Finite Group Databasebeta

← #16846757

Subgroups — #16846757

Order 3968.

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

normal subgroups only

This group has 370 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×#11758519C212yesmaximal, complemented
2#14521630C211yesmaximal, characteristic
3C2×#11758393C212yesmaximal, complemented
4#14520818C211yesmaximal, characteristic, complemented
5C31×#391C211yesmaximal, characteristic, complemented
6C22×Q8×C31C2211yescharacteristic
7C2×#92495C2212yes—
8C2×C4⋊C4×C31C2211yescharacteristic
9C2×C42×C31C2211yescharacteristic
10C2×#92482—22no—
11#11758519—24no—
12#11758519—24no—
13C2×#92481—22no—
14#11758507—22no—
15C2×#92474C2212yes—
16#11758474—22no—
17#11758472—22no—
18C31×#95—22no—
19#11758393—24no—
20C2×Q8×C31—21no—
21C2×Q8×C31—22no—
22C2×Q8×C31—22no—
23C2×Q8×C31D412yescomplemented
24C22×C4×C31—21no—
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—
38C42×C31—22no—
39#92482—28no—
40#92481—28no—
41(C2×D31)⋊C4—24no—
42C4⋊Dic31—22no—
43#92474—22no—
44#92474D414yescomplemented
45C2×C31⋊C8—22no—
46C23×C31C2×D411yescharacteristic
47C22×D31—22no—
48Q8×C31—24no—
49Q8×C31—42no—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31—42no—
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D412yes—
60C2×C4×C31C2×D412yes—
61C2×C4×C31#4111yescharacteristic
62C22⋊D31—42no—
63C22⋊D31—42no—
64C2×Dic31—22no—
65D124—22no—
66D124—22no—
67D124—82no—
68C4×D31—42no—
69C4×D31—42no—
70Dic62—22no—
71Dic62—22no—
72C31⋊C8—24no—
73#2007—311nomaximal, Sylow
74C22×C31—21no—
75C22×C31—21no—
76C22×C31#12011yescharacteristic
77C22×C31#12111yescharacteristic
78C22×C31#12711yescharacteristic
79C2×D31—42no—
80C2×D31—42no—
81C2×D31—42no—
82C4×C31—42no—
83C4×C31—42no—
84C4×C31—42no—
85C4×C31#12012yes—
86C4×C31#12112yes—
87Dic31—42no—
88C2×#137—312no—
89#537—311no—
90C2×#104—312no—
91#391D3111yescharacteristic, complemented
92#343—311no—
93C2×C31—21no—
94C2×C31—21no—
95C2×C31#39211yescharacteristic
96C2×C31#45511yescharacteristic
97C2×C31#45611yescharacteristic
98D31—82no—
99C2×#41—312no—
100C22×Q8C2×D3111yescharacteristic
101#137—624no—
102#137—624no—
103C2×Q16—622no—
104C2×SD16—622no—
105C2×M16—312no—
106C22⋊Q8—622no—
107#121—622no—
108#121—622no—
109C2×C4⋊C4C2×D3111yescharacteristic
110C2×C42C2×D3111yescharacteristic
111#104—624no—
112#95—22no—
113C31#200711yescharacteristic, complemented, Sylow
114#41—622no—
115#41—622no—
116#41—622no—
117#41—622no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—312no—
122C2×Q8D12412yescomplemented
123C2×D4—312no—
124C2×D4—622no—
125C2×D4—622no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—622no—
129C22×C4C22⋊D3112yes—
130C22×C4C22×D3111yescharacteristic
131Q16—628no—
132SD16—628no—
133M16—314no—
134M16—622no—
135C2×C8—622no—
136C4⋊C4—22no—
137C4⋊C4—622no—
138C22⋊C4—624no—
139C42—22no—
140C23—622no—
141C23C2×C22⋊D3111yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—622no—
145Q8—622no—
146D4—622no—
147D4—622no—
148D4—1242no—
149D4—1242no—
150D4—2482no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—622no—
160C2×C4—1242no—
161C2×C4—1242no—
162C2×C4C2×D12411yescharacteristic
163C2×C4#9249511yescharacteristic
164C2×C4D4×D3112yes—
165C2×C4D4×D3112yes—
166C8—624no—
167C22—21no—
168C22—21no—
169C22—1242no—
170C22—1242no—
171C22—1242no—
172C22#1175850711yescharacteristic
173C22#1175851411yescharacteristic
174C22#1175851711yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—1242no—
179C4#1175845912yes—
180C4#1175846112yes—
181C2—21no—
182C2—21no—
183C2—2482no—
184C2#1452095811yescharacteristic
185C2#1452122611yescharacteristic
186C2#1452123111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#391C2
socleC22×C31#120
prime radical#14521630C2
hypercenter#391D31
hypocenterC31#2007
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#11758519C2semidirect
3. C2×#11758393C2semidirect
4. #14520818C2semidirect
5. C31×#391C2semidirect
23. C2×Q8×C31D4semidirect
44. #92474D4semidirect
91. #391D31semidirect
113. C31#2007semidirect
122. C2×Q8D124semidirect

Maximal subgroups

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

subgroupindex
C2×#117585192
#145216302
C2×#117583932
#145208182
C31×#3912
#200731