Finite Group Databasebeta

← #16846739

Subgroups — #16846739

Order 3968.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#11758528C211yesmaximal, characteristic, complemented
2#14521613C211yesmaximal, characteristic
3C2×#11758452C211yesmaximal, characteristic, complemented
4#14521059C211yesmaximal, characteristic, complemented
5C2×#11758411C211yesmaximal, characteristic, complemented
6#14520809C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C22×D124C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13#11758528—22no—
14#11758528—22no—
15#11758524—21no—
16C2×#92482—21no—
17#11758517—21no—
18#11758514—22no—
19C2×#92480—21no—
20#11758507—22no—
21C2×(C2×D31)⋊C4—22no—
22#11758503C2211yescharacteristic
23C2×#92474C2211yescharacteristic
24#11758452—22no—
25#11758452—22no—
26C31×#104—22no—
27#11758411—22no—
28#11758404—22no—
29C23×D31D412yes—
30#41×C31—21no—
31#41×C31—21no—
32#41×C31—21no—
33#41×C31—21no—
34C2×Q8×C31D411yescharacteristic
35C2×D4×C31—21no—
36C2×D4×C31D411yescharacteristic
37C22×C4×C31—21no—
38C22×C4×C31—21no—
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—24no—
41C22×Dic31—21no—
42C2×D124—21no—
43C2×D124—21no—
44C2×D124—21no—
45C2×D124—21no—
46C2×D124—21no—
47C2×D124—21no—
48C2×Dic62—21no—
49C2×Dic62—21no—
50C2×Dic62—21no—
51C2×Dic62—21no—
52C2×Dic62—21no—
53C2×Dic62D412yescomplemented
54M16×C31—21no—
55M16×C31—21no—
56C2×C8×C31—21no—
57C42×C31—21no—
58C42×C31D412yescomplemented
59C22⋊Dic31—21no—
60#92482—24no—
61#92480—24no—
62(C2×D31)⋊C4—28no—
63(C2×D31)⋊C4—24no—
64C4⋊Dic31D412yes—
65C4×Dic31—21no—
66#92474—21no—
67#92474D412yescomplemented
68C2×C31⋊C8—21no—
69C23×C31—21no—
70C23×C31C2×D411yescharacteristic
71C22×D31—22no—
72C22×D31—22no—
73C22×D31—22no—
74C22×D31—44no—
75Q8×C31—21no—
76Q8×C31—21no—
77D4×C31—21no—
78D4×C31—21no—
79D4×C31—41no—
80D4×C31—41no—
81C2×C4×C31—22no—
82C2×C4×C31—21no—
83C2×C4×C31—42no—
84C2×C4×C31—41no—
85C2×C4×C31—41no—
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31C2×D411yescharacteristic
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31C2×D411yescharacteristic
91C2×C4×C31#4111yescharacteristic
92C22⋊D31—84no—
93C2×Dic31—22no—
94C2×Dic31—22no—
95C2×Dic31—41no—
96C2×Dic31—41no—
97D124—41no—
98D124—41no—
99D124—41no—
100D124—41no—
101Dic62—22no—
102Dic62—22no—
103Dic62—41no—
104Dic62—41no—
105C8×C31—41no—
106C31⋊C8—22no—
107#2004—311nomaximal, Sylow
108C22×C31—22no—
109C22×C31—41no—
110C22×C31—42no—
111C22×C31#12011yescharacteristic
112C22×C31#12011yescharacteristic
113C22×C31#12111yescharacteristic
114C2×D31—44no—
115C2×D31—42no—
116C2×D31—44no—
117C2×D31—82no—
118C4×C31—42no—
119C4×C31—41no—
120C4×C31#12011yescharacteristic
121C4×C31#12111yescharacteristic
122C4×C31#12111yescharacteristic
123C4×C31#12711yescharacteristic
124Dic31—42no—
125Dic31—42no—
126C2×#137—311no—
127#535—311no—
128C2×#124—311no—
129C2×#104D3111yescharacteristic, complemented
130#419—311no—
131C2×#100—311no—
132#339—311no—
133C2×C31—21no—
134C2×C31—21no—
135C2×C31—81no—
136C2×C31#39211yescharacteristic
137C2×C31#45512yes—
138D31—82no—
139C2×#41C2×D3111yescharacteristic
140C22×Q8—311no—
141C22×D4—311no—
142#137—622no—
143#137—622no—
144C2×Q16—621no—
145C2×SD16—621no—
146C2×M16—311no—
147C2×M16C2×D3111yescharacteristic
148#127—621no—
149#124—622no—
150#124—621no—
151#124—622no—
152#121—622no—
153#120—622no—
154#117—311no—
155C2×C22⋊C4—622no—
156C2×C42C2×D3111yescharacteristic
157#104—22no—
158#103—622no—
159#100—622no—
160C31#200411yescharacteristic, complemented, Sylow
161C24—312no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—312no—
167C2×Q8—621no—
168C2×Q8—621no—
169C2×Q8—621no—
170C2×Q8—621no—
171C2×Q8—621no—
172C2×Q8D12411yescharacteristic
173C2×D4—21no—
174C2×D4—624no—
175C2×D4—621no—
176C2×D4—621no—
177C2×D4—621no—
178C2×D4—621no—
179C2×D4—621no—
180C2×D4—621no—
181C2×D4D12411yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—621no—
185C22×C4C22×D3111yescharacteristic
186Q16—624no—
187SD16—624no—
188M16—21no—
189M16—21no—
190M16—312no—
191M16—621no—
192C2×C8—21no—
193C2×C8—621no—
194C4⋊C4—312no—
195C22⋊C4—628no—
196C22⋊C4—624no—
197C22⋊C4—621no—
198C42—21no—
199C42—621no—
200C42C22⋊D3112yescomplemented
201C23—21no—
202C23—622no—
203C23—622no—
204C23—622no—
205C23—1244no—
206C23D4×D3111yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—622no—
210Q8—622no—
211Q8—1241no—
212Q8—1241no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—1241no—
218D4—1241no—
219D4—1241no—
220D4—1241no—
221D4—2484no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—622no—
228C2×C4—622no—
229C2×C4—1241no—
230C2×C4—1241no—
231C2×C4C2×D12411yescharacteristic
232C2×C4#9249511yescharacteristic
233C2×C4D4×D3111yescharacteristic
234C2×C4D4×D3111yescharacteristic
235C2×C4D4×D3111yescharacteristic
236C2×C4C2×C22⋊D3111yescharacteristic
237C8—41no—
238C8—622no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—1244no—
243C22—1242no—
244C22—1244no—
245C22—2482no—
246C22#1175845911yescharacteristic
247C22#1175846111yescharacteristic
248C22#1175851411yescharacteristic
249C4—42no—
250C4—41no—
251C4—1242no—
252C4—1242no—
253C4#1175845911yescharacteristic
254C4#1175846111yescharacteristic
255C4#1175850711yescharacteristic
256C4#1175851711yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—2482no—
261C2#1452095811yescharacteristic
262C2#1452122812yes—
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31#120
prime radical#14521613C2
hypercenterC2×#104D31
hypocenterC31#2004
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#11758528C2semidirect
3. C2×#11758452C2semidirect
4. #14521059C2semidirect
5. C2×#11758411C2semidirect
6. #14520809C2semidirect
7. C2×C31×#104C2semidirect
53. C2×Dic62D4semidirect
58. C42×C31D4semidirect
67. #92474D4semidirect
129. C2×#104D31semidirect
160. C31#2004semidirect
200. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585282
#145216132
C2×#117584522
#145210592
C2×#117584112
#145208092
C2×C31×#1042
#200431