Finite Group Databasebeta

← #30605535

Subgroups — #30605535

Order 15616.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462188C212yesmaximal, complemented
2#21460824C212yesmaximal, complemented
3#21460821C212yesmaximal, complemented
4#21456219C211yesmaximal, characteristic
5#16840685—22no—
6#16840658—22no—
7#16840654C2214yes—
8C2×#14519769C411yescharacteristic
9#16840130C411yescharacteristic
10#16840130C2211yescharacteristic
11#16840126C411yescharacteristic
12#16840126C2211yescharacteristic
13#16840116—22no—
14#16839763—22no—
15C4×#11758194C2211yescharacteristic
16C61×#532C411yescharacteristic
17#14519851—24no—
18C2×#11758194D412yes—
19#14519769—21no—
20#14519769—41no—
21#14519769C2×C411yescharacteristic
22#14519769C2×C411yescharacteristic
23C2×C4⋊Dic61—21no—
24C2×#11758196—41no—
25#14519701—22no—
26#14519701—22no—
27#14519698—22no—
28#14519698—22no—
29#14519688C2×C411yescharacteristic
30#14519688C2311yescharacteristic
31C4×#92418D412yes—
32C2×#41×C61—21no—
33C4⋊Q8×C61C2×C411yescharacteristic
34#127×C61C2×C411yescharacteristic
35#124×C61—21no—
36#121×C61—41no—
37C4×D4×C61—41no—
38C2×C42×C61C2×C411yescharacteristic
39#41×C61—44no—
40C2×Q8×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61—41no—
43C2×D4×C61—41no—
44C22×C4×C61—21no—
45C22×C4×C61—41no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×Dic61—41no—
48C4⋊C4×C61—41no—
49C22⋊C4×C61—42no—
50C42×C61—21no—
51C42×C61C22⋊C411yescharacteristic
52C42×C61C22×C411yescharacteristic
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—41no—
56#11758196—42no—
57#11758196—41no—
58#11758196—41no—
59#11758194—42no—
60C2×#92418C22⋊C412yes—
61C2×#92418C2×D412yes—
62#11758187—44no—
63C23×C61—41no—
64C23×C61#10011yescharacteristic
65Q8×C61—42no—
66D4×C61—42no—
67D4×C61—82no—
68D4×C61—82no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—82no—
74C2×C4×C61—81no—
75C2×C4×C61#10011yescharacteristic
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—82no—
80#92418—22no—
81#92418—22no—
82#11917—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—41no—
85C22×C61—82no—
86C22×C61—81no—
87C22×C61C2×#10011yescharacteristic
88C4×C61—21no—
89C4×C61—41no—
90C4×C61—41no—
91C4×C61—81no—
92C4×C61#42112yes—
93Dic61—81no—
94Dic61—81no—
95#3142—611no—
96#2165—612no—
97#1356—612no—
98#1355—612no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61—161no—
102C2×C61#153311yescharacteristic
103#532#692311yescharacteristic
104C2×#125—611no—
105#491—611no—
106#491—611no—
107#490—611no—
108#490—611no—
109#488—1222no—
110#417—1222no—
111C4×M16—611no—
112#364—1222no—
113#349—1222no—
114#347—614no—
115C61#1191711yescharacteristic, complemented, Sylow
116C2×#41—21no—
117C2×M16—612no—
118C4⋊Q8C2×#692311yescharacteristic
119#127C2×#692311yescharacteristic
120#125—611no—
121#125—611no—
122#125—1221no—
123#125—2441no—
124#124—21no—
125#121—41no—
126C4×D4—41no—
127C2×C4⋊C4—1221no—
128C2×C4⋊C4—2441no—
129C2×C42C2×#692311yescharacteristic
130M32—1224no—
131#103—1222no—
132#103—1222no—
133#102—1222no—
134#102—1222no—
135#97—611no—
136#97—611no—
137C4×C8—612no—
138#41—44no—
139C2×Q8—21no—
140C2×D4—21no—
141C2×D4—41no—
142C2×D4—41no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—2441no—
146C22×C4C22⋊#692311yescharacteristic
147M16—2442no—
148C2×C8—612no—
149C2×C8—612no—
150C4⋊C4—41no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—2441no—
154C4⋊C4—2441no—
155C4⋊C4—2442no—
156C4⋊C4—2441no—
157C22⋊C4—42no—
158C42—21no—
159C42C22⋊#692311yescharacteristic
160C42C22×#692311yescharacteristic
161C16—2444no—
162C23—41no—
163C23#1451983711yescharacteristic
164Q8—42no—
165D4—42no—
166D4—82no—
167D4—82no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—4882no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4#1451983711yescharacteristic
178C2×C4C2×C22⋊#692311yescharacteristic
179C8—1222no—
180C8—1222no—
181C22—21no—
182C22—41no—
183C22—82no—
184C22—81no—
185C22C2×#1451983711yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—4881no—
191C4—4881no—
192C4#1684076012yes—
193C2—21no—
194C2—41no—
195C2—161no—
196C2#2146129811yescharacteristic
subgroupG/H
centerC2#21461298
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
Fitting, prime radicalC61×#532C4
socleC2×C61#1533
cosocle#14519688C23
hypercenter#532#6923
hypocenterC61#11917
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460824C2semidirect
3. #21460821C2semidirect
115. C61#11917semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214608242
#214608212
#214562192
#1191761