Finite Group Databasebeta

← #30594936

Subgroups — #30594936

Order 15616.

258 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460907C211yesmaximal, characteristic, complemented
2#21460754C211yesmaximal, characteristic, complemented
3#21446926C211yesmaximal, characteristic
4#16840741—21no—
5#16840658—21no—
6C2×#14519803—21no—
7C2×#14519694—21no—
8#16839728C2211yescharacteristic
9#16839527C411yescharacteristic, complemented
10C22×D8×C61C411yescharacteristic, complemented
11#14519856—41no—
12#14519851—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16#14519803—42no—
17#14519803—42no—
18C2×#11758200—41no—
19C2×#11758199—41no—
20C2×#11758194—21no—
21C2×#11758194D411yescharacteristic
22#14519694—42no—
23#14519689—41no—
24C22×D4×C61—21no—
25C2×D8×C61—41no—
26C2×D8×C61—42no—
27C22×C8×C61C2×C411yescharacteristic
28C24×C61—41no—
29C2×D4×C61—22no—
30C2×D4×C61—41no—
31C2×D4×C61—41no—
32C2×D4×C61—41no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C22×C4×C61C22⋊C411yescharacteristic
36C2×C22⋊D61—21no—
37#11758222—41no—
38#11758222—41no—
39C2×D244D811yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122SD1611yescharacteristic
42C22⋊#6923—42no—
43C4⋊#6923—81no—
44C4×#6923—81no—
45D8×C61—42no—
46D8×C61—42no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49#11758200—44no—
50#11758199—44no—
51#11758194—22no—
52#11758194—41no—
53#11758194—41no—
54C2×#92418—21no—
55C2×#92418—41no—
56#11758187—81no—
57C23×C61—42no—
58C23×C61—81no—
59C23×C61—81no—
60C23×C61—162no—
61C23×C61#10411yescharacteristic
62C22×D61—21no—
63C2×#6923—82no—
64D4×C61—42no—
65D4×C61—42no—
66D4×C61—81no—
67D4×C61—81no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61#9911yescharacteristic
71C2×C4×C61#10211yescharacteristic
72C22⋊D61—81no—
73C2×Dic61—21no—
74D244—41no—
75C4×D61—41no—
76C4×D61—41no—
77Dic122—41no—
78C8×C61—41no—
79#92418—42no—
80#92418—41no—
81#7398—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—82no—
85C22×C61—162no—
86C22×C61—162no—
87C22×C61—162no—
88C22×C61#32711yescharacteristic
89C2×D61—41no—
90C2×D61—81no—
91#6923—162no—
92C4×C61—21no—
93C4×C61AΣL(1,𝔽16)11yescharacteristic
94C4×C61#35311yescharacteristic
95Dic61—41no—
96#2018—611no—
97#1391—611no—
98#1321—611no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61—162no—
102C2×C61#134311yescharacteristic
103D61—81no—
104C2×AGL(1,ℤ/8)—1221no—
105C22×D8#692311yescharacteristic, complemented
106C2×#100—1221no—
107#410—1221no—
108#408—611no—
109#349—1221no—
110#341—611no—
111C61#739811yescharacteristic, complemented, Sylow
112C2×#41—611no—
113C22×D4—21no—
114AGL(1,ℤ/8)—2442no—
115AGL(1,ℤ/8)—2442no—
116C2×SD16—2441no—
117C2×D8—41no—
118C2×D8—42no—
119C2×D8—2441no—
120C2×M16—611no—
121C2×M16—1221no—
122C22×C8C2×#692311yescharacteristic
123#117—2441no—
124M32—2441no—
125#100—2442no—
126#99—1222no—
127#99—2441no—
128C22⋊C8—2441no—
129C24—41no—
130#41—2441no—
131#41—2441no—
132C2×Q8—611no—
133C2×D4—22no—
134C2×D4—41no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4—611no—
140C2×D4—1221no—
141C22×C4—1221no—
142C22×C4C22⋊#692311yescharacteristic
143SD16—2444no—
144D8—42no—
145D8—42no—
146D8—2444no—
147M16—1222no—
148M16—2441no—
149M16—2441no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—1221no—
153C2×C8—2441no—
154C4⋊C4—4881no—
155C22⋊C4—2442no—
156C42—4881no—
157C16—4881no—
158C23—42no—
159C23—81no—
160C23—81no—
161C23—162no—
162C23—1221no—
163C23#1451984111yescharacteristic
164Q8—2441no—
165D4—42no—
166D4—42no—
167D4—81no—
168D4—81no—
169D4—4881no—
170D4—2441no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—1221no—
174C2×C4—4882no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4#1451983511yescharacteristic
178C2×C4#1451983911yescharacteristic
179C8—41no—
180C8—2442no—
181C8—2441no—
182C22—21no—
183C22—41no—
184C22—82no—
185C22—162no—
186C22—162no—
187C22—162no—
188C22—4881no—
189C22—2441no—
190C22#1684061311yescharacteristic
191C4—21no—
192C4—9762no—
193C4—2441no—
194C4#1684066211yescharacteristic
195C4#1684066611yescharacteristic
196C2—21no—
197C2—41no—
198C2—162no—
199C2—4881no—
200C2#2146079711yescharacteristic
subgroupG/H
centerC2#21460797
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC22×D8×C61C4
socleC2×C61#1343
prime radical#21446926C2
cosocle#16839728C22
hypercenterC22×D8#6923
hypocenterC61#7398
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. #21460907C2semidirect
2. #21460754C2semidirect
9. #16839527C4semidirect
10. C22×D8×C61C4semidirect
105. C22×D8#6923semidirect
111. C61#7398semidirect

Maximal subgroups

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

subgroupindex
#214609072
#214607542
#214469262
#739861