Finite Group Databasebeta

← #16846752

Subgroups — #16846752

Order 3968.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11758509C212yesmaximal, complemented
2#14521630C211yesmaximal, characteristic, complemented
3C2×#11758393C212yesmaximal, complemented
4#14520818C211yesmaximal, characteristic, complemented
5C31×#390C211yesmaximal, characteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C2×#92495C2212yes—
8C2×C4⋊C4×C31C2211yescharacteristic
9C2×C22⋊C4×C31—22no—
10C2×C42×C31C2211yescharacteristic
11C2×#92480—22no—
12#11758509—24no—
13#11758509—24no—
14C2×#92479—22no—
15#11758507—22no—
16C2×#92474C2212yes—
17#11758474—22no—
18#11758472—22no—
19#11758393—24no—
20C24×C31—21no—
21C2×D4×C31—22no—
22C2×D4×C31—22no—
23C2×D4×C31—21no—
24C2×D4×C31D412yescomplemented
25C22×C4×C31—21no—
26C22×C4×C31D412yes—
27C22×C4×C31C2311yescharacteristic
28C2×C22⋊D31—22no—
29#92495—22no—
30#92495—22no—
31#92495—22no—
32#92495—22no—
33C2×D124—22no—
34C2×D124D412yes—
35C2×C4×D31—22no—
36C2×Dic62D412yes—
37C4⋊C4×C31—22no—
38C22⋊C4×C31—44no—
39C42×C31—22no—
40#92480—28no—
41#92479—28no—
42(C2×D31)⋊C4—24no—
43C4⋊Dic31—22no—
44#92474—22no—
45#92474D414yescomplemented
46C2×C31⋊C8—22no—
47C23×C31—22no—
48C23×C31—42no—
49C23×C31—42no—
50C23×C31—41no—
51C23×C31—41no—
52C23×C31C2×D411yescharacteristic
53C22×D31—22no—
54D4×C31—24no—
55D4×C31—42no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—42no—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D412yes—
63C2×C4×C31C2×D412yes—
64C2×C4×C31#4111yescharacteristic
65C22⋊D31—42no—
66C22⋊D31—42no—
67C2×Dic31—22no—
68D124—22no—
69D124—22no—
70D124—82no—
71C4×D31—42no—
72C4×D31—42no—
73Dic62—22no—
74Dic62—22no—
75C31⋊C8—24no—
76#2006—311nomaximal, Sylow
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—44no—
80C22×C31—42no—
81C22×C31—82no—
82C22×C31—81no—
83C22×C31—81no—
84C22×C31#12011yescharacteristic
85C22×C31#12111yescharacteristic
86C22×C31#12711yescharacteristic
87C2×D31—42no—
88C2×D31—42no—
89C2×D31—42no—
90C4×C31—42no—
91C4×C31—42no—
92C4×C31#12012yes—
93C4×C31#12112yes—
94Dic31—42no—
95C2×AGL(1,ℤ/8)—312no—
96#537—311no—
97C2×#104—312no—
98#390D3111yescharacteristic, complemented
99#343—311no—
100C2×C31—21no—
101C2×C31—21no—
102C2×C31—82no—
103C2×C31#39211yescharacteristic
104C2×C31#45311yescharacteristic
105C2×C31#45411yescharacteristic
106D31—82no—
107C2×#41—312no—
108C22×D4C2×D3111yescharacteristic
109AGL(1,ℤ/8)—624no—
110AGL(1,ℤ/8)—624no—
111C2×SD16—622no—
112C2×D8—622no—
113C2×M16—312no—
114C22⋊Q8—622no—
115#121—622no—
116#121—622no—
117C2×C4⋊C4C2×D3111yescharacteristic
118C2×C22⋊C4—22no—
119C2×C42C2×D3111yescharacteristic
120#104—624no—
121C31#200611yescharacteristic, complemented, Sylow
122C24—21no—
123#41—622no—
124#41—622no—
125#41—622no—
126#41—622no—
127C2×Q8—312no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—312no—
132C2×D4—622no—
133C2×D4—622no—
134C2×D4D12412yescomplemented
135C22×C4—21no—
136C22×C4—622no—
137C22×C4C22⋊D3112yes—
138C22×C4C22×D3111yescharacteristic
139SD16—628no—
140D8—628no—
141M16—314no—
142M16—622no—
143C2×C8—622no—
144C4⋊C4—22no—
145C4⋊C4—622no—
146C22⋊C4—44no—
147C22⋊C4—624no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—622no—
155C23C2×C22⋊D3111yescharacteristic
156Q8—622no—
157Q8—622no—
158D4—24no—
159D4—42no—
160D4—622no—
161D4—622no—
162D4—1242no—
163D4—1242no—
164D4—2482no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—622no—
171C2×C4—1242no—
172C2×C4—1242no—
173C2×C4C2×D12411yescharacteristic
174C2×C4#9249511yescharacteristic
175C2×C4D4×D3112yes—
176C2×C4D4×D3112yes—
177C8—624no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—1242no—
186C22—1242no—
187C22—1242no—
188C22#1175850711yescharacteristic
189C22#1175851411yescharacteristic
190C22#1175851711yescharacteristic
191C4—42no—
192C4—42no—
193C4—1242no—
194C4#1175845912yes—
195C4#1175846112yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2482no—
200C2#1452095811yescharacteristic
201C2#1452121611yescharacteristic
202C2#1452122111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#390C2
socleC22×C31#120
hypercenter#390D31
hypocenterC31#2006
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#11758509C2semidirect
2. #14521630C2semidirect
3. C2×#11758393C2semidirect
4. #14520818C2semidirect
5. C31×#390C2semidirect
24. C2×D4×C31D4semidirect
45. #92474D4semidirect
98. #390D31semidirect
121. C31#2006semidirect
134. C2×D4D124semidirect

Maximal subgroups

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

subgroupindex
C2×#117585092
#145216302
C2×#117583932
#145208182
C31×#3902
#200631