Finite Group Databasebeta

← #34054784

Subgroups — #34054784

Order 19072.

488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#23750176C211yesmaximal, characteristic, complemented
2C4×D4×D149C211yesmaximal, characteristic, complemented
3#23749945C212yesmaximal, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749821C211yesmaximal, characteristic, complemented
6#23749820C211yesmaximal, characteristic, complemented
7#23749760C212yesmaximal, complemented
8#23749736C212yesmaximal, complemented
9#23749734C212yesmaximal, complemented
10#23749681C211yesmaximal, characteristic, complemented
11#476×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—21no—
13C2×D4×D149C2211yescharacteristic
14C22×C4×D149—21no—
15C2×D1192C2212yes—
16C2×#14558721C2212yes—
17#18011908C2211yescharacteristic, complemented
18#18011900—21no—
19#18011886—21no—
20#18011886C2212yes—
21C4×D596C2211yescharacteristic
22D4×Dic149C2211yescharacteristic
23#18011873—21no—
24#18011873C2211yescharacteristic
25#18011873C2212yescomplemented
26C4×C22⋊D149—21no—
27#18011871—21no—
28C4⋊C4×D149C2211yescharacteristic
29C22⋊C4×D149—21no—
30C42×D149C2211yescharacteristic
31#18011842C2212yescomplemented
32C4⋊#11924746C2211yescharacteristic, complemented
33#18011833C2212yescomplemented
34#18011831C2212yes—
35#18011831C2212yescomplemented
36#18011823C2212yes—
37#18011821C2212yescomplemented
38C4⋊Q8×C149C2211yescharacteristic, complemented
39C4×D4×C149C2211yescharacteristic
40#106×C149C2212yescomplemented
41C4⋊C8×C149C2211yescharacteristic, complemented
42#102×C149C2212yes—
43C23×D149—21no—
44#14558737—44no—
45C2×D596—22no—
46C2×D596—21no—
47C2×D596—21no—
48C2×D596C2312yes—
49C2×D596C2311yescharacteristic
50C2×C22⋊D149—21no—
51D4×D149—22no—
52D4×D149—22no—
53C22×Dic149—21no—
54C2×C4×D149—21no—
55C2×C4×D149—21no—
56C2×C4×D149—22no—
57C2×C4×D149—21no—
58C2×C4×D149—44no—
59C2×C4×D149D411yescharacteristic
60C2×C4×D149D411yescharacteristic
61C2×C4×D149C2311yescharacteristic
62D1192—24no—
63#14558721—24no—
64C2×#11924746C2312yes—
65C4⋊Dic149C2311yescharacteristic
66#14558715—21no—
67C22⋊Dic149—21no—
68#14558713—21no—
69#14558713—22no—
70#14558713—22no—
71#14558713—21no—
72C4×Dic149D411yescharacteristic
73C4×Dic149D411yescharacteristic
74C4×Dic149C2311yescharacteristic
75C2×Q8×C149—21no—
76C2×D4×C149C2311yescharacteristic
77C22×C4×C149—21no—
78C2×C8×C149C2312yes—
79C4⋊C4×C149—21no—
80C4⋊C4×C149C2312yes—
81C4⋊C4×C149C2311yescharacteristic
82C22⋊C4×C149—21no—
83C42×C149C2311yescharacteristic
84C22×D149—24no—
85C22×D149—21no—
86C22×D149—22no—
87C22×D149—42no—
88C22×D149—42no—
89C22×D149C2×D411yescharacteristic
90D596—21no—
91D596—22no—
92D596—22no—
93D596—42no—
94D596—44no—
95D596—42no—
96D596#4112yescomplemented
97C22⋊D149—24no—
98C2×Dic149—21no—
99C2×Dic149—42no—
100C2×Dic149C2×D411yescharacteristic
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C4×D149—22no—
104C4×D149—22no—
105C4×D149—21no—
106C4×D149—21no—
107C4×D149—42no—
108C4×D149—44no—
109C4×D149—42no—
110C4×D149—42no—
111#11924746—22no—
112C23×C149—21no—
113Q8×C149—42no—
114D4×C149—21no—
115D4×C149#4112yescomplemented
116C2×C4×C149—21no—
117C2×C4×C149—22no—
118C2×C4×C149—42no—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2411yescharacteristic
122C8×C149—22no—
123C22×C149—22no—
124C22×C149—41no—
125C22×C149—41no—
126C22×C149C22×D411yescharacteristic
127C2×D149—21no—
128C2×D149—21no—
129C2×D149—22no—
130C2×D149—48no—
131C2×D149—41no—
132C2×D149—41no—
133C2×D149—42no—
134C2×D149—42no—
135C2×D149—42no—
136C2×D149AGL(1,ℤ/8)12yes—
137C4×C149—21no—
138C4×C149—41no—
139C4×C149—42no—
140C4×C149AGL(1,ℤ/8)12yes—
141C4×C149C2×#4111yescharacteristic
142C4×C149C2×#4111yescharacteristic
143Dic149—21no—
144Dic149—21no—
145Dic149—21no—
146Dic149—41no—
147C2×C149—42no—
148C2×C149#52511yescharacteristic
149C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
151D149—22no—
152D149—42no—
153D149—82no—
154C149#310911yescharacteristic, complemented, Sylow
155#3109—1491nomaximal, Sylow
156#532—1491no—
157C2×C4×D4—1491no—
158#481—1492no—
159#476—1491no—
160#476D14911yescharacteristic, complemented
161#459—1491no—
162#459—1491no—
163#447—1492no—
164#442—1492no—
165#442—1492no—
166#432—1491no—
167C2×#41—2981no—
168C22×D4—1491no—
169C23×C4—2981no—
170C2×D8—1492no—
171C2×D8—1492no—
172C4⋊Q8C2×D14911yescharacteristic, complemented
173#127—1491no—
174#124—2981no—
175#121—2981no—
176#121—1492no—
177C4×D4—2981no—
178C4×D4—2981no—
179C4×D4—2981no—
180C4×D4—1491no—
181C4×D4—1491no—
182C4×D4—1492no—
183C4×D4—1491no—
184C4×D4C2×D14911yescharacteristic
185C2×C4⋊C4—1491no—
186C2×C22⋊C4—2981no—
187C2×C42—1491no—
188#106—1492no—
189#106C2×D14912yescomplemented
190C4⋊C8—1491no—
191C4⋊C8C2×D14911yescharacteristic, complemented
192#102—1492no—
193#102—1492no—
194#102—1492no—
195#102C2×D14912yes—
196C22⋊C8—1492no—
197#97—1492no—
198C24—2981no—
199#41—5964no—
200C2×Q8—21no—
201C2×D4—2982no—
202C2×D4—2982no—
203C2×D4—2982no—
204C2×D4—2981no—
205C2×D4—2981no—
206C2×D4—2981no—
207C2×D4—1492no—
208C2×D4—1491no—
209C2×D4C22×D14911yescharacteristic
210C22×C4—21no—
211C22×C4—2981no—
212C22×C4—2981no—
213C22×C4—2982no—
214C22×C4—2981no—
215C22×C4—2981no—
216C22×C4—5964no—
217C22×C4—1491no—
218C22×C4—1491no—
219C22×C4—1491no—
220D8—2984no—
221D8—2984no—
222C2×C8—1492no—
223C2×C8C22×D14912yes—
224C4⋊C4—21no—
225C4⋊C4—2981no—
226C4⋊C4—1491no—
227C4⋊C4C22×D14911yescharacteristic
228C4⋊C4C22×D14912yes—
229C22⋊C4—21no—
230C22⋊C4—2981no—
231C22⋊C4—2982no—
232C22⋊C4—2982no—
233C22⋊C4—2981no—
234C22⋊C4—2981no—
235C42—1491no—
236C42—1491no—
237C42—1491no—
238C42C22×D14911yescharacteristic
239C23—21no—
240C23—2984no—
241C23—2981no—
242C23—2982no—
243C23—5962no—
244C23—5962no—
245C23—1491no—
246Q8—42no—
247D4—21no—
248D4—2984no—
249D4—2982no—
250D4—2981no—
251D4—2982no—
252D4—5962no—
253D4—5964no—
254D4—5962no—
255D4—1492no—
256D4#1455873712yescomplemented
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—2982no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—2981no—
264C2×C4—2981no—
265C2×C4—5962no—
266C2×C4—5964no—
267C2×C4—5962no—
268C2×C4—5962no—
269C2×C4—5962no—
270C2×C4—1491no—
271C2×C4—1491no—
272C2×C4—1491no—
273C2×C4D4×D14911yescharacteristic
274C2×C4D4×D14911yescharacteristic
275C2×C4C23×D14911yescharacteristic
276C8—22no—
277C8—2982no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—2981no—
282C22—2981no—
283C22—2982no—
284C22—5968no—
285C22—5961no—
286C22—5961no—
287C22—5962no—
288C22—5962no—
289C22—5962no—
290C22—1492no—
291C22C2×D4×D14911yescharacteristic
292C4—21no—
293C4—42no—
294C4—41no—
295C4—2981no—
296C4—2981no—
297C4—2981no—
298C4—5961no—
299C4#1801193812yes—
300C4#41×D14911yescharacteristic
301C4C2×#1455873711yescharacteristic
302C2—42no—
303C2—2982no—
304C2—5962no—
305C2—11922no—
306C2#2375013811yescharacteristic
307C2AGL(1,ℤ/8)×D14911yescharacteristic
308C2C2×#1801193811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#476×C149C2
socleC22×C149C22×D4
hypercenter#476D149
hypocenterC149#3109
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #23750176C2semidirect
2. C4×D4×D149C2semidirect
3. #23749945C2semidirect
4. #23749912C2semidirect
5. #23749821C2semidirect
6. #23749820C2semidirect
7. #23749760C2semidirect
8. #23749736C2semidirect
9. #23749734C2semidirect
10. #23749681C2semidirect
11. #476×C149C2semidirect
17. #18011908C22semidirect
25. #18011873C22semidirect
31. #18011842C22semidirect
32. C4⋊#11924746C22semidirect
33. #18011833C22semidirect
35. #18011831C22semidirect
37. #18011821C22semidirect
38. C4⋊Q8×C149C22semidirect
40. #106×C149C22semidirect
41. C4⋊C8×C149C22semidirect
96. D596#41semidirect
115. D4×C149#41semidirect
154. C149#3109semidirect
160. #476D149semidirect
172. C4⋊Q8C2×D149semidirect
189. #106C2×D149semidirect
191. C4⋊C8C2×D149semidirect
256. D4#14558737semidirect

Maximal subgroups

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

subgroupindex
#237501762
C4×D4×D1492
#237499452
#237499122
#237498212
#237498202
#237497602
#237497362
#237497342
#237496812
#476×C1492
#3109149