Finite Group Databasebeta

← #16845025

Subgroups — #16845025

Order 3968.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521793C211yesmaximal, characteristic
2#14521455C211yesmaximal, characteristic, complemented
3#14521411C211yesmaximal, characteristic, complemented
4#14520790C211yesmaximal, characteristic, complemented
5#14520789C211yesmaximal, characteristic, complemented
6#14520788C211yesmaximal, characteristic, complemented
7C31×#497C211yesmaximal, characteristic, complemented
8C2×Q16×C31—21no—
9C2×SD16×C31—21no—
10C31×C4⋊Q8C2211yescharacteristic
11C31×#124C2211yescharacteristic
12#11758523—21no—
13#11758516—21no—
14#11758463—21no—
15#11758461—21no—
16#11758460—21no—
17#11758455—21no—
18#11758452C2211yescharacteristic
19#11758447C2211yescharacteristic
20C31×#97C2211yescharacteristic
21#11758398—21no—
22#11758397—21no—
23#11758396—21no—
24#11758395—21no—
25#11758391C2211yescharacteristic
26#11758391C2211yescharacteristic
27C2×Q8×C31—21no—
28C2×Q8×C31D411yescharacteristic
29C2×D4×C31D411yescharacteristic
30C2×C22⋊D31—21no—
31C2×C22⋊D31—21no—
32C22×Dic31—21no—
33C2×D124D411yescharacteristic
34C2×C4×D31—21no—
35C2×Dic62D411yescharacteristic
36Q16×C31—42no—
37SD16×C31—42no—
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—21no—
41C22⋊C4×C31—21no—
42C22⋊C4×C31—21no—
43C42×C31C2311yescharacteristic
44C22⋊Dic31—21no—
45(C2×D31)⋊C4—21no—
46(C2×D31)⋊C4—21no—
47(C2×D31)⋊C4—21no—
48C4⋊Dic31—21no—
49C4⋊Dic31D411yescharacteristic
50C4⋊Dic31D411yescharacteristic
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53Dic31⋊C4—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8—21no—
56C23×C31—21no—
57C22×D31—21no—
58Q8×C31—41no—
59Q8×C31—41no—
60Q8×C31—41no—
61D4×C31—41no—
62C2×C4×C31—21no—
63C2×C4×C31—41no—
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C22⋊D31—81no—
68C22⋊D31—81no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—21no—
72C2×Dic31—81no—
73D124—41no—
74C4×D31—81no—
75Dic62—41no—
76C8×C31—22no—
77C31⋊C8—22no—
78C31⋊C8—41no—
79#1661—311nomaximal, Sylow
80C22×C31—41no—
81C22×C31—41no—
82C22×C31—41no—
83C22×C31#12011yescharacteristic
84C2×D31—41no—
85C2×D31—41no—
86C2×D31—41no—
87C4×C31—21no—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31—41no—
91C4×C31—81no—
92Dic31—41no—
93Dic31—41no—
94Dic31—41no—
95#562—311no—
96#501—311no—
97#497D3111yescharacteristic, complemented
98#489—311no—
99#330—311no—
100#329—311no—
101#329—311no—
102C2×C31—81no—
103C2×C31#45311yescharacteristic
104C2×C31#45511yescharacteristic
105C2×C31#45611yescharacteristic
106D31—81no—
107C2×Q16—21no—
108C2×SD16—21no—
109C4⋊Q8C2×D3111yescharacteristic
110#125—311no—
111#124—311no—
112#124C2×D3111yescharacteristic
113#123—621no—
114#123—621no—
115C22⋊Q8—621no—
116C22⋊Q8—621no—
117#121—621no—
118#121—621no—
119#107—621no—
120#106—621no—
121#103—621no—
122#102—621no—
123#97—311no—
124#97—311no—
125#97C2×D3111yescharacteristic
126C31#166111yescharacteristic, complemented, Sylow
127C2×Q8—21no—
128C2×Q8—311no—
129C2×Q8C22⋊D3111yescharacteristic
130C2×D4—311no—
131C2×D4—621no—
132C2×D4—621no—
133C2×D4C22⋊D3111yescharacteristic
134C22×C4—621no—
135C22×C4—621no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—621no—
140C2×C8—621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—311no—
144C4⋊C4—311no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—621no—
152C22⋊C4—621no—
153C22⋊C4—621no—
154C22⋊C4—621no—
155C42C22×D3111yescharacteristic
156C23—21no—
157C23—621no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—1241no—
162D4—41no—
163D4—1241no—
164D4—2481no—
165D4—2481no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—621no—
169C2×C4—621no—
170C2×C4—621no—
171C2×C4—2481no—
172C2×C4—2481no—
173C2×C4D4×D3111yescharacteristic
174C2×C4D4×D3111yescharacteristic
175C2×C4C2×C22⋊D3111yescharacteristic
176C8—22no—
177C8—622no—
178C8—1241no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—1241no—
183C22—1241no—
184C22—1241no—
185C22#1175851411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—1241no—
192C4—1241no—
193C4—1241no—
194C2—81no—
195C2—2481no—
196C2#1452121611yescharacteristic
197C2#1452122511yescharacteristic
198C2#1452123011yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#497C2
socleC22×C31#120
prime radical#14521793C2
hypercenter#497D31
hypocenterC31#1661
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #14521455C2semidirect
3. #14521411C2semidirect
4. #14520790C2semidirect
5. #14520789C2semidirect
6. #14520788C2semidirect
7. C31×#497C2semidirect
97. #497D31semidirect
126. C31#1661semidirect

Maximal subgroups

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

subgroupindex
#145217932
#145214552
#145214112
#145207902
#145207892
#145207882
C31×#4972
#166131