Finite Group Databasebeta

← C2×#14521181 #16854885

Subgroups — C2×#14521181 #16854885

Order 3968.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×D4×D31C211yesmaximal, characteristic, complemented
2C22×#92479C211yesmaximal, characteristic, complemented
3C2×#11758515C211yesmaximal, characteristic, complemented
4#14521181C218yesmaximal, direct product factor
5C2×#11758409C211yesmaximal, characteristic, complemented
6C2×#11758420C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C31C211yesmaximal, characteristic, complemented
9C24×D31—21no—
10C22×D4×C31C2211yescharacteristic
11C22×D4×C31C2211yescharacteristic, complemented
12C22×C22⋊D31—21no—
13C22×C22⋊D31—21no—
14C2×D4×D31—24no—
15C2×D4×D31—24no—
16C2×D4×D31—22no—
17C2×D4×D31C2214yescomplemented
18C22×D124C2211yescharacteristic
19C22×C4×D31C2211yescharacteristic
20C2×D8×C31—24no—
21C2×D8×C31C2214yescomplemented
22C22×C8×C31C2211yescharacteristic, complemented
23C2×C22⋊Dic31—21no—
24#11758515—22no—
25#11758515C2214yescomplemented
26C2×#92479—24no—
27C2×#92479C2214yescomplemented
28C2×C4⋊Dic31C2211yescharacteristic, complemented
29C22×C31⋊C8C2211yescharacteristic, complemented
30#11758420C2214yescomplemented
31#11758409C2214yescomplemented
32(C2×D31)⋊C8C2214yescomplemented
33C24×C31—21no—
34C24×C31—21no—
35C23×D31—28no—
36C23×D31—21no—
37C23×D31—24no—
38C23×D31—44no—
39C23×D31—44no—
40C23×D31D411yescharacteristic
41C2×D4×C31—21no—
42C2×D4×C31—22no—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—21no—
46C2×D4×C31D414yescomplemented
47C2×D4×C31C2312yes—
48C2×D4×C31C2312yescomplemented
49C22×C4×C31C2311yescharacteristic
50C2×C22⋊D31—28no—
51C2×C22⋊D31—24no—
52C2×C22⋊D31—24no—
53C2×C22⋊D31—44no—
54C22×Dic31—21no—
55C22×Dic31D411yescharacteristic
56D4×D31—216no—
57D4×D31—28no—
58D4×D31—28no—
59C2×D124—21no—
60C2×D124—22no—
61C2×D124D414yescomplemented
62C2×D124C2312yes—
63C2×C4×D31—22no—
64C2×C4×D31—22no—
65C2×C4×D31D412yes—
66C2×C4×D31C2312yes—
67D8×C31—28no—
68C2×C8×C31—22no—
69C2×C8×C31C2312yescomplemented
70C22⋊Dic31—24no—
71#92479—28no—
72C4⋊Dic31—21no—
73C4⋊Dic31C2312yescomplemented
74C2×C31⋊C8—22no—
75C2×C31⋊C8C2312yescomplemented
76C23×C31—24no—
77C23×C31—22no—
78C23×C31—22no—
79C23×C31—42no—
80C23×C31—42no—
81C23×C31—42no—
82C23×C31—42no—
83C23×C31—42no—
84C23×C31C2×D411yescharacteristic
85C22×D31—22no—
86C22×D31—22no—
87C22×D31—216no—
88C22×D31—24no—
89C22×D31—22no—
90C22×D31—48no—
91C22×D31—432no—
92C22×D31—42no—
93C22×D31—42no—
94C22×D31—48no—
95C22×D31D814yescomplemented
96C22×D31C2×D412yes—
97D4×C31—24no—
98D4×C31—22no—
99D4×C31—22no—
100D4×C31—22no—
101D4×C31—42no—
102D4×C31C2×D414yescomplemented
103C2×C4×C31C2×D411yescharacteristic
104C2×C4×C31C2×D412yes—
105C2×C4×C31C2×D412yes—
106C2×C4×C31C2411yescharacteristic
107C22⋊D31—216no—
108C22⋊D31—48no—
109C2×Dic31—22no—
110C2×Dic31—22no—
111C2×Dic31—42no—
112C2×Dic31C2×D412yes—
113D124—24no—
114D124—22no—
115D124C2×D414yescomplemented
116C4×D31—24no—
117C4×D31—22no—
118C4×D31—22no—
119C8×C31—22no—
120C31⋊C8—22no—
121C2×#447—311nomaximal, Sylow
122C22×C31—24no—
123C22×C31—42no—
124C22×C31—42no—
125C22×C31—48no—
126C22×C31—42no—
127C22×C31—42no—
128C22×C31—42no—
129C22×C31—84no—
130C22×C31#12012yes—
131C22×C31C2×D812yes—
132C22×C31AGL(1,ℤ/8)12yes—
133C22×C31C22×D411yescharacteristic
134C2×D31—22no—
135C2×D31—22no—
136C2×D31—28no—
137C2×D31—24no—
138C2×D31—432no—
139C2×D31—42no—
140C2×D31—42no—
141C2×D31—48no—
142C2×D31C2×D814yescomplemented
143C4×C31#12012yes—
144C4×C31C22×D411yescharacteristic
145C4×C31C22×D411yescharacteristic
146Dic31—22no—
147Dic31—42no—
148C23×D4—311no—
149C22×D8—311no—
150C22×D8D3111yescharacteristic, complemented
151C2×#121—311no—
152#447—318no—
153C2×#102—311no—
154C2×#102—311no—
155C2×C22⋊C8—311no—
156C2×C31—44no—
157C2×C31—82no—
158C2×C31#44714yescomplemented
159C2×C31C2×#12011yescharacteristic
160C2×C31C22×D811yescharacteristic
161C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
162D31—24no—
163D31—44no—
164C25—621no—
165C22×D4—314no—
166C22×D4—311no—
167C22×D4—622no—
168C22×D4—621no—
169C22×D4—624no—
170C22×D4—624no—
171C22×D4—621no—
172C22×D4C2×D3111yescharacteristic
173C22×D4C2×D3111yescharacteristic, complemented
174C23×C4—311no—
175C2×D8—24no—
176C2×D8—314no—
177C2×D8—624no—
178C2×D8C2×D3114yescomplemented
179C22×C8—311no—
180C22×C8C2×D3111yescharacteristic, complemented
181#121—314no—
182#121—622no—
183C2×C4⋊C4—311no—
184C2×C22⋊C4—621no—
185#102—314no—
186#102—314no—
187C22⋊C8—314no—
188C31C2×#44711yescharacteristic, complemented, Sylow
189C24—21no—
190C24—21no—
191C24—311no—
192C24—624no—
193C24—628no—
194C24—621no—
195C24—1244no—
196C24—1244no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—314no—
203C2×D4—312no—
204C2×D4—624no—
205C2×D4—628no—
206C2×D4—6216no—
207C2×D4—628no—
208C2×D4—628no—
209C2×D4—624no—
210C2×D4—621no—
211C2×D4—622no—
212C2×D4—1244no—
213C2×D4C22⋊D3114yescomplemented
214C2×D4C22×D3112yes—
215C2×D4C22×D3112yescomplemented
216C22×C4—311no—
217C22×C4—312no—
218C22×C4—312no—
219C22×C4—622no—
220C22×C4—622no—
221C22×C4—621no—
222C22×C4C22×D3111yescharacteristic
223D8—28no—
224D8—628no—
225C2×C8—22no—
226C2×C8—312no—
227C2×C8—622no—
228C2×C8C22×D3112yescomplemented
229C4⋊C4—312no—
230C4⋊C4—621no—
231C22⋊C4—624no—
232C23—24no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—314no—
241C23—312no—
242C23—6216no—
243C23—622no—
244C23—622no—
245C23—624no—
246C23—622no—
247C23—1248no—
248C23—12432no—
249C23—1248no—
250C23—1242no—
251C23—1242no—
252C23D4×D3111yescharacteristic
253D4—24no—
254D4—22no—
255D4—22no—
256D4—22no—
257D4—42no—
258D4—314no—
259D4—6216no—
260D4—624no—
261D4—622no—
262D4—1248no—
263D4C2×C22⋊D3114yescomplemented
264C2×C4—312no—
265C2×C4—622no—
266C2×C4—624no—
267C2×C4—622no—
268C2×C4—622no—
269C2×C4—622no—
270C2×C4—1242no—
271C2×C4D4×D3111yescharacteristic
272C2×C4D4×D3112yes—
273C2×C4C2×C22⋊D3112yes—
274C2×C4C23×D3111yescharacteristic
275C8—22no—
276C8—622no—
277C22—24no—
278C22—48no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—314no—
286C22—628no—
287C22—622no—
288C22—622no—
289C22—624no—
290C22—12432no—
291C22—1248no—
292C22—1242no—
293C22—1242no—
294C22D8×D3112yes—
295C22#1175848812yes—
296C22#1175851412yes—
297C22C2×D4×D3111yescharacteristic
298C4—622no—
299C4—1242no—
300C4#1175851412yes—
301C4C2×D4×D3111yescharacteristic
302C4C22×C22⋊D3111yescharacteristic
303C2—44no—
304C2—82no—
305C2—624no—
306C2—1244no—
307C2#1452118114yesdirect product factor
308C2C2×#1175851411yescharacteristic
309C2C2×D8×D3111yescharacteristic
310C2C2×#1175848811yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×D8×C31C2
socleC23×C31C2×D4
hypercenterC22×D8D31
hypocenterC31C2×#447
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D31C2semidirect
2. C22×#92479C2semidirect
3. C2×#11758515C2semidirect
4. #14521181C2direct (N × H)
5. C2×#11758409C2semidirect
6. C2×#11758420C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C22×D8×C31C2semidirect
11. C22×D4×C31C22semidirect
17. C2×D4×D31C22semidirect
21. C2×D8×C31C22semidirect
22. C22×C8×C31C22semidirect
25. #11758515C22semidirect
27. C2×#92479C22semidirect
28. C2×C4⋊Dic31C22semidirect
29. C22×C31⋊C8C22semidirect
30. #11758420C22semidirect
31. #11758409C22semidirect
32. (C2×D31)⋊C8C22semidirect
46. C2×D4×C31D4semidirect
48. C2×D4×C31C23semidirect
61. C2×D124D4semidirect
69. C2×C8×C31C23semidirect
73. C4⋊Dic31C23semidirect
75. C2×C31⋊C8C23semidirect
95. C22×D31D8semidirect
102. D4×C31C2×D4semidirect
115. D124C2×D4semidirect
142. C2×D31C2×D8semidirect
150. C22×D8D31semidirect
158. C2×C31#447semidirect
173. C22×D4C2×D31semidirect
178. C2×D8C2×D31semidirect
180. C22×C8C2×D31semidirect
188. C31C2×#447semidirect
213. C2×D4C22⋊D31semidirect
215. C2×D4C22×D31semidirect
228. C2×C8C22×D31semidirect
263. D4C2×C22⋊D31semidirect
307. C2#14521181direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D312
C22×#924792
C2×#117585152
#145211812
C2×#117584092
C2×#117584202
C2×(C2×D31)⋊C82
C22×D8×C312
C2×#44731