Finite Group Databasebeta

← #16847242

Subgroups — #16847242

Order 3968.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758405C211yesmaximal, characteristic, complemented
2C2×#11758396C211yesmaximal, characteristic, complemented
3C2×#11758420C211yesmaximal, characteristic
4#14520952C211yesmaximal, characteristic
5#14520918C211yesmaximal, characteristic, complemented
6#14520803C211yesmaximal, characteristic, complemented
7C2×C31×#102C211yesmaximal, characteristic
8C22×D4×C31C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C22⋊Dic31—22no—
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—22no—
15C2×C4×Dic31C2211yescharacteristic
16C22×C31⋊C8C2211yescharacteristic
17C31×#102—22no—
18#11758420—22no—
19#11758405—22no—
20#11758396—22no—
21C24×C31—21no—
22C2×D4×C31—21no—
23C2×D4×C31—21no—
24C2×D4×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31Q812yes—
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31—21no—
32C22×Dic31D412yes—
33C2×C8×C31—21no—
34C2×C8×C31—21no—
35C2×C8×C31D412yes—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C22⋊Dic31—44no—
39C4⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43Dic31⋊C4—44no—
44C4×Dic31—21no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C2×C31⋊C8D412yes—
49C23×C31—22no—
50C23×C31—41no—
51C23×C31—41no—
52C23×C31—42no—
53C23×C31—42no—
54C23×C31C2×D411yescharacteristic
55D4×C31—22no—
56D4×C31—22no—
57D4×C31—41no—
58D4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—42no—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×Q811yescharacteristic
64C2×C4×C31#4111yescharacteristic
65C2×C4×C31#4111yescharacteristic
66C2×C4×C31#4111yescharacteristic
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—41no—
70C2×Dic31—41no—
71C2×Dic31—42no—
72C2×Dic31—42no—
73C2×Dic31SD1614yes—
74C8×C31—22no—
75C31⋊C8—22no—
76#2094—311nomaximal, Sylow
77C22×C31—42no—
78C22×C31—44no—
79C22×C31—82no—
80C22×C31—81no—
81C22×C31—81no—
82C22×C31C22⋊Q811yescharacteristic
83C22×C31#12311yescharacteristic
84C22×C31#12711yescharacteristic
85C22×C31C2×SD1612yes—
86C22×C31AGL(1,ℤ/8)12yes—
87C4×C31—81no—
88C4×C31C22⋊Q811yescharacteristic
89C4×C31C22⋊Q811yescharacteristic
90C4×C31#12311yescharacteristic
91C4×C31#12311yescharacteristic
92Dic31—24no—
93Dic31—81no—
94Dic31—81no—
95C2×#106—311no—
96C2×#106—311no—
97C2×#102—311no—
98C2×#102D3111yescharacteristic
99#390—311no—
100#384—311no—
101#336—311no—
102C2×C31—82no—
103C2×C31#39911yescharacteristic
104C2×C31#47612yes—
105C2×C31#48112yes—
106C2×C31#49211yescharacteristic
107C2×C31#49611yescharacteristic
108C22×D4C2×D3111yescharacteristic
109C22×C8—311no—
110C22×C8C2×D3111yescharacteristic
111C2×C4⋊C4—311no—
112C2×C4⋊C4—311no—
113C2×C4⋊C4—622no—
114C2×C4⋊C4C2×D3111yescharacteristic
115C2×C22⋊C4—622no—
116C2×C42—311no—
117#106—622no—
118#106—622no—
119#102—22no—
120#102—622no—
121C31#209411yescharacteristic, complemented, Sylow
122C24—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4Dic6212yes—
129C22×C4—21no—
130C22×C4—312no—
131C22×C4—621no—
132C22×C4—621no—
133C22×C4C22×D3111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—312no—
137C2×C8—621no—
138C2×C8—621no—
139C2×C8C22⋊D3112yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—1244no—
147C22⋊C4—1244no—
148C42—621no—
149C42—621no—
150C23—22no—
151C23—41no—
152C23—42no—
153C23—42no—
154C23—41no—
155C23D4×D3111yescharacteristic
156D4—22no—
157D4—22no—
158D4—41no—
159D4—41no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—314no—
163C2×C4—622no—
164C2×C4—622no—
165C2×C4—1242no—
166C2×C4—1242no—
167C2×C4—1241no—
168C2×C4—1241no—
169C2×C4C2×Dic6211yescharacteristic
170C2×C4#9249511yescharacteristic
171C2×C4D4×D3111yescharacteristic
172C2×C4#9249711yescharacteristic
173C2×C4#9249711yescharacteristic
174C2×C4C2×C22⋊D3111yescharacteristic
175C8—22no—
176C8—622no—
177C22—42no—
178C22—44no—
179C22—82no—
180C22—81no—
181C22—81no—
182C22#1175845511yescharacteristic
183C22#1175846011yescharacteristic
184C22#1175848812yes—
185C22SD16×D3112yes—
186C22#1175851711yescharacteristic
187C4—81no—
188C4—624no—
189C4—2481no—
190C4—2481no—
191C4#1175845511yescharacteristic
192C4#1175846011yescharacteristic
193C4#1175850111yescharacteristic
194C4#1175851211yescharacteristic
195C2—82no—
196C2#1452098511yescharacteristic
197C2#1452133712yes—
198C2#1452136612yes—
199C2#1452142011yescharacteristic
200C2#1452143711yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC22×D4×C31C22
hypercenterC2×#102D31
hypocenterC31#2094
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#11758405C2semidirect
2. C2×#11758396C2semidirect
5. #14520918C2semidirect
6. #14520803C2semidirect
121. C31#2094semidirect

Maximal subgroups

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

subgroupindex
C2×#117584052
C2×#117583962
C2×#117584202
#145209522
#145209182
#145208032
C2×C31×#1022
#209431