#214608362
#214563302
#1197061