Finite Group Databasebeta

← #30594982

Subgroups — #30594982

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#21447040C211yesmaximal, characteristic
4C2×#14519844—21no—
5#16840607—21no—
6C2×#14519704—21no—
7#16839763—21no—
8#16839631C2211yescharacteristic
9#16839531C411yescharacteristic
10C61×#537C411yescharacteristic
11C22×#92420—41no—
12#14519844—22no—
13#14519844—41no—
14C22⋊#92420—41no—
15C2×#11758194—21no—
16C2×C4⋊Dic61D411yescharacteristic
17C2×#11758196—41no—
18C2×C4×Dic61D411yescharacteristic
19#14519704—41no—
20#14519704—41no—
21#14519701—41no—
22#14519698—41no—
23C2×#41×C61—21no—
24C22⋊Q8×C61—41no—
25#121×C61—41no—
26#121×C61—41no—
27C2×C4⋊C4×C61C2×C411yescharacteristic
28#41×C61—41no—
29#41×C61—41no—
30#41×C61—41no—
31#41×C61—41no—
32C2×Q8×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—41no—
35C2×D4×C61—41no—
36C22×C4×C61—21no—
37C22×C4×C61—41no—
38C22×C4×C61C22⋊C411yescharacteristic
39C22×Dic61—21no—
40C22×Dic61—21no—
41C2×#92420—42no—
42C2×#92420—81no—
43C2×#92420—81no—
44C2×#92420—81no—
45C4⋊C4×C61—41no—
46C4⋊C4×C61—41no—
47C22⋊C4×C61—42no—
48C4⋊Dic61—41no—
49#11758196—81no—
50#11758196—81no—
51C4×Dic61—21no—
52C4×Dic61D811yescharacteristic
53C4×Dic61SD1611yescharacteristic
54#11758194—41no—
55#11758194—41no—
56C2×#92418—41no—
57C23×C61—41no—
58C23×C61#9911yescharacteristic
59Q8×C61—41no—
60Q8×C61—41no—
61D4×C61—41no—
62D4×C61—41no—
63D4×C61—81no—
64D4×C61—81no—
65D4×C61—161no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—81no—
71C2×C4×C61—81no—
72C2×C4×C61—81no—
73C2×C4×C61#10211yescharacteristic
74C2×C4×C61#10411yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—81no—
83#92420—82no—
84#92420—161no—
85#92418—81no—
86#7417—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—81no—
90C22×C61—81no—
91C22×C61—81no—
92C22×C61#32711yescharacteristic
93C22×C61AΣL(1,𝔽16)11yescharacteristic
94C22×C61#35511yescharacteristic
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—81no—
98C4×C61—81no—
99Dic61—21no—
100Dic61—21no—
101Dic61—21no—
102Dic61—21no—
103Dic61—81no—
104#2039—611no—
105#1325—611no—
106#1296—611no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—161no—
110C2×C61#134511yescharacteristic
111C2×C61#140211yescharacteristic
112C2×C61#140511yescharacteristic
113#537#692311yescharacteristic
114C2×C4⋊C8—1221no—
115C2×#104—1221no—
116#417—1221no—
117#384—611no—
118#343—611no—
119#324—1221no—
120C61#741711yescharacteristic, complemented, Sylow
121C2×#41—21no—
122C2×M16—1221no—
123C22×C8—2441no—
124C22⋊Q8—41no—
125#121—41no—
126#121—41no—
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—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142C2×Q8—21no—
143C2×D4—21no—
144C2×D4—41no—
145C2×D4—41no—
146C22×C4—21no—
147C22×C4—41no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C22⋊#692311yescharacteristic
151M16—2441no—
152M16—2441no—
153C2×C8—4881no—
154C2×C8—4881no—
155C2×C8—4881no—
156C2×C8—2441no—
157C2×C8—2442no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—4881no—
161C4⋊C4—4881no—
162C4⋊C4—2441no—
163C22⋊C4—42no—
164C42—611no—
165C42—611no—
166C42—1221no—
167C23—41no—
168C23#1451983511yescharacteristic
169Q8—41no—
170Q8—41no—
171D4—41no—
172D4—41no—
173D4—81no—
174D4—81no—
175D4—161no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—4881no—
190C2×C4—2441no—
191C2×C4#1451983911yescharacteristic
192C2×C4#1451984111yescharacteristic
193C8—9761no—
194C8—4881no—
195C8—4882no—
196C22—21no—
197C22—21no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22#1684061311yescharacteristic
202C22#1684066211yescharacteristic
203C22#1684067011yescharacteristic
204C4—21no—
205C4—21no—
206C4—81no—
207C4—81no—
208C4—1221no—
209C4—1221no—
210C4—1221no—
211C4—1221no—
212C4—4881no—
213C2—21no—
214C2—21no—
215C2—161no—
216C2#2146080111yescharacteristic
217C2#2146093811yescharacteristic
218C2#2146094411yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
Fitting, prime radicalC61×#537C4
socleC22×C61AΣL(1,𝔽16)
cosocle#16839631C22
hypercenter#537#6923
hypocenterC61#7417
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #537

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
#214470402
#741761