Finite Group Databasebeta

← #16847708

Subgroups — #16847708

Order 3968.

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

normal subgroups only

This group has 246 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#14521783C211yesmaximal, characteristic, complemented
2#14521240C211yesmaximal, characteristic, complemented
3#14521238C211yesmaximal, characteristic, complemented
4#14521219C211yesmaximal, characteristic
5#14520841C211yesmaximal, characteristic, complemented
6#14520840C211yesmaximal, characteristic, complemented
7C31×#352C211yesmaximal, characteristic, complemented
8#11758561C2211yescharacteristic
9C31×#123C2211yescharacteristic
10#11758517C2211yescharacteristic
11#11758512C2211yescharacteristic
12#11758506—21no—
13C4×C22⋊D31—21no—
14#11758485—21no—
15#11758471—21no—
16#11758464—21no—
17#11758463—21no—
18#11758462—21no—
19#11758462—21no—
20(C22⋊D31)⋊C4—21no—
21C31×#100C2211yescharacteristic
22C31×#99C2211yescharacteristic
23#11758422C2211yescharacteristic
24#11758413—21no—
25#11758394—21no—
26#11758394—21no—
27C2×D4×C31C2311yescharacteristic
28C22×C4×C31D411yescharacteristic
29C2×C22⋊D31—21no—
30C2×C22⋊D31—21no—
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C22×Dic31D411yescharacteristic
34#92497—41no—
35D4×D31—41no—
36#92495—21no—
37C2×D124D411yescharacteristic
38C2×C4×D31—21no—
39C2×Dic62—21no—
40M16×C31—21no—
41C4⋊C4×C31—21no—
42C22⋊C4×C31—21no—
43C22⋊C4×C31—21no—
44C22⋊C4×C31D411yescharacteristic
45C22⋊Dic31—21no—
46C22⋊Dic31—21no—
47C22⋊Dic31D411yescharacteristic
48(C2×D31)⋊C4—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—41no—
52(C2×D31)⋊C4—41no—
53C4⋊Dic31—41no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56Dic31⋊C4—41no—
57C4×Dic31—21no—
58C4×Dic31—21no—
59C4×Dic31D411yescharacteristic
60D248—41no—
61#92470—41no—
62C23×C31C2×D411yescharacteristic
63C23×C31C2×D411yescharacteristic
64C22×D31—21no—
65C22×D31—21no—
66C22×D31—21no—
67D4×C31—41no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—41no—
71C2×C4×C31—41no—
72C2×C4×C31C2×D411yescharacteristic
73C22⋊D31—42no—
74C22⋊D31—42no—
75C22⋊D31—41no—
76C22⋊D31—41no—
77C22⋊D31—41no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—21no—
81C2×Dic31—21no—
82C2×Dic31—21no—
83C2×Dic31—41no—
84C2×Dic31—41no—
85D124—21no—
86D124—41no—
87C4×D31—41no—
88C4×D31—81no—
89Dic62—21no—
90Dic62—42no—
91C8×C31—41no—
92#2198—311nomaximal, Sylow
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31#12011yescharacteristic
98C2×D31—41no—
99C2×D31—41no—
100C2×D31—41no—
101C2×D31—41no—
102C2×D31—81no—
103C2×D31—81no—
104C4×C31—21no—
105C4×C31—41no—
106C4×C31—41no—
107C4×C31—81no—
108Dic31—22no—
109Dic31—41no—
110Dic31—41no—
111Dic31—41no—
112Dic31—81no—
113#559—311no—
114#458—311no—
115#458—311no—
116#453—311no—
117#353—311no—
118#352—311no—
119#352D3111yescharacteristic, complemented
120C2×C31—21no—
121C2×C31—41no—
122C2×C31—41no—
123C2×C31B(4,𝔽2)11yescharacteristic
124D31—81no—
125D31—81no—
126H(5,𝔽2)—311no—
127AGL(1,ℤ/8)—621no—
128#127—311no—
129#124—621no—
130#124—621no—
131#123—311no—
132#123—621no—
133#123—621no—
134#123—621no—
135#123C2×D3111yescharacteristic
136C4×Q8—621no—
137C4×D4—621no—
138C4×D4—621no—
139#104—621no—
140#100C2×D3111yescharacteristic
141#99—311no—
142#99—621no—
143#99—621no—
144#99C2×D3111yescharacteristic
145C31#219811yescharacteristic, complemented, Sylow
146#41—621no—
147#41—1241no—
148C2×Q8—621no—
149C2×D4—311no—
150C2×D4—621no—
151C2×D4—621no—
152C2×D4—621no—
153C2×D4—621no—
154C2×D4—1241no—
155C2×D4C22×D3111yescharacteristic
156C22×C4—311no—
157C22×C4—621no—
158C22×C4D12411yescharacteristic
159SD16—1241no—
160D8—1241no—
161M16—21no—
162C4⋊C4—21no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C4⋊C4—1241no—
166C4⋊C4—1241no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—311no—
170C22⋊C4—621no—
171C22⋊C4—621no—
172C22⋊C4—621no—
173C22⋊C4—621no—
174C22⋊C4—621no—
175C22⋊C4—1241no—
176C22⋊C4—1241no—
177C22⋊C4D12411yescharacteristic
178C42—311no—
179C42—621no—
180C42—621no—
181C23—621no—
182C23—621no—
183C23—621no—
184C23C2×D12411yescharacteristic
185C23D4×D3111yescharacteristic
186Q8—621no—
187Q8—1242no—
188D4—41no—
189D4—621no—
190D4—1241no—
191D4—1242no—
192D4—1242no—
193D4—1241no—
194D4—1241no—
195D4—1241no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—621no—
201C2×C4—621no—
202C2×C4—621no—
203C2×C4—621no—
204C2×C4—621no—
205C2×C4—1241no—
206C2×C4—1241no—
207C2×C4—1241no—
208C2×C4—2481no—
209C2×C4D4×D3111yescharacteristic
210C8—41no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—1241no—
216C22—1241no—
217C22—1241no—
218C22—1241no—
219C22—2481no—
220C22—2481no—
221C22#1175845911yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—81no—
226C4—622no—
227C4—1241no—
228C4—1241no—
229C4—1241no—
230C4—2481no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—2481no—
235C2—2481no—
236C2#1452123711yescharacteristic
subgroupG/H
centerC2#14521237
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingC31×#352C2
socleC2×C31B(4,𝔽2)
prime radical#14521219C2
hypercenter#352D31
hypocenterC31#2198
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #14521783C2semidirect
2. #14521240C2semidirect
3. #14521238C2semidirect
5. #14520841C2semidirect
6. #14520840C2semidirect
7. C31×#352C2semidirect
119. #352D31semidirect
145. C31#2198semidirect

Maximal subgroups

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

subgroupindex
#145217832
#145212402
#145212382
#145212192
#145208412
#145208402
C31×#3522
#219831