Finite Group Databasebeta

← #30594983

Subgroups — #30594983

Order 15616.

228 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460762C211yesmaximal, characteristic, complemented
2#21460697C211yesmaximal, characteristic, complemented
3#21447044C211yesmaximal, characteristic
4C2×#14519844—21no—
5#16840607—21no—
6#16840343C411yescharacteristic
7C2×#14519703—21no—
8#16839764—21no—
9#16839631C2211yescharacteristic
10C61×#343C411yescharacteristic
11C22×#92420—41no—
12#14519844—22no—
13#14519844—41no—
14C22⋊#92420—41no—
15C2×#11758222—21no—
16#14519757—41no—
17#14519752—41no—
18#14519751—41no—
19C2×C4⋊Dic61D411yescharacteristic
20C2×#11758196—41no—
21C2×C4×Dic61D411yescharacteristic
22#14519703—41no—
23#14519703—41no—
24#14519702—41no—
25#14519699—41no—
26C2×M16×C61—21no—
27C2×C4⋊C4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×C22⋊D61—41no—
31C22×Dic61—21no—
32C22×Dic61—21no—
33#11758222—41no—
34#11758222—41no—
35#11758222—41no—
36#11758222—41no—
37C2×D244—21no—
38C2×D244—41no—
39C2×C4×D61—41no—
40C2×Dic122—21no—
41C2×#92420—42no—
42C2×#92420—81no—
43C2×#92420—81no—
44C2×#92420—81no—
45M16×C61—41no—
46M16×C61—41no—
47C2×C8×C61—41no—
48C4⋊C4×C61—41no—
49#11758198—42no—
50C4⋊Dic61—41no—
51C4⋊Dic61—41no—
52#11758196—81no—
53#11758196—81no—
54C4×Dic61—21no—
55C4×Dic61D811yescharacteristic
56C4×Dic61SD1611yescharacteristic
57C23×C61#9911yescharacteristic
58C22×D61—41no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—81no—
63C2×C4×C61#10211yescharacteristic
64C2×C4×C61#10411yescharacteristic
65C22⋊D61—81no—
66C22⋊D61—81no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—81no—
76D244—41no—
77D244—41no—
78D244—161no—
79C4×D61—81no—
80C4×D61—81no—
81Dic122—41no—
82Dic122—41no—
83#92420—82no—
84#92420—161no—
85C8×C61—81no—
86#7417—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—21no—
89C22×C61#32711yescharacteristic
90C22×C61AΣL(1,𝔽16)11yescharacteristic
91C22×C61#35511yescharacteristic
92C2×D61—81no—
93C2×D61—81no—
94C2×D61—81no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—81no—
98Dic61—21no—
99Dic61—21no—
100Dic61—21no—
101Dic61—21no—
102Dic61—81no—
103Dic61—81no—
104#2039—611no—
105#1325—611no—
106#1296—611no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61#134511yescharacteristic
110C2×C61#140211yescharacteristic
111C2×C61#140511yescharacteristic
112D61—161no—
113#537—611no—
114C2×C4⋊C8—1221no—
115C2×#104—1221no—
116#417—1221no—
117#384—611no—
118#343#692311yescharacteristic
119#324—1221no—
120C61#741711yescharacteristic, complemented, Sylow
121C2×#41—1221no—
122C2×M16—21no—
123C22×C8—2441no—
124C22⋊Q8—2441no—
125#121—2441no—
126#121—2441no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—2441no—
129C2×C4⋊C4C2×#692311yescharacteristic
130C2×C42—611no—
131C4⋊C8—1222no—
132C4⋊C8—2441no—
133#104—2441no—
134#104—2441no—
135#103—2441no—
136#102—2441no—
137C22⋊C8—2441no—
138#41—2441no—
139#41—2441no—
140#41—2441no—
141#41—2441no—
142C2×Q8—1221no—
143C2×D4—1221no—
144C2×D4—2441no—
145C2×D4—2441no—
146C22×C4—21no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—2441no—
150C22×C4C22⋊#692311yescharacteristic
151M16—41no—
152M16—41no—
153C2×C8—41no—
154C2×C8—4881no—
155C2×C8—4881no—
156C2×C8—4881no—
157C2×C8—2442no—
158C4⋊C4—41no—
159C4⋊C4—4881no—
160C4⋊C4—4881no—
161C4⋊C4—2441no—
162C4⋊C4—2441no—
163C22⋊C4—2442no—
164C42—611no—
165C42—611no—
166C42—1221no—
167C23—2441no—
168C23#1451983611yescharacteristic
169Q8—2441no—
170Q8—2441no—
171D4—9761no—
172D4—4881no—
173D4—4881no—
174D4—2441no—
175D4—2441no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—81no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—4881no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4#1451983911yescharacteristic
192C2×C4#1451984211yescharacteristic
193C8—81no—
194C8—9761no—
195C8—4882no—
196C22—21no—
197C22—21no—
198C22—4881no—
199C22—4881no—
200C22—4881no—
201C22#1684061411yescharacteristic
202C22#1684066311yescharacteristic
203C22#1684067111yescharacteristic
204C4—21no—
205C4—21no—
206C4—81no—
207C4—1221no—
208C4—1221no—
209C4—1221no—
210C4—1221no—
211C4—4881no—
212C4—4881no—
213C2—21no—
214C2—21no—
215C2—9761no—
216C2#2146080211yescharacteristic
217C2#2146093911yescharacteristic
218C2#2146094511yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61AΣL(1,𝔽16)
prime radical#16840343C4
cosocle#16839631C22
hypercenter#343#6923
hypocenterC61#7417
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #21460762C2semidirect
2. #21460697C2semidirect
120. C61#7417semidirect

Maximal subgroups

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

subgroupindex
#214607622
#214606972
#214470442
#741761