Finite Group Databasebeta

← D8×C22⋊D151 #34080781

Subgroups — D8×C22⋊D151 #34080781

Order 19328.

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×D151C211yesmaximal, characteristic, complemented
2D4×C22⋊D151C212yesmaximal, complemented
3#23752587C211yesmaximal, characteristic, complemented
4#23752448C211yesmaximal, characteristic, complemented
5#23752445C211yesmaximal, characteristic, complemented
6#23752405C212yesmaximal, complemented
7#23752346C212yesmaximal, complemented
8#23752344C212yesmaximal, complemented
9D8×Dic151C211yesmaximal, characteristic, complemented
10C8×C22⋊D151C211yesmaximal, characteristic, complemented
11C22×D8×C151C211yesmaximal, characteristic, complemented
12C22×C22⋊D151—22no—
13C2×D4×D151C2212yescomplemented
14C2×D1208C2211yescharacteristic, complemented
15C2×#14558989C2212yescomplemented
16C2×#14558989C2212yescomplemented
17D8×D151—24no—
18C2×C8×D151C2211yescharacteristic, complemented
19#18012735C2212yescomplemented
20#18012713C2212yescomplemented
21#18012711—22no—
22#18012710C2212yescomplemented
23#18012708—22no—
24#18012707—22no—
25D4×Dic151C2212yescomplemented
26C4×C22⋊D151C2211yescharacteristic
27#18012673C2211yescharacteristic, complemented
28Dic151⋊C8C2211yescharacteristic, complemented
29#18012661C2212yescomplemented
30#18012660C2212yescomplemented
31#18012660C2212yescomplemented
32C22⋊(C151⋊C8)C2211yescharacteristic, complemented
33(C2×D151)⋊C8C2211yescharacteristic, complemented
34C8×Dic151C2211yescharacteristic, complemented
35C22×D4×C151C2212yescomplemented
36C2×D8×C151—24no—
37C2×D8×C151C2211yescharacteristic
38C2×D8×C151C2211yescharacteristic, complemented
39C2×D8×C151C2212yescomplemented
40C22×C8×C151C2211yescharacteristic, complemented
41C23×D151—22no—
42C2×D604C2312yes—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—22no—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—48no—
49C2×C22⋊D151D411yescharacteristic
50D4×D151—24no—
51D4×D151—42no—
52C22×Dic151—22no—
53C2×C4×D151C2311yescharacteristic
54D1208—22no—
55#14558989—24no—
56#14558989—42no—
57C2×C151⋊C8C2311yescharacteristic
58C2×C151⋊C8C2311yescharacteristic
59C8×D151—22no—
60C4⋊Dic151C2312yes—
61Dic151⋊C4D411yescharacteristic
62C22⋊Dic151—22no—
63C22⋊Dic151—22no—
64C22⋊Dic151D411yescharacteristic
65(C2×D151)⋊C4—22no—
66(C2×D151)⋊C4D411yescharacteristic
67C4×Dic151C2311yescharacteristic
68C24×C151—22no—
69C2×D4×C151—24no—
70C2×D4×C151—22no—
71C2×D4×C151—42no—
72C2×D4×C151C2312yes—
73C2×D4×C151C2312yes—
74C22×C4×C151C2311yescharacteristic
75D8×C151—24no—
76D8×C151—22no—
77D8×C151D414yescomplemented
78C2×C8×C151—22no—
79C2×C8×C151C2311yescharacteristic
80C2×C8×C151C2311yescharacteristic
81C22×D151—22no—
82C22×D151—44no—
83C22×D151—44no—
84C22×D151—82no—
85C22×D151C2×D411yescharacteristic
86D604—22no—
87D604—22no—
88C22⋊D151—44no—
89C22⋊D151—44no—
90C22⋊D151—44no—
91C22⋊D151—44no—
92C22⋊D151—82no—
93C22⋊D151D814yesdirect product factor
94C2×Dic151—22no—
95C2×Dic151—44no—
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C2×Dic151C2×D411yescharacteristic
99C4×D151—21no—
100C4×D151—21no—
101C151⋊C8—21no—
102C151⋊C8—21no—
103C23×C151—22no—
104C23×C151—22no—
105C23×C151—44no—
106C23×C151—44no—
107C23×C151—82no—
108C23×C151C2×D411yescharacteristic
109D4×C151—22no—
110D4×C151—22no—
111D4×C151—22no—
112D4×C151—44no—
113D4×C151C2×D414yescomplemented
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—21no—
119C8×C151C2×D412yescomplemented
120C22×C151—21no—
121C22×C151—21no—
122C22×C151—24no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—88no—
129C22×C151C2×D812yescomplemented
130C22×C151C22×D411yescharacteristic
131C2×D151—21no—
132C2×D151—21no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—42no—
136C2×D151—88no—
137C2×D151C2×D812yescomplemented
138C4×C151—21no—
139C4×C151C22×D411yescharacteristic
140C4×C151H(5,𝔽2)11yescharacteristic
141Dic151—21no—
142Dic151—21no—
143Dic151—42no—
144Dic151C2×D812yescomplemented
145C2×C151—22no—
146C2×C151—44no—
147C2×C151—82no—
148C2×C151D4211yescharacteristic
149C2×C151C22×D811yescharacteristic
150C2×C151#57611yescharacteristic
151D151—22no—
152D151—82no—
153C151D4×D811yescharacteristic, complemented, Sylow
154D4×D8—1511nomaximal, Sylow
155C22×D8—1511no—
156C22×D8D15111yescharacteristic, complemented
157D42—1512no—
158#493—1511no—
159#466—1511no—
160#466—1511no—
161#459—1512no—
162#447—1512no—
163#447—1512no—
164C4×D8—1511no—
165C8×D4—1511no—
166C22×D4—3022no—
167C22×D4—1512no—
168C22×D4C2×D15112yescomplemented
169C2×D8—24no—
170C2×D8—3024no—
171C2×D8—1512no—
172C2×D8—1512no—
173C2×D8—1511no—
174C2×D8C2×D15111yescharacteristic
175C2×D8C2×D15112yescomplemented
176C2×D8C2×D15111yescharacteristic, complemented
177C22×C8—1511no—
178C22×C8C2×D15111yescharacteristic, complemented
179#127—1512no—
180#121—3022no—
181#121—1512no—
182#121—1512no—
183#120—3022no—
184#120—3022no—
185C4×D4—1512no—
186C4×D4—1511no—
187#107—1511no—
188C4⋊C8—1511no—
189#102—1512no—
190#102—1512no—
191#102—1512no—
192C22⋊C8—1511no—
193C22⋊C8—1511no—
194C4×C8—1511no—
195C24—22no—
196C24—3022no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—3024no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—3022no—
204C2×D4—3022no—
205C2×D4—3022no—
206C2×D4—6042no—
207C2×D4—6048no—
208C2×D4—1511no—
209C2×D4—1512no—
210C2×D4C22×D15112yes—
211C2×D4C22×D15112yes—
212C22×C4—3022no—
213C22×C4—1511no—
214C22×C4C22×D15111yescharacteristic
215D8—24no—
216D8—22no—
217D8—3024no—
218D8—3022no—
219D8—6042no—
220D8C22⋊D15114yesdirect product factor
221C2×C8—22no—
222C2×C8—3022no—
223C2×C8—1511no—
224C2×C8—1511no—
225C2×C8C22×D15111yescharacteristic
226C2×C8C22×D15111yescharacteristic
227C4⋊C4—1512no—
228C4⋊C4—1511no—
229C22⋊C4—3022no—
230C22⋊C4—3022no—
231C22⋊C4—3022no—
232C22⋊C4—1511no—
233C22⋊C4—1511no—
234C42—1511no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—3022no—
241C23—6044no—
242C23—6044no—
243C23—1511no—
244C23—12082no—
245C23D4×D15111yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—3022no—
251D4—3022no—
252D4—6044no—
253D4—6044no—
254D4—6044no—
255D4—6044no—
256D4—1514no—
257D4—12082no—
258D4C2×C22⋊D15114yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—3021no—
262C2×C4—3021no—
263C2×C4—3022no—
264C2×C4—6044no—
265C2×C4—1511no—
266C2×C4—1511no—
267C2×C4—1511no—
268C2×C4D4×D15111yescharacteristic
269C2×C4C23×D15111yescharacteristic
270C8—21no—
271C8—3021no—
272C8—3021no—
273C8C2×C22⋊D15112yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—3021no—
284C22—3021no—
285C22—6042no—
286C22—6042no—
287C22—6042no—
288C22—1512no—
289C22—12088no—
290C22D8×D15112yescomplemented
291C22C2×D4×D15111yescharacteristic
292C4—21no—
293C4—3021no—
294C4—3021no—
295C4—6042no—
296C4—1512no—
297C4C22×C22⋊D15111yescharacteristic
298C4#1801278411yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—3022no—
303C2—12082no—
304C2D4×C22⋊D15111yescharacteristic
305C2C2×D8×D15111yescharacteristic
306C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×D8×C151C2
socleC22×C151C22×D4
hypercenterC22×D8D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D151C2semidirect
2. D4×C22⋊D151C2semidirect
3. #23752587C2semidirect
4. #23752448C2semidirect
5. #23752445C2semidirect
6. #23752405C2semidirect
7. #23752346C2semidirect
8. #23752344C2semidirect
9. D8×Dic151C2semidirect
10. C8×C22⋊D151C2semidirect
11. C22×D8×C151C2semidirect
13. C2×D4×D151C22semidirect
14. C2×D1208C22semidirect
15. C2×#14558989C22semidirect
16. C2×#14558989C22semidirect
18. C2×C8×D151C22semidirect
19. #18012735C22semidirect
20. #18012713C22semidirect
22. #18012710C22semidirect
25. D4×Dic151C22semidirect
27. #18012673C22semidirect
28. Dic151⋊C8C22semidirect
29. #18012661C22semidirect
30. #18012660C22semidirect
31. #18012660C22semidirect
32. C22⋊(C151⋊C8)C22semidirect
33. (C2×D151)⋊C8C22semidirect
34. C8×Dic151C22semidirect
35. C22×D4×C151C22semidirect
38. C2×D8×C151C22semidirect
39. C2×D8×C151C22semidirect
40. C22×C8×C151C22semidirect
77. D8×C151D4semidirect
93. C22⋊D151D8direct (N × H)
113. D4×C151C2×D4semidirect
119. C8×C151C2×D4semidirect
129. C22×C151C2×D8semidirect
137. C2×D151C2×D8semidirect
144. Dic151C2×D8semidirect
153. C151D4×D8semidirect
156. C22×D8D151semidirect
168. C22×D4C2×D151semidirect
175. C2×D8C2×D151semidirect
176. C2×D8C2×D151semidirect
178. C22×C8C2×D151semidirect
220. D8C22⋊D151direct (N × H)
258. D4C2×C22⋊D151semidirect
273. C8C2×C22⋊D151semidirect
290. C22D8×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
D4×C22⋊D1512
#237525872
#237524482
#237524452
#237524052
#237523462
#237523442
D8×Dic1512
C8×C22⋊D1512
C22×D8×C1512
D4×D8151