Finite Group Databasebeta

← C2×#14521235 #16855094

Subgroups — C2×#14521235 #16855094

Order 3968.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758561C211yesmaximal, characteristic, complemented
2C2×#11758530C212yesmaximal, complemented
3#14521235C218yesmaximal, direct product factor
4C2×#11758422C211yesmaximal, characteristic, complemented
5C2×#11758394C212yesmaximal, complemented
6C2×C31×#120C211yesmaximal, characteristic, complemented
7C25×C31C2211yescharacteristic, complemented
8C22×D4×C31—21no—
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31—21no—
11C22×C22⋊D31—22no—
12C22×C22⋊D31C2212yes—
13#11758561—22no—
14#11758561—24no—
15#11758561C2214yescomplemented
16C2×#92497—22no—
17C2×D4×D31—22no—
18C2×#92495—21no—
19C31×#120—22no—
20C31×#120C2214yescomplemented
21C2×C22⋊C4×C31—21no—
22C2×C22⋊C4×C31C2211yescharacteristic, complemented
23#11758530—24no—
24#11758530C2218yescomplemented
25C2×C22⋊Dic31—22no—
26C2×C22⋊Dic31C2212yescomplemented
27#11758422C2214yescomplemented
28#11758394C2218yescomplemented
29C24×C31—22no—
30C24×C31—21no—
31C24×C31—22no—
32C24×C31—21no—
33C24×C31—44no—
34C24×C31D411yescharacteristic, complemented
35C24×C31C2311yescharacteristic
36C24×C31C2312yescomplemented
37C23×D31—21no—
38C23×D31D412yescomplemented
39C2×D4×C31—22no—
40C2×D4×C31—22no—
41C2×D4×C31—24no—
42C2×D4×C31—44no—
43C2×D4×C31D412yescomplemented
44C2×D4×C31C2312yes—
45C22×C4×C31—21no—
46C22×C4×C31D411yescharacteristic, complemented
47C2×C22⋊D31—22no—
48C2×C22⋊D31—24no—
49C2×C22⋊D31—22no—
50C2×C22⋊D31—22no—
51C2×C22⋊D31—22no—
52C2×C22⋊D31—22no—
53C2×C22⋊D31—24no—
54C2×C22⋊D31—28no—
55C2×C22⋊D31—48no—
56C2×C22⋊D31D414yescomplemented
57C2×C22⋊D31C2314yes—
58C22×Dic31—21no—
59C22×Dic31—22no—
60C22×Dic31D412yescomplemented
61#92497—28no—
62#92497—28no—
63D4×D31—28no—
64D4×D31—28no—
65#92495—24no—
66#92495—24no—
67C2×D124—21no—
68C2×C4×D31—22no—
69C2×Dic62—21no—
70C22⋊C4×C31—21no—
71C22⋊C4×C31—24no—
72C22⋊C4×C31C2312yescomplemented
73C22⋊Dic31—22no—
74C22⋊Dic31—28no—
75C22⋊Dic31C2314yescomplemented
76C23×C31—28no—
77C23×C31—24no—
78C23×C31—21no—
79C23×C31—24no—
80C23×C31—22no—
81C23×C31—21no—
82C23×C31—42no—
83C23×C31—44no—
84C23×C31—44no—
85C23×C31—42no—
86C23×C31—48no—
87C23×C31—44no—
88C23×C31—42no—
89C23×C31—42no—
90C23×C31—41no—
91C23×C31—41no—
92C23×C31C2×D412yes—
93C23×C31C2×D412yes—
94C23×C31C2×D411yescharacteristic
95C23×C31C2×D411yescharacteristic
96C23×C31C2×D412yescomplemented
97C23×C31C2411yescharacteristic
98C22×D31—22no—
99C22×D31—24no—
100C22×D31—22no—
101C22×D31—44no—
102C22×D31—82no—
103C22×D31C2×D414yescomplemented
104D4×C31—24no—
105D4×C31—24no—
106D4×C31—48no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—22no—
110C2×C4×C31—42no—
111C2×C4×C31C2×D412yescomplemented
112C22⋊D31—28no—
113C22⋊D31—24no—
114C22⋊D31—24no—
115C22⋊D31—24no—
116C22⋊D31—24no—
117C22⋊D31—416no—
118C2×Dic31—24no—
119C2×Dic31—22no—
120C2×Dic31—22no—
121C2×Dic31—24no—
122C2×Dic31—44no—
123C2×Dic31C2×D414yescomplemented
124D124—24no—
125C4×D31—28no—
126Dic62—24no—
127C2×B(4,𝔽2)—311nomaximal, Sylow
128C22×C31—24no—
129C22×C31—22no—
130C22×C31—28no—
131C22×C31—24no—
132C22×C31—22no—
133C22×C31—42no—
134C22×C31—41no—
135C22×C31—41no—
136C22×C31—42no—
137C22×C31—44no—
138C22×C31—42no—
139C22×C31—48no—
140C22×C31—44no—
141C22×C31—42no—
142C22×C31—42no—
143C22×C31—44no—
144C22×C31—81no—
145C22×C31#12012yes—
146C22×C31#12011yescharacteristic
147C22×C31#12011yescharacteristic
148C22×C31C22×D412yes—
149C22×C31C22×D411yescharacteristic
150C2×D31—24no—
151C2×D31—44no—
152C2×D31—44no—
153C2×D31—82no—
154C2×D31—84no—
155C4×C31—22no—
156C4×C31—42no—
157Dic31—24no—
158Dic31—44no—
159C2×H(5,𝔽2)—311no—
160C2×#120—312no—
161C2×#120D3111yescharacteristic, complemented
162B(4,𝔽2)—318no—
163C2×#99—311no—
164C2×#99—312no—
165C2×C31—22no—
166C2×C31—21no—
167C2×C31—22no—
168C2×C31—21no—
169C2×C31—42no—
170C2×C31—44no—
171C2×C31B(4,𝔽2)12yescomplemented
172C2×C31C2×#12011yescharacteristic
173D31—44no—
174C25C2×D3111yescharacteristic, complemented
175H(5,𝔽2)—314no—
176H(5,𝔽2)—624no—
177H(5,𝔽2)—622no—
178C2×#41—622no—
179C2×#41—621no—
180C22×D4—21no—
181C22×D4—312no—
182C22×D4—622no—
183C22×D4—621no—
184C22×D4—622no—
185C22×D4C2×D3111yescharacteristic
186#120—22no—
187#120—318no—
188#120—624no—
189#120C2×D3114yescomplemented
190C2×C22⋊C4—21no—
191C2×C22⋊C4—312no—
192C2×C22⋊C4—622no—
193C2×C22⋊C4C2×D3111yescharacteristic, complemented
194#99—314no—
195#99—318no—
196C31C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
197C24—22no—
198C24—21no—
199C24—22no—
200C24—21no—
201C24—44no—
202C24—312no—
203C24—621no—
204C24C22⋊D3111yescharacteristic, complemented
205C24C22×D3111yescharacteristic
206C24C22×D3112yescomplemented
207#41—624no—
208#41—628no—
209#41—628no—
210#41—624no—
211C2×Q8—621no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—24no—
215C2×D4—44no—
216C2×D4—314no—
217C2×D4—314no—
218C2×D4—621no—
219C2×D4—628no—
220C2×D4—628no—
221C2×D4—622no—
222C2×D4—624no—
223C2×D4—622no—
224C2×D4—622no—
225C2×D4—622no—
226C2×D4—622no—
227C2×D4—624no—
228C2×D4—628no—
229C2×D4—1248no—
230C2×D4C22⋊D3112yescomplemented
231C2×D4C22×D3112yes—
232C22×C4—21no—
233C22×C4—312no—
234C22×C4—622no—
235C22×C4—621no—
236C22×C4—622no—
237C22×C4C22⋊D3111yescharacteristic, complemented
238C22⋊C4—21no—
239C22⋊C4—24no—
240C22⋊C4—314no—
241C22⋊C4—628no—
242C22⋊C4—622no—
243C22⋊C4C22×D3112yescomplemented
244C23—24no—
245C23—28no—
246C23—21no—
247C23—24no—
248C23—22no—
249C23—21no—
250C23—42no—
251C23—44no—
252C23—42no—
253C23—44no—
254C23—44no—
255C23—48no—
256C23—42no—
257C23—41no—
258C23—42no—
259C23—41no—
260C23—314no—
261C23—624no—
262C23—622no—
263C23—622no—
264C23—1244no—
265C23—2482no—
266C23D4×D3112yes—
267C23D4×D3112yes—
268C23C2×C22⋊D3111yescharacteristic
269C23C2×C22⋊D3111yescharacteristic
270C23C2×C22⋊D3112yescomplemented
271C23C23×D3111yescharacteristic
272Q8—624no—
273D4—24no—
274D4—24no—
275D4—48no—
276D4—624no—
277D4—628no—
278D4—624no—
279D4—624no—
280D4—624no—
281D4—624no—
282D4—12416no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—314no—
288C2×C4—628no—
289C2×C4—624no—
290C2×C4—622no—
291C2×C4—622no—
292C2×C4—624no—
293C2×C4—1244no—
294C2×C4C2×C22⋊D3112yescomplemented
295C22—22no—
296C22—24no—
297C22—24no—
298C22—28no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—42no—
305C22—44no—
306C22—44no—
307C22—48no—
308C22—44no—
309C22—42no—
310C22—42no—
311C22—81no—
312C22—624no—
313C22—1244no—
314C22—1244no—
315C22—2482no—
316C22—2484no—
317C22#1175851411yescharacteristic
318C22#1175851412yes—
319C22#1175851411yescharacteristic
320C22C2×D4×D3112yes—
321C22C22×C22⋊D3111yescharacteristic
322C4—22no—
323C4—42no—
324C4—624no—
325C4—1244no—
326C2—21no—
327C2—22no—
328C2—21no—
329C2—22no—
330C2—44no—
331C2—42no—
332C2—1244no—
333C2#1452123512yesdirect product factor
334C2C2×#1175851411yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC2×C31×#120C2
socleC22×C31#120
hypercenterC2×#120D31
hypocenterC31C2×B(4,𝔽2)
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#11758561C2semidirect
2. C2×#11758530C2semidirect
3. #14521235C2direct (N × H)
4. C2×#11758422C2semidirect
5. C2×#11758394C2semidirect
6. C2×C31×#120C2semidirect
7. C25×C31C22semidirect
15. #11758561C22semidirect
20. C31×#120C22semidirect
22. C2×C22⋊C4×C31C22semidirect
24. #11758530C22semidirect
26. C2×C22⋊Dic31C22semidirect
27. #11758422C22semidirect
28. #11758394C22semidirect
34. C24×C31D4semidirect
36. C24×C31C23semidirect
38. C23×D31D4semidirect
43. C2×D4×C31D4semidirect
46. C22×C4×C31D4semidirect
56. C2×C22⋊D31D4semidirect
60. C22×Dic31D4semidirect
72. C22⋊C4×C31C23semidirect
75. C22⋊Dic31C23semidirect
96. C23×C31C2×D4semidirect
103. C22×D31C2×D4semidirect
111. C2×C4×C31C2×D4semidirect
123. C2×Dic31C2×D4semidirect
161. C2×#120D31semidirect
171. C2×C31B(4,𝔽2)semidirect
174. C25C2×D31semidirect
189. #120C2×D31semidirect
193. C2×C22⋊C4C2×D31semidirect
196. C31C2×B(4,𝔽2)semidirect
204. C24C22⋊D31semidirect
206. C24C22×D31semidirect
230. C2×D4C22⋊D31semidirect
237. C22×C4C22⋊D31semidirect
243. C22⋊C4C22×D31semidirect
270. C23C2×C22⋊D31semidirect
294. C2×C4C2×C22⋊D31semidirect
333. C2#14521235direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585612
C2×#117585302
#145212352
C2×#117584222
C2×#117583942
C2×C31×#1202
C2×B(4,𝔽2)31