Finite Group Databasebeta

← D4×#14558721 #34056364

Subgroups — D4×#14558721 #34056364

Order 19072.

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×#14558721C212yesmaximal, complemented
2D4×D596C211yesmaximal, characteristic, complemented
3#23750001C211yesmaximal, characteristic, complemented
4#23749859C212yesmaximal, complemented
5#23749820C211yesmaximal, characteristic, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749759C212yesmaximal, complemented
8#23749758C212yesmaximal, complemented
9C4×#14558721C211yesmaximal, characteristic, complemented
10D4×#11924746C211yesmaximal, characteristic, complemented
11D42×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yescomplemented
13C2×D4×D149—21no—
14C2×#14558721—28no—
15C2×#14558721C2211yescharacteristic
16C2×#14558721C2212yescomplemented
17C2×#14558721C2212yescomplemented
18C2×#14558721C2212yescomplemented
19C2×#14558721C2212yescomplemented
20C22×#11924746C2212yescomplemented
21#18011908C2211yescharacteristic, complemented
22#18011886—21no—
23#18011885C2212yescomplemented
24#18011881—22no—
25C4×D596C2211yescharacteristic, complemented
26#18011844C2211yescharacteristic, complemented
27C4⋊#11924746C2211yescharacteristic, complemented
28#18011832C2211yescharacteristic, complemented
29#18011832C2212yescomplemented
30#18011831C2211yescharacteristic, complemented
31#18011831C2212yescomplemented
32C22⋊#11924746C2212yescomplemented
33C4×#11924746C2211yescharacteristic, complemented
34C22×D4×C149—21no—
35C22×D4×C149C2212yescomplemented
36#127×C149C2211yescharacteristic, complemented
37#121×C149—21no—
38#121×C149C2212yescomplemented
39#120×C149—22no—
40C4×D4×C149C2211yescharacteristic
41C4×D4×C149C2211yescharacteristic, complemented
42C23×D149—22no—
43C2×D596—24no—
44C2×D596—21no—
45C2×D596—22no—
46C2×D596—21no—
47C2×D596—42no—
48C2×D596C2312yes—
49C2×D596C2311yescharacteristic
50C2×C22⋊D149—22no—
51D4×D149—44no—
52C2×C4×D149—21no—
53#14558721—24no—
54#14558721—24no—
55#14558721—24no—
56#14558721—42no—
57#14558721D414yesdirect product factor
58C2×#11924746—24no—
59C2×#11924746C2312yes—
60C2×#11924746C2311yescharacteristic
61C2×#11924746C2311yescharacteristic
62C4⋊Dic149C2311yescharacteristic
63#14558713—21no—
64#14558713—22no—
65C24×C149—22no—
66C2×D4×C149—24no—
67C2×D4×C149—22no—
68C2×D4×C149—22no—
69C2×D4×C149—21no—
70C2×D4×C149—21no—
71C2×D4×C149—42no—
72C2×D4×C149—44no—
73C2×D4×C149D411yescharacteristic
74C2×D4×C149C2312yes—
75C2×D4×C149C2311yescharacteristic
76C22×C4×C149—21no—
77C22×C4×C149C2312yes—
78C4⋊C4×C149D411yescharacteristic
79C4⋊C4×C149C2311yescharacteristic
80C22⋊C4×C149—21no—
81C22⋊C4×C149—22no—
82C22⋊C4×C149D412yes—
83C42×C149C2311yescharacteristic
84C22×D149—21no—
85C22×D149—22no—
86C22×D149—44no—
87C22×D149—44no—
88C22×D149—82no—
89D596—22no—
90D596—21no—
91D596—22no—
92D596—44no—
93D596—42no—
94D596—81no—
95D596C2×D412yescomplemented
96C22⋊D149—44no—
97C2×Dic149—21no—
98C4×D149—42no—
99#11924746—22no—
100#11924746—21no—
101#11924746C2×D412yescomplemented
102C23×C149—21no—
103C23×C149—22no—
104C23×C149—44no—
105C23×C149—44no—
106C23×C149—82no—
107C23×C149C2×D412yes—
108D4×C149—22no—
109D4×C149—21no—
110D4×C149—22no—
111D4×C149—44no—
112D4×C149—44no—
113D4×C149—42no—
114D4×C149—81no—
115D4×C149D814yescomplemented
116D4×C149C2×D412yescomplemented
117C2×C4×C149—22no—
118C2×C4×C149—22no—
119C2×C4×C149—21no—
120C2×C4×C149—42no—
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D412yes—
123C2×C4×C149C2×D411yescharacteristic
124C2×C4×C149C2411yescharacteristic
125C22×C149—22no—
126C22×C149—22no—
127C22×C149—22no—
128C22×C149—41no—
129C22×C149—41no—
130C22×C149—42no—
131C22×C149—42no—
132C22×C149—42no—
133C22×C149—88no—
134C22×C149C2×D814yescomplemented
135C22×C149C22×D411yescharacteristic
136C2×D149—22no—
137C2×D149—41no—
138C2×D149—41no—
139C2×D149—42no—
140C2×D149—42no—
141C2×D149—42no—
142C2×D149—88no—
143C4×C149—22no—
144C4×C149—21no—
145C4×C149—41no—
146C4×C149C2×D812yescomplemented
147C4×C149C22×D411yescharacteristic
148C4×C149H(5,𝔽2)11yescharacteristic
149Dic149—41no—
150C2×C149—24no—
151C2×C149—42no—
152C2×C149—82no—
153C2×C149D4211yescharacteristic
154C2×C149C22×D811yescharacteristic
155C2×C149#57611yescharacteristic
156D149—42no—
157D149—82no—
158C149D4×D811yescharacteristic, complemented, Sylow
159D4×D8—1491nomaximal, Sylow
160C22×D8—1492no—
161D42—1491no—
162D42D14911yescharacteristic, complemented
163#493—1491no—
164#466—1492no—
165#459—1491no—
166#459—1491no—
167#447—1492no—
168#447—1492no—
169C4×D8—1491no—
170C8×D4—1491no—
171C22×D4—21no—
172C22×D4—2981no—
173C22×D4—1492no—
174C22×D4C2×D14912yescomplemented
175C2×D8—2988no—
176C2×D8—1492no—
177C2×D8—1492no—
178C2×D8—1492no—
179C2×D8—1492no—
180C2×D8—1491no—
181C22×C8—1492no—
182#127—1491no—
183#127C2×D14911yescharacteristic, complemented
184#121—21no—
185#121—2981no—
186#121—1492no—
187#121C2×D14912yescomplemented
188#120—22no—
189#120—2982no—
190C4×D4—1491no—
191C4×D4C2×D14911yescharacteristic
192C4×D4C2×D14911yescharacteristic, complemented
193#107—1491no—
194C4⋊C8—1491no—
195#102—1491no—
196#102—1492no—
197#102—1491no—
198#102—1492no—
199C22⋊C8—1492no—
200C4×C8—1491no—
201C24—22no—
202C24—2982no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—2984no—
211C2×D4—2982no—
212C2×D4—2982no—
213C2×D4—2981no—
214C2×D4—2981no—
215C2×D4—5962no—
216C2×D4—5964no—
217C2×D4—1492no—
218C2×D4—1491no—
219C2×D4C22⋊D14911yescharacteristic
220C2×D4C22×D14912yes—
221C2×D4C22×D14911yescharacteristic
222C22×C4—21no—
223C22×C4—2981no—
224C22×C4C22×D14912yes—
225D8—2984no—
226D8—2984no—
227D8—2984no—
228D8—5962no—
229D8—1494no—
230C2×C8—2984no—
231C2×C8—1491no—
232C2×C8—1492no—
233C2×C8—1491no—
234C4⋊C4—1491no—
235C4⋊C4C22⋊D14911yescharacteristic
236C4⋊C4C22×D14911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—2981no—
240C22⋊C4—2982no—
241C22⋊C4C22⋊D14912yes—
242C42C22×D14911yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—2981no—
249C23—2982no—
250C23—5964no—
251C23—5964no—
252C23—11922no—
253C23C2×C22⋊D14912yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—2982no—
262D4—2981no—
263D4—2982no—
264D4—5964no—
265D4—5964no—
266D4—5962no—
267D4—1492no—
268D4—11921no—
269D4#1455872114yesdirect product factor
270D4D4×D14912yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—2981no—
276C2×C4—5962no—
277C2×C4C2×C22⋊D14911yescharacteristic
278C2×C4C2×C22⋊D14912yes—
279C2×C4C2×C22⋊D14911yescharacteristic
280C2×C4C23×D14911yescharacteristic
281C8—2982no—
282C8—2981no—
283C8—1492no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—2982no—
294C22—5961no—
295C22—5961no—
296C22—5962no—
297C22—5962no—
298C22—5962no—
299C22—11928no—
300C22C2×#1455872114yescomplemented
301C22C22×C22⋊D14911yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—5961no—
306C4C2×#1455872112yescomplemented
307C4C2×D4×D14911yescharacteristic
308C4#1801195611yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—5962no—
313C2—11922no—
314C2D4×C22⋊D14911yescharacteristic
315C2C22×#1455872111yescharacteristic
316C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149D4×D8
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#14558721C2semidirect
2. D4×D596C2semidirect
3. #23750001C2semidirect
4. #23749859C2semidirect
5. #23749820C2semidirect
6. #23749817C2semidirect
7. #23749759C2semidirect
8. #23749758C2semidirect
9. C4×#14558721C2semidirect
10. D4×#11924746C2semidirect
11. D42×C149C2semidirect
12. C22×D596C22semidirect
16. C2×#14558721C22semidirect
17. C2×#14558721C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558721C22semidirect
20. C22×#11924746C22semidirect
21. #18011908C22semidirect
23. #18011885C22semidirect
25. C4×D596C22semidirect
26. #18011844C22semidirect
27. C4⋊#11924746C22semidirect
28. #18011832C22semidirect
29. #18011832C22semidirect
30. #18011831C22semidirect
31. #18011831C22semidirect
32. C22⋊#11924746C22semidirect
33. C4×#11924746C22semidirect
35. C22×D4×C149C22semidirect
36. #127×C149C22semidirect
38. #121×C149C22semidirect
41. C4×D4×C149C22semidirect
57. #14558721D4direct (N × H)
95. D596C2×D4semidirect
101. #11924746C2×D4semidirect
115. D4×C149D8semidirect
116. D4×C149C2×D4semidirect
134. C22×C149C2×D8semidirect
146. C4×C149C2×D8semidirect
158. C149D4×D8semidirect
162. D42D149semidirect
174. C22×D4C2×D149semidirect
183. #127C2×D149semidirect
187. #121C2×D149semidirect
192. C4×D4C2×D149semidirect
269. D4#14558721direct (N × H)
270. D4D4×D149semidirect
300. C22C2×#14558721semidirect
306. C4C2×#14558721semidirect

Maximal subgroups

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

subgroupindex
C22×#145587212
D4×D5962
#237500012
#237498592
#237498202
#237498172
#237497592
#237497582
C4×#145587212
D4×#119247462
D42×C1492
D4×D8149