Finite Group Databasebeta

← D4×#14558724 #34056383

Subgroups — D4×#14558724 #34056383

Order 19072.

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

normal subgroups only

This group has 546 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×#14558724C212yesmaximal, complemented
2D4×Dic298C211yesmaximal, characteristic, complemented
3#23749997C211yesmaximal, characteristic, complemented
4#23749852C212yesmaximal, complemented
5#23749830C211yesmaximal, characteristic, complemented
6#23749822C211yesmaximal, characteristic, complemented
7#23749776C212yesmaximal, complemented
8#23749763C212yesmaximal, complemented
9C4×#14558724C211yesmaximal, characteristic, complemented
10D4×#11924746C211yesmaximal, characteristic, complemented
11D42×C149C211yesmaximal, characteristic
12C22×Dic298C2212yescomplemented
13C2×#14558724—28no—
14C2×#14558724C2212yes—
15C2×#14558724C2211yescharacteristic
16C2×#14558724C2212yescomplemented
17C2×#14558724C2212yescomplemented
18C2×#14558724C2212yescomplemented
19C22×#11924746C2212yescomplemented
20#18011911C2211yescharacteristic, complemented
21#18011910—21no—
22#18011890C2212yescomplemented
23#18011888—22no—
24C4×Dic298C2211yescharacteristic, complemented
25D4×Dic149—21no—
26#18011842C2211yescharacteristic, complemented
27C4⋊#11924746C2211yescharacteristic, complemented
28#18011834C2211yescharacteristic, complemented
29#18011834C2212yescomplemented
30#18011832C2211yescharacteristic
31#18011832C2212yescomplemented
32C22⋊#11924746C2212yescomplemented
33C4×#11924746C2211yescharacteristic, complemented
34C22×D4×C149—21no—
35C22×D4×C149C2212yes—
36#127×C149C2211yescharacteristic
37#121×C149—21no—
38#121×C149C2212yes—
39#120×C149—22no—
40C4×D4×C149C2211yescharacteristic
41C4×D4×C149C2211yescharacteristic
42C2×Dic298—24no—
43C2×Dic298—22no—
44C2×Dic298—42no—
45C2×Dic298C2312yes—
46C2×Dic298C2311yescharacteristic
47C22×Dic149—22no—
48#14558724—24no—
49#14558724—24no—
50#14558724—24no—
51#14558724—42no—
52#14558724D414yesdirect product factor
53C2×#11924746—24no—
54C2×#11924746C2312yes—
55C2×#11924746C2311yescharacteristic
56C2×#11924746C2311yescharacteristic
57C4⋊Dic149—21no—
58C4⋊Dic149—21no—
59C4⋊Dic149C2311yescharacteristic
60#14558715—22no—
61#14558715—21no—
62C22⋊Dic149—22no—
63C4×Dic149—21no—
64C24×C149—22no—
65C2×D4×C149—24no—
66C2×D4×C149—22no—
67C2×D4×C149—22no—
68C2×D4×C149—21no—
69C2×D4×C149—21no—
70C2×D4×C149—42no—
71C2×D4×C149—44no—
72C2×D4×C149D411yescharacteristic
73C2×D4×C149C2312yes—
74C2×D4×C149C2311yescharacteristic
75C22×C4×C149—21no—
76C22×C4×C149C2312yes—
77C4⋊C4×C149D411yescharacteristic
78C4⋊C4×C149C2311yescharacteristic
79C22⋊C4×C149—21no—
80C22⋊C4×C149—22no—
81C22⋊C4×C149D412yes—
82C42×C149C2311yescharacteristic
83Dic298—21no—
84Dic298—22no—
85Dic298—22no—
86Dic298—44no—
87Dic298C2×D412yescomplemented
88C2×Dic149—21no—
89C2×Dic149—22no—
90C2×Dic149—21no—
91C2×Dic149—44no—
92#11924746—22no—
93#11924746—21no—
94#11924746C2×D412yescomplemented
95C23×C149—21no—
96C23×C149—22no—
97C23×C149—44no—
98C23×C149—44no—
99C23×C149—82no—
100C23×C149C2×D412yes—
101D4×C149—22no—
102D4×C149—21no—
103D4×C149—22no—
104D4×C149—44no—
105D4×C149—44no—
106D4×C149—42no—
107D4×C149—81no—
108D4×C149SD1614yescomplemented
109D4×C149C2×D412yes—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149—21no—
113C2×C4×C149—42no—
114C2×C4×C149C2×D412yes—
115C2×C4×C149C2×D411yescharacteristic
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C22×C149—22no—
119C22×C149—22no—
120C22×C149—22no—
121C22×C149—41no—
122C22×C149—41no—
123C22×C149—42no—
124C22×C149—42no—
125C22×C149—42no—
126C22×C149—88no—
127C22×C149C2×SD1614yescomplemented
128C22×C149C22×D411yescharacteristic
129C4×C149—22no—
130C4×C149—21no—
131C4×C149—41no—
132C4×C149C2×SD1612yescomplemented
133C4×C149C22×D411yescharacteristic
134C4×C149H(5,𝔽2)11yescharacteristic
135Dic149—22no—
136Dic149—42no—
137Dic149—41no—
138C2×C149—24no—
139C2×C149—42no—
140C2×C149—82no—
141C2×C149D4211yescharacteristic
142C2×C149C22×SD1611yescharacteristic
143C2×C149#57711yescharacteristic
144C149D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1491nomaximal, Sylow
146C22×SD16—1492no—
147D4×Q8—1491no—
148D42D14911yescharacteristic
149#492—1491no—
150#465—1492no—
151#461—1491no—
152#460—1491no—
153#450—1492no—
154#448—1492no—
155C4×SD16—1491no—
156C8×D4—1491no—
157C22×Q8—1492no—
158C22×D4—21no—
159C22×D4C2×D14912yes—
160C2×SD16—2988no—
161C2×SD16—1492no—
162C2×SD16—1492no—
163C2×SD16—1492no—
164C2×SD16—1492no—
165C2×SD16—1491no—
166C22×C8—1492no—
167C4⋊Q8—2981no—
168C4⋊Q8—1491no—
169#127C2×D14911yescharacteristic
170C22⋊Q8—2982no—
171C22⋊Q8—1492no—
172#121—21no—
173#121C2×D14912yes—
174#120—22no—
175C4×Q8—1491no—
176C4×D4—2981no—
177C4×D4C2×D14911yescharacteristic
178C4×D4C2×D14911yescharacteristic
179#106—1491no—
180C4⋊C8—1491no—
181#103—1491no—
182#103—1492no—
183#102—1491no—
184#102—1492no—
185C22⋊C8—1492no—
186C4×C8—1491no—
187C24—22no—
188C2×Q8—2984no—
189C2×Q8—2982no—
190C2×Q8—5962no—
191C2×Q8—1492no—
192C2×Q8—1491no—
193C2×D4—24no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—42no—
199C2×D4—44no—
200C2×D4C22⋊D14911yescharacteristic
201C2×D4C22×D14912yes—
202C2×D4C22×D14911yescharacteristic
203C22×C4—21no—
204C22×C4—2982no—
205C22×C4C22×D14912yes—
206SD16—2984no—
207SD16—2984no—
208SD16—2984no—
209SD16—5962no—
210SD16—1494no—
211C2×C8—2984no—
212C2×C8—1491no—
213C2×C8—1492no—
214C2×C8—1491no—
215C4⋊C4—2981no—
216C4⋊C4—2981no—
217C4⋊C4—2981no—
218C4⋊C4—2982no—
219C4⋊C4—1491no—
220C4⋊C4C22⋊D14911yescharacteristic
221C4⋊C4C22×D14911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—22no—
224C22⋊C4—2982no—
225C22⋊C4C22⋊D14912yes—
226C42—2981no—
227C42C22×D14911yescharacteristic
228C23—21no—
229C23—22no—
230C23—44no—
231C23—44no—
232C23—82no—
233C23C2×C22⋊D14912yes—
234Q8—2981no—
235Q8—2982no—
236Q8—2982no—
237Q8—5964no—
238Q8—1492no—
239D4—22no—
240D4—21no—
241D4—22no—
242D4—44no—
243D4—44no—
244D4—42no—
245D4—81no—
246D4#1455872414yesdirect product factor
247D4D4×D14912yes—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—2981no—
253C2×C4—2981no—
254C2×C4—2982no—
255C2×C4—5964no—
256C2×C4C2×C22⋊D14911yescharacteristic
257C2×C4C2×C22⋊D14912yes—
258C2×C4C2×C22⋊D14911yescharacteristic
259C2×C4C23×D14911yescharacteristic
260C8—2982no—
261C8—2981no—
262C8—1492no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—88no—
272C22C2×#1455872414yescomplemented
273C22C22×C22⋊D14911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—2982no—
278C4—5961no—
279C4—5962no—
280C4C2×#1455872412yescomplemented
281C4C2×D4×D14911yescharacteristic
282C4#1801195611yescharacteristic
283C2—24no—
284C2—42no—
285C2—82no—
286C2D4×C22⋊D14911yescharacteristic
287C2C22×#1455872411yescharacteristic
288C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radicalD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149D4×SD16
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×#14558724C2semidirect
2. D4×Dic298C2semidirect
3. #23749997C2semidirect
4. #23749852C2semidirect
5. #23749830C2semidirect
6. #23749822C2semidirect
7. #23749776C2semidirect
8. #23749763C2semidirect
9. C4×#14558724C2semidirect
10. D4×#11924746C2semidirect
12. C22×Dic298C22semidirect
16. C2×#14558724C22semidirect
17. C2×#14558724C22semidirect
18. C2×#14558724C22semidirect
19. C22×#11924746C22semidirect
20. #18011911C22semidirect
22. #18011890C22semidirect
24. C4×Dic298C22semidirect
26. #18011842C22semidirect
27. C4⋊#11924746C22semidirect
28. #18011834C22semidirect
29. #18011834C22semidirect
31. #18011832C22semidirect
32. C22⋊#11924746C22semidirect
33. C4×#11924746C22semidirect
52. #14558724D4direct (N × H)
87. Dic298C2×D4semidirect
94. #11924746C2×D4semidirect
108. D4×C149SD16semidirect
127. C22×C149C2×SD16semidirect
132. C4×C149C2×SD16semidirect
144. C149D4×SD16semidirect
246. D4#14558724direct (N × H)
272. C22C2×#14558724semidirect
280. C4C2×#14558724semidirect

Maximal subgroups

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

subgroupindex
C22×#145587242
D4×Dic2982
#237499972
#237498522
#237498302
#237498222
#237497762
#237497632
C4×#145587242
D4×#119247462
D42×C1492
D4×SD16149