Finite Group Databasebeta

← #34055490

Subgroups — #34055490

Order 19072.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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×#18011886C211yesmaximal, characteristic, complemented
2#121×D149C211yesmaximal, characteristic, complemented
3#23749945C212yesmaximal, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749879C212yesmaximal, complemented
6#23749877C212yesmaximal, complemented
7#23749761C211yesmaximal, characteristic, complemented
8#23749760C212yesmaximal, complemented
9#23749758C211yesmaximal, characteristic, complemented
10#23749587C211yesmaximal, characteristic, complemented
11#481×C149C211yesmaximal, characteristic, complemented
12C22×D596—21no—
13C22×D596C2211yescharacteristic, complemented
14C2×D4×D149—21no—
15C2×D4×D149C2211yescharacteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C2×D1192C2212yescomplemented
18C2×#14558721C2212yescomplemented
19C2×#14558719C2212yescomplemented
20#18011886—21no—
21#18011886—21no—
22#18011886C2212yes—
23#18011886C2211yescharacteristic, complemented
24#18011886C2212yescomplemented
25#18011885C2211yescharacteristic
26#18011884—21no—
27#18011883—21no—
28#18011882C2211yescharacteristic, complemented
29C4⋊C4×D149C2211yescharacteristic, complemented
30C2×#14558713—21no—
31C22⋊C4×D149—21no—
32#18011842C2212yescomplemented
33#18011833C2212yescomplemented
34#18011831C2212yescomplemented
35#18011831C2212yescomplemented
36C22⋊#11924746C2211yescharacteristic, complemented
37#18011823C2212yescomplemented
38#121×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic, complemented
40#106×C149C2212yescomplemented
41#102×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44C23×D149—21no—
45C23×D149D411yescharacteristic
46C2×D596—21no—
47C2×D596—22no—
48C2×D596—22no—
49C2×D596—21no—
50C2×D596—42no—
51C2×D596—44no—
52C2×D596C2312yes—
53C2×D596C2311yescharacteristic
54C2×C22⋊D149—21no—
55C2×C22⋊D149—21no—
56C2×C22⋊D149—21no—
57D4×D149—42no—
58D4×D149—44no—
59C22×Dic149D411yescharacteristic
60C2×C4×D149—21no—
61C2×C4×D149—42no—
62C2×C4×D149D411yescharacteristic
63C2×C4×D149D411yescharacteristic
64C2×C4×D149C2311yescharacteristic
65C2×C4×D149C2311yescharacteristic
66D1192—42no—
67#14558721—42no—
68#14558719—42no—
69C2×#11924746C2312yes—
70C4⋊Dic149C2311yescharacteristic
71#14558715—21no—
72C22⋊Dic149—21no—
73#14558713—21no—
74#14558713—22no—
75#14558713—22no—
76#14558713—21no—
77C2×D4×C149—21no—
78C2×D4×C149C2311yescharacteristic
79C22×C4×C149—21no—
80C22×C4×C149C2311yescharacteristic
81C2×C8×C149C2312yes—
82C4⋊C4×C149—21no—
83C4⋊C4×C149C2312yes—
84C4⋊C4×C149C2311yescharacteristic
85C22⋊C4×C149—21no—
86C22×D149—22no—
87C22×D149—22no—
88C22×D149—21no—
89C22×D149—22no—
90C22×D149—41no—
91C22×D149—42no—
92C22×D149—42no—
93C22×D149—42no—
94C22×D149—42no—
95C22×D149—42no—
96C22×D149—42no—
97C22×D149C2×D411yescharacteristic
98C22×D149C2×D411yescharacteristic
99D596—22no—
100D596—22no—
101D596—22no—
102D596—42no—
103D596—42no—
104D596—44no—
105D596—44no—
106C22⋊D149—42no—
107C22⋊D149—42no—
108C22⋊D149—42no—
109C2×Dic149—21no—
110C2×Dic149—41no—
111C2×Dic149C2×D411yescharacteristic
112C2×Dic149C2×D411yescharacteristic
113C4×D149—22no—
114C4×D149—22no—
115C4×D149—41no—
116C4×D149—41no—
117C4×D149—42no—
118#11924746—22no—
119C23×C149—21no—
120C23×C149C2×D411yescharacteristic
121D4×C149—22no—
122D4×C149—42no—
123C2×C4×C149—22no—
124C2×C4×C149—21no—
125C2×C4×C149—22no—
126C2×C4×C149—42no—
127C2×C4×C149C2×D411yescharacteristic
128C2×C4×C149C2411yescharacteristic
129C8×C149—22no—
130C22×C149—21no—
131C22×C149—21no—
132C22×C149—41no—
133C22×C149—41no—
134C22×C149—41no—
135C22×C149AGL(1,ℤ/8)12yes—
136C22×C149C22×D411yescharacteristic
137C2×D149—21no—
138C2×D149—21no—
139C2×D149—21no—
140C2×D149—21no—
141C2×D149—21no—
142C2×D149—44no—
143C2×D149—41no—
144C2×D149—42no—
145C2×D149—41no—
146C2×D149—42no—
147C2×D149—41no—
148C2×D149—42no—
149C2×D149—84no—
150C2×D149—84no—
151C2×D149AGL(1,ℤ/8)12yes—
152C4×C149—21no—
153C4×C149—42no—
154C4×C149—41no—
155C4×C149H(5,𝔽2)12yes—
156Dic149—21no—
157Dic149—21no—
158Dic149—41no—
159C2×C149—22no—
160C2×C149—81no—
161C2×C149#53411yescharacteristic
162C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
164D149—22no—
165D149—41no—
166D149—81no—
167D149—82no—
168C149#319211yescharacteristic, complemented, Sylow
169#3192—1491nomaximal, Sylow
170C2×#121—1491no—
171C2×#121—1491no—
172#481—1491no—
173#481—1492no—
174#481D14911yescharacteristic, complemented
175#469—1492no—
176#469—1492no—
177#447—1491no—
178#447—1492no—
179#447—1491no—
180#407—1491no—
181C22×D4—2981no—
182C22×D4—2981no—
183C22×D4—1491no—
184C22×D4—1491no—
185C23×C4—1491no—
186C2×D8—1492no—
187C2×D8—1492no—
188C2×M16—1492no—
189#121—2981no—
190#121—2981no—
191#121—2981no—
192#121—2981no—
193#121—1491no—
194#121—1491no—
195#121—1492no—
196#121—1491no—
197#121—1492no—
198#121C2×D14911yescharacteristic
199C2×C4⋊C4—1491no—
200C2×C4⋊C4C2×D14911yescharacteristic, complemented
201C2×C22⋊C4—2981no—
202C2×C22⋊C4—2981no—
203#106—1492no—
204#106C2×D14912yescomplemented
205#102—1492no—
206#102—1492no—
207#102—1492no—
208#102C2×D14912yescomplemented
209C22⋊C8—1491no—
210C22⋊C8—1492no—
211C22⋊C8C2×D14911yescharacteristic, complemented
212C24—2981no—
213C24—2981no—
214C24—1491no—
215C2×D4—21no—
216C2×D4—2981no—
217C2×D4—2982no—
218C2×D4—2982no—
219C2×D4—2981no—
220C2×D4—2981no—
221C2×D4—2981no—
222C2×D4—2981no—
223C2×D4—5962no—
224C2×D4—5964no—
225C2×D4—5962no—
226C2×D4—5964no—
227C2×D4—1492no—
228C2×D4—1491no—
229C2×D4C22×D14911yescharacteristic
230C22×C4—21no—
231C22×C4—2981no—
232C22×C4—5962no—
233C22×C4—1491no—
234C22×C4—1491no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4C22×D14911yescharacteristic
239D8—5962no—
240D8—5962no—
241M16—5962no—
242C2×C8—1492no—
243C2×C8C22×D14912yes—
244C4⋊C4—21no—
245C4⋊C4—2981no—
246C4⋊C4—1491no—
247C4⋊C4C22×D14911yescharacteristic
248C4⋊C4C22×D14912yes—
249C22⋊C4—21no—
250C22⋊C4—2981no—
251C22⋊C4—2982no—
252C22⋊C4—2982no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C23—21no—
256C23—2982no—
257C23—2982no—
258C23—2982no—
259C23—2981no—
260C23—5961no—
261C23—5962no—
262C23—5962no—
263C23—5962no—
264C23—5962no—
265C23—5962no—
266C23—5962no—
267C23—1491no—
268C23—1491no—
269C23D4×D14911yescharacteristic
270D4—22no—
271D4—42no—
272D4—2982no—
273D4—2982no—
274D4—2982no—
275D4—5962no—
276D4—5964no—
277D4—5962no—
278D4—5964no—
279D4—5962no—
280D4—5962no—
281D4—5962no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—2982no—
287C2×C4—2982no—
288C2×C4—2981no—
289C2×C4—5961no—
290C2×C4—5961no—
291C2×C4—5962no—
292C2×C4—5961no—
293C2×C4—1491no—
294C2×C4—1491no—
295C2×C4D4×D14911yescharacteristic
296C2×C4C23×D14911yescharacteristic
297C8—22no—
298C8—2982no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—2981no—
305C22—2981no—
306C22—2981no—
307C22—2981no—
308C22—2981no—
309C22—5964no—
310C22—5962no—
311C22—5961no—
312C22—5961no—
313C22—5962no—
314C22—5962no—
315C22—5961no—
316C22—1492no—
317C22—11924no—
318C22—11924no—
319C22#1801193812yes—
320C22C2×D4×D14911yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—2981no—
325C4—2981no—
326C4—5961no—
327C4#1801195712yes—
328C2—22no—
329C2—81no—
330C2—2982no—
331C2—5961no—
332C2—11922no—
333C2—11921no—
334C2#2375018611yescharacteristic
335C2AGL(1,ℤ/8)×D14911yescharacteristic
336C2C2×#1801193811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#481×C149C2
socleC22×C149C22×D4
hypercenter#481D149
hypocenterC149#3192
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#18011886C2semidirect
2. #121×D149C2semidirect
3. #23749945C2semidirect
4. #23749943C2semidirect
5. #23749879C2semidirect
6. #23749877C2semidirect
7. #23749761C2semidirect
8. #23749760C2semidirect
9. #23749758C2semidirect
10. #23749587C2semidirect
11. #481×C149C2semidirect
13. C22×D596C22semidirect
15. C2×D4×D149C22semidirect
17. C2×D1192C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558719C22semidirect
23. #18011886C22semidirect
24. #18011886C22semidirect
28. #18011882C22semidirect
29. C4⋊C4×D149C22semidirect
32. #18011842C22semidirect
33. #18011833C22semidirect
34. #18011831C22semidirect
35. #18011831C22semidirect
36. C22⋊#11924746C22semidirect
37. #18011823C22semidirect
39. C2×C4⋊C4×C149C22semidirect
40. #106×C149C22semidirect
41. #102×C149C22semidirect
42. C22⋊C8×C149C22semidirect
168. C149#3192semidirect
174. #481D149semidirect
200. C2×C4⋊C4C2×D149semidirect
204. #106C2×D149semidirect
208. #102C2×D149semidirect
211. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118862
#121×D1492
#237499452
#237499432
#237498792
#237498772
#237497612
#237497602
#237497582
#237495872
#481×C1492
#3192149