Finite Group Databasebeta

← #16858308

Subgroups — #16858308

Order 3968.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#14521764C211yesmaximal, characteristic, complemented
2#14521704C211yesmaximal, characteristic, complemented
3#14521447C211yesmaximal, characteristic, complemented
4#14521372C212yesmaximal, complemented
5#14521366C212yesmaximal, complemented
6#14521339C211yesmaximal, characteristic, complemented
7#14521329C211yesmaximal, characteristic, complemented
8#14521299C212yesmaximal, complemented
9#14521128C211yesmaximal, characteristic, complemented
10#14521090C212yesmaximal, complemented
11C4×D8×C31C211yesmaximal, characteristic, complemented
12C2×#92495—21no—
13C2×D8×C31C2211yescharacteristic
14C4×D4×C31C2211yescharacteristic
15C4×D4×C31C2211yescharacteristic
16#11758515C2212yes—
17#11758515C2212yes—
18#11758507—21no—
19#11758503—21no—
20#11758501—21no—
21C2×#92469C2212yes—
22#11758469C2212yes—
23C4⋊C4×D31C2212yes—
24#11758462—22no—
25#11758460—22no—
26C4×D124C2211yescharacteristic
27#11758446C2211yescharacteristic
28#11758446C2211yescharacteristic
29C31×#107C2211yescharacteristic
30C31×#102C2211yescharacteristic
31C31×#102C2211yescharacteristic
32C4×C8×C31C2211yescharacteristic
33#11758420C2212yes—
34#11758420C2212yes—
35(C2×D31)⋊C8C2212yes—
36#11758405C2212yes—
37#11758405C2212yes—
38#11758396C2212yes—
39#11758395C2212yes—
40C4⋊(C31⋊C8)C2211yescharacteristic
41C2×D4×C31C2311yescharacteristic
42C2×D4×C31C2311yescharacteristic
43C22×C4×C31—21no—
44C22×C4×C31—21no—
45C2×C22⋊D31—22no—
46C2×C22⋊D31—22no—
47#92495—44no—
48C2×D124D411yescharacteristic
49C2×C4×D31—22no—
50C2×C4×D31C2312yes—
51C2×Dic62—21no—
52C2×Dic62—21no—
53D8×C31—22no—
54C2×C8×C31C2311yescharacteristic
55C2×C8×C31C2311yescharacteristic
56C4⋊C4×C31C2311yescharacteristic
57C4⋊C4×C31C2311yescharacteristic
58C22⋊C4×C31—21no—
59C22⋊C4×C31—21no—
60C42×C31C2311yescharacteristic
61C22⋊Dic31—22no—
62C22⋊Dic31—22no—
63(C2×D31)⋊C4—22no—
64(C2×D31)⋊C4D412yes—
65C4⋊Dic31—21no—
66C4⋊Dic31—21no—
67C4⋊Dic31D411yescharacteristic
68C4⋊Dic31C2312yes—
69C4⋊Dic31C2312yes—
70Dic31⋊C4—22no—
71C4×Dic31—22no—
72C2×C31⋊C8C2312yes—
73#92469—24no—
74C23×C31—21no—
75C23×C31—21no—
76C22×D31C2×D412yes—
77D4×C31—21no—
78D4×C31—21no—
79D4×C31—21no—
80D4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—42no—
84C2×C4×C31—42no—
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31C2411yescharacteristic
88C22⋊D31—44no—
89C22⋊D31—82no—
90C2×Dic31—22no—
91C2×Dic31—22no—
92C2×Dic31C2×D412yes—
93D124—22no—
94C4×D31—22no—
95C4×D31—22no—
96C4×D31—44no—
97Dic62—42no—
98Dic62—81no—
99C8×C31—21no—
100C8×C31#4112yescomplemented
101C31⋊C8—22no—
102#3354—311nomaximal, Sylow
103C22×C31—41no—
104C22×C31—41no—
105C22×C31—41no—
106C22×C31—41no—
107C22×C31—41no—
108C22×C31—41no—
109C22×C31C22×D411yescharacteristic
110C2×D31—22no—
111C2×D31—22no—
112C2×D31—22no—
113C4×C31—21no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31AGL(1,ℤ/8)12yes—
117C4×C31C2×#4111yescharacteristic
118C4×C312−1+411yescharacteristic
119Dic31—22no—
120Dic31—42no—
121Dic31—42no—
122#555—311no—
123#547—311no—
124#498—311no—
125#482—312no—
126#481—312no—
127#476—311no—
128#474—311no—
129#469—312no—
130C4×D8D3111yescharacteristic, complemented
131#436—311no—
132#428—312no—
133C2×C31—81no—
134C2×C31—81no—
135C2×C31#54711yescharacteristic
136C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C31#57711yescharacteristic
138D31—42no—
139C2×#41—621no—
140C2×D8C2×D3111yescharacteristic
141C2×M16—312no—
142C4⋊Q8—311no—
143C4⋊Q8—311no—
144#124—622no—
145#123—622no—
146C22⋊Q8—621no—
147#121—312no—
148#121—312no—
149#121—621no—
150C4×D4—311no—
151C4×D4C2×D3111yescharacteristic
152C4×D4C2×D3111yescharacteristic
153#117—312no—
154#117—621no—
155C2×C4⋊C4—312no—
156#107—312no—
157#107C2×D3111yescharacteristic
158#106—312no—
159#106—312no—
160#106—312no—
161C4⋊C8—311no—
162#102—312no—
163#102—312no—
164#102C2×D3111yescharacteristic
165#102C2×D3111yescharacteristic
166C22⋊C8—312no—
167C4×C8C2×D3111yescharacteristic
168C31#335411yescharacteristic, complemented, Sylow
169#41—1244no—
170C2×Q8—621no—
171C2×Q8—621no—
172C2×D4—311no—
173C2×D4—622no—
174C2×D4—622no—
175C2×D4C22×D3111yescharacteristic
176C2×D4C22×D3111yescharacteristic
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—312no—
180C22×C4—622no—
181D8—22no—
182M16—624no—
183C2×C8—312no—
184C2×C8C22×D3111yescharacteristic
185C2×C8C22×D3111yescharacteristic
186C4⋊C4—311no—
187C4⋊C4—312no—
188C4⋊C4—312no—
189C4⋊C4—622no—
190C4⋊C4—621no—
191C4⋊C4—621no—
192C4⋊C4C22×D3111yescharacteristic
193C4⋊C4C22×D3111yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—312no—
197C22⋊C4—622no—
198C22⋊C4—622no—
199C22⋊C4—622no—
200C42—622no—
201C42C22×D3111yescharacteristic
202C23—21no—
203C23—21no—
204C23—312no—
205Q8—1242no—
206Q8—2481no—
207D4—21no—
208D4—21no—
209D4—21no—
210D4—21no—
211D4—622no—
212D4—1244no—
213D4—2482no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—312no—
219C2×C4—622no—
220C2×C4—622no—
221C2×C4—622no—
222C2×C4—622no—
223C2×C4—1244no—
224C2×C4D4×D3111yescharacteristic
225C2×C4D4×D3111yescharacteristic
226C2×C4C23×D3111yescharacteristic
227C8—21no—
228C8—622no—
229C8#9249512yescomplemented
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—622no—
237C22—622no—
238C22—622no—
239C22C2×D4×D3111yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—622no—
244C4—1242no—
245C4—1242no—
246C4#1175848812yes—
247C4C2×#9249511yescharacteristic
248C4#1175856711yescharacteristic
249C2—81no—
250C2—81no—
251C2—1242no—
252C2#1452170411yescharacteristic
253C2C2×#1175848811yescharacteristic
254C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
hypercenterC4×D8D31
hypocenterC31#3354
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14521764C2semidirect
2. #14521704C2semidirect
3. #14521447C2semidirect
4. #14521372C2semidirect
5. #14521366C2semidirect
6. #14521339C2semidirect
7. #14521329C2semidirect
8. #14521299C2semidirect
9. #14521128C2semidirect
10. #14521090C2semidirect
11. C4×D8×C31C2semidirect
100. C8×C31#41semidirect
130. C4×D8D31semidirect
168. C31#3354semidirect
229. C8#92495semidirect

Maximal subgroups

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

subgroupindex
#145217642
#145217042
#145214472
#145213722
#145213662
#145213392
#145213292
#145212992
#145211282
#145210902
C4×D8×C312
#335431