Finite Group Databasebeta

← #30594082

Subgroups — #30594082

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#21447131C211yesmaximal, characteristic
4#16840765—21no—
5C22⋊#11758187—21no—
6C22×D488C411yescharacteristic
7C2×#14519706C2211yescharacteristic
8C2×#14519697—21no—
9#16839663—21no—
10C61×#340C411yescharacteristic
11C2×#11758217—41no—
12C2×#11758187—41no—
13#14519844—22no—
14C4⋊#92420—41no—
15C22×D244—21no—
16C2×D488—41no—
17C2×D488—42no—
18C22×#92418D411yescharacteristic
19C2×#11758198—41no—
20C2×#11758198—41no—
21C2×C4×Dic61D411yescharacteristic
22#14519706—41no—
23#14519697—42no—
24C22×C8×C61C2×C411yescharacteristic
25C2×C4⋊C4×C61—21no—
26C23×D61—41no—
27C22×C4×C61—41no—
28C22×C4×C61C22⋊C411yescharacteristic
29C22×Dic61D811yescharacteristic
30C22×Dic61SD1611yescharacteristic
31C2×D244—22no—
32C2×D244—41no—
33C2×D244—41no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—41no—
37#11758217—81no—
38#11758217—81no—
39C2×#92420—42no—
40C2×C8×C61—21no—
41C2×C8×C61—41no—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—41no—
44#11758198—82no—
45#11758198—81no—
46#11758198—81no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C2×#92418—41no—
51D488—42no—
52D488—42no—
53#11758187—81no—
54C23×C61#10211yescharacteristic
55C22×D61—42no—
56C22×D61—81no—
57C22×D61—81no—
58C22×D61—81no—
59C22×D61—81no—
60C22×D61—81no—
61C22×D61—81no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—81no—
65C2×C4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61#9911yescharacteristic
68C2×C4×C61#10411yescharacteristic
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—41no—
73C2×Dic61D1611yescharacteristic
74C2×Dic61SD3211yescharacteristic
75D244—42no—
76D244—42no—
77D244—81no—
78D244—81no—
79#92420—82no—
80C8×C61—41no—
81#92418—41no—
82#7088—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61#32711yescharacteristic
86C22×C61#35711yescharacteristic
87C22×C61#36011yescharacteristic
88C2×D61—82no—
89C2×D61—82no—
90C2×D61—82no—
91C2×D61—161no—
92C2×D61—161no—
93C2×D61—161no—
94C2×D61—161no—
95C4×C61—21no—
96C4×C61—161no—
97C4×C61AΣL(1,𝔽16)11yescharacteristic
98C4×C61#35511yescharacteristic
99Dic61—21no—
100Dic61—21no—
101Dic61—41no—
102#2054—611no—
103#1322—611no—
104#1292—611no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#134111yescharacteristic
108C2×C61#134511yescharacteristic
109C2×C61#134711yescharacteristic
110D61—162no—
111C22×D8—611no—
112#423—1221no—
113C2×C4⋊C8—611no—
114C2×#102—1221no—
115#390—1221no—
116C22⋊C16—1221no—
117#340#692311yescharacteristic
118C61#708811yescharacteristic, complemented, Sylow
119C22×D4—1221no—
120C2×D8—2441no—
121C2×D8—2442no—
122C2×M16—2441no—
123C22×C8—611no—
124C22×C8C2×#692311yescharacteristic
125C2×C4⋊C4—21no—
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—2441no—
135C2×D4—1222no—
136C2×D4—2441no—
137C2×D4—2441no—
138C2×D4—2441no—
139C2×D4—2441no—
140C2×D4—2441no—
141C22×C4—41no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4C22⋊#692311yescharacteristic
145D8—2442no—
146D8—2442no—
147M16—4881no—
148M16—4881no—
149C2×C8—21no—
150C2×C8—41no—
151C2×C8—1221no—
152C2×C8—2442no—
153C2×C8—2441no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C22⋊C4—4881no—
157C22⋊C4—4881no—
158C22⋊C4—4882no—
159C42—1221no—
160C42—1221no—
161C16—4881no—
162C23—4881no—
163C23—4881no—
164C23—4881no—
165C23—4881no—
166C23—4881no—
167C23—4881no—
168C23—2442no—
169C23#1451983911yescharacteristic
170D4—4881no—
171D4—4881no—
172D4—2442no—
173D4—2442no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2441no—
185C2×C4#1451983611yescharacteristic
186C2×C4#1451984211yescharacteristic
187C8—41no—
188C8—4882no—
189C8—2441no—
190C22—21no—
191C22—21no—
192C22—9761no—
193C22—9761no—
194C22—9761no—
195C22—9761no—
196C22—4882no—
197C22—4882no—
198C22—4882no—
199C22#1684061411yescharacteristic
200C22#1684067411yescharacteristic
201C22#1684067911yescharacteristic
202C4—21no—
203C4—161no—
204C4—1221no—
205C4—1221no—
206C4—2441no—
207C4#1684066311yescharacteristic
208C4#1684067111yescharacteristic
209C2—21no—
210C2—21no—
211C2—9762no—
212C2#2146079411yescharacteristic
213C2#2146080211yescharacteristic
214C2#2146080611yescharacteristic
subgroupG/H
centerC22#16840614
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#327
prime radicalC22×D488C4
cosocleC2×#14519706C22
hypercenter#340#6923
hypocenterC61#7088
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

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
#214471312
#708861