Finite Group Databasebeta

← D4×#11765850 #22600013

Subgroups — D4×#11765850 #22600013

Order 9088.

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×#11765850C212yesmaximal, complemented
2D4×D284C211yesmaximal, characteristic, complemented
3#17986375C211yesmaximal, characteristic, complemented
4#17986233C212yesmaximal, complemented
5#17986194C211yesmaximal, characteristic, complemented
6#17986191C211yesmaximal, characteristic, complemented
7#17986133C212yesmaximal, complemented
8#17986132C212yesmaximal, complemented
9C4×#11765850C211yesmaximal, characteristic, complemented
10D4×C71⋊C8C211yesmaximal, characteristic, complemented
11D42×C71C211yesmaximal, characteristic, complemented
12C22×D284C2212yescomplemented
13C2×D4×D71—21no—
14C2×#11765850—28no—
15C2×#11765850C2211yescharacteristic
16C2×#11765850C2212yescomplemented
17C2×#11765850C2212yescomplemented
18C2×#11765850C2212yescomplemented
19C2×#11765850C2212yescomplemented
20C22×C71⋊C8C2212yescomplemented
21#14556125C2211yescharacteristic, complemented
22#14556103—21no—
23#14556102C2212yescomplemented
24#14556098—22no—
25C4×D284C2211yescharacteristic, complemented
26#14556061C2211yescharacteristic, complemented
27C4⋊(C71⋊C8)C2211yescharacteristic, complemented
28#14556049C2211yescharacteristic, complemented
29#14556049C2212yescomplemented
30#14556048C2211yescharacteristic, complemented
31#14556048C2212yescomplemented
32C22⋊(C71⋊C8)C2212yescomplemented
33C4×C71⋊C8C2211yescharacteristic, complemented
34C22×D4×C71—21no—
35C22×D4×C71C2212yescomplemented
36#127×C71C2211yescharacteristic, complemented
37#121×C71—21no—
38#121×C71C2212yescomplemented
39#120×C71—22no—
40C4×D4×C71C2211yescharacteristic
41C4×D4×C71C2211yescharacteristic, complemented
42C23×D71—22no—
43C2×D284—24no—
44C2×D284—21no—
45C2×D284—22no—
46C2×D284—21no—
47C2×D284—42no—
48C2×D284C2312yes—
49C2×D284C2311yescharacteristic
50C2×C22⋊D71—22no—
51D4×D71—44no—
52C2×C4×D71—21no—
53#11765850—24no—
54#11765850—24no—
55#11765850—24no—
56#11765850—42no—
57#11765850D414yesdirect product factor
58C2×C71⋊C8—24no—
59C2×C71⋊C8C2311yescharacteristic
60C2×C71⋊C8C2312yes—
61C2×C71⋊C8C2311yescharacteristic
62C4⋊Dic71C2311yescharacteristic
63(C2×D71)⋊C4—21no—
64(C2×D71)⋊C4—22no—
65C24×C71—22no—
66C2×D4×C71—24no—
67C2×D4×C71—22no—
68C2×D4×C71—22no—
69C2×D4×C71—21no—
70C2×D4×C71—21no—
71C2×D4×C71—42no—
72C2×D4×C71—44no—
73C2×D4×C71D411yescharacteristic
74C2×D4×C71C2312yes—
75C2×D4×C71C2311yescharacteristic
76C22×C4×C71—21no—
77C22×C4×C71C2312yes—
78C4⋊C4×C71D411yescharacteristic
79C4⋊C4×C71C2311yescharacteristic
80C22⋊C4×C71—21no—
81C22⋊C4×C71—22no—
82C22⋊C4×C71D412yes—
83C42×C71C2311yescharacteristic
84C23×C71—21no—
85C23×C71—22no—
86C23×C71—44no—
87C23×C71—44no—
88C23×C71—82no—
89C23×C71C2×D412yes—
90C22×D71—21no—
91C22×D71—22no—
92C22×D71—44no—
93C22×D71—44no—
94C22×D71—82no—
95D4×C71—22no—
96D4×C71—21no—
97D4×C71—22no—
98D4×C71—44no—
99D4×C71—44no—
100D4×C71—42no—
101D4×C71—81no—
102D4×C71D814yescomplemented
103D4×C71C2×D412yescomplemented
104C2×C4×C71—22no—
105C2×C4×C71—22no—
106C2×C4×C71—21no—
107C2×C4×C71—42no—
108C2×C4×C71C2×D411yescharacteristic
109C2×C4×C71C2×D412yes—
110C2×C4×C71C2×D411yescharacteristic
111C2×C4×C71C2411yescharacteristic
112C22⋊D71—44no—
113C2×Dic71—21no—
114D284—22no—
115D284—21no—
116D284—22no—
117D284—44no—
118D284—42no—
119D284—81no—
120D284C2×D412yescomplemented
121C4×D71—42no—
122C71⋊C8—22no—
123C71⋊C8—21no—
124C71⋊C8C2×D412yescomplemented
125C22×C71—22no—
126C22×C71—22no—
127C22×C71—22no—
128C22×C71—41no—
129C22×C71—41no—
130C22×C71—42no—
131C22×C71—42no—
132C22×C71—42no—
133C22×C71—88no—
134C22×C71C2×D814yescomplemented
135C22×C71C22×D411yescharacteristic
136C2×D71—22no—
137C2×D71—41no—
138C2×D71—41no—
139C2×D71—42no—
140C2×D71—42no—
141C2×D71—42no—
142C2×D71—88no—
143C4×C71—22no—
144C4×C71—21no—
145C4×C71—41no—
146C4×C71C2×D812yescomplemented
147C4×C71C22×D411yescharacteristic
148C4×C71H(5,𝔽2)11yescharacteristic
149Dic71—41no—
150C2×C71—24no—
151C2×C71—42no—
152C2×C71—82no—
153C2×C71D4211yescharacteristic
154C2×C71C22×D811yescharacteristic
155C2×C71#57611yescharacteristic
156D71—42no—
157D71—82no—
158D4×D8—711nomaximal, Sylow
159C71D4×D811yescharacteristic, complemented, Sylow
160C22×D8—712no—
161D42—711no—
162D42D7111yescharacteristic, complemented
163#493—711no—
164#466—712no—
165#459—711no—
166#459—711no—
167#447—712no—
168#447—712no—
169C4×D8—711no—
170C8×D4—711no—
171C22×D4—21no—
172C22×D4—712no—
173C22×D4—1421no—
174C22×D4C2×D7112yescomplemented
175C2×D8—712no—
176C2×D8—711no—
177C2×D8—712no—
178C2×D8—712no—
179C2×D8—712no—
180C2×D8—1428no—
181C22×C8—712no—
182#127—711no—
183#127C2×D7111yescharacteristic, complemented
184#121—21no—
185#121—712no—
186#121—1421no—
187#121C2×D7112yescomplemented
188#120—22no—
189#120—1422no—
190C4×D4—711no—
191C4×D4C2×D7111yescharacteristic
192C4×D4C2×D7111yescharacteristic, complemented
193#107—711no—
194C4⋊C8—711no—
195#102—711no—
196#102—712no—
197#102—711no—
198#102—712no—
199C22⋊C8—712no—
200C4×C8—711no—
201C24—22no—
202C24—1422no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—2842no—
211C2×D4—2844no—
212C2×D4—711no—
213C2×D4—712no—
214C2×D4—1424no—
215C2×D4—1422no—
216C2×D4—1422no—
217C2×D4—1421no—
218C2×D4—1421no—
219C2×D4C22⋊D7111yescharacteristic
220C2×D4C22×D7112yes—
221C2×D4C22×D7111yescharacteristic
222C22×C4—21no—
223C22×C4—1421no—
224C22×C4C22×D7112yes—
225D8—2842no—
226D8—714no—
227D8—1424no—
228D8—1424no—
229D8—1424no—
230C2×C8—711no—
231C2×C8—711no—
232C2×C8—712no—
233C2×C8—1424no—
234C4⋊C4—711no—
235C4⋊C4C22⋊D7111yescharacteristic
236C4⋊C4C22×D7111yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—1421no—
240C22⋊C4—1422no—
241C22⋊C4C22⋊D7112yes—
242C42C22×D7111yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—2844no—
249C23—2844no—
250C23—5682no—
251C23—1422no—
252C23—1421no—
253C23C2×C22⋊D7112yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—2844no—
262D4—2844no—
263D4—2842no—
264D4—5681no—
265D4—712no—
266D4—1422no—
267D4—1422no—
268D4—1421no—
269D4#1176585014yesdirect product factor
270D4D4×D7112yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—2842no—
276C2×C4—1421no—
277C2×C4C2×C22⋊D7111yescharacteristic
278C2×C4C2×C22⋊D7112yes—
279C2×C4C2×C22⋊D7111yescharacteristic
280C2×C4C23×D7111yescharacteristic
281C8—712no—
282C8—1422no—
283C8—1421no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—2841no—
294C22—2841no—
295C22—2842no—
296C22—2842no—
297C22—2842no—
298C22—5688no—
299C22—1422no—
300C22C2×#1176585014yescomplemented
301C22C22×C22⋊D7111yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—2841no—
306C4C2×#1176585012yescomplemented
307C4C2×D4×D7111yescharacteristic
308C4#1455617311yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—2842no—
313C2—5682no—
314C2D4×C22⋊D7111yescharacteristic
315C2C22×#1176585011yescharacteristic
316C2#1798680211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingD42×C71C2
socleC22×C71C22×D4
hypercenterD42D71
hypocenterC71D4×D8
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#11765850C2semidirect
2. D4×D284C2semidirect
3. #17986375C2semidirect
4. #17986233C2semidirect
5. #17986194C2semidirect
6. #17986191C2semidirect
7. #17986133C2semidirect
8. #17986132C2semidirect
9. C4×#11765850C2semidirect
10. D4×C71⋊C8C2semidirect
11. D42×C71C2semidirect
12. C22×D284C22semidirect
16. C2×#11765850C22semidirect
17. C2×#11765850C22semidirect
18. C2×#11765850C22semidirect
19. C2×#11765850C22semidirect
20. C22×C71⋊C8C22semidirect
21. #14556125C22semidirect
23. #14556102C22semidirect
25. C4×D284C22semidirect
26. #14556061C22semidirect
27. C4⋊(C71⋊C8)C22semidirect
28. #14556049C22semidirect
29. #14556049C22semidirect
30. #14556048C22semidirect
31. #14556048C22semidirect
32. C22⋊(C71⋊C8)C22semidirect
33. C4×C71⋊C8C22semidirect
35. C22×D4×C71C22semidirect
36. #127×C71C22semidirect
38. #121×C71C22semidirect
41. C4×D4×C71C22semidirect
57. #11765850D4direct (N × H)
102. D4×C71D8semidirect
103. D4×C71C2×D4semidirect
120. D284C2×D4semidirect
124. C71⋊C8C2×D4semidirect
134. C22×C71C2×D8semidirect
146. C4×C71C2×D8semidirect
159. C71D4×D8semidirect
162. D42D71semidirect
174. C22×D4C2×D71semidirect
183. #127C2×D71semidirect
187. #121C2×D71semidirect
192. C4×D4C2×D71semidirect
269. D4#11765850direct (N × H)
270. D4D4×D71semidirect
300. C22C2×#11765850semidirect
306. C4C2×#11765850semidirect