Finite Group Databasebeta

← #16858386

Subgroups — #16858386

Order 3968.

336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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#14521779C211yesmaximal, characteristic
2#14521774C211yesmaximal, characteristic
3#14521398C212yesmaximal
4#14521342C212yesmaximal
5#14521341C211yesmaximal, characteristic
6#14521258C212yesmaximal
7#14521256C211yesmaximal, characteristic
8C8×Dic62C211yesmaximal, characteristic
9C4×Dic124C211yesmaximal, characteristic
10#14521141C212yesmaximal
11C31×#487C211yesmaximal, characteristic
12C31×C4⋊Q8C2211yescharacteristic
13C31×C4⋊Q8C2211yescharacteristic
14Q8×Dic31C2212yes—
15#11758521—22no—
16#11758521C2212yes—
17C2×#92482C2212yes—
18C2×Dic124C2211yescharacteristic
19#11758467—21no—
20#11758466—22no—
21#11758465—21no—
22#11758465C2212yes—
23#11758464—21no—
24#11758464—21no—
25#11758464C2212yes—
26C4×Dic62C2211yescharacteristic
27C4×Dic62C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×#103C2212yes—
30C31×#103C2212yes—
31C4×C8×C31C2211yescharacteristic
32#11758423C2212yes—
33#11758406C2211yescharacteristic
34#11758404C2211yescharacteristic
35#11758404C2211yescharacteristic
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
38#11758398C2212yes—
39#11758395C2212yes—
40C4⋊(C31⋊C8)C2211yescharacteristic
41C2×Q8×C31—21no—
42C2×Q8×C31C2312yes—
43C2×Dic62—22no—
44C2×Dic62D411yescharacteristic
45C2×Dic62C2311yescharacteristic
46C2×Dic62C2311yescharacteristic
47C2×C8×C31C2311yescharacteristic
48C2×C8×C31C2311yescharacteristic
49C4⋊C4×C31—21no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31—21no—
52C4⋊C4×C31C2312yes—
53C42×C31C2311yescharacteristic
54#92482—24no—
55C4⋊Dic31—22no—
56C4⋊Dic31D411yescharacteristic
57C4⋊Dic31C2311yescharacteristic
58C4⋊Dic31C2311yescharacteristic
59Dic31⋊C4—21no—
60Dic31⋊C4—21no—
61Dic31⋊C4—22no—
62Dic31⋊C4—22no—
63Dic31⋊C4—22no—
64Dic31⋊C4—22no—
65Dic31⋊C4D412yes—
66C4×Dic31—21no—
67C4×Dic31—21no—
68C4×Dic31—22no—
69C4×Dic31—22no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2312yes—
72Dic124—22no—
73Q8×C31—22no—
74Q8×C31—22no—
75Q8×C31—81no—
76C2×C4×C31—22no—
77C2×C4×C31—22no—
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2411yescharacteristic
81C2×Dic31—21no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31C2×D412yes—
86C2×Dic31C2×D412yes—
87Dic62—21no—
88Dic62—21no—
89Dic62—21no—
90Dic62—82no—
91Dic62Q1614yescomplemented
92Dic62#4112yes—
93C8×C31—21no—
94C8×C31—21no—
95C31⋊C8—22no—
96#3363—311nomaximal, Sylow
97C22×C31C22×D411yescharacteristic
98C4×C31—21no—
99C4×C31—42no—
100C4×C31—42no—
101C4×C31C2×Q1612yes—
102C4×C31C2×#4111yescharacteristic
103C4×C312−1+411yescharacteristic
104Dic31—22no—
105Dic31—22no—
106Dic31—41no—
107Dic31—41no—
108Dic31—41no—
109Dic31C2×Q1614yes—
110Q82—311no—
111#557—311no—
112#487—312no—
113#487D3111yescharacteristic
114#477—311no—
115#477—312no—
116#462—311no—
117#462—312no—
118C8×Q8—311no—
119C4×Q16—312no—
120C4×Q16—311no—
121C2×C31#54811yescharacteristic
122C2×C31C22×Q1611yescharacteristic
123C2×C31#57711yescharacteristic
124C2×Q16—312no—
125C2×Q16—311no—
126C4⋊Q8—312no—
127C4⋊Q8—312no—
128C4⋊Q8—621no—
129C4⋊Q8—622no—
130C4⋊Q8C2×D3111yescharacteristic
131C4⋊Q8C2×D3111yescharacteristic
132#125—622no—
133#125—621no—
134C4×Q8—311no—
135C4×Q8—312no—
136C4×Q8—312no—
137C4×Q8—311no—
138C4×Q8—311no—
139C4×Q8—621no—
140C4×Q8—621no—
141#107—311no—
142#107—312no—
143C4⋊C8—312no—
144C4⋊C8—311no—
145#103—312no—
146#103—311no—
147#103—311no—
148#103—312no—
149#103C2×D3112yes—
150#103C2×D3112yes—
151C4×C8—312no—
152C4×C8C2×D3111yescharacteristic
153C31#336311yescharacteristic, complemented, Sylow
154C2×Q8—21no—
155C2×Q8—311no—
156C2×Q8—311no—
157C2×Q8—311no—
158C2×Q8—622no—
159C2×Q8C22×D3112yes—
160Q16—622no—
161Q16—624no—
162C2×C8—312no—
163C2×C8C22×D3111yescharacteristic
164C2×C8C22×D3111yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—312no—
169C4⋊C4—311no—
170C4⋊C4—311no—
171C4⋊C4—311no—
172C4⋊C4—622no—
173C4⋊C4—622no—
174C4⋊C4—622no—
175C4⋊C4—622no—
176C4⋊C4—622no—
177C4⋊C4—621no—
178C4⋊C4—621no—
179C4⋊C4C22×D3112yes—
180C42—312no—
181C42—622no—
182C42—622no—
183C42—621no—
184C42—621no—
185C42C22×D3111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—81no—
189Q8—314no—
190Q8—312no—
191Q8—621no—
192Q8—621no—
193Q8—621no—
194Q8—2482no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—312no—
198C2×C4—312no—
199C2×C4—621no—
200C2×C4—621no—
201C2×C4—621no—
202C2×C4—621no—
203C2×C4D4×D3111yescharacteristic
204C2×C4D4×D3111yescharacteristic
205C2×C4C23×D3111yescharacteristic
206C8—21no—
207C8—21no—
208C8—622no—
209C22C2×D4×D3111yescharacteristic
210C4—21no—
211C4—42no—
212C4—42no—
213C4—314no—
214C4—622no—
215C4—622no—
216C4—1241no—
217C4—1241no—
218C4—1241no—
219C4Q16×D3112yes—
220C4#41×D3111yescharacteristic
221C4#1175856711yescharacteristic
222C2#1452170711yescharacteristic
223C2C2×Q16×D3111yescharacteristic
224C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#487C2
socle, prime radicalC22×C31C22×D4
hypercenter#487D31
hypocenterC31#3363
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
91. Dic62Q16semidirect
153. C31#3363semidirect

Maximal subgroups

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

subgroupindex
#145217792
#145217742
#145213982
#145213422
#145213412
#145212582
#145212562
C8×Dic622
C4×Dic1242
#145211412
C31×#4872
#336331