Finite Group Databasebeta

← #16846753

Subgroups — #16846753

Order 3968.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11758526C212yesmaximal, complemented
2C2×#11758425C212yesmaximal, complemented
3#14520950C211yesmaximal, characteristic, complemented
4#14520818C211yesmaximal, characteristic, complemented
5C31×#537C211yesmaximal, characteristic, complemented
6C2×#41×C31C2212yes—
7C22×D124C2211yescharacteristic
8C31×C22⋊Q8—22no—
9C31×#121—22no—
10C31×#121—22no—
11C2×C4⋊C4×C31C2211yescharacteristic
12#11758526—24no—
13#11758526—24no—
14C2×#92481—22no—
15C2×#92479—22no—
16C2×(C2×D31)⋊C4—22no—
17C2×C4×Dic31C2211yescharacteristic
18C2×#92474C2212yes—
19#11758425—24no—
20C23×D31—21no—
21#41×C31—22no—
22#41×C31—22no—
23#41×C31—22no—
24#41×C31—22no—
25C2×Q8×C31D412yes—
26C2×D4×C31—22no—
27C2×D4×C31—22no—
28C2×D4×C31D412yes—
29C22×C4×C31—22no—
30C22×C4×C31D412yes—
31C22×C4×C31C2311yescharacteristic
32C22×Dic31—21no—
33C2×D124—22no—
34C2×D124—22no—
35C2×D124—21no—
36C2×D124D412yescomplemented
37C4⋊C4×C31—22no—
38C4⋊C4×C31—22no—
39C22⋊C4×C31—24no—
40#92481—28no—
41#92479—28no—
42(C2×D31)⋊C4—44no—
43C4×Dic31—22no—
44#92474—22no—
45#92474D414yescomplemented
46C2×C31⋊C8—22no—
47C23×C31—22no—
48C23×C31C2×D411yescharacteristic
49C22×D31—22no—
50C22×D31—42no—
51C22×D31—42no—
52C22×D31—41no—
53C22×D31—41no—
54Q8×C31—22no—
55Q8×C31—22no—
56D4×C31—22no—
57D4×C31—22no—
58D4×C31—42no—
59D4×C31—42no—
60D4×C31—82no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D412yes—
68C2×C4×C31C2×D412yes—
69C2×C4×C31#4111yescharacteristic
70C2×Dic31—22no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73D124—24no—
74D124—42no—
75C31⋊C8—24no—
76#2006—311nomaximal, Sylow
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—42no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31#12011yescharacteristic
83C22×C31#12111yescharacteristic
84C22×C31#12711yescharacteristic
85C2×D31—44no—
86C2×D31—42no—
87C2×D31—82no—
88C2×D31—81no—
89C2×D31—81no—
90C4×C31—42no—
91C4×C31—42no—
92C4×C31#12012yes—
93C4×C31#12112yes—
94Dic31—42no—
95C2×AGL(1,ℤ/8)—312no—
96#537D3111yescharacteristic, complemented
97C2×#104—312no—
98#390—311no—
99#343—311no—
100C2×C31—21no—
101C2×C31—21no—
102C2×C31—82no—
103C2×C31#39211yescharacteristic
104C2×C31#45311yescharacteristic
105C2×C31#45411yescharacteristic
106D31—82no—
107C2×#41C2×D3112yes—
108C22×D4—311no—
109AGL(1,ℤ/8)—624no—
110AGL(1,ℤ/8)—624no—
111C2×SD16—622no—
112C2×D8—622no—
113C2×M16—312no—
114C22⋊Q8—22no—
115#121—22no—
116#121—22no—
117C2×C4⋊C4C2×D3111yescharacteristic
118C2×C22⋊C4—622no—
119C2×C42—311no—
120#104—624no—
121C31#200611yescharacteristic, complemented, Sylow
122C24—621no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D3112yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—312no—
131C2×D4—622no—
132C2×D4—621no—
133C2×D4—622no—
134C2×D4C22⋊D3112yes—
135C22×C4—22no—
136C22×C4—621no—
137C22×C4C22⋊D3112yes—
138C22×C4C22×D3111yescharacteristic
139SD16—628no—
140D8—628no—
141M16—314no—
142M16—622no—
143C2×C8—622no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—1244no—
148C42—622no—
149C23—22no—
150C23—622no—
151C23—1242no—
152C23—1242no—
153C23—1241no—
154C23—1241no—
155C23C2×C22⋊D3111yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—624no—
164D4—1242no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—622no—
171C2×C4—1241no—
172C2×C4—1241no—
173C2×C4D4×D3111yescharacteristic
174C2×C4D4×D3112yes—
175C2×C4#9249711yescharacteristic
176C2×C4C2×C22⋊D3112yes—
177C8—624no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—1244no—
184C22—1242no—
185C22—2482no—
186C22—2481no—
187C22—2481no—
188C22#1175851511yescharacteristic
189C22#1175851711yescharacteristic
190C22#1175853011yescharacteristic
191C4—42no—
192C4—42no—
193C4—1242no—
194C4#1175851412yes—
195C4#1175851612yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2482no—
200C2#1452095711yescharacteristic
201C2#1452121711yescharacteristic
202C2#1452122211yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#537C2
socleC22×C31#120
hypercenter#537D31
hypocenterC31#2006
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#11758526C2semidirect
2. C2×#11758425C2semidirect
3. #14520950C2semidirect
4. #14520818C2semidirect
5. C31×#537C2semidirect
36. C2×D124D4semidirect
45. #92474D4semidirect
96. #537D31semidirect
121. C31#2006semidirect

Maximal subgroups

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

subgroupindex
C2×#117585262
C2×#117584252
#145209502
#145208182
C31×#5372
#200631