Finite Group Databasebeta

← #30594942

Subgroups — #30594942

Order 15616.

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

normal subgroups only

This group has 234 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#21460910C211yesmaximal, characteristic
2#21460754C211yesmaximal, characteristic
3#21446938C211yesmaximal, characteristic
4#16840748—21no—
5#16840658—21no—
6C2×#14519808—21no—
7C2×#14519696—21no—
8#16839728C2211yescharacteristic
9#16839527C411yescharacteristic
10C22×Q16×C61C411yescharacteristic
11D61⋊M16—41no—
12#14519851—41no—
13#14519838—41no—
14#14519837—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×D244SD1611yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122D811yescharacteristic
42#11758217—42no—
43#11758213—81no—
44D61⋊C8—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—
59Q8×C61—42no—
60Q8×C61—42no—
61Q8×C61—81no—
62Q8×C61—81no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—42no—
66C2×C4×C61—81no—
67C2×C4×C61—81no—
68C2×C4×C61#9911yescharacteristic
69C2×C4×C61#10211yescharacteristic
70C22⋊D61—81no—
71C2×Dic61—21no—
72D244—41no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—41no—
76#92420—82no—
77C8×C61—41no—
78#92418—42no—
79#92418—41no—
80#7401—611nomaximal, Sylow
81C22×C61—21no—
82C22×C61—41no—
83C22×C61#32711yescharacteristic
84C2×D61—41no—
85C2×D61—81no—
86C4×C61—21no—
87C4×C61—82no—
88C4×C61AΣL(1,𝔽16)11yescharacteristic
89C4×C61#35311yescharacteristic
90Dic61—41no—
91#2020—611no—
92#1392—611no—
93#1321—611no—
94C2×C61—21no—
95C2×C61—41no—
96C2×C61#134311yescharacteristic
97D61—81no—
98C2×#137—1221no—
99C22×Q16#692311yescharacteristic
100#413—1221no—
101C2×#101—1221no—
102#408—611no—
103#349—1221no—
104#341—611no—
105C61#740111yescharacteristic, complemented, Sylow
106C2×#41—611no—
107C22×Q8—21no—
108#137—2442no—
109#137—2442no—
110C2×Q16—41no—
111C2×Q16—42no—
112C2×Q16—2441no—
113C2×SD16—2441no—
114C2×M16—611no—
115C2×M16—1221no—
116C2×M16—2441no—
117C22×C8C2×#692311yescharacteristic
118M32—2441no—
119#101—2442no—
120#101—2441no—
121#100—1222no—
122C22⋊C8—2441no—
123#41—2441no—
124#41—2441no—
125C2×Q8—22no—
126C2×Q8—41no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8—41no—
131C2×Q8—611no—
132C2×D4—611no—
133C2×D4—1221no—
134C22×C4—41no—
135C22×C4—1221no—
136C22×C4C22⋊#692311yescharacteristic
137Q16—42no—
138Q16—42no—
139Q16—2444no—
140SD16—2444no—
141M16—1222no—
142M16—4881no—
143M16—2442no—
144M16—2441no—
145M16—2441no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8—1221no—
149C2×C8—4881no—
150C2×C8—2441no—
151C16—4881no—
152C23—1221no—
153C23#1451984111yescharacteristic
154Q8—42no—
155Q8—42no—
156Q8—81no—
157Q8—81no—
158Q8—2441no—
159D4—4881no—
160D4—2441no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—1221no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4#1451983511yescharacteristic
170C2×C4#1451983911yescharacteristic
171C8—41no—
172C8—4882no—
173C8—2442no—
174C8—2441no—
175C22—21no—
176C22—41no—
177C22—4881no—
178C22—2441no—
179C22#1684061311yescharacteristic
180C4—21no—
181C4—82no—
182C4—2441no—
183C4#1684066211yescharacteristic
184C4#1684066611yescharacteristic
185C2—21no—
186C2—41no—
187C2—4881no—
188C2#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#7401
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
105. C61#7401semidirect

Maximal subgroups

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

subgroupindex
#214609102
#214607542
#214469382
#740161