Finite Group Databasebeta

← #16858384

Subgroups — #16858384

Order 3968.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic62C211yesmaximal, characteristic
2#14521774C211yesmaximal, characteristic
3#14521399C211yesmaximal, characteristic
4#14521398C212yesmaximal
5#14521345C211yesmaximal, characteristic
6#14521342C212yesmaximal
7#14521257C212yesmaximal
8#14521173C211yesmaximal, characteristic
9Q16×Dic31C212yesmaximal
10C4×#92482C211yesmaximal, characteristic
11C31×#462C211yesmaximal, characteristic
12C2×Q16×C31C2212yes—
13C31×C4⋊Q8C2211yescharacteristic
14C4×Q8×C31C2211yescharacteristic
15Q8×Dic31C2212yes—
16Q8×Dic31C2212yes—
17#11758521C2212yes—
18C2×#92482C2211yescharacteristic
19#11758467—21no—
20#11758466—22no—
21#11758465—22no—
22#11758465C2212yes—
23#11758464—21no—
24#11758446—21no—
25#11758446C2211yescharacteristic
26C4×Dic62—21no—
27C4×Dic62C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×C4⋊C8C2211yescharacteristic
30C31×#103C2212yes—
31#11758423C2211yescharacteristic
32#11758423C2212yes—
33#11758423C2212yes—
34#11758406C2212yes—
35#11758404C2212yes—
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
38#11758398C2211yescharacteristic
39#11758395C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41C2×Q8×C31C2312yes—
42C2×Q8×C31C2311yescharacteristic
43C2×Dic62—21no—
44C2×Dic62—22no—
45C2×Dic62D411yescharacteristic
46C2×Dic62C2311yescharacteristic
47Q16×C31—24no—
48C2×C8×C31C2312yes—
49C4⋊C4×C31—21no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31—21no—
52C4⋊C4×C31C2311yescharacteristic
53C42×C31—21no—
54C42×C31C2311yescharacteristic
55#92482—22no—
56C4⋊Dic31—21no—
57C4⋊Dic31—22no—
58C4⋊Dic31—22no—
59C4⋊Dic31D411yescharacteristic
60C4⋊Dic31C2311yescharacteristic
61C4⋊Dic31C2312yes—
62Dic31⋊C4—21no—
63Dic31⋊C4—22no—
64Dic31⋊C4—22no—
65Dic31⋊C4—22no—
66Dic31⋊C4D412yes—
67C4×Dic31—21no—
68C4×Dic31—22no—
69C4×Dic31—22no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2311yescharacteristic
72C2×C31⋊C8C2311yescharacteristic
73Q8×C31—21no—
74Q8×C31—22no—
75Q8×C31—22no—
76Q8×C31#4112yes—
77C2×C4×C31—21no—
78C2×C4×C31—22no—
79C2×C4×C31—21no—
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2411yescharacteristic
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31—22no—
86C2×Dic31C2×D412yes—
87C2×Dic31C2×D412yes—
88Dic62—21no—
89Dic62—21no—
90Dic62—82no—
91Dic62—81no—
92Dic62Q1614yescomplemented
93C8×C31—22no—
94C31⋊C8—21no—
95C31⋊C8—21no—
96#3363—311nomaximal, Sylow
97C22×C31C22×D411yescharacteristic
98C4×C31—22no—
99C4×C31—21no—
100C4×C31—42no—
101C4×C31—41no—
102C4×C31C2×Q1612yes—
103C4×C31C2×#4111yescharacteristic
104C4×C312−1+411yescharacteristic
105Dic31—22no—
106Dic31—41no—
107Dic31—42no—
108Dic31—41no—
109Dic31C2×Q1614yes—
110Q82—311no—
111#557—311no—
112#487—311no—
113#487—312no—
114#477—311no—
115#477—312no—
116#462—312no—
117#462D3111yescharacteristic
118C8×Q8—311no—
119C4×Q16—312no—
120C4×Q16—311no—
121C2×C31#54811yescharacteristic
122C2×C31C22×Q1611yescharacteristic
123C2×C31#57711yescharacteristic
124C2×Q16—311no—
125C2×Q16C2×D3112yes—
126C4⋊Q8—312no—
127C4⋊Q8—312no—
128C4⋊Q8—311no—
129C4⋊Q8—621no—
130C4⋊Q8—622no—
131C4⋊Q8C2×D3111yescharacteristic
132#125—622no—
133#125—621no—
134C4×Q8—311no—
135C4×Q8—312no—
136C4×Q8—312no—
137C4×Q8—311no—
138C4×Q8—621no—
139C4×Q8—621no—
140C4×Q8C2×D3111yescharacteristic
141#107—312no—
142#107—311no—
143C4⋊C8—312no—
144C4⋊C8C2×D3111yescharacteristic
145#103—311no—
146#103—312no—
147#103—312no—
148#103—312no—
149#103—311no—
150#103C2×D3112yes—
151C4×C8—312no—
152C4×C8—311no—
153C31#336311yescharacteristic, complemented, Sylow
154C2×Q8—311no—
155C2×Q8—311no—
156C2×Q8—622no—
157C2×Q8—621no—
158C2×Q8C22×D3112yes—
159C2×Q8C22×D3111yescharacteristic
160Q16—24no—
161Q16—622no—
162C2×C8—311no—
163C2×C8—311no—
164C2×C8C22×D3112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—312no—
169C4⋊C4—311no—
170C4⋊C4—312no—
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×D3111yescharacteristic
180C42—21no—
181C42—312no—
182C42—622no—
183C42—622no—
184C42—621no—
185C42C22×D3111yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—314no—
190Q8—621no—
191Q8—621no—
192Q8—2481no—
193Q8—2482no—
194Q8#9249712yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—312no—
199C2×C4—312no—
200C2×C4—621no—
201C2×C4—622no—
202C2×C4—621no—
203C2×C4D4×D3111yescharacteristic
204C2×C4D4×D3111yescharacteristic
205C2×C4C23×D3111yescharacteristic
206C8—22no—
207C8—621no—
208C8—621no—
209C22C2×D4×D3111yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—314no—
215C4—622no—
216C4—1242no—
217C4—1241no—
218C4—1241no—
219C4Q16×D3112yes—
220C4C2×#9249711yescharacteristic
221C4#1175856711yescharacteristic
222C2#1452170511yescharacteristic
223C2C2×Q16×D3111yescharacteristic
224C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#462C2
socle, prime radicalC22×C31C22×D4
hypercenter#462D31
hypocenterC31#3363
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

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

Maximal subgroups

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

subgroupindex
Q8×Dic622
#145217742
#145213992
#145213982
#145213452
#145213422
#145212572
#145211732
Q16×Dic312
C4×#924822
C31×#4622
#336331