Finite Group Databasebeta

← D4×#14558989 #34080783

Subgroups — D4×#14558989 #34080783

Order 19328.

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

normal subgroups only

This group has 620 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
1C22×#14558989C212yesmaximal, complemented
2D4×D604C211yesmaximal, characteristic, complemented
3#23752588C211yesmaximal, characteristic, complemented
4#23752446C212yesmaximal, complemented
5#23752407C211yesmaximal, characteristic, complemented
6#23752404C211yesmaximal, characteristic, complemented
7#23752346C212yesmaximal, complemented
8#23752345C212yesmaximal, complemented
9C4×#14558989C211yesmaximal, characteristic, complemented
10D4×C151⋊C8C211yesmaximal, characteristic, complemented
11D42×C151C211yesmaximal, characteristic, complemented
12C22×D604C2212yescomplemented
13C2×D4×D151—21no—
14C2×#14558989—28no—
15C2×#14558989C2211yescharacteristic
16C2×#14558989C2212yescomplemented
17C2×#14558989C2212yescomplemented
18C2×#14558989C2212yescomplemented
19C2×#14558989C2212yescomplemented
20C22×C151⋊C8C2212yescomplemented
21#18012736C2211yescharacteristic, complemented
22#18012714—21no—
23#18012713C2212yescomplemented
24#18012709—22no—
25C4×D604C2211yescharacteristic, complemented
26#18012672C2211yescharacteristic, complemented
27C4⋊(C151⋊C8)C2211yescharacteristic, complemented
28#18012660C2211yescharacteristic, complemented
29#18012660C2212yescomplemented
30#18012659C2211yescharacteristic, complemented
31#18012659C2212yescomplemented
32C22⋊(C151⋊C8)C2212yescomplemented
33C4×C151⋊C8C2211yescharacteristic, complemented
34C22×D4×C151—21no—
35C22×D4×C151C2212yescomplemented
36#127×C151C2211yescharacteristic, complemented
37#121×C151—21no—
38#121×C151C2212yescomplemented
39#120×C151—22no—
40C4×D4×C151C2211yescharacteristic
41C4×D4×C151C2211yescharacteristic, complemented
42C23×D151—22no—
43C2×D604—24no—
44C2×D604—22no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—42no—
48C2×D604C2312yes—
49C2×D604C2311yescharacteristic
50C2×C22⋊D151—22no—
51D4×D151—44no—
52C2×C4×D151—21no—
53#14558989—24no—
54#14558989—24no—
55#14558989—24no—
56#14558989—42no—
57#14558989D414yesdirect product factor
58C2×C151⋊C8—24no—
59C2×C151⋊C8C2312yes—
60C2×C151⋊C8C2311yescharacteristic
61C2×C151⋊C8C2311yescharacteristic
62C4⋊Dic151C2311yescharacteristic
63(C2×D151)⋊C4—21no—
64(C2×D151)⋊C4—22no—
65C24×C151—22no—
66C2×D4×C151—24no—
67C2×D4×C151—22no—
68C2×D4×C151—22no—
69C2×D4×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—42no—
72C2×D4×C151—44no—
73C2×D4×C151D411yescharacteristic
74C2×D4×C151C2312yes—
75C2×D4×C151C2311yescharacteristic
76C22×C4×C151—21no—
77C22×C4×C151C2312yes—
78C4⋊C4×C151D411yescharacteristic
79C4⋊C4×C151C2311yescharacteristic
80C22⋊C4×C151—21no—
81C22⋊C4×C151—22no—
82C22⋊C4×C151D412yes—
83C42×C151C2311yescharacteristic
84C22×D151—21no—
85C22×D151—22no—
86C22×D151—44no—
87C22×D151—44no—
88C22×D151—82no—
89D604—22no—
90D604—21no—
91D604—22no—
92D604—44no—
93D604—42no—
94D604—81no—
95D604C2×D412yescomplemented
96C22⋊D151—44no—
97C2×Dic151—21no—
98C4×D151—42no—
99C151⋊C8—22no—
100C151⋊C8—21no—
101C151⋊C8C2×D412yescomplemented
102C23×C151—21no—
103C23×C151—22no—
104C23×C151—44no—
105C23×C151—44no—
106C23×C151—82no—
107C23×C151C2×D412yes—
108D4×C151—22no—
109D4×C151—21no—
110D4×C151—22no—
111D4×C151—44no—
112D4×C151—44no—
113D4×C151—42no—
114D4×C151—81no—
115D4×C151D814yescomplemented
116D4×C151C2×D412yescomplemented
117C2×C4×C151—22no—
118C2×C4×C151—22no—
119C2×C4×C151—21no—
120C2×C4×C151—42no—
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151C2411yescharacteristic
125C22×C151—22no—
126C22×C151—22no—
127C22×C151—22no—
128C22×C151—41no—
129C22×C151—41no—
130C22×C151—42no—
131C22×C151—42no—
132C22×C151—42no—
133C22×C151—88no—
134C22×C151C2×D814yescomplemented
135C22×C151C22×D411yescharacteristic
136C2×D151—22no—
137C2×D151—41no—
138C2×D151—41no—
139C2×D151—42no—
140C2×D151—42no—
141C2×D151—42no—
142C2×D151—88no—
143C4×C151—22no—
144C4×C151—21no—
145C4×C151—41no—
146C4×C151C2×D812yescomplemented
147C4×C151C22×D411yescharacteristic
148C4×C151H(5,𝔽2)11yescharacteristic
149Dic151—41no—
150C2×C151—24no—
151C2×C151—42no—
152C2×C151—82no—
153C2×C151D4211yescharacteristic
154C2×C151C22×D811yescharacteristic
155C2×C151#57611yescharacteristic
156D151—42no—
157D151—82no—
158C151D4×D811yescharacteristic, complemented, Sylow
159D4×D8—1511nomaximal, Sylow
160C22×D8—1512no—
161D42—1511no—
162D42D15111yescharacteristic, complemented
163#493—1511no—
164#466—1512no—
165#459—1511no—
166#459—1511no—
167#447—1512no—
168#447—1512no—
169C4×D8—1511no—
170C8×D4—1511no—
171C22×D4—21no—
172C22×D4—3021no—
173C22×D4—1512no—
174C22×D4C2×D15112yescomplemented
175C2×D8—3028no—
176C2×D8—1512no—
177C2×D8—1512no—
178C2×D8—1512no—
179C2×D8—1512no—
180C2×D8—1511no—
181C22×C8—1512no—
182#127—1511no—
183#127C2×D15111yescharacteristic, complemented
184#121—21no—
185#121—3021no—
186#121—1512no—
187#121C2×D15112yescomplemented
188#120—22no—
189#120—3022no—
190C4×D4—1511no—
191C4×D4C2×D15111yescharacteristic
192C4×D4C2×D15111yescharacteristic, complemented
193#107—1511no—
194C4⋊C8—1511no—
195#102—1511no—
196#102—1512no—
197#102—1511no—
198#102—1512no—
199C22⋊C8—1512no—
200C4×C8—1511no—
201C24—22no—
202C24—3022no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—3024no—
211C2×D4—3022no—
212C2×D4—3022no—
213C2×D4—3021no—
214C2×D4—3021no—
215C2×D4—6042no—
216C2×D4—6044no—
217C2×D4—1512no—
218C2×D4—1511no—
219C2×D4C22⋊D15111yescharacteristic
220C2×D4C22×D15112yes—
221C2×D4C22×D15111yescharacteristic
222C22×C4—21no—
223C22×C4—3021no—
224C22×C4C22×D15112yes—
225D8—3024no—
226D8—3024no—
227D8—3024no—
228D8—6042no—
229D8—1514no—
230C2×C8—3024no—
231C2×C8—1511no—
232C2×C8—1512no—
233C2×C8—1511no—
234C4⋊C4—1511no—
235C4⋊C4C22⋊D15111yescharacteristic
236C4⋊C4C22×D15111yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—3021no—
240C22⋊C4—3022no—
241C22⋊C4C22⋊D15112yes—
242C42C22×D15111yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—3021no—
249C23—3022no—
250C23—6044no—
251C23—6044no—
252C23—12082no—
253C23C2×C22⋊D15112yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—3022no—
262D4—3021no—
263D4—3022no—
264D4—6044no—
265D4—6044no—
266D4—6042no—
267D4—1512no—
268D4—12081no—
269D4#1455898914yesdirect product factor
270D4D4×D15112yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—3021no—
276C2×C4—6042no—
277C2×C4C2×C22⋊D15111yescharacteristic
278C2×C4C2×C22⋊D15112yes—
279C2×C4C2×C22⋊D15111yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—3022no—
282C8—3021no—
283C8—1512no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—3022no—
294C22—6041no—
295C22—6041no—
296C22—6042no—
297C22—6042no—
298C22—6042no—
299C22—12088no—
300C22C2×#1455898914yescomplemented
301C22C22×C22⋊D15111yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—6041no—
306C4C2×#1455898912yescomplemented
307C4C2×D4×D15111yescharacteristic
308C4#1801278411yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—6042no—
313C2—12082no—
314C2D4×C22⋊D15111yescharacteristic
315C2C22×#1455898911yescharacteristic
316C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingD42×C151C2
socleC22×C151C22×D4
hypercenterD42D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#14558989C2semidirect
2. D4×D604C2semidirect
3. #23752588C2semidirect
4. #23752446C2semidirect
5. #23752407C2semidirect
6. #23752404C2semidirect
7. #23752346C2semidirect
8. #23752345C2semidirect
9. C4×#14558989C2semidirect
10. D4×C151⋊C8C2semidirect
11. D42×C151C2semidirect
12. C22×D604C22semidirect
16. C2×#14558989C22semidirect
17. C2×#14558989C22semidirect
18. C2×#14558989C22semidirect
19. C2×#14558989C22semidirect
20. C22×C151⋊C8C22semidirect
21. #18012736C22semidirect
23. #18012713C22semidirect
25. C4×D604C22semidirect
26. #18012672C22semidirect
27. C4⋊(C151⋊C8)C22semidirect
28. #18012660C22semidirect
29. #18012660C22semidirect
30. #18012659C22semidirect
31. #18012659C22semidirect
32. C22⋊(C151⋊C8)C22semidirect
33. C4×C151⋊C8C22semidirect
35. C22×D4×C151C22semidirect
36. #127×C151C22semidirect
38. #121×C151C22semidirect
41. C4×D4×C151C22semidirect
57. #14558989D4direct (N × H)
95. D604C2×D4semidirect
101. C151⋊C8C2×D4semidirect
115. D4×C151D8semidirect
116. D4×C151C2×D4semidirect
134. C22×C151C2×D8semidirect
146. C4×C151C2×D8semidirect
158. C151D4×D8semidirect
162. D42D151semidirect
174. C22×D4C2×D151semidirect
183. #127C2×D151semidirect
187. #121C2×D151semidirect
192. C4×D4C2×D151semidirect
269. D4#14558989direct (N × H)
270. D4D4×D151semidirect
300. C22C2×#14558989semidirect
306. C4C2×#14558989semidirect

Maximal subgroups

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

subgroupindex
C22×#145589892
D4×D6042
#237525882
#237524462
#237524072
#237524042
#237523462
#237523452
C4×#145589892
D4×C151⋊C82
D42×C1512
D4×D8151