Finite Group Databasebeta

← #34055708

Subgroups — #34055708

Order 19072.

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

normal subgroups only

This group has 490 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
1#127×D149C211yesmaximal, characteristic, complemented
2#23750157C211yesmaximal, characteristic, complemented
3#23750013C212yesmaximal, complemented
4#23749988C212yesmaximal, complemented
5#23749826C211yesmaximal, characteristic, complemented
6#23749822C211yesmaximal, characteristic, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749777C212yesmaximal, complemented
9#23749757C212yesmaximal, complemented
10#23749681C211yesmaximal, characteristic, complemented
11#459×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15C2×#14558725C2212yescomplemented
16C2×#14558724C2212yescomplemented
17C2×#14558721C2212yescomplemented
18#18011908C2211yescharacteristic
19#18011907—21no—
20#18011907—21no—
21#18011907C2212yes—
22#18011904—21no—
23#18011902C2211yescharacteristic, complemented
24#18011898C2211yescharacteristic, complemented
25#18011893—21no—
26#18011891C2211yescharacteristic
27#18011882C2211yescharacteristic
28C4×Dic298C2211yescharacteristic, complemented
29C4×C22⋊D149—21no—
30#18011870—21no—
31C42×D149C2211yescharacteristic
32C4⋊#11924746C2211yescharacteristic, complemented
33#18011833C2212yescomplemented
34#18011832C2212yescomplemented
35#18011831C2212yescomplemented
36#18011823C2212yes—
37#18011821C2212yescomplemented
38C2×D8×C149C2212yescomplemented
39#127×C149C2211yescharacteristic
40C4×D4×C149C2211yescharacteristic, complemented
41C4⋊C8×C149C2211yescharacteristic, complemented
42#102×C149C2212yescomplemented
43C23×D149—22no—
44C2×Dic298C2311yescharacteristic
45C2×D596—21no—
46C2×D596—21no—
47C2×D596C2312yes—
48C2×C22⋊D149—21no—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51C2×C22⋊D149—22no—
52D4×D149—42no—
53D4×D149—42no—
54D4×D149—44no—
55D4×D149—44no—
56C2×C4×D149D411yescharacteristic
57C2×C4×D149D411yescharacteristic
58C2×C4×D149C2311yescharacteristic
59#14558725—42no—
60#14558724—42no—
61#14558721—42no—
62C2×#11924746C2312yes—
63C4⋊Dic149—21no—
64C4⋊Dic149—21no—
65C4⋊Dic149C2311yescharacteristic
66#14558715—21no—
67#14558715—21no—
68C22⋊Dic149—21no—
69C22⋊Dic149—21no—
70C22⋊Dic149—21no—
71#14558713—21no—
72C4×Dic149—21no—
73C4×Dic149D411yescharacteristic
74C4×Dic149D411yescharacteristic
75C4×Dic149C2311yescharacteristic
76C2×D4×C149—21no—
77C2×D4×C149—21no—
78C2×D4×C149C2312yes—
79C2×D4×C149C2311yescharacteristic
80C22×C4×C149—21no—
81D8×C149—42no—
82C2×C8×C149C2312yes—
83C4⋊C4×C149C2311yescharacteristic
84C22⋊C4×C149—21no—
85C42×C149C2311yescharacteristic
86C22×D149—22no—
87C22×D149—44no—
88C22×D149—44no—
89C22×D149—44no—
90C22×D149C2×D411yescharacteristic
91Dic298—21no—
92Dic298—21no—
93D596—22no—
94D596—22no—
95D596—42no—
96D596—42no—
97C22⋊D149—44no—
98C22⋊D149—44no—
99C22⋊D149—44no—
100C22⋊D149—42no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149C2×D411yescharacteristic
104C2×Dic149C2×D411yescharacteristic
105C2×Dic149C2×D411yescharacteristic
106C4×D149—22no—
107C4×D149—22no—
108C4×D149—21no—
109C4×D149—21no—
110#11924746—22no—
111C23×C149—22no—
112C23×C149—21no—
113D4×C149—21no—
114D4×C149—22no—
115D4×C149—22no—
116D4×C149—21no—
117D4×C149—42no—
118D4×C149—42no—
119C2×C4×C149—21no—
120C2×C4×C149—42no—
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2411yescharacteristic
124C8×C149—22no—
125C22×C149—41no—
126C22×C149—42no—
127C22×C149—41no—
128C22×C149—42no—
129C22×C149—42no—
130C22×C149—41no—
131C22×C149C22×D411yescharacteristic
132C2×D149—21no—
133C2×D149—21no—
134C2×D149—42no—
135C2×D149—42no—
136C2×D149—42no—
137C2×D149—88no—
138C2×D149AGL(1,ℤ/8)12yes—
139C4×C149—21no—
140C4×C149—41no—
141C4×C149AGL(1,ℤ/8)12yes—
142C4×C149H(5,𝔽2)11yescharacteristic
143C4×C149H(5,𝔽2)11yescharacteristic
144Dic149—21no—
145Dic149—21no—
146Dic149—21no—
147Dic149—41no—
148Dic149—41no—
149C2×C149—82no—
150C2×C149—81no—
151C2×C149#53511yescharacteristic
152C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
154D149—22no—
155D149—82no—
156C149#321711yescharacteristic, complemented, Sylow
157#3217—1491nomaximal, Sylow
158C2×#127—1491no—
159#529—1491no—
160#496—1492no—
161#490—1492no—
162#460—1491no—
163#460—1491no—
164#459—1491no—
165#459D14911yescharacteristic, complemented
166#450—1492no—
167#447—1492no—
168#432—1491no—
169C22×D4—2981no—
170C22×D4—2981no—
171C22×D4—1492no—
172C2×SD16—1492no—
173C2×SD16—1492no—
174C2×D8—1492no—
175C2×D8C2×D14912yescomplemented
176#127—2981no—
177#127—2981no—
178#127—1492no—
179#127—1491no—
180#127C2×D14911yescharacteristic
181#126—2981no—
182#125—1491no—
183#124—1491no—
184#123—2981no—
185C22⋊Q8—1491no—
186#121—1491no—
187C4×Q8—1491no—
188C4×D4—2981no—
189C4×D4C2×D14911yescharacteristic, complemented
190#117—2981no—
191C2×C42—1491no—
192C4⋊C8—1491no—
193C4⋊C8C2×D14911yescharacteristic, complemented
194#102—1492no—
195#102—1492no—
196#102—1492no—
197#102C2×D14912yescomplemented
198C22⋊C8—1492no—
199#97—1492no—
200C24—2982no—
201C2×Q8—1491no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—2981no—
205C2×D4—2982no—
206C2×D4—2982no—
207C2×D4—2982no—
208C2×D4—2981no—
209C2×D4—2981no—
210C2×D4—5962no—
211C2×D4—5962no—
212C2×D4—5964no—
213C2×D4—5964no—
214C2×D4—1492no—
215C2×D4C22×D14912yes—
216C2×D4C22×D14911yescharacteristic
217C22×C4—21no—
218C22×C4—1491no—
219C22×C4—1491no—
220C22×C4—1491no—
221SD16—5962no—
222SD16—5962no—
223D8—42no—
224D8—5962no—
225C2×C8—1492no—
226C2×C8C22×D14912yes—
227C4⋊C4—2981no—
228C4⋊C4—2981no—
229C4⋊C4—2981no—
230C4⋊C4—2981no—
231C4⋊C4—1491no—
232C4⋊C4C22×D14911yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—2981no—
235C22⋊C4—2981no—
236C22⋊C4—2981no—
237C22⋊C4—2981no—
238C42—2981no—
239C42—1491no—
240C42—1491no—
241C42—1491no—
242C42C22×D14911yescharacteristic
243C23—21no—
244C23—22no—
245C23—2982no—
246C23—5964no—
247C23—5964no—
248C23—5964no—
249C23—1491no—
250Q8—2981no—
251Q8—2981no—
252D4—21no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—2982no—
259D4—2982no—
260D4—5962no—
261D4—5964no—
262D4—5964no—
263D4—5964no—
264D4—5962no—
265D4—5962no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—2982no—
269C2×C4—2982no—
270C2×C4—2981no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—2981no—
274C2×C4—1491no—
275C2×C4—1491no—
276C2×C4—1491no—
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C23×D14911yescharacteristic
280C8—22no—
281C8—2982no—
282C22—42no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—2981no—
289C22—2981no—
290C22—5962no—
291C22—5962no—
292C22—5962no—
293C22—1492no—
294C22—11928no—
295C22C2×D4×D14911yescharacteristic
296C4—21no—
297C4—41no—
298C4—2981no—
299C4—2981no—
300C4—2981no—
301C4—5961no—
302C4—5961no—
303C4#1801193512yes—
304C4#1801195611yescharacteristic
305C4#1801195711yescharacteristic
306C2—82no—
307C2—81no—
308C2—2982no—
309C2—11922no—
310C2#2375019111yescharacteristic
311C2AGL(1,ℤ/8)×D14911yescharacteristic
312C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3217
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. #127×D149C2semidirect
2. #23750157C2semidirect
3. #23750013C2semidirect
4. #23749988C2semidirect
5. #23749826C2semidirect
6. #23749822C2semidirect
7. #23749820C2semidirect
8. #23749777C2semidirect
9. #23749757C2semidirect
10. #23749681C2semidirect
11. #459×C149C2semidirect
15. C2×#14558725C22semidirect
16. C2×#14558724C22semidirect
17. C2×#14558721C22semidirect
23. #18011902C22semidirect
24. #18011898C22semidirect
28. C4×Dic298C22semidirect
32. C4⋊#11924746C22semidirect
33. #18011833C22semidirect
34. #18011832C22semidirect
35. #18011831C22semidirect
37. #18011821C22semidirect
38. C2×D8×C149C22semidirect
40. C4×D4×C149C22semidirect
41. C4⋊C8×C149C22semidirect
42. #102×C149C22semidirect
156. C149#3217semidirect
165. #459D149semidirect
175. C2×D8C2×D149semidirect
189. C4×D4C2×D149semidirect
193. C4⋊C8C2×D149semidirect
197. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#127×D1492
#237501572
#237500132
#237499882
#237498262
#237498222
#237498202
#237497772
#237497572
#237496812
#459×C1492
#3217149