Finite Group Databasebeta

← #29600882

Subgroups — #29600882

Order 15616.

180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#16839602C211yesmaximal, characteristic, complemented
2#21448114C211yesmaximal, characteristic
3#21447945C211yesmaximal, characteristic
4#21447941C211yesmaximal, characteristic
5#21444022C211yesmaximal, characteristic, complemented
6#21444013C211yesmaximal, characteristic, complemented
7C61×#1420C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9#16840178C2211yescharacteristic
10#16840038—21no—
11#16840034—21no—
12#16839602—21no—
13#16839602—21no—
14#16839595—21no—
15C2×#14519683C2211yescharacteristic
16C32×D61—21no—
17#16839592C2211yescharacteristic
18#16839578—21no—
19#16839577—21no—
20C2×Q32×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519810—41no—
24#14519808—41no—
25C2×Dic244—21no—
26#14519783D411yescharacteristic
27Dic488—21no—
28Dic488—21no—
29#14519717D411yescharacteristic
30#14519716—21no—
31C16×D61—21no—
32#14519713—21no—
33#14519696—41no—
34#14519695—41no—
35#14519683D411yescharacteristic
36#14519683D411yescharacteristic
37C2×Q16×C61—21no—
38Q32×C61—21no—
39Q32×C61—21no—
40C2×C16×C61C2311yescharacteristic
41#108×C61—21no—
42C32×C61—21no—
43C2×Q8×C61—41no—
44#11758222D811yescharacteristic
45C2×Dic122—41no—
46Q16×C61—41no—
47Q16×C61—41no—
48M16×C61—41no—
49C2×C8×C61C2×D411yescharacteristic
50#11758202—81no—
51#11758201—81no—
52#11758194—41no—
53#11758194D811yescharacteristic
54Dic244—41no—
55Dic244—41no—
56Dic244—81no—
57#11758190—81no—
58#11758189—21no—
59C8×D61—21no—
60C16×C61C2×D411yescharacteristic
61C16×C61#4111yescharacteristic
62#11758185—21no—
63Q8×C61—81no—
64Q8×C61—81no—
65C2×C4×C61—81no—
66C2×C4×C61C2×D811yescharacteristic
67C22⋊D61—21no—
68C2×Dic61—81no—
69D244D1611yescharacteristic
70C4×D61—21no—
71Dic122—81no—
72Dic122—81no—
73Dic122D1611yescharacteristic
74C8×C61—81no—
75C8×C61#12111yescharacteristic
76C8×C61#13511yescharacteristic
77#92418—21no—
78#92418—81no—
79#13701—611nomaximal, Sylow
80C22×C61#50811yescharacteristic
81C2×D61—21no—
82C4×C61—161no—
83C4×C61#46611yescharacteristic
84C4×C61C2×D1611yescharacteristic
85Dic61—21no—
86Dic61—161no—
87C2×Q64—611no—
88#2258—611no—
89#2222—611no—
90#2222—611no—
91#1425—611no—
92#1420—611no—
93#1420D6111yescharacteristic, complemented
94C2×C61—21no—
95C2×C61#221511yescharacteristic
96D61—41no—
97C2×Q32—611no—
98C2×Q32C2×D6111yescharacteristic
99#504—611no—
100#473—1221no—
101#473—1221no—
102Q64—1221no—
103Q64—1221no—
104M64—1221no—
105M64C2×D6111yescharacteristic
106C2×C32—611no—
107C2×C32—1221no—
108#368—611no—
109#368C2×D6111yescharacteristic
110#362—1221no—
111#362—1221no—
112C61#1370111yescharacteristic, complemented, Sylow
113#137—2441no—
114#137—2441no—
115C2×Q16—21no—
116C2×Q16—1221no—
117#131—611no—
118Q32—21no—
119Q32—21no—
120Q32—1221no—
121Q32—1221no—
122M32—611no—
123M32—1221no—
124C2×C16—1221no—
125C2×C16C22×D6111yescharacteristic
126#108—21no—
127#108—1221no—
128#101—2441no—
129#101—2441no—
130C32—21no—
131C32—611no—
132C32—611no—
133#41—611no—
134C2×Q8—41no—
135C2×Q8—2441no—
136Q16—41no—
137Q16—41no—
138Q16—4881no—
139Q16—4881no—
140Q16—2441no—
141Q16—2441no—
142SD16—4881no—
143SD16—4881no—
144M16—41no—
145M16—611no—
146M16—1221no—
147M16—2441no—
148C2×C8—1221no—
149C2×C8D4×D6111yescharacteristic
150C16—1221no—
151C16#1175822211yescharacteristic
152C16D4×D6111yescharacteristic
153Q8—81no—
154Q8—81no—
155Q8—611no—
156Q8—4881no—
157Q8—4881no—
158D4—611no—
159D4—1221no—
160C2×C4—81no—
161C2×C4—1221no—
162C2×C4—4881no—
163C2×C4D8×D6111yescharacteristic
164C8—81no—
165C8—1221no—
166C8—4881no—
167C8#1451975011yescharacteristic
168C8#1451979811yescharacteristic
169C22—1221no—
170C22#1684019311yescharacteristic
171C4—161no—
172C4—1221no—
173C4—9761no—
174C4#1683999711yescharacteristic
175C4D16×D6111yescharacteristic
176C2—21no—
177C2—2441no—
178C2#2144790411yescharacteristic
subgroupG/H
centerC2#21447904
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1420C2
socleC2×C61#2215
prime radical#11758222D8
hypercenter#1420D61
hypocenterC61#13701
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. C2×#16839602C2semidirect
5. #21444022C2semidirect
6. #21444013C2semidirect
7. C61×#1420C2semidirect
93. #1420D61semidirect
112. C61#13701semidirect

Maximal subgroups

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

subgroupindex
C2×#168396022
#214481142
#214479452
#214479412
#214440222
#214440132
C61×#14202
#1370161