Finite Group Databasebeta

← #30605665

Subgroups — #30605665

Order 15616.

296 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462178C211yesmaximal, characteristic
2#21461375C211yesmaximal, characteristic
3#21460835C214yesmaximal, complemented
4#21456330C211yesmaximal, characteristic
5#16840766—21no—
6#16840683C2212yes—
7#16840657—21no—
8C4×#11758187—21no—
9#16840624—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×#11758213—41no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23C4⋊#92420—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—
51#11758213—82no—
52C2×C8×C61C22⋊C411yescharacteristic
53C2×C8×C61C22×C411yescharacteristic
54C4⋊C4×C61—22no—
55C4⋊C4×C61—41no—
56C42×C61C22⋊C411yescharacteristic
57#11758198—42no—
58C4⋊Dic61—22no—
59C4⋊Dic61—41no—
60C4⋊Dic61—42no—
61#11758196—42no—
62C4×Dic61—42no—
63C4×Dic61D811yescharacteristic
64C4×Dic61SD1611yescharacteristic
65C4×Dic61C2×D411yescharacteristic
66C2×#92418C22⋊C411yescharacteristic
67C2×#92418C2×D411yescharacteristic
68C8×D61—22no—
69C8×D61—22no—
70#11758187—42no—
71C22×D61#10211yescharacteristic
72Q8×C61—82no—
73C2×C4×C61—42no—
74C2×C4×C61#10211yescharacteristic
75C2×C4×C61#10211yescharacteristic
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×Dic61—42no—
78C2×Dic61#10211yescharacteristic
79C2×Dic61C2×D811yescharacteristic
80C2×Dic61C2×SD1611yescharacteristic
81C4×D61—22no—
82C4×D61—22no—
83C4×D61—21no—
84C4×D61—21no—
85Dic122—82no—
86#92420—82no—
87C8×C61—21no—
88C8×C61—21no—
89#92418#10112yes—
90#92418#13712yes—
91#11968—611nomaximal, Sylow
92C22×C61C2×#10211yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C4×C61—82no—
97C4×C61#35912yes—
98C4×C61#36012yes—
99C4×C61C2×#10111yescharacteristic
100C4×C61#41911yescharacteristic
101Dic61—21no—
102Dic61—21no—
103Dic61—21no—
104Dic61—82no—
105#3160—611no—
106#2162—611no—
107#1566—611no—
108#1363—614no—
109C2×C61#154611yescharacteristic
110C2×C61C2×#35911yescharacteristic
111C2×C61C2×#36011yescharacteristic
112D61—41no—
113#533—1221no—
114#500—611no—
115#500#692311yescharacteristic
116#499—612no—
117#499—1221no—
118#498—1221no—
119#427—612no—
120#427—1221no—
121#423—1221no—
122C2×C4×C8—611no—
123C4⋊C16—612no—
124C22⋊C16—1221no—
125C4×C16—1221no—
126#334—612no—
127#334—1221no—
128C61#1196811yescharacteristic, complemented, Sylow
129C2×M16—2441no—
130C22×C8—611no—
131C22×C8—611no—
132C4⋊Q8—21no—
133C4⋊Q8—1221no—
134#125—1222no—
135C22⋊Q8—2441no—
136C22⋊Q8—2441no—
137C4×Q8—2441no—
138C4×Q8—2441no—
139#117—1222no—
140C2×C42—611no—
141C2×C16—1222no—
142#107—21no—
143#107—612no—
144#107—1221no—
145#107C2×#692312yes—
146#106—1222no—
147#106—1222no—
148C4⋊C8—1222no—
149C4⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—611no—
153C4×C8C2×#692311yescharacteristic
154C2×Q8—41no—
155C2×Q8—2441no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159M16—4882no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—1222no—
163C2×C8—1222no—
164C2×C8—2442no—
165C2×C8C22⋊#692311yescharacteristic
166C2×C8C22×#692311yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—1222no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C4⋊C4—2441no—
173C22⋊C4—2442no—
174C42—611no—
175C42—611no—
176C42—611no—
177C42—2442no—
178C42C22⋊#692311yescharacteristic
179C16—2442no—
180C23—611no—
181Q8—82no—
182Q8—4882no—
183C2×C4—42no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—2442no—
192C2×C4#1451983911yescharacteristic
193C2×C4#1451983911yescharacteristic
194C2×C4C2×C22⋊#692311yescharacteristic
195C8—21no—
196C8—21no—
197C8—612no—
198C8—612no—
199C8—4882no—
200C22—1221no—
201C22—1221no—
202C22—1221no—
203C22C2×#1451983911yescharacteristic
204C4—82no—
205C4—1221no—
206C4—1221no—
207C4—1221no—
208C4—4882no—
209C4#1684067612yes—
210C4#1684067912yes—
211C4D61⋊#10111yescharacteristic
212C4#1684075511yescharacteristic
213C2—2441no—
214C2#2146132911yescharacteristic
215C2C2×#1684067611yescharacteristic
216C2C2×#1684067911yescharacteristic
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#11968
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. #21460835C2semidirect
128. C61#11968semidirect

Maximal subgroups

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

subgroupindex
#214621782
#214613752
#214608352
#214563302
#1196861