Finite Group Databasebeta

← #30594943

Subgroups — #30594943

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#21446941C211yesmaximal, characteristic
4#16840748—21no—
5#16840658—21no—
6C2×#14519810—21no—
7C22×Dic244C411yescharacteristic
8C2×#14519695—21no—
9#16839728C2211yescharacteristic
10C61×#341C411yescharacteristic
11D61⋊M16—41no—
12#14519851—41no—
13#14519838—41no—
14#14519837—22no—
15C2×#11758222D411yescharacteristic
16C22×Dic122—21no—
17#14519810—42no—
18#14519810—42no—
19C2×Dic244—41no—
20C2×Dic244—41no—
21C2×Dic244—42no—
22C2×#11758190—41no—
23C2×#11758194D411yescharacteristic
24#14519695—42no—
25#14519689—41no—
26C2×M16×C61—21no—
27C22×C8×C61C2×C411yescharacteristic
28C22×C4×C61C22⋊C411yescharacteristic
29C2×C22⋊D61—21no—
30C22×Dic61—41no—
31#11758222—41no—
32#11758222—41no—
33C2×D244SD1611yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122—22no—
36C2×Dic122—41no—
37C2×Dic122—41no—
38C2×Dic122—41no—
39C2×Dic122—41no—
40C2×Dic122—41no—
41C2×Dic122D811yescharacteristic
42#11758217—42no—
43#11758213—81no—
44D61⋊C8—81no—
45M16×C61—22no—
46M16×C61—41no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50#11758194—41no—
51C2×#92418—21no—
52Dic244—44no—
53Dic244—42no—
54Dic244—42no—
55#11758190—44no—
56#11758187—81no—
57C23×C61#10411yescharacteristic
58C22×D61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61#9911yescharacteristic
62C2×C4×C61#10211yescharacteristic
63C22⋊D61—81no—
64C2×Dic61—21no—
65C2×Dic61—42no—
66C2×Dic61—81no—
67C2×Dic61—81no—
68D244—41no—
69C4×D61—41no—
70C4×D61—41no—
71Dic122—41no—
72Dic122—42no—
73Dic122—42no—
74Dic122—81no—
75Dic122—81no—
76#92420—82no—
77C8×C61—42no—
78C8×C61—41no—
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×C61AΣL(1,𝔽16)11yescharacteristic
88C4×C61#35311yescharacteristic
89Dic61—41no—
90Dic61—82no—
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—611no—
100#413—1221no—
101C2×#101—1221no—
102#408—611no—
103#349—1221no—
104#341#692311yescharacteristic
105C61#740111yescharacteristic, complemented, Sylow
106C2×#41—611no—
107C22×Q8—1221no—
108#137—2442no—
109#137—2442no—
110C2×Q16—2441no—
111C2×Q16—2441no—
112C2×Q16—2442no—
113C2×SD16—2441no—
114C2×M16—21no—
115C2×M16—611no—
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—611no—
126C2×Q8—1222no—
127C2×Q8—2441no—
128C2×Q8—2441no—
129C2×Q8—2441no—
130C2×Q8—2441no—
131C2×Q8—2441no—
132C2×D4—611no—
133C2×D4—1221no—
134C22×C4—1221no—
135C22×C4—2441no—
136C22×C4C22⋊#692311yescharacteristic
137Q16—2442no—
138Q16—2442no—
139Q16—2444no—
140SD16—2444no—
141M16—22no—
142M16—41no—
143M16—4881no—
144M16—2442no—
145M16—2441no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8—1221no—
150C2×C8—4881no—
151C16—4881no—
152C23—1221no—
153C23#1451984211yescharacteristic
154Q8—4881no—
155Q8—4881no—
156Q8—2442no—
157Q8—2441no—
158Q8—2442no—
159D4—4881no—
160D4—2441no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—1221no—
164C2×C4—4881no—
165C2×C4—4881no—
166C2×C4—2442no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4#1451983611yescharacteristic
170C2×C4#1451983911yescharacteristic
171C8—42no—
172C8—41no—
173C8—4882no—
174C8—2441no—
175C22—21no—
176C22—41no—
177C22—4881no—
178C22—2441no—
179C22#1684061411yescharacteristic
180C4—21no—
181C4—4882no—
182C4—2441no—
183C4#1684066311yescharacteristic
184C4#1684066711yescharacteristic
185C2—21no—
186C2—41no—
187C2—4881no—
188C2#2146079811yescharacteristic
subgroupG/H
centerC2#21460798
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC2×C61#1343
prime radicalC2×#11758222D4
cosocle#16839728C22
hypercenter#341#6923
hypocenterC61#7401
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

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
#214469412
#740161