Finite Group Databasebeta

← #16847730

Subgroups — #16847730

Order 3968.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#14521798C211yesmaximal, characteristic, complemented
2#14521232C211yesmaximal, characteristic, complemented
3#14521222C211yesmaximal, characteristic
4#14520848C211yesmaximal, characteristic, complemented
5#14520847C211yesmaximal, characteristic, complemented
6#14520845C211yesmaximal, characteristic, complemented
7C31×#456C211yesmaximal, characteristic, complemented
8C31×2−1+4C2211yescharacteristic
9C31×#137—21no—
10C31×C4⋊Q8C2211yescharacteristic
11#11758528—21no—
12#11758526—21no—
13#11758524C2211yescharacteristic
14#11758523—21no—
15#11758521C2211yescharacteristic
16#11758475—21no—
17#11758473—21no—
18#11758471—21no—
19#11758466—21no—
20#11758453—21no—
21C31×#104—21no—
22C31×#101C2211yescharacteristic
23#11758425—21no—
24#11758425—21no—
25#11758424C2211yescharacteristic
26#11758424C2211yescharacteristic
27#41×C31—21no—
28#41×C31—21no—
29#41×C31—21no—
30#41×C31—41no—
31C2×Q8×C31—41no—
32C2×Q8×C31D411yescharacteristic
33C2×Q8×C31C2311yescharacteristic
34C2×D124D411yescharacteristic
35C2×C4×D31—21no—
36C2×Dic62D411yescharacteristic
37Q16×C31—41no—
38SD16×C31—41no—
39M16×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C42×C31D411yescharacteristic
43#92482—41no—
44#92481—41no—
45#92480—41no—
46#92479—41no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52C4⋊Dic31—21no—
53Dic31⋊C4—21no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56Dic31⋊C4—21no—
57Dic31⋊C4—21no—
58C4×Dic31D411yescharacteristic
59C4×Dic31D411yescharacteristic
60#92474—21no—
61#92474—21no—
62C22×D31—21no—
63Q8×C31—21no—
64Q8×C31—21no—
65Q8×C31—21no—
66Q8×C31—41no—
67Q8×C31—41no—
68D4×C31—21no—
69D4×C31—21no—
70D4×C31—21no—
71D4×C31—41no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×Dic31—21no—
81C2×Dic31—21no—
82C2×Dic31—21no—
83D124—41no—
84C4×D31—81no—
85Dic62—41no—
86C8×C31—41no—
87C31⋊C8—41no—
88C31⋊C8—41no—
89#2203—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31#12011yescharacteristic
92C2×D31—42no—
93C2×D31—41no—
94C4×C31—21no—
95C4×C31—21no—
96C4×C31—21no—
97C4×C31—41no—
98C4×C31—41no—
99C4×C31—41no—
100Dic31—41no—
101Dic31—41no—
102Dic31—41no—
103#563—311no—
104#456—311no—
105#456D3111yescharacteristic, complemented
106#454—311no—
107#356—311no—
108#356—311no—
109#355—311no—
110C2×C31—21no—
111C2×C31—81no—
112C2×C31B(4,𝔽2)11yescharacteristic
113D31—81no—
1142−1+4C2×D3111yescharacteristic
115#137—21no—
116#137—621no—
117AGL(1,ℤ/8)—621no—
118C4⋊Q8—311no—
119C4⋊Q8C2×D3111yescharacteristic
120#126—621no—
121#126—621no—
122#125—621no—
123#124—311no—
124#123—621no—
125C22⋊Q8—621no—
126C22⋊Q8—621no—
127#104—21no—
128#104—621no—
129#104—621no—
130#101—311no—
131#101—311no—
132#101C2×D3111yescharacteristic
133C31#220311yescharacteristic, complemented, Sylow
134#41—21no—
135#41—21no—
136#41—21no—
137#41—41no—
138C2×Q8—41no—
139C2×Q8—311no—
140C2×Q8C22⋊D3111yescharacteristic
141C2×Q8C22×D3111yescharacteristic
142C2×D4—311no—
143C22×C4—621no—
144Q16—41no—
145Q16—1241no—
146SD16—41no—
147SD16—1241no—
148SD16—1241no—
149D8—1241no—
150M16—21no—
151M16—621no—
152M16—621no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—621no—
156C4⋊C4—621no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C4⋊C4—621no—
160C4⋊C4—621no—
161C22⋊C4—621no—
162C22⋊C4—621no—
163C22⋊C4—621no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C42—311no—
167C42—311no—
168C42C22⋊D3111yescharacteristic
169C23—621no—
170Q8—21no—
171Q8—21no—
172Q8—21no—
173Q8—41no—
174Q8—41no—
175Q8—1241no—
176D4—21no—
177D4—21no—
178D4—21no—
179D4—41no—
180D4—1241no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—621no—
187C2×C4—621no—
188C2×C4—621no—
189C2×C4—2481no—
190C2×C4D4×D3111yescharacteristic
191C2×C4D4×D3111yescharacteristic
192C2×C4C2×C22⋊D3111yescharacteristic
193C8—41no—
194C8—1241no—
195C8—1241no—
196C22—41no—
197C22—1242no—
198C22—1241no—
199C22#1175851411yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—41no—
206C4—1241no—
207C4—1241no—
208C4—1241no—
209C2—21no—
210C2—81no—
211C2—2481no—
212C2#1452123511yescharacteristic
subgroupG/H
centerC2#14521235
commutator, cosocleC2×Q8×C31C23
FrattiniC2×Q8C22×D31
FittingC31×#456C2
socleC2×C31B(4,𝔽2)
prime radical#14521222C2
hypercenter#456D31
hypocenterC31#2203
LCSG ▷ C2×Q8×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14521798C2semidirect
2. #14521232C2semidirect
4. #14520848C2semidirect
5. #14520847C2semidirect
6. #14520845C2semidirect
7. C31×#456C2semidirect
105. #456D31semidirect
133. C31#2203semidirect

Maximal subgroups

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

subgroupindex
#145217982
#145212322
#145212222
#145208482
#145208472
#145208452
C31×#4562
#220331