Finite Group Databasebeta

← D8×C22⋊D149 #34056362

Subgroups — D8×C22⋊D149 #34056362

Order 19072.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D8×D149C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C212yesmaximal, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749861C211yesmaximal, characteristic, complemented
5#23749858C211yesmaximal, characteristic, complemented
6#23749818C212yesmaximal, complemented
7#23749759C212yesmaximal, complemented
8#23749757C212yesmaximal, complemented
9D8×Dic149C211yesmaximal, characteristic, complemented
10C8×C22⋊D149C211yesmaximal, characteristic, complemented
11C22×D8×C149C211yesmaximal, characteristic, complemented
12C22×C22⋊D149—22no—
13C2×D4×D149C2212yescomplemented
14C2×D1192C2211yescharacteristic, complemented
15C2×#14558721C2212yescomplemented
16C2×#14558721C2212yescomplemented
17D8×D149—24no—
18C2×C8×D149C2211yescharacteristic, complemented
19#18011907C2212yescomplemented
20#18011885C2212yescomplemented
21#18011883—22no—
22#18011882C2212yescomplemented
23#18011880—22no—
24#18011879—22no—
25D4×Dic149C2212yescomplemented
26C4×C22⋊D149C2211yescharacteristic
27#18011845C2211yescharacteristic, complemented
28#18011840C2211yescharacteristic, complemented
29#18011833C2212yescomplemented
30#18011832C2212yescomplemented
31#18011832C2212yescomplemented
32C22⋊#11924746C2211yescharacteristic, complemented
33#18011823C2211yescharacteristic, complemented
34C8×Dic149C2211yescharacteristic, complemented
35C22×D4×C149C2212yescomplemented
36C2×D8×C149—24no—
37C2×D8×C149C2211yescharacteristic
38C2×D8×C149C2211yescharacteristic, complemented
39C2×D8×C149C2212yescomplemented
40C22×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C2×D596C2312yes—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45C2×C22⋊D149—22no—
46C2×C22⋊D149—22no—
47C2×C22⋊D149—22no—
48C2×C22⋊D149—48no—
49C2×C22⋊D149D411yescharacteristic
50D4×D149—24no—
51D4×D149—42no—
52C22×Dic149—22no—
53C2×C4×D149C2311yescharacteristic
54D1192—22no—
55#14558721—24no—
56#14558721—42no—
57C2×#11924746C2311yescharacteristic
58C2×#11924746C2311yescharacteristic
59C8×D149—22no—
60C4⋊Dic149C2312yes—
61#14558715D411yescharacteristic
62C22⋊Dic149—22no—
63C22⋊Dic149—22no—
64C22⋊Dic149D411yescharacteristic
65#14558713—22no—
66#14558713D411yescharacteristic
67C4×Dic149C2311yescharacteristic
68C24×C149—22no—
69C2×D4×C149—24no—
70C2×D4×C149—22no—
71C2×D4×C149—42no—
72C2×D4×C149C2312yes—
73C2×D4×C149C2312yes—
74C22×C4×C149C2311yescharacteristic
75D8×C149—24no—
76D8×C149—22no—
77D8×C149D414yescomplemented
78C2×C8×C149—22no—
79C2×C8×C149C2311yescharacteristic
80C2×C8×C149C2311yescharacteristic
81C22×D149—22no—
82C22×D149—44no—
83C22×D149—44no—
84C22×D149—82no—
85C22×D149C2×D411yescharacteristic
86D596—22no—
87D596—22no—
88C22⋊D149—44no—
89C22⋊D149—44no—
90C22⋊D149—44no—
91C22⋊D149—44no—
92C22⋊D149—82no—
93C22⋊D149D814yesdirect product factor
94C2×Dic149—22no—
95C2×Dic149—44no—
96C2×Dic149C2×D411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C2×Dic149C2×D411yescharacteristic
99C4×D149—21no—
100C4×D149—21no—
101#11924746—21no—
102#11924746—21no—
103C23×C149—22no—
104C23×C149—22no—
105C23×C149—44no—
106C23×C149—44no—
107C23×C149—82no—
108C23×C149C2×D411yescharacteristic
109D4×C149—22no—
110D4×C149—22no—
111D4×C149—22no—
112D4×C149—44no—
113D4×C149C2×D414yescomplemented
114C2×C4×C149—21no—
115C2×C4×C149—21no—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—21no—
119C8×C149C2×D412yescomplemented
120C22×C149—21no—
121C22×C149—21no—
122C22×C149—24no—
123C22×C149—42no—
124C22×C149—42no—
125C22×C149—42no—
126C22×C149—42no—
127C22×C149—42no—
128C22×C149—88no—
129C22×C149C2×D812yescomplemented
130C22×C149C22×D411yescharacteristic
131C2×D149—21no—
132C2×D149—21no—
133C2×D149—42no—
134C2×D149—42no—
135C2×D149—42no—
136C2×D149—88no—
137C2×D149C2×D812yescomplemented
138C4×C149—21no—
139C4×C149C22×D411yescharacteristic
140C4×C149H(5,𝔽2)11yescharacteristic
141Dic149—21no—
142Dic149—21no—
143Dic149—42no—
144Dic149C2×D812yescomplemented
145C2×C149—22no—
146C2×C149—44no—
147C2×C149—82no—
148C2×C149D4211yescharacteristic
149C2×C149C22×D811yescharacteristic
150C2×C149#57611yescharacteristic
151D149—22no—
152D149—82no—
153C149D4×D811yescharacteristic, complemented, Sylow
154D4×D8—1491nomaximal, Sylow
155C22×D8—1491no—
156C22×D8D14911yescharacteristic, complemented
157D42—1492no—
158#493—1491no—
159#466—1491no—
160#466—1491no—
161#459—1492no—
162#447—1492no—
163#447—1492no—
164C4×D8—1491no—
165C8×D4—1491no—
166C22×D4—2982no—
167C22×D4—1492no—
168C22×D4C2×D14912yescomplemented
169C2×D8—24no—
170C2×D8—2984no—
171C2×D8—1492no—
172C2×D8—1492no—
173C2×D8—1491no—
174C2×D8C2×D14911yescharacteristic
175C2×D8C2×D14912yescomplemented
176C2×D8C2×D14911yescharacteristic, complemented
177C22×C8—1491no—
178C22×C8C2×D14911yescharacteristic, complemented
179#127—1492no—
180#121—2982no—
181#121—1492no—
182#121—1492no—
183#120—2982no—
184#120—2982no—
185C4×D4—1492no—
186C4×D4—1491no—
187#107—1491no—
188C4⋊C8—1491no—
189#102—1492no—
190#102—1492no—
191#102—1492no—
192C22⋊C8—1491no—
193C22⋊C8—1491no—
194C4×C8—1491no—
195C24—22no—
196C24—2982no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—2984no—
201C2×D4—2982no—
202C2×D4—2982no—
203C2×D4—2982no—
204C2×D4—2982no—
205C2×D4—2982no—
206C2×D4—5962no—
207C2×D4—5968no—
208C2×D4—1491no—
209C2×D4—1492no—
210C2×D4C22×D14912yes—
211C2×D4C22×D14912yes—
212C22×C4—2982no—
213C22×C4—1491no—
214C22×C4C22×D14911yescharacteristic
215D8—24no—
216D8—22no—
217D8—2984no—
218D8—2982no—
219D8—5962no—
220D8C22⋊D14914yesdirect product factor
221C2×C8—22no—
222C2×C8—2982no—
223C2×C8—1491no—
224C2×C8—1491no—
225C2×C8C22×D14911yescharacteristic
226C2×C8C22×D14911yescharacteristic
227C4⋊C4—1492no—
228C4⋊C4—1491no—
229C22⋊C4—2982no—
230C22⋊C4—2982no—
231C22⋊C4—2982no—
232C22⋊C4—1491no—
233C22⋊C4—1491no—
234C42—1491no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—2982no—
241C23—5964no—
242C23—5964no—
243C23—1491no—
244C23—11922no—
245C23D4×D14911yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—2982no—
251D4—2982no—
252D4—5964no—
253D4—5964no—
254D4—5964no—
255D4—5964no—
256D4—1494no—
257D4—11922no—
258D4C2×C22⋊D14914yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—2981no—
262C2×C4—2981no—
263C2×C4—2982no—
264C2×C4—5964no—
265C2×C4—1491no—
266C2×C4—1491no—
267C2×C4—1491no—
268C2×C4D4×D14911yescharacteristic
269C2×C4C23×D14911yescharacteristic
270C8—21no—
271C8—2981no—
272C8—2981no—
273C8C2×C22⋊D14912yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—2981no—
284C22—2981no—
285C22—5962no—
286C22—5962no—
287C22—5962no—
288C22—1492no—
289C22—11928no—
290C22D8×D14912yescomplemented
291C22C2×D4×D14911yescharacteristic
292C4—21no—
293C4—2981no—
294C4—2981no—
295C4—5962no—
296C4—1492no—
297C4C22×C22⋊D14911yescharacteristic
298C4#1801195611yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—2982no—
303C2—11922no—
304C2D4×C22⋊D14911yescharacteristic
305C2C2×D8×D14911yescharacteristic
306C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×D8×C149C2
socleC22×C149C22×D4
hypercenterC22×D8D149
hypocenterC149D4×D8
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D149C2semidirect
2. D4×C22⋊D149C2semidirect
3. #23750000C2semidirect
4. #23749861C2semidirect
5. #23749858C2semidirect
6. #23749818C2semidirect
7. #23749759C2semidirect
8. #23749757C2semidirect
9. D8×Dic149C2semidirect
10. C8×C22⋊D149C2semidirect
11. C22×D8×C149C2semidirect
13. C2×D4×D149C22semidirect
14. C2×D1192C22semidirect
15. C2×#14558721C22semidirect
16. C2×#14558721C22semidirect
18. C2×C8×D149C22semidirect
19. #18011907C22semidirect
20. #18011885C22semidirect
22. #18011882C22semidirect
25. D4×Dic149C22semidirect
27. #18011845C22semidirect
28. #18011840C22semidirect
29. #18011833C22semidirect
30. #18011832C22semidirect
31. #18011832C22semidirect
32. C22⋊#11924746C22semidirect
33. #18011823C22semidirect
34. C8×Dic149C22semidirect
35. C22×D4×C149C22semidirect
38. C2×D8×C149C22semidirect
39. C2×D8×C149C22semidirect
40. C22×C8×C149C22semidirect
77. D8×C149D4semidirect
93. C22⋊D149D8direct (N × H)
113. D4×C149C2×D4semidirect
119. C8×C149C2×D4semidirect
129. C22×C149C2×D8semidirect
137. C2×D149C2×D8semidirect
144. Dic149C2×D8semidirect
153. C149D4×D8semidirect
156. C22×D8D149semidirect
168. C22×D4C2×D149semidirect
175. C2×D8C2×D149semidirect
176. C2×D8C2×D149semidirect
178. C22×C8C2×D149semidirect
220. D8C22⋊D149direct (N × H)
258. D4C2×C22⋊D149semidirect
273. C8C2×C22⋊D149semidirect
290. C22D8×D149semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1492
D4×C22⋊D1492
#237500002
#237498612
#237498582
#237498182
#237497592
#237497572
D8×Dic1492
C8×C22⋊D1492
C22×D8×C1492
D4×D8149