Finite Group Databasebeta

← #34056293

Subgroups — #34056293

Order 19072.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011939C212yesmaximal, complemented
2#23750280C211yesmaximal, characteristic, complemented
3D4×D596C211yesmaximal, characteristic, complemented
4#23749998C211yesmaximal, characteristic, complemented
5#23749871C212yesmaximal, complemented
6#23749831C211yesmaximal, characteristic, complemented
7#23749821C211yesmaximal, characteristic, complemented
8#23749778C212yesmaximal, complemented
9#23749772C212yesmaximal, complemented
10C4×D1192C211yesmaximal, characteristic, complemented
11#436×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2212yescomplemented
13C22×D596C2212yes—
14C2×D4×D149—21no—
15#18011939—28no—
16C2×#14558725C2212yes—
17C2×#14558725C2212yescomplemented
18C2×#14558725C2212yescomplemented
19C2×D1192C2211yescharacteristic
20C2×D1192C2212yescomplemented
21#18011911C2211yescharacteristic, complemented
22#18011908C2211yescharacteristic
23#18011893—22no—
24#18011890C2212yescomplemented
25#18011886—21no—
26#18011885C2212yes—
27#18011882—21no—
28#18011881—22no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic, complemented
31C4⋊C4×D149—21no—
32#18011845C2211yescharacteristic, complemented
33#18011836C2212yescomplemented
34#18011833C2211yescharacteristic
35#18011833C2211yescharacteristic, complemented
36#18011833C2212yescomplemented
37C2×M16×C149C2212yescomplemented
38C4×D4×C149C2211yescharacteristic
39C4⋊C8×C149C2211yescharacteristic, complemented
40C22⋊C8×C149C2212yescomplemented
41C4×C8×C149C2211yescharacteristic, complemented
42C23×D149—22no—
43#14558736—24no—
44#14558736—42no—
45C2×Dic298C2312yes—
46C2×D596—24no—
47C2×D596—21no—
48C2×D596—22no—
49C2×D596—21no—
50C2×D596—42no—
51C2×D596C2312yes—
52C2×D596C2311yescharacteristic
53C2×D596C2311yescharacteristic
54C2×C22⋊D149—22no—
55C2×C22⋊D149—22no—
56D4×D149—44no—
57C2×C4×D149—21no—
58C2×C4×D149—22no—
59C2×C4×D149—21no—
60#14558725—24no—
61#14558725—24no—
62#14558725—42no—
63D1192—24no—
64D1192D414yescomplemented
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149C2311yescharacteristic
68C4⋊Dic149C2311yescharacteristic
69#14558715—22no—
70C22⋊Dic149—22no—
71#14558713—21no—
72#14558713—21no—
73#14558713—22no—
74C2×D4×C149D411yescharacteristic
75C22×C4×C149C2312yes—
76M16×C149—24no—
77C2×C8×C149C2312yes—
78C2×C8×C149C2311yescharacteristic
79C2×C8×C149C2311yescharacteristic
80C4⋊C4×C149D411yescharacteristic
81C22⋊C4×C149D412yes—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—21no—
85C22×D149—22no—
86C22×D149—44no—
87C22×D149—44no—
88C22×D149—82no—
89Dic298—22no—
90Dic298—22no—
91D596—22no—
92D596—21no—
93D596—21no—
94D596—22no—
95D596—44no—
96D596—42no—
97D596—81no—
98D596C2×D412yes—
99D596C2×D412yescomplemented
100C22⋊D149—44no—
101C22⋊D149—44no—
102C2×Dic149—21no—
103C2×Dic149—22no—
104C2×Dic149—21no—
105C4×D149—44no—
106C4×D149—42no—
107C4×D149—42no—
108C23×C149C2×D412yes—
109D4×C149—22no—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149C2×D412yes—
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2411yescharacteristic
116C8×C149—22no—
117C8×C149—21no—
118C8×C149C2×D412yescomplemented
119C22×C149—22no—
120C22×C149—22no—
121C22×C149—22no—
122C22×C149C22×D411yescharacteristic
123C2×D149—22no—
124C2×D149—22no—
125C2×D149—41no—
126C2×D149—41no—
127C2×D149—41no—
128C2×D149—41no—
129C2×D149—42no—
130C2×D149—42no—
131C2×D149—42no—
132C2×D149—88no—
133C4×C149—22no—
134C4×C149—21no—
135C4×C149AGL(1,ℤ/8)12yescomplemented
136C4×C149C22×D411yescharacteristic
137C4×C149H(5,𝔽2)11yescharacteristic
138Dic149—42no—
139Dic149—41no—
140Dic149—41no—
141C2×C149—42no—
142C2×C149D4211yescharacteristic
143C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C149#57711yescharacteristic
145D149—42no—
146D149—42no—
147D149—82no—
148C149#327211yescharacteristic, complemented, Sylow
149#3272—1491nomaximal, Sylow
150C2×AGL(1,ℤ/8)—1492no—
151#547—1491no—
152D42—1491no—
153#492—1491no—
154#468—1492no—
155#461—1491no—
156#459—1491no—
157#450—1492no—
158#449—1492no—
159C4×D8—1491no—
160#436D14911yescharacteristic, complemented
161C2×#41—1492no—
162C22×D4—2981no—
163C22×D4—1492no—
164AGL(1,ℤ/8)—2988no—
165C2×SD16—1492no—
166C2×SD16—1492no—
167C2×SD16—1492no—
168C2×D8—1492no—
169C2×D8—1491no—
170C2×M16C2×D14912yescomplemented
171C4⋊Q8—1491no—
172#127—1491no—
173#123—2982no—
174C22⋊Q8—1492no—
175#121—2981no—
176#121—2981no—
177#121—1492no—
178#120—2982no—
179C4×D4—1491no—
180C4×D4—1491no—
181C4×D4C2×D14911yescharacteristic
182C2×C4⋊C4—2981no—
183#107—1491no—
184C4⋊C8C2×D14911yescharacteristic, complemented
185#103—1492no—
186#102—1491no—
187#102—1491no—
188#102—1492no—
189C22⋊C8C2×D14912yescomplemented
190C4×C8C2×D14911yescharacteristic, complemented
191C24—2982no—
192#41—2984no—
193#41—5962no—
194C2×Q8—1492no—
195C2×D4—2984no—
196C2×D4—2982no—
197C2×D4—2982no—
198C2×D4—2982no—
199C2×D4—2981no—
200C2×D4—2981no—
201C2×D4—5962no—
202C2×D4—5964no—
203C2×D4—1492no—
204C2×D4—1491no—
205C2×D4—1491no—
206C2×D4D59611yescharacteristic
207C22×C4—2981no—
208C22×C4—2982no—
209C22×C4—2981no—
210C22×C4C22×D14912yes—
211SD16—2984no—
212SD16—2984no—
213SD16—5962no—
214D8—2984no—
215D8—1494no—
216M16—24no—
217C2×C8C22×D14911yescharacteristic
218C2×C8C22×D14912yes—
219C2×C8C22×D14911yescharacteristic
220C4⋊C4—2981no—
221C4⋊C4—2982no—
222C4⋊C4—2981no—
223C4⋊C4—1491no—
224C4⋊C4—1491no—
225C4⋊C4D59611yescharacteristic
226C22⋊C4—2982no—
227C22⋊C4—2981no—
228C22⋊C4—2981no—
229C22⋊C4—2982no—
230C22⋊C4D59612yes—
231C42C22×D14911yescharacteristic
232C23—2981no—
233C23—2981no—
234C23—2982no—
235C23—5964no—
236C23—5964no—
237C23—11922no—
238C23C2×D59612yes—
239Q8—2982no—
240Q8—2982no—
241D4—22no—
242D4—2982no—
243D4—2981no—
244D4—2981no—
245D4—2982no—
246D4—5964no—
247D4—5964no—
248D4—5964no—
249D4—5962no—
250D4—1492no—
251D4—1492no—
252D4—11921no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—2981no—
256C2×C4—2981no—
257C2×C4—2982no—
258C2×C4—5964no—
259C2×C4—5962no—
260C2×C4—5962no—
261C2×C4C2×D59611yescharacteristic
262C2×C4C2×D59612yes—
263C2×C4C2×D59611yescharacteristic
264C2×C4C23×D14911yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D14912yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—2982no—
272C22—2982no—
273C22—5961no—
274C22—5961no—
275C22—5961no—
276C22—5961no—
277C22—5962no—
278C22—5962no—
279C22—5962no—
280C22—11928no—
281C22C22×D59611yescharacteristic
282C4—21no—
283C4—22no—
284C4—5961no—
285C4—5961no—
286C4—5962no—
287C4#1801193912yescomplemented
288C4C2×D4×D14911yescharacteristic
289C4#1801195711yescharacteristic
290C2—42no—
291C2—5962no—
292C2—5962no—
293C2—11922no—
294C2D4×D59611yescharacteristic
295C2C2×#1801193911yescharacteristic
296C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#436×C149C2
socleC22×C149C22×D4
hypercenter#436D149
hypocenterC149#3272
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. #23750280C2semidirect
3. D4×D596C2semidirect
4. #23749998C2semidirect
5. #23749871C2semidirect
6. #23749831C2semidirect
7. #23749821C2semidirect
8. #23749778C2semidirect
9. #23749772C2semidirect
10. C4×D1192C2semidirect
11. #436×C149C2semidirect
12. C2×#14558736C22semidirect
17. C2×#14558725C22semidirect
18. C2×#14558725C22semidirect
20. C2×D1192C22semidirect
21. #18011911C22semidirect
24. #18011890C22semidirect
30. C4×D596C22semidirect
32. #18011845C22semidirect
33. #18011836C22semidirect
35. #18011833C22semidirect
36. #18011833C22semidirect
37. C2×M16×C149C22semidirect
39. C4⋊C8×C149C22semidirect
40. C22⋊C8×C149C22semidirect
41. C4×C8×C149C22semidirect
64. D1192D4semidirect
99. D596C2×D4semidirect
118. C8×C149C2×D4semidirect
135. C4×C149AGL(1,ℤ/8)semidirect
148. C149#3272semidirect
160. #436D149semidirect
170. C2×M16C2×D149semidirect
184. C4⋊C8C2×D149semidirect
189. C22⋊C8C2×D149semidirect
190. C4×C8C2×D149semidirect
267. C8D4×D149semidirect
287. C4#18011939semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
#237502802
D4×D5962
#237499982
#237498712
#237498312
#237498212
#237497782
#237497722
C4×D11922
#436×C1492
#3272149