Finite Group Databasebeta

← #16847230

Subgroups — #16847230

Order 3968.

274 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11758406C211yesmaximal, characteristic, complemented
2C2×#11758396C211yesmaximal, characteristic, complemented
3C2×#11758420C211yesmaximal, characteristic
4#14520952C211yesmaximal, characteristic
5#14520914C211yesmaximal, 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×C4×Dic31C2211yescharacteristic
15C22×C31⋊C8C2211yescharacteristic
16C31×#102—22no—
17#11758420—22no—
18C31⋊#95—22no—
19#11758406—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—
43C4×Dic31—21no—
44C4×Dic31—21no—
45C2×C31⋊C8—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8D412yes—
48C23×C31—22no—
49C23×C31—41no—
50C23×C31—41no—
51C23×C31—42no—
52C23×C31—42no—
53C23×C31C2×D411yescharacteristic
54D4×C31—22no—
55D4×C31—22no—
56D4×C31—41no—
57D4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31—42no—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×Q811yescharacteristic
63C2×C4×C31#4111yescharacteristic
64C2×C4×C31#4111yescharacteristic
65C2×C4×C31#4111yescharacteristic
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—41no—
70C2×Dic31—41no—
71C2×Dic31—42no—
72C2×Dic31—42no—
73C8×C31—22no—
74C31⋊C8—22no—
75#2092—311nomaximal, Sylow
76C22×C31—42no—
77C22×C31—44no—
78C22×C31—82no—
79C22×C31—81no—
80C22×C31—81no—
81C22×C31C22⋊Q811yescharacteristic
82C22×C31#12311yescharacteristic
83C22×C31#12711yescharacteristic
84C22×C31#13512yes—
85C22×C31AGL(1,ℤ/8)12yes—
86C4×C31—81no—
87C4×C31C22⋊Q811yescharacteristic
88C4×C31C22⋊Q811yescharacteristic
89C4×C31#12311yescharacteristic
90C4×C31#12311yescharacteristic
91Dic31—42no—
92Dic31—81no—
93Dic31—81no—
94C2×#107—311no—
95C2×#106—311no—
96C2×#102—311no—
97C2×#102D3111yescharacteristic
98#390—311no—
99#382—311no—
100#336—311no—
101C2×C31—82no—
102C2×C31#39911yescharacteristic
103C2×C31#47812yes—
104C2×C31#48212yes—
105C2×C31#49511yescharacteristic
106C2×C31#49611yescharacteristic
107C22×D4C2×D3111yescharacteristic
108C22×C8—311no—
109C22×C8C2×D3111yescharacteristic
110C2×C4⋊C4—311no—
111C2×C4⋊C4—311no—
112C2×C4⋊C4C2×D3111yescharacteristic
113C2×C22⋊C4—622no—
114C2×C42—311no—
115#107—622no—
116#106—622no—
117#102—22no—
118#102—622no—
119#95—622no—
120C31#209211yescharacteristic, complemented, Sylow
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic6212yes—
128C22×C4—21no—
129C22×C4—312no—
130C22×C4—621no—
131C22×C4—621no—
132C22×C4C22×D3111yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—312no—
136C2×C8—621no—
137C2×C8—621no—
138C2×C8C22⋊D3112yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C22⋊C4—1244no—
146C42—621no—
147C42—621no—
148C23—22no—
149C23—41no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23D4×D3111yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—622no—
161C2×C4—622no—
162C2×C4—622no—
163C2×C4—1242no—
164C2×C4—1242no—
165C2×C4—1241no—
166C2×C4—1241no—
167C2×C4C2×Dic6211yescharacteristic
168C2×C4#9249511yescharacteristic
169C2×C4D4×D3111yescharacteristic
170C2×C4#9249711yescharacteristic
171C2×C4#9249711yescharacteristic
172C2×C4C2×C22⋊D3111yescharacteristic
173C8—22no—
174C8—622no—
175C22—44no—
176C22—42no—
177C22—82no—
178C22—81no—
179C22—81no—
180C22#1175845511yescharacteristic
181C22#1175846011yescharacteristic
182C22#1175848912yes—
183C22#1175849112yes—
184C22#1175851711yescharacteristic
185C4—81no—
186C4—1242no—
187C4—2481no—
188C4—2481no—
189C4#1175845511yescharacteristic
190C4#1175846011yescharacteristic
191C4#1175850111yescharacteristic
192C4#1175851211yescharacteristic
193C2—82no—
194C2#1452098511yescharacteristic
195C2#1452134712yes—
196C2#1452137112yes—
197C2#1452143211yescharacteristic
198C2#1452143511yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC22×D4×C31C22
hypercenterC2×#102D31
hypocenterC31#2092
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×#11758406C2semidirect
2. C2×#11758396C2semidirect
5. #14520914C2semidirect
6. #14520803C2semidirect
120. C31#2092semidirect

Maximal subgroups

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

subgroupindex
C2×#117584062
C2×#117583962
C2×#117584202
#145209522
#145209142
#145208032
C2×C31×#1022
#209231