Finite Group Databasebeta

← #34054166

Subgroups — #34054166

Order 19072.

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

normal subgroups only

This group has 584 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×#18011935C212yesmaximal, complemented
2#127×D149C211yesmaximal, characteristic, complemented
3C4×#14558735C211yesmaximal, characteristic, complemented
4#23749826C211yesmaximal, characteristic, complemented
5#23749824C212yesmaximal, complemented
6#23749822C211yesmaximal, characteristic, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749818C212yesmaximal, complemented
9#23749647C211yesmaximal, characteristic, complemented
10#23749628C212yesmaximal, complemented
11#459×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2211yescharacteristic
13C2×D4×D149—21no—
14C2×D4×D149—21no—
15C2×D4×D149C2212yes—
16#18011935—28no—
17C2×#14558725C2212yescomplemented
18C2×#14558724C2212yescomplemented
19C2×#14558721C2212yescomplemented
20C2×#14558719C2212yes—
21#18011908C2211yescharacteristic
22#18011907—21no—
23#18011907—21no—
24#18011907C2212yes—
25C4×Dic298C2211yescharacteristic, complemented
26#18011876C2211yescharacteristic, complemented
27D4×Dic149C2211yescharacteristic, complemented
28C4×C22⋊D149—21no—
29#18011871—21no—
30#18011869C2211yescharacteristic
31#18011867—21no—
32C2×C4×Dic149—21no—
33C42×D149C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic, complemented
35#18011840C2212yescomplemented
36#18011833C2212yescomplemented
37#18011832C2212yescomplemented
38#18011831C2212yescomplemented
39C2×D8×C149C2212yescomplemented
40#127×C149C2211yescharacteristic
41C4×D4×C149C2211yescharacteristic, complemented
42C4⋊C8×C149C2211yescharacteristic, complemented
43#102×C149C2212yescomplemented
44C23×D149—22no—
45#14558735—22no—
46#14558735D414yescomplemented
47C2×Dic298C2311yescharacteristic
48C2×D596—21no—
49C2×D596—21no—
50C2×D596C2312yes—
51C2×C22⋊D149—21no—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54C2×C22⋊D149—22no—
55D4×D149—24no—
56D4×D149—24no—
57D4×D149—44no—
58D4×D149—44no—
59C22×Dic149—21no—
60C22×Dic149—21no—
61C2×C4×D149D411yescharacteristic
62C2×C4×D149D411yescharacteristic
63C2×C4×D149C2311yescharacteristic
64#14558725—24no—
65#14558724—24no—
66#14558721—24no—
67#14558719—24no—
68C2×#11924746C2312yes—
69C4⋊Dic149C2311yescharacteristic
70#14558715—21no—
71#14558715—21no—
72C22⋊Dic149—21no—
73#14558713—21no—
74C4×Dic149—21no—
75C4×Dic149—21no—
76C4×Dic149—21no—
77C4×Dic149D411yescharacteristic
78C4×Dic149D411yescharacteristic
79C4×Dic149C2311yescharacteristic
80C2×D4×C149—21no—
81C2×D4×C149—21no—
82C2×D4×C149C2312yes—
83C2×D4×C149C2311yescharacteristic
84C22×C4×C149—21no—
85D8×C149—24no—
86C2×C8×C149C2312yes—
87C4⋊C4×C149C2311yescharacteristic
88C22⋊C4×C149—21no—
89C42×C149C2311yescharacteristic
90C22×D149—22no—
91C22×D149—44no—
92C22×D149—44no—
93C22×D149—44no—
94C22×D149C2×D411yescharacteristic
95Dic298—21no—
96Dic298C2×D412yescomplemented
97D596—22no—
98D596—22no—
99D596—42no—
100D596—42no—
101C22⋊D149—24no—
102C22⋊D149—44no—
103C22⋊D149—44no—
104C22⋊D149—44no—
105C2×Dic149—21no—
106C2×Dic149—24no—
107C2×Dic149—21no—
108C2×Dic149—42no—
109C2×Dic149C2×D411yescharacteristic
110C2×Dic149C2×D411yescharacteristic
111C2×Dic149C2×D411yescharacteristic
112C4×D149—22no—
113C4×D149—22no—
114C4×D149C2×D412yes—
115C4×D149#4112yes—
116#11924746—22no—
117C23×C149—21no—
118C23×C149—22no—
119D4×C149—22no—
120D4×C149—21no—
121D4×C149—22no—
122D4×C149—42no—
123D4×C149—42no—
124D4×C149C2×D412yescomplemented
125C2×C4×C149—21no—
126C2×C4×C149—42no—
127C2×C4×C149C2×D411yescharacteristic
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2411yescharacteristic
130C8×C149—22no—
131C22×C149—22no—
132C22×C149—41no—
133C22×C149—41no—
134C22×C149—42no—
135C22×C149—42no—
136C22×C149—42no—
137C22×C149C22×D411yescharacteristic
138C2×D149—21no—
139C2×D149—21no—
140C2×D149—42no—
141C2×D149—42no—
142C2×D149—42no—
143C2×D149—88no—
144C2×D149#12112yes—
145C4×C149—21no—
146C4×C149—41no—
147C4×C149AGL(1,ℤ/8)12yescomplemented
148C4×C149C22×D411yescharacteristic
149C4×C149C2×#4111yescharacteristic
150Dic149—22no—
151Dic149—21no—
152Dic149—41no—
153Dic149#12112yes—
154Dic149AGL(1,ℤ/8)12yescomplemented
155C2×C149—42no—
156C2×C149—82no—
157C2×C149C2×#12111yescharacteristic
158C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
160D149—22no—
161D149—82no—
162C149#303811yescharacteristic, complemented, Sylow
163#3038—1491nomaximal, Sylow
164C2×AGL(1,ℤ/8)—1492no—
165C2×#127—1491no—
166C4×#41—1491no—
167#460—1491no—
168#460—1491no—
169#460—1492no—
170#459—1492no—
171#459—1491no—
172#459D14911yescharacteristic, complemented
173#423—1491no—
174#418—1492no—
175C2×#41—1491no—
176C22×D4—2981no—
177C22×D4—2981no—
178C22×D4—1492no—
179AGL(1,ℤ/8)—2988no—
180C2×SD16—1492no—
181C2×SD16—1492no—
182C2×D8—1492no—
183C2×D8C2×D14912yescomplemented
184C2×M16—1492no—
185#127—2981no—
186#127—2981no—
187#127—1492no—
188#127—1491no—
189#127C2×D14911yescharacteristic
190C4×Q8—1491no—
191C4×Q8—1491no—
192C4×D4—2981no—
193C4×D4—2981no—
194C4×D4—1491no—
195C4×D4C2×D14911yescharacteristic, complemented
196#117—2981no—
197#117—1491no—
198C2×C42—2981no—
199C2×C42—1491no—
200C4⋊C8—1492no—
201C4⋊C8—1491no—
202C4⋊C8C2×D14911yescharacteristic, complemented
203#102—1492no—
204#102—1492no—
205#102—1492no—
206#102C2×D14912yescomplemented
207C24—2982no—
208#41—2982no—
209#41—1494no—
210C2×Q8—1491no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—2981no—
214C2×D4—2984no—
215C2×D4—2984no—
216C2×D4—2982no—
217C2×D4—2982no—
218C2×D4—2982no—
219C2×D4—2981no—
220C2×D4—2981no—
221C2×D4—5964no—
222C2×D4—5964no—
223C2×D4—1492no—
224C2×D4C22×D14912yes—
225C2×D4C22×D14911yescharacteristic
226C22×C4—21no—
227C22×C4—2981no—
228C22×C4—2981no—
229C22×C4—1491no—
230C22×C4—1491no—
231C22×C4—1491no—
232SD16—2984no—
233SD16—2984no—
234D8—24no—
235D8—2984no—
236M16—2984no—
237C2×C8—1492no—
238C2×C8C22×D14912yes—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—1491no—
242C4⋊C4C22×D14911yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—2981no—
245C22⋊C4—2981no—
246C42—2981no—
247C42—2981no—
248C42—2981no—
249C42—1491no—
250C42—1491no—
251C42—1491no—
252C42C22×D14911yescharacteristic
253C23—21no—
254C23—22no—
255C23—2982no—
256C23—5964no—
257C23—5964no—
258C23—5964no—
259C23—1491no—
260Q8—2981no—
261Q8—1492no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—2984no—
268D4—2982no—
269D4—2982no—
270D4—5962no—
271D4—5964no—
272D4—5964no—
273D4—5964no—
274D4—5962no—
275D4D4×D14912yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—2982no—
279C2×C4—2981no—
280C2×C4—2984no—
281C2×C4—2982no—
282C2×C4—2981no—
283C2×C4—5962no—
284C2×C4—1491no—
285C2×C4—1491no—
286C2×C4—1491no—
287C2×C4—1492no—
288C2×C4—1492no—
289C2×C4D4×D14911yescharacteristic
290C2×C4D4×D14911yescharacteristic
291C2×C4C23×D14911yescharacteristic
292C8—22no—
293C8—2982no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—2981no—
301C22—2981no—
302C22—5962no—
303C22—5962no—
304C22—5962no—
305C22—1492no—
306C22—11928no—
307C22C2×D4×D14911yescharacteristic
308C4—21no—
309C4—41no—
310C4—2981no—
311C4—2982no—
312C4—5961no—
313C4—1492no—
314C4—1492no—
315C4#1801193512yescomplemented
316C4C2×D4×D14911yescharacteristic
317C4#41×D14911yescharacteristic
318C2—42no—
319C2—82no—
320C2—2982no—
321C2—11922no—
322C2#121×D14911yescharacteristic
323C2AGL(1,ℤ/8)×D14911yescharacteristic
324C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3038
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. #127×D149C2semidirect
3. C4×#14558735C2semidirect
4. #23749826C2semidirect
5. #23749824C2semidirect
6. #23749822C2semidirect
7. #23749820C2semidirect
8. #23749818C2semidirect
9. #23749647C2semidirect
10. #23749628C2semidirect
11. #459×C149C2semidirect
17. C2×#14558725C22semidirect
18. C2×#14558724C22semidirect
19. C2×#14558721C22semidirect
25. C4×Dic298C22semidirect
26. #18011876C22semidirect
27. D4×Dic149C22semidirect
34. C4⋊#11924746C22semidirect
35. #18011840C22semidirect
36. #18011833C22semidirect
37. #18011832C22semidirect
38. #18011831C22semidirect
39. C2×D8×C149C22semidirect
41. C4×D4×C149C22semidirect
42. C4⋊C8×C149C22semidirect
43. #102×C149C22semidirect
46. #14558735D4semidirect
96. Dic298C2×D4semidirect
124. D4×C149C2×D4semidirect
147. C4×C149AGL(1,ℤ/8)semidirect
154. Dic149AGL(1,ℤ/8)semidirect
162. C149#3038semidirect
172. #459D149semidirect
183. C2×D8C2×D149semidirect
195. C4×D4C2×D149semidirect
202. C4⋊C8C2×D149semidirect
206. #102C2×D149semidirect
275. D4D4×D149semidirect
315. C4#18011935semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
#127×D1492
C4×#145587352
#237498262
#237498242
#237498222
#237498202
#237498182
#237496472
#237496282
#459×C1492
#3038149