Finite Group Databasebeta

← #30594081

Subgroups — #30594081

Order 15616.

248 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 42 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#21460756C211yesmaximal, characteristic, complemented
2#21460689C211yesmaximal, characteristic, complemented
3#21447127C211yesmaximal, characteristic
4#16840765—21no—
5C22⋊#11758187—21no—
6C2×#14519706C2211yescharacteristic
7C2×#14519698—21no—
8#16839665—21no—
9#16839525C411yescharacteristic
10C22×D8×C61C411yescharacteristic
11C2×#11758217—41no—
12C2×#11758187—41no—
13#14519844—22no—
14C4⋊#92420—41no—
15C22×#92418D411yescharacteristic
16C2×C4⋊Dic61—21no—
17C2×C22⋊Dic61—41no—
18C2×C22⋊Dic61—41no—
19C2×C4×Dic61D411yescharacteristic
20#14519706—41no—
21#14519698—42no—
22C22×D4×C61—21no—
23C2×D8×C61—41no—
24C2×D8×C61—42no—
25C22×C8×C61C2×C411yescharacteristic
26C24×C61—41no—
27C2×D4×C61—22no—
28C2×D4×C61—41no—
29C2×D4×C61—41no—
30C2×D4×C61—41no—
31C2×D4×C61—41no—
32C2×D4×C61—41no—
33C22×C4×C61C22⋊C411yescharacteristic
34C22×Dic61—41no—
35C22×Dic61D811yescharacteristic
36C22×Dic61SD1611yescharacteristic
37#11758217—81no—
38#11758217—81no—
39C2×#92420—42no—
40D8×C61—42no—
41D8×C61—42no—
42C2×C8×C61—21no—
43C2×C8×C61—41no—
44C22⋊Dic61—82no—
45C22⋊Dic61—81no—
46C22⋊Dic61—81no—
47C4⋊Dic61—41no—
48C4⋊Dic61—41no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C2×#92418—21no—
52C2×#92418—41no—
53#11758187—81no—
54C23×C61—42no—
55C23×C61—81no—
56C23×C61—81no—
57C23×C61—81no—
58C23×C61—81no—
59C23×C61—81no—
60C23×C61—81no—
61C23×C61#10211yescharacteristic
62D4×C61—42no—
63D4×C61—42no—
64D4×C61—81no—
65D4×C61—81no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61#9911yescharacteristic
69C2×C4×C61#10411yescharacteristic
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61—81no—
75C2×Dic61—81no—
76C2×Dic61—81no—
77C2×Dic61D1611yescharacteristic
78C2×Dic61SD3211yescharacteristic
79#92420—82no—
80C8×C61—41no—
81#92418—41no—
82#7088—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—82no—
86C22×C61—82no—
87C22×C61—82no—
88C22×C61—161no—
89C22×C61—161no—
90C22×C61—161no—
91C22×C61—161no—
92C22×C61#32711yescharacteristic
93C22×C61#35711yescharacteristic
94C22×C61#36011yescharacteristic
95C4×C61—21no—
96C4×C61AΣL(1,𝔽16)11yescharacteristic
97C4×C61#35511yescharacteristic
98Dic61—21no—
99Dic61—21no—
100Dic61—41no—
101Dic61—161no—
102#2054—611no—
103#1322—611no—
104#1292—611no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—162no—
108C2×C61#134111yescharacteristic
109C2×C61#134511yescharacteristic
110C2×C61#134711yescharacteristic
111C22×D8#692311yescharacteristic
112#423—1221no—
113C2×C4⋊C8—611no—
114C2×#102—1221no—
115#390—1221no—
116C22⋊C16—1221no—
117#340—611no—
118C61#708811yescharacteristic, complemented, Sylow
119C22×D4—21no—
120C2×D8—41no—
121C2×D8—42no—
122C2×M16—2441no—
123C22×C8—611no—
124C22×C8C2×#692311yescharacteristic
125C2×C4⋊C4—1221no—
126C2×C22⋊C4—2441no—
127C2×C22⋊C4—2441no—
128C2×C42—611no—
129C2×C16—2441no—
130C4⋊C8—1222no—
131C4⋊C8—2441no—
132C4⋊C8—2441no—
133#102—2442no—
134C24—41no—
135C2×D4—22no—
136C2×D4—41no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4—41no—
140C2×D4—41no—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—2441no—
144C22×C4C22⋊#692311yescharacteristic
145D8—42no—
146D8—42no—
147M16—4881no—
148M16—4881no—
149C2×C8—21no—
150C2×C8—41no—
151C2×C8—1221no—
152C2×C8—2442no—
153C2×C8—2441no—
154C4⋊C4—2441no—
155C4⋊C4—2441no—
156C22⋊C4—4881no—
157C22⋊C4—4881no—
158C22⋊C4—4882no—
159C42—1221no—
160C42—1221no—
161C16—4881no—
162C23—42no—
163C23—81no—
164C23—81no—
165C23—81no—
166C23—81no—
167C23—81no—
168C23—81no—
169C23#1451983911yescharacteristic
170D4—42no—
171D4—42no—
172D4—81no—
173D4—81no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—4881no—
182C2×C4—4881no—
183C2×C4—4881no—
184C2×C4—2441no—
185C2×C4#1451983511yescharacteristic
186C2×C4#1451984111yescharacteristic
187C8—41no—
188C8—4882no—
189C8—2441no—
190C22—21no—
191C22—21no—
192C22—82no—
193C22—82no—
194C22—82no—
195C22—161no—
196C22—161no—
197C22—161no—
198C22—161no—
199C22#1684061311yescharacteristic
200C22#1684067411yescharacteristic
201C22#1684067811yescharacteristic
202C4—21no—
203C4—1221no—
204C4—1221no—
205C4—9761no—
206C4—2441no—
207C4#1684066211yescharacteristic
208C4#1684067011yescharacteristic
209C2—21no—
210C2—21no—
211C2—162no—
212C2#2146079311yescharacteristic
213C2#2146080111yescharacteristic
214C2#2146080511yescharacteristic
subgroupG/H
centerC22#16840613
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
Fitting, prime radicalC22×D8×C61C4
socleC22×C61#327
cosocleC2×#14519706C22
hypercenterC22×D8#6923
hypocenterC61#7088
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. #21460756C2semidirect
2. #21460689C2semidirect
118. C61#7088semidirect

Maximal subgroups

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

subgroupindex
#214607562
#214606892
#214471272
#708861