Finite Group Databasebeta

← #30604218

Subgroups — #30604218

Order 15616.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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#21462193C212yesmaximal
2#21460767C212yesmaximal
3#21460766C212yesmaximal
4#21454751C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8#16840315C411yescharacteristic
9#16839890—22no—
10C8×Dic122—22no—
11#16839790C411yescharacteristic
12#16839789C2211yescharacteristic
13#16839785C2211yescharacteristic
14#16839717C2211yescharacteristic
15C2×C8×Dic61C411yescharacteristic
16C61×#405C411yescharacteristic
17#14519851—24no—
18C2×#11758194C2311yescharacteristic
19C22×#92418C2×C411yescharacteristic
20#14519776—21no—
21#14519768—21no—
22#14519754—22no—
23C4×Dic122—22no—
24#14519736C2×C411yescharacteristic
25C2×C4×Dic61C2×C411yescharacteristic
26C4⋊#92418—22no—
27#14519706—22no—
28#14519706—22no—
29#14519687D412yes—
30C8×Dic61—21no—
31C8×Dic61—21no—
32C8×Dic61D412yes—
33C2×M16×C61C2×C411yescharacteristic
34C22×C8×C61C2×C411yescharacteristic
35#117×C61C2×C411yescharacteristic
36#97×C61—21no—
37C4×C8×C61—21no—
38C22×C4×C61C22×C411yescharacteristic
39C22×Dic61—21no—
40C2×Dic122—22no—
41M16×C61—41no—
42C2×C8×C61—22no—
43C2×C8×C61—21no—
44C2×C8×C61C22⋊C411yescharacteristic
45C2×C8×C61C22⋊C411yescharacteristic
46C4⋊C4×C61—21no—
47C22⋊C4×C61M1612yes—
48C42×C61—21no—
49C22⋊Dic61—21no—
50C4⋊Dic61—22no—
51C4⋊Dic61—21no—
52#11758196—22no—
53#11758196—22no—
54C4×Dic61—21no—
55C4×Dic61C22⋊C412yes—
56C4×Dic61M1611yescharacteristic
57C4×Dic61M1611yescharacteristic
58#11758194—41no—
59C2×#92418—21no—
60C2×#92418—41no—
61C2×#92418C2×D412yes—
62#11758187—44no—
63C23×C61C2×M1611yescharacteristic
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61C2×C22⋊C411yescharacteristic
68C2×C4×C61C2×M1611yescharacteristic
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—22no—
72C2×Dic61—42no—
73Dic122—44no—
74C8×C61—21no—
75C8×C61—41no—
76C8×C61#10112yes—
77#92418—22no—
78#92418—41no—
79#11539—611nomaximal, Sylow
80C22×C61—21no—
81C22×C61—41no—
82C22×C61#40711yescharacteristic
83C4×C61—21no—
84C4×C61—42no—
85C4×C61#41011yescharacteristic
86C4×C61C2×#10111yescharacteristic
87Dic61—22no—
88Dic61—42no—
89Dic61—41no—
90#2960—611no—
91#2166—612no—
92#1328—612no—
93#1327—612no—
94C2×C61—21no—
95C2×C61—41no—
96C2×C61#146711yescharacteristic
97#533—611no—
98#446—1222no—
99C8×Q8—1222no—
100#424—611no—
101#424—611no—
102#423—611no—
103#405—611no—
104#405#692311yescharacteristic
105C2×C4×C8—611no—
106#364—1222no—
107#349—614no—
108#347—1222no—
109C61#1153911yescharacteristic, complemented, Sylow
110C2×M16—611no—
111C2×M16C2×#692311yescharacteristic
112C22×C8—611no—
113C22×C8C2×#692311yescharacteristic
114C4⋊Q8—1221no—
115#125—1221no—
116C22⋊Q8—1222no—
117C4×Q8—1222no—
118#117—611no—
119#117C2×#692311yescharacteristic
120C2×C42—611no—
121M32—1224no—
122C4⋊C8—1222no—
123C4⋊C8—1222no—
124C4⋊C8—1222no—
125#97—21no—
126#97—612no—
127C4×C8—21no—
128C4×C8—612no—
129C4×C8—1221no—
130C4×C8—1221no—
131C2×Q8—1222no—
132C22×C4—1221no—
133C22×C4C22×#692311yescharacteristic
134M16—41no—
135M16—2441no—
136C2×C8—22no—
137C2×C8—21no—
138C2×C8—612no—
139C2×C8—1221no—
140C2×C8—2441no—
141C2×C8C22⋊#692311yescharacteristic
142C2×C8C22⋊#692311yescharacteristic
143C4⋊C4—21no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1221no—
148C22⋊C4—1221no—
149C22⋊C4#1175821312yes—
150C42—21no—
151C42—612no—
152C42—611no—
153C42—611no—
154C42—1221no—
155C16—2444no—
156C23C2×#1175821311yescharacteristic
157Q8—2444no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—1222no—
164C2×C4—2442no—
165C2×C4C2×C22⋊#692311yescharacteristic
166C2×C4D61⋊M1611yescharacteristic
167C8—21no—
168C8—41no—
169C8—1222no—
170C8—2441no—
171C8#1451983812yes—
172C22—21no—
173C22—41no—
174C22#1684073311yescharacteristic
175C4—21no—
176C4—42no—
177C4—1222no—
178C4—2441no—
179C4—2442no—
180C4#1684074111yescharacteristic
181C4C2×#1451983811yescharacteristic
182C2—21no—
183C2—41no—
184C2#2146108111yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC2×C61#1467
prime radicalC23×C61C2×M16
cosocleC2×#11758194C23
hypercenter#405#6923
hypocenterC61#11539
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
109. C61#11539semidirect

Maximal subgroups

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

subgroupindex
#214621932
#214607672
#214607662
#214547512
#1153961