Finite Group Databasebeta

← #30594938

Subgroups — #30594938

Order 15616.

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

normal subgroups only

This group has 238 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
2#21460754C211yesmaximal, characteristic
3#21446938C211yesmaximal, characteristic
4#16840741—21no—
5#16840658—21no—
6C2×#14519808—21no—
7C2×#14519696—21no—
8#16839728C2211yescharacteristic
9#16839527C411yescharacteristic, complemented
10C22×Q16×C61C411yescharacteristic, complemented
11#14519856—41no—
12#14519851—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16#14519808—42no—
17#14519808—42no—
18C2×#11758202—41no—
19C2×#11758201—41no—
20C2×#11758194—21no—
21C2×#11758194D411yescharacteristic
22#14519696—42no—
23#14519689—41no—
24C22×Q8×C61—21no—
25C2×Q16×C61—41no—
26C2×Q16×C61—42no—
27C22×C8×C61C2×C411yescharacteristic
28C2×Q8×C61—22no—
29C2×Q8×C61—41no—
30C2×Q8×C61—41no—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61—41no—
34C22×C4×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—
45Q16×C61—42no—
46Q16×C61—42no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49#11758202—44no—
50#11758201—44no—
51#11758194—22no—
52#11758194—41no—
53#11758194—41no—
54C2×#92418—21no—
55C2×#92418—41no—
56#11758187—81no—
57C23×C61#10411yescharacteristic
58C22×D61—21no—
59C2×#6923—82no—
60Q8×C61—42no—
61Q8×C61—42no—
62Q8×C61—81no—
63Q8×C61—81no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—42no—
67C2×C4×C61—81no—
68C2×C4×C61—81no—
69C2×C4×C61#9911yescharacteristic
70C2×C4×C61#10211yescharacteristic
71C22⋊D61—81no—
72C2×Dic61—21no—
73D244—41no—
74C4×D61—41no—
75C4×D61—41no—
76Dic122—41no—
77C8×C61—41no—
78#92418—42no—
79#92418—41no—
80#7399—611nomaximal, Sylow
81C22×C61—21no—
82C22×C61—41no—
83C22×C61#32711yescharacteristic
84C2×D61—41no—
85C2×D61—81no—
86#6923—162no—
87C4×C61—21no—
88C4×C61—82no—
89C4×C61AΣL(1,𝔽16)11yescharacteristic
90C4×C61#35311yescharacteristic
91Dic61—41no—
92#2020—611no—
93#1391—611no—
94#1321—611no—
95C2×C61—21no—
96C2×C61—41no—
97C2×C61#134311yescharacteristic
98D61—81no—
99C2×#137—1221no—
100C22×Q16#692311yescharacteristic, complemented
101C2×#101—1221no—
102#410—1221no—
103#408—611no—
104#349—1221no—
105#341—611no—
106C61#739911yescharacteristic, complemented, Sylow
107C2×#41—611no—
108C22×Q8—21no—
109#137—2442no—
110#137—2442no—
111C2×Q16—41no—
112C2×Q16—42no—
113C2×Q16—2441no—
114C2×SD16—2441no—
115C2×M16—611no—
116C2×M16—1221no—
117C22×C8C2×#692311yescharacteristic
118#117—2441no—
119M32—2441no—
120#101—2442no—
121#99—1222no—
122#99—2441no—
123C22⋊C8—2441no—
124#41—2441no—
125#41—2441no—
126C2×Q8—22no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—611no—
133C2×D4—611no—
134C2×D4—1221no—
135C22×C4—41no—
136C22×C4—1221no—
137C22×C4C22⋊#692311yescharacteristic
138Q16—42no—
139Q16—42no—
140Q16—2444no—
141SD16—2444no—
142M16—1222no—
143M16—2441no—
144M16—2441no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—1221no—
148C2×C8—2441no—
149C4⋊C4—4881no—
150C22⋊C4—2442no—
151C42—4881no—
152C16—4881no—
153C23—1221no—
154C23#1451984111yescharacteristic
155Q8—42no—
156Q8—42no—
157Q8—81no—
158Q8—81no—
159Q8—2441no—
160D4—4881no—
161D4—2441no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—1221no—
168C2×C4—4882no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4#1451983511yescharacteristic
172C2×C4#1451983911yescharacteristic
173C8—41no—
174C8—2442no—
175C8—2441no—
176C22—21no—
177C22—41no—
178C22—4881no—
179C22—2441no—
180C22#1684061311yescharacteristic
181C4—21no—
182C4—82no—
183C4—9762no—
184C4—2441no—
185C4#1684066211yescharacteristic
186C4#1684066611yescharacteristic
187C2—21no—
188C2—41no—
189C2—4881no—
190C2#2146079711yescharacteristic
subgroupG/H
centerC2#21460797
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC22×Q16×C61C4
socleC2×C61#1343
prime radicalC2×#11758222D4
cosocle#16839728C22
hypercenterC22×Q16#6923
hypocenterC61#7399
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
9. #16839527C4semidirect
10. C22×Q16×C61C4semidirect
100. C22×Q16#6923semidirect
106. C61#7399semidirect

Maximal subgroups

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

subgroupindex
#214609072
#214607542
#214469382
#739961