Finite Group Databasebeta

← #30604157

Subgroups — #30604157

Order 15616.

288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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#21462189C212yesmaximal, complemented
2#21460768C212yesmaximal, complemented
3#21460753C212yesmaximal
4#21454459C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8#41×Dic61C411yescharacteristic
9#16839820—22no—
10#16839812—22no—
11#16839790C411yescharacteristic
12#16839788C2211yescharacteristic
13#16839729C2211yescharacteristic
14M16×Dic61C2211yescharacteristic
15C2×C8×Dic61C411yescharacteristic
16C61×#408C411yescharacteristic
17#14519851—24no—
18C2×#11758194C2311yescharacteristic
19C22×#92418C2×C411yescharacteristic
20Q8×Dic61—21no—
21D4×Dic61—21no—
22D4×Dic61—22no—
23#14519736—21no—
24#14519736C2×C411yescharacteristic
25C2×C4×Dic61—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27#14519706—22no—
28#14519706—22no—
29C22⋊#92418—22no—
30#14519687D412yes—
31C8×Dic61—21no—
32C8×Dic61—21no—
33C8×Dic61D412yes—
34C2×#41×C61C2×C411yescharacteristic
35C2×M16×C61C2×C411yescharacteristic
36C22×C8×C61C2×C411yescharacteristic
37C22⋊C8×C61—22no—
38#41×C61—41no—
39#41×C61—41no—
40C2×Q8×C61M1611yescharacteristic
41C2×D4×C61—21no—
42C2×D4×C61M1611yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—22no—
46C22×Dic61—21no—
47M16×C61—41no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61C22⋊C412yes—
51C22⋊Dic61—22no—
52C22⋊Dic61M1612yes—
53C4⋊Dic61—22no—
54C4⋊Dic61—21no—
55C4×Dic61—22no—
56C4×Dic61—21no—
57C4×Dic61—21no—
58C4×Dic61C22⋊C411yescharacteristic
59C4×Dic61C22⋊C411yescharacteristic
60#11758194—41no—
61C2×#92418—21no—
62C2×#92418—41no—
63C2×#92418C2×D412yes—
64#11758187—44no—
65C23×C61—21no—
66C23×C61C2×M1611yescharacteristic
67Q8×C61—41no—
68D4×C61—41no—
69D4×C61—42no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C2×C4×C61C2×M1611yescharacteristic
77C2×Dic61—21no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80C2×Dic61—42no—
81C2×Dic61—44no—
82C8×C61—22no—
83C8×C61—41no—
84#92418—22no—
85#92418—41no—
86#11524—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61—42no—
90C22×C61—41no—
91C22×C61#40711yescharacteristic
92C4×C61—21no—
93C4×C61—41no—
94C4×C61#41011yescharacteristic
95C4×C61#41311yescharacteristic
96Dic61—22no—
97Dic61—42no—
98Dic61—41no—
99#2922—611no—
100#2165—612no—
101#1328—612no—
102#1321—612no—
103C2×C61—21no—
104C2×C61—41no—
105C2×C61—81no—
106C2×C61#146411yescharacteristic
107C4×#41—611no—
108#433—1222no—
109#431—1222no—
110#424—611no—
111#424—611no—
112#408—611no—
113#408#692311yescharacteristic
114C4×M16—611no—
115C2×C4×C8—611no—
116#364—1222no—
117#349—614no—
118#347—1222no—
119C61#1152411yescharacteristic, complemented, Sylow
120C2×#41C2×#692311yescharacteristic
121C2×M16—611no—
122C2×M16C2×#692311yescharacteristic
123C22×C8—611no—
124C22×C8C2×#692311yescharacteristic
125C4×Q8—1221no—
126C4×D4—1222no—
127C4×D4—1221no—
128#117—611no—
129#117—1221no—
130C2×C42—611no—
131C2×C42—1221no—
132M32—1224no—
133C4⋊C8—1222no—
134C4⋊C8—1222no—
135C22⋊C8—22no—
136C22⋊C8—1222no—
137#97—612no—
138C4×C8—612no—
139C4×C8—1221no—
140C4×C8—1221no—
141#41—41no—
142#41—41no—
143C2×Q8#1175821311yescharacteristic
144C2×D4—21no—
145C2×D4#1175821311yescharacteristic
146C22×C4—21no—
147C22×C4—1222no—
148C22×C4—1221no—
149C22×C4C22×#692311yescharacteristic
150M16—41no—
151M16—2441no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8—612no—
155C2×C8—1221no—
156C2×C8—2441no—
157C2×C8C22⋊#692312yes—
158C4⋊C4—1222no—
159C4⋊C4—1221no—
160C22⋊C4—612no—
161C22⋊C4—1222no—
162C42—611no—
163C42—611no—
164C42—1222no—
165C42—1221no—
166C42—1221no—
167C16—2444no—
168C23—21no—
169C23D61⋊M1611yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1222no—
181C2×C4—2442no—
182C2×C4—2444no—
183C2×C4C2×C22⋊#692311yescharacteristic
184C2×C4C2×#1175821311yescharacteristic
185C8—22no—
186C8—41no—
187C8—1222no—
188C8—2441no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#1684073311yescharacteristic
194C4—21no—
195C4—41no—
196C4—1222no—
197C4—2441no—
198C4—2442no—
199C4#1684074211yescharacteristic
200C4#1684074911yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2#2146107111yescharacteristic
subgroupG/H
centerC4#16840742
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1464
prime radicalC2×#41×C61C2×C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11524
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462189C2semidirect
2. #21460768C2semidirect
119. C61#11524semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214607682
#214607532
#214544592
#1152461