Finite Group Databasebeta

← #16855447

Subgroups — #16855447

Order 3968.

446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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#14521849C211yesmaximal, characteristic
2C2×#11758519C211yesmaximal, characteristic, complemented
3C2×#11758519C211yesmaximal, characteristic, complemented
4#14521815C211yesmaximal, characteristic, complemented
5#14521323C214yesmaximal, complemented
6#14521315C214yesmaximal, complemented
7#14521097C211yesmaximal, characteristic, complemented
8#14521031C211yesmaximal, characteristic, complemented
9C2×C31×#101C211yesmaximal, characteristic, complemented
10C22×Q8×C31C2211yescharacteristic
11C2×#92495C2211yescharacteristic
12C2×#92495C2211yescharacteristic
13C2×M16×C31C2211yescharacteristic
14C2×M16×C31C2211yescharacteristic
15C2×#92482—21no—
16C2×#92482C2212yescomplemented
17#11758519—22no—
18#11758519—22no—
19#11758519—22no—
20#11758519C2214yes—
21C2×#92481—21no—
22C2×#92481C2212yescomplemented
23C2×#92474C2211yescharacteristic
24C2×#92474C2211yescharacteristic
25#11758486—21no—
26#11758486C2212yes—
27#11758485—21no—
28#11758485C2212yes—
29#11758484C2214yes—
30M16×D31—22no—
31#11758481—22no—
32#11758478—22no—
33C31×#101C2214yescomplemented
34#11758412C2212yescomplemented
35#11758411C2212yescomplemented
36#11758410C2214yescomplemented
37C2×Q8×C31—21no—
38C2×Q8×C31—21no—
39C2×Q8×C31—21no—
40C2×Q8×C31—21no—
41C2×Q8×C31—21no—
42C2×Q8×C31C2312yes—
43C22×C4×C31—21no—
44C22×C4×C31C2311yescharacteristic
45C2×C22⋊D31—21no—
46C2×C22⋊D31—21no—
47#92495—21no—
48#92495—21no—
49#92495—21no—
50#92495—21no—
51#92495—21no—
52#92495—21no—
53#92495D412yes—
54#92495C2312yes—
55C2×D124D411yescharacteristic
56C2×D124C2311yescharacteristic
57C2×C4×D31—21no—
58C2×C4×D31—21no—
59C2×Dic62D411yescharacteristic
60C2×Dic62C2311yescharacteristic
61M16×C31—21no—
62M16×C31—21no—
63M16×C31C2312yes—
64M16×C31C2312yes—
65C2×C8×C31—21no—
66C2×C8×C31—21no—
67#92482—24no—
68#92482—24no—
69#92481—24no—
70#92481—24no—
71#92474—21no—
72#92474D412yes—
73#92474D412yes—
74#92474C2312yes—
75C2×C31⋊C8—21no—
76C2×C31⋊C8C2312yes—
77Dic124—22no—
78D248—22no—
79#92470—22no—
80#92470—22no—
81#92469—24no—
82C8×D31—24no—
83C23×C31#4111yescharacteristic
84C22×D31—21no—
85C22×D31—21no—
86Q8×C31—22no—
87Q8×C31—22no—
88Q8×C31—41no—
89Q8×C31—41no—
90C2×C4×C31—22no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2×D411yescharacteristic
97C2×C4×C31#4111yescharacteristic
98C2×C4×C31C2411yescharacteristic
99C22⋊D31—22no—
100C22⋊D31—22no—
101C22⋊D31—41no—
102C22⋊D31—41no—
103C2×Dic31—21no—
104C2×Dic31—21no—
105D124—21no—
106D124—21no—
107D124—21no—
108D124C2×D412yes—
109C4×D31—22no—
110C4×D31—22no—
111C4×D31—41no—
112C4×D31—41no—
113Dic62—21no—
114Dic62—21no—
115Dic62—21no—
116Dic62C2×D412yes—
117C8×C31—22no—
118C8×C31—22no—
119C31⋊C8—22no—
120C31⋊C8C2×D414yes—
121#3069—311nomaximal, Sylow
122C22×C31—41no—
123C22×C31#12111yescharacteristic
124C22×C31#12111yescharacteristic
125C22×C31C2×#4111yescharacteristic
126C2×D31—22no—
127C2×D31—41no—
128C2×D31—81no—
129C2×D31—81no—
130C4×C31—42no—
131C4×C31#12111yescharacteristic
132C4×C31#12111yescharacteristic
133C4×C31C22×D411yescharacteristic
134C4×C31C22×D411yescharacteristic
135Dic31—22no—
136Dic31—41no—
137#575—311no—
138C2×#137—311no—
139C2×#137—311no—
140#568—311no—
141#473—314no—
142#471—314no—
143#430—311no—
144#413—311no—
145C2×#101D3111yescharacteristic, complemented
146C2×C31—21no—
147C2×C31—21no—
148C2×C31—21no—
149C2×C31C2×#12111yescharacteristic
150D31—42no—
151D31—81no—
152C2×#41—311no—
153C2×#41—311no—
154C22×Q8C2×D3111yescharacteristic
155#137—314no—
156#137—312no—
157#137—621no—
158#137—622no—
159#137—622no—
160#137—622no—
161AGL(1,ℤ/8)—312no—
162AGL(1,ℤ/8)—621no—
163#135—622no—
164C2×Q16—312no—
165C2×Q16—621no—
166C2×SD16—312no—
167C2×SD16—621no—
168#131—314no—
169#131—622no—
170C2×M16—311no—
171C2×M16—311no—
172C2×M16—622no—
173C2×M16C2×D3111yescharacteristic
174C2×M16C2×D3111yescharacteristic
175#108—314no—
176#101—312no—
177#101C2×D3114yescomplemented
178#100—312no—
179C31#306911yescharacteristic, complemented, Sylow
180#41—312no—
181#41—312no—
182#41—621no—
183#41—621no—
184#41—621no—
185#41—621no—
186#41—621no—
187#41—621no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—311no—
194C2×Q8—311no—
195C2×Q8C22×D3112yes—
196C2×D4—311no—
197C2×D4—311no—
198C2×D4—621no—
199C2×D4—621no—
200C22×C4—21no—
201C22×C4—621no—
202C22×C4—621no—
203C22×C4C22×D3111yescharacteristic
204Q16—622no—
205Q16—624no—
206Q16—624no—
207SD16—622no—
208SD16—622no—
209SD16—624no—
210SD16—624no—
211D8—622no—
212M16—21no—
213M16—21no—
214M16—312no—
215M16—312no—
216M16—312no—
217M16—624no—
218M16—621no—
219M16C22×D3112yes—
220M16C22×D3112yes—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—312no—
224C2×C8—624no—
225C2×C8—621no—
226C23—621no—
227C23—621no—
228C23#9249511yescharacteristic
229Q8—22no—
230Q8—22no—
231Q8—41no—
232Q8—41no—
233Q8—312no—
234Q8—621no—
235Q8—621no—
236Q8—621no—
237D4—312no—
238D4—622no—
239D4—622no—
240D4—621no—
241D4—621no—
242D4—621no—
243D4—1241no—
244D4—1241no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—621no—
249C2×C4—622no—
250C2×C4—622no—
251C2×C4—621no—
252C2×C4—1241no—
253C2×C4—1241no—
254C2×C4#9249511yescharacteristic
255C2×C4D4×D3111yescharacteristic
256C2×C4D4×D3111yescharacteristic
257C2×C4D4×D3111yescharacteristic
258C2×C4D4×D3111yescharacteristic
259C2×C4C23×D3111yescharacteristic
260C8—22no—
261C8—22no—
262C8—314no—
263C8—622no—
264C22—41no—
265C22—622no—
266C22—1241no—
267C22—2481no—
268C22—2481no—
269C22#1175846111yescharacteristic
270C22#1175846111yescharacteristic
271C22C2×#9249511yescharacteristic
272C4—42no—
273C4—622no—
274C4—1241no—
275C4#1175846111yescharacteristic
276C4#1175846111yescharacteristic
277C4C2×D4×D3111yescharacteristic
278C4C2×D4×D3111yescharacteristic
279C2—21no—
280C2—21no—
281C2—21no—
282C2—1242no—
283C2—2481no—
284C2C2×#1175846111yescharacteristic
subgroupG/H
centerC2C2×#11758461
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#101C2
socleC2×C31C2×#121
prime radical#14521849C2
hypercenterC2×#101D31
hypocenterC31#3069
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#11758519C2semidirect
3. C2×#11758519C2semidirect
4. #14521815C2semidirect
5. #14521323C2semidirect
6. #14521315C2semidirect
7. #14521097C2semidirect
8. #14521031C2semidirect
9. C2×C31×#101C2semidirect
16. C2×#92482C22semidirect
22. C2×#92481C22semidirect
33. C31×#101C22semidirect
34. #11758412C22semidirect
35. #11758411C22semidirect
36. #11758410C22semidirect
145. C2×#101D31semidirect
177. #101C2×D31semidirect
179. C31#3069semidirect

Maximal subgroups

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

subgroupindex
#145218492
C2×#117585192
#145218152
#145213232
#145213152
#145210972
#145210312
C2×C31×#1012
#306931