Finite Group Databasebeta

← #30594939

Subgroups — #30594939

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#21446941C211yesmaximal, characteristic
4#16840741—21no—
5#16840658—21no—
6C2×#14519810—21no—
7C22×Dic244C411yescharacteristic, complemented
8C2×#14519695—21no—
9#16839728C2211yescharacteristic
10C61×#341C411yescharacteristic, complemented
11#14519856—41no—
12#14519851—41no—
13#14519836—41no—
14#14519835—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×D244D811yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122—22no—
36C2×Dic122—41no—
37C2×Dic122—41no—
38C2×Dic122—41no—
39C2×Dic122—41no—
40C2×Dic122—41no—
41C2×Dic122SD1611yescharacteristic
42C22⋊#6923—42no—
43C4⋊#6923—81no—
44C4×#6923—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×#6923—82no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61#9911yescharacteristic
63C2×C4×C61#10211yescharacteristic
64C22⋊D61—81no—
65C2×Dic61—21no—
66C2×Dic61—42no—
67C2×Dic61—81no—
68C2×Dic61—81no—
69D244—41no—
70C4×D61—41no—
71C4×D61—41no—
72Dic122—41no—
73Dic122—42no—
74Dic122—42no—
75Dic122—81no—
76Dic122—81no—
77C8×C61—42no—
78C8×C61—41no—
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×C61AΣL(1,𝔽16)11yescharacteristic
89C4×C61#35311yescharacteristic
90Dic61—41no—
91Dic61—82no—
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—611no—
101C2×#101—1221no—
102#410—1221no—
103#408—611no—
104#349—1221no—
105#341#692311yescharacteristic, complemented
106C61#739911yescharacteristic, complemented, Sylow
107C2×#41—611no—
108C22×Q8—1221no—
109#137—2442no—
110#137—2442no—
111C2×Q16—2441no—
112C2×Q16—2441no—
113C2×Q16—2442no—
114C2×SD16—2441no—
115C2×M16—21no—
116C2×M16—611no—
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—611no—
127C2×Q8—1222no—
128C2×Q8—2441no—
129C2×Q8—2441no—
130C2×Q8—2441no—
131C2×Q8—2441no—
132C2×Q8—2441no—
133C2×D4—611no—
134C2×D4—1221no—
135C22×C4—1221no—
136C22×C4—2441no—
137C22×C4C22⋊#692311yescharacteristic
138Q16—2442no—
139Q16—2442no—
140Q16—2444no—
141SD16—2444no—
142M16—22no—
143M16—41no—
144M16—2441no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—41no—
148C2×C8—1221no—
149C4⋊C4—4881no—
150C22⋊C4—2442no—
151C42—4881no—
152C16—4881no—
153C23—1221no—
154C23#1451984211yescharacteristic
155Q8—4881no—
156Q8—4881no—
157Q8—2442no—
158Q8—2441no—
159Q8—2442no—
160D4—4881no—
161D4—2441no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—1221no—
165C2×C4—4882no—
166C2×C4—4881no—
167C2×C4—4881no—
168C2×C4—2442no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4#1451983611yescharacteristic
172C2×C4#1451983911yescharacteristic
173C8—42no—
174C8—41no—
175C8—2441no—
176C22—21no—
177C22—41no—
178C22—4881no—
179C22—2441no—
180C22#1684061411yescharacteristic
181C4—21no—
182C4—9762no—
183C4—4882no—
184C4—2441no—
185C4#1684066311yescharacteristic
186C4#1684066711yescharacteristic
187C2—21no—
188C2—41no—
189C2—4881no—
190C2#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#7399
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
7. C22×Dic244C4semidirect
10. C61×#341C4semidirect
105. #341#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
#214469412
#739961