Finite Group Databasebeta

← #34055705

Subgroups — #34055705

Order 19072.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750154C211yesmaximal, characteristic, complemented
3#23750015C211yesmaximal, characteristic, complemented
4#23749990C211yesmaximal, characteristic, complemented
5#23749989C211yesmaximal, characteristic, complemented
6#23749823C212yesmaximal, complemented
7#23749818C212yesmaximal, complemented
8#23749774C212yesmaximal, complemented
9#23749757C212yesmaximal, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#496×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15C2×#14558723C2212yescomplemented
16C2×#14558721C2212yescomplemented
17#18011908C2211yescharacteristic
18#18011907—21no—
19#18011907—21no—
20#18011907C2212yes—
21#18011904—21no—
22#18011903C2211yescharacteristic, complemented
23#18011893—21no—
24#18011887C2211yescharacteristic
25#18011882C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic, complemented
27D4×Dic149C2211yescharacteristic, complemented
28#18011871—21no—
29#18011867—21no—
30C42×D149C2211yescharacteristic
31#18011840C2212yescomplemented
32#18011833C2212yescomplemented
33#18011833C2212yescomplemented
34#18011832C2212yescomplemented
35#18011832C2212yescomplemented
36#18011823C2212yes—
37#18011822C2211yescharacteristic, complemented
38C2×SD16×C149C2212yescomplemented
39C2×D8×C149C2212yescomplemented
40#127×C149C2211yescharacteristic
41#124×C149C2211yescharacteristic, complemented
42#97×C149C2211yescharacteristic, complemented
43C23×D149—22no—
44C2×D596—21no—
45C2×D596—21no—
46C2×D596C2312yes—
47C2×C22⋊D149—21no—
48C2×C22⋊D149—22no—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51D4×D149—42no—
52D4×D149—42no—
53D4×D149—44no—
54D4×D149—44no—
55C22×Dic149—21no—
56C2×C4×D149D411yescharacteristic
57C2×C4×D149D411yescharacteristic
58C2×C4×D149C2311yescharacteristic
59#14558723—42no—
60#14558721—42no—
61C2×#11924746C2312yes—
62C4⋊Dic149—21no—
63C4⋊Dic149C2311yescharacteristic
64C4⋊Dic149C2311yescharacteristic
65#14558715—21no—
66#14558715—21no—
67#14558715—21no—
68C22⋊Dic149—21no—
69C22⋊Dic149—21no—
70#14558713—21no—
71C4×Dic149—21no—
72C4×Dic149D411yescharacteristic
73C4×Dic149D411yescharacteristic
74C4×Dic149C2311yescharacteristic
75C2×Q8×C149C2311yescharacteristic
76C2×D4×C149—21no—
77C2×D4×C149—21no—
78C2×D4×C149C2312yes—
79C2×D4×C149C2311yescharacteristic
80SD16×C149—42no—
81D8×C149—42no—
82C2×C8×C149C2312yes—
83C22⋊C4×C149—21no—
84C22⋊C4×C149—21no—
85C42×C149C2311yescharacteristic
86C22×D149—22no—
87C22×D149—44no—
88C22×D149—44no—
89C22×D149—44no—
90C22×D149C2×D411yescharacteristic
91D596—22no—
92D596—22no—
93D596—42no—
94D596—42no—
95C22⋊D149—44no—
96C22⋊D149—44no—
97C22⋊D149—42no—
98C22⋊D149—44no—
99C2×Dic149—21no—
100C2×Dic149—21no—
101C2×Dic149—42no—
102C2×Dic149C2×D411yescharacteristic
103C2×Dic149C2×D411yescharacteristic
104C2×Dic149C2×D411yescharacteristic
105C4×D149—22no—
106C4×D149—22no—
107C4×D149—22no—
108#11924746—22no—
109C23×C149—21no—
110C23×C149—22no—
111Q8×C149—22no—
112D4×C149—22no—
113D4×C149—22no—
114D4×C149—22no—
115D4×C149—42no—
116D4×C149—42no—
117C2×C4×C149—21no—
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2411yescharacteristic
121C8×C149—22no—
122C22×C149—41no—
123C22×C149—42no—
124C22×C149—42no—
125C22×C149—42no—
126C22×C149—41no—
127C22×C149—41no—
128C22×C149C22×D411yescharacteristic
129C2×D149—21no—
130C2×D149—21no—
131C2×D149—42no—
132C2×D149—42no—
133C2×D149—42no—
134C2×D149—88no—
135C2×D149AGL(1,ℤ/8)12yes—
136C4×C149—21no—
137C4×C149—21no—
138C4×C149—41no—
139C4×C149H(5,𝔽2)12yes—
140Dic149—21no—
141Dic149—21no—
142Dic149—41no—
143Dic149—41no—
144Dic149AGL(1,ℤ/8)12yes—
145C2×C149—82no—
146C2×C149—81no—
147C2×C149#53511yescharacteristic
148C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
150D149—22no—
151D149—82no—
152C149#321711yescharacteristic, complemented, Sylow
153#3217—1491nomaximal, Sylow
154C2×#127—1491no—
155#529—1491no—
156#496—1491no—
157#496D14911yescharacteristic, complemented
158#490—1491no—
159#490—1491no—
160#460—1492no—
161#459—1492no—
162#450—1492no—
163#447—1492no—
164#432—1491no—
165C22×D4—2981no—
166C22×D4—2981no—
167C22×D4—1492no—
168C2×SD16—1492no—
169C2×SD16C2×D14912yescomplemented
170C2×D8—1492no—
171C2×D8C2×D14912yescomplemented
172#127—2981no—
173#127—2981no—
174#127—1492no—
175#127—1491no—
176#127C2×D14911yescharacteristic
177#126—2981no—
178#125—1491no—
179#124C2×D14911yescharacteristic, complemented
180#123—2981no—
181C22⋊Q8—1491no—
182#121—1491no—
183C4×Q8—1491no—
184C4×D4—2981no—
185C4×D4—1491no—
186#117—2981no—
187C2×C42—1491no—
188C4⋊C8—1492no—
189#102—1492no—
190#102—1492no—
191#102—1492no—
192#102—1492no—
193C22⋊C8—1492no—
194#97—1491no—
195#97C2×D14911yescharacteristic, complemented
196C24—2982no—
197C2×Q8C22×D14911yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—2981no—
201C2×D4—2982no—
202C2×D4—2982no—
203C2×D4—2982no—
204C2×D4—2981no—
205C2×D4—2981no—
206C2×D4—5962no—
207C2×D4—5962no—
208C2×D4—5964no—
209C2×D4—5964no—
210C2×D4—1492no—
211C2×D4C22×D14912yes—
212C2×D4C22×D14911yescharacteristic
213C22×C4—2981no—
214C22×C4—1491no—
215C22×C4—1491no—
216C22×C4—1491no—
217SD16—42no—
218SD16—5962no—
219D8—42no—
220D8—5962no—
221C2×C8—1492no—
222C2×C8C22×D14912yes—
223C4⋊C4—2981no—
224C4⋊C4—2981no—
225C4⋊C4—2981no—
226C4⋊C4—2981no—
227C4⋊C4—1491no—
228C4⋊C4—1491no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—2981no—
232C22⋊C4—2981no—
233C22⋊C4—2981no—
234C42—2981no—
235C42—1491no—
236C42—1491no—
237C42—1491no—
238C42C22×D14911yescharacteristic
239C23—21no—
240C23—22no—
241C23—2982no—
242C23—5964no—
243C23—5964no—
244C23—5964no—
245C23—1491no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—2982no—
253D4—2982no—
254D4—5962no—
255D4—5962no—
256D4—5964no—
257D4—5964no—
258D4—5962no—
259D4—5964no—
260C2×C4—21no—
261C2×C4—2982no—
262C2×C4—2982no—
263C2×C4—2982no—
264C2×C4—2981no—
265C2×C4—2981no—
266C2×C4—5962no—
267C2×C4—1491no—
268C2×C4—1491no—
269C2×C4—1491no—
270C2×C4D4×D14911yescharacteristic
271C2×C4D4×D14911yescharacteristic
272C2×C4C23×D14911yescharacteristic
273C8—22no—
274C8—2982no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—2981no—
282C22—2981no—
283C22—5962no—
284C22—5962no—
285C22—5962no—
286C22—1492no—
287C22—11928no—
288C22C2×D4×D14911yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—2981no—
293C4—2981no—
294C4—5961no—
295C4—5961no—
296C4—1492no—
297C4#1801195612yes—
298C2—82no—
299C2—81no—
300C2—2982no—
301C2—11922no—
302C2#2375018811yescharacteristic
303C2AGL(1,ℤ/8)×D14911yescharacteristic
304C2AGL(1,ℤ/8)×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#496×C149C2
socleC22×C149C22×D4
hypercenter#496D149
hypocenterC149#3217
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D149C2semidirect
2. #23750154C2semidirect
3. #23750015C2semidirect
4. #23749990C2semidirect
5. #23749989C2semidirect
6. #23749823C2semidirect
7. #23749818C2semidirect
8. #23749774C2semidirect
9. #23749757C2semidirect
10. #23749680C2semidirect
11. #496×C149C2semidirect
15. C2×#14558723C22semidirect
16. C2×#14558721C22semidirect
22. #18011903C22semidirect
26. Q8×Dic149C22semidirect
27. D4×Dic149C22semidirect
31. #18011840C22semidirect
32. #18011833C22semidirect
33. #18011833C22semidirect
34. #18011832C22semidirect
35. #18011832C22semidirect
37. #18011822C22semidirect
38. C2×SD16×C149C22semidirect
39. C2×D8×C149C22semidirect
41. #124×C149C22semidirect
42. #97×C149C22semidirect
152. C149#3217semidirect
157. #496D149semidirect
169. C2×SD16C2×D149semidirect
171. C2×D8C2×D149semidirect
179. #124C2×D149semidirect
195. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#127×D1492
#237501542
#237500152
#237499902
#237499892
#237498232
#237498182
#237497742
#237497572
#237496802
#496×C1492
#3217149