Finite Group Databasebeta

← #30604155

Subgroups — #30604155

Order 15616.

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

normal subgroups only

This group has 280 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#21460767C212yesmaximal, complemented
3#21460754C212yesmaximal
4#21454469C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8#16840230C411yescharacteristic
9#16839822—22no—
10#16839818—22no—
11#16839789C2211yescharacteristic
12#16839730C411yescharacteristic
13#16839728C2211yescharacteristic
14M16×Dic61C2211yescharacteristic
15C2×#14519687C411yescharacteristic
16C61×#424C411yescharacteristic
17#14519851—24no—
18C2×#11758222C2×C411yescharacteristic
19C2×#11758194C2311yescharacteristic
20C22×#92418C2×C411yescharacteristic
21#14519742—21no—
22#14519739—21no—
23#14519737—22no—
24#14519734—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C42×D61—21no—
27C4⋊#92418—22no—
28#14519689—22no—
29#14519689—22no—
30#14519687—21no—
31#14519687—21no—
32#14519687D412yes—
33C8×Dic61D412yes—
34C2×M16×C61C2×C411yescharacteristic
35C22×C8×C61C2×C411yescharacteristic
36#117×C61C2×C411yescharacteristic
37C4⋊C8×C61—22no—
38C22×C4×C61C22×C411yescharacteristic
39C2×C22⋊D61—21no—
40C22×Dic61—21no—
41#11758222—41no—
42#11758222—41no—
43C2×D244M1611yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122M1611yescharacteristic
47M16×C61—41no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61C22⋊C412yes—
51C4⋊C4×C61—21no—
52C22⋊C4×C61M1612yes—
53C42×C61—21no—
54#11758198—22no—
55#11758196—22no—
56C4×Dic61—22no—
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×C61C2×M1611yescharacteristic
66C22×D61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61C2×C22⋊C411yescharacteristic
71C2×C4×C61C2×M1611yescharacteristic
72C22⋊D61—42no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—81no—
77D244—41no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—82no—
81Dic122—41no—
82C8×C61—22no—
83C8×C61—41no—
84#92418—22no—
85#92418—41no—
86#11523—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61#40711yescharacteristic
90C2×D61—42no—
91C2×D61—41no—
92C4×C61—21no—
93C4×C61—42no—
94C4×C61#41011yescharacteristic
95C4×C61#41311yescharacteristic
96Dic61—41no—
97Dic61—41no—
98Dic61—41no—
99#2923—611no—
100#2165—612no—
101#1328—612no—
102#1321—612no—
103C2×C61—21no—
104C2×C61—41no—
105C2×C61#146411yescharacteristic
106D61—81no—
107C4×#41—611no—
108#433—1222no—
109#432—1222no—
110#424—611no—
111#424#692311yescharacteristic
112#408—611no—
113#408—611no—
114C4×M16—611no—
115C2×#97—611no—
116#364—1222no—
117#349—614no—
118#347—1222no—
119C61#1152311yescharacteristic, complemented, Sylow
120C2×#41—611no—
121C2×M16—611no—
122C2×M16C2×#692311yescharacteristic
123C22×C8—611no—
124C22×C8C2×#692311yescharacteristic
125C4×Q8—1221no—
126C4×D4—1221no—
127C4×D4—1222no—
128#117—1221no—
129#117C2×#692311yescharacteristic
130C2×C42—611no—
131C2×C42—1221no—
132M32—1224no—
133C4⋊C8—22no—
134C4⋊C8—1222no—
135C22⋊C8—1222no—
136C22⋊C8—1222no—
137#97—612no—
138#97—1221no—
139#97—1221no—
140C4×C8—612no—
141#41—2441no—
142#41—2441no—
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—1222no—
147C22×C4—1221no—
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—21no—
159C4⋊C4—1222no—
160C22⋊C4—1222no—
161C22⋊C4#1175821312yes—
162C42—21no—
163C42—611no—
164C42—611no—
165C42—1222no—
166C42—1221no—
167C16—2444no—
168C23—1221no—
169C23C2×#1175821311yescharacteristic
170Q8—2441no—
171D4—2441no—
172D4—2442no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—4882no—
180C2×C4—4881no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C22⋊#692311yescharacteristic
184C2×C4D61⋊M1611yescharacteristic
185C8—22no—
186C8—41no—
187C8—1222no—
188C8—2441no—
189C22—21no—
190C22—41no—
191C22—2442no—
192C22—2441no—
193C22#1684073311yescharacteristic
194C4—21no—
195C4—42no—
196C4—2441no—
197C4—2441no—
198C4—2441no—
199C4#1684074311yescharacteristic
200C4#1684074911yescharacteristic
201C2—21no—
202C2—41no—
203C2—4881no—
204C2#2146107311yescharacteristic
subgroupG/H
centerC4#16840743
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC2×C61#1464
prime radicalC2×#11758222C2×C4
cosocleC2×#11758194C23
hypercenter#424#6923
hypocenterC61#11523
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #21462189C2semidirect
2. #21460767C2semidirect
119. C61#11523semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214607672
#214607542
#214544692
#1152361