Finite Group Databasebeta

← #34053545

Subgroups — #34053545

Order 19072.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D149C211yesmaximal, characteristic
2#23750101C211yesmaximal, characteristic, complemented
3#23750097C211yesmaximal, characteristic
4#23749728C211yesmaximal, characteristic, complemented
5#23749725C211yesmaximal, characteristic, complemented
6#23749723C211yesmaximal, characteristic, complemented
7#23749722C211yesmaximal, characteristic, complemented
8C4×#14558725C211yesmaximal, characteristic, complemented
9SD16×Dic149C211yesmaximal, characteristic, complemented
10#23749712C211yesmaximal, characteristic, complemented
11#23749660C211yesmaximal, characteristic, complemented
12#23749632C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic
14#23749579C211yesmaximal, characteristic, complemented
15C4×SD16×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21SD16×D149C418yescomplemented
22C2×#14558719C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24Q8×Dic149C2211yescharacteristic, complemented
25C4×Dic298—21no—
26C4×Dic298C2211yescharacteristic, complemented
27#18011876—21no—
28#18011876C2211yescharacteristic, complemented
29C4×D596C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011869—21no—
35#18011869C2211yescharacteristic
36#18011869C2211yescharacteristic
37#18011868—21no—
38#18011868C2211yescharacteristic
39C2×#14558713—21no—
40C22⋊C4×D149—21no—
41#18011844C2211yescharacteristic, complemented
42#18011844C2211yescharacteristic, complemented
43#18011843C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011834C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011822C2211yescharacteristic, complemented
51#18011821C2211yescharacteristic, complemented
52C8×Dic149C2211yescharacteristic, complemented
53C2×SD16×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic, complemented
55C4×D4×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic
59C4×C8×C149C2211yescharacteristic, complemented
60C23×D149—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63Q8×D149—22no—
64Q8×D149C2×C414yescomplemented
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67D4×D149—22no—
68D4×D149C2×C414yes—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149C2311yescharacteristic
74#14558725C2×C414yescomplemented
75#14558724C2×C414yescomplemented
76#14558723C2×C414yescomplemented
77#14558719—22no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C8×D149C2×C414yescomplemented
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715D411yescharacteristic
87#14558715D411yescharacteristic
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104SD16×C149C2×C414yescomplemented
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C22×D149—21no—
114C22×D149—24no—
115C22×D149—81no—
116C22×D149—81no—
117C22×D149C2×D411yescharacteristic
118Dic298—21no—
119Dic298—24no—
120Dic298C22×C412yes—
121D596—21no—
122D596C22×C412yes—
123C22⋊D149—24no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—81no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—24no—
132C4×D149—81no—
133C4×D149—81no—
134C4×D149C22×C412yes—
135C4×D149#4112yes—
136#11924746—21no—
137#11924746C22×C412yes—
138C23×C149—21no—
139Q8×C149—21no—
140Q8×C149C22×C412yes—
141D4×C149—21no—
142D4×C149C22×C412yes—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—81no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149C22×C412yes—
152C22×C149—22no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—22no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—84no—
162C2×D149C4×D412yes—
163C4×C149—22no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149C23×C411yescharacteristic
169C4×C149C2×#4111yescharacteristic
170Dic149—22no—
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149C4×D412yes—
176C2×C149—42no—
177C2×C149C2×C4×D411yescharacteristic
178C2×C149#57711yescharacteristic
179C2×C149#57711yescharacteristic
180D149—22no—
181D149—42no—
182C149#294911yescharacteristic, complemented, Sylow
183#2949—1491nomaximal, Sylow
184C22×SD16—1491no—
185#519—1491no—
186#518—1491no—
187#440—1491no—
188#440—1491no—
189#440—1491no—
190#440—1491no—
191C4×SD16—1491no—
192C4×SD16—1491no—
193C4×SD16—1491no—
194C4×SD16D14911yescharacteristic, complemented
195#427—1491no—
196#419—1491no—
197#418—1491no—
198#405—1491no—
199C22×Q8—1491no—
200C22×D4—1491no—
201C2×SD16—1491no—
202C2×SD16—1491no—
203C2×SD16—1498no—
204C2×SD16—1491no—
205C2×SD16C2×D14911yescharacteristic
206C2×M16—1491no—
207C22×C8—1491no—
208C4×Q8—2981no—
209C4×Q8—2981no—
210C4×Q8—1491no—
211C4×Q8—1491no—
212C4×Q8—1491no—
213C4×Q8C2×D14911yescharacteristic, complemented
214C4×D4—2981no—
215C4×D4—2981no—
216C4×D4—1491no—
217C4×D4—1491no—
218C4×D4—1491no—
219C4×D4C2×D14911yescharacteristic
220#117—2981no—
221#117—2981no—
222#117—1491no—
223#117—1491no—
224#117—1491no—
225C2×C22⋊C4—2981no—
226C2×C22⋊C4—2981no—
227#107—1491no—
228#107—1491no—
229#106—1491no—
230#106C2×D14911yescharacteristic, complemented
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103C2×D14911yescharacteristic, complemented
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102C2×D14911yescharacteristic
239#97—1491no—
240#97—1491no—
241C4×C8—1491no—
242C4×C8C2×D14911yescharacteristic, complemented
243C24—2981no—
244C2×Q8—2981no—
245C2×Q8—2982no—
246C2×Q8—1494no—
247C2×Q8—1491no—
248C2×Q8C22×D14911yescharacteristic
249C2×D4—2982no—
250C2×D4—2981no—
251C2×D4—1494no—
252C2×D4—1491no—
253C2×D4C22×D14911yescharacteristic
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—1491no—
260SD16—1494no—
261SD16—1494no—
262SD16—1494no—
263SD16C4×D14914yescomplemented
264M16—2982no—
265C2×C8—1491no—
266C2×C8—1491no—
267C2×C8—1494no—
268C2×C8C22×D14911yescharacteristic
269C2×C8C22×D14911yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4C22×D14911yescharacteristic
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—1491no—
287C22⋊C4—1491no—
288C42—21no—
289C42—2981no—
290C42—2981no—
291C42—2981no—
292C42—2981no—
293C42—2981no—
294C42—1491no—
295C42C22×D14911yescharacteristic
296C23—21no—
297C23—2984no—
298C23—2981no—
299C23—1491no—
300C23—11921no—
301C23—11921no—
302Q8—21no—
303Q8—2984no—
304Q8—2981no—
305Q8—1492no—
306Q8C2×C4×D14912yes—
307D4—21no—
308D4—2984no—
309D4—2981no—
310D4—1492no—
311D4C2×C4×D14912yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—2984no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1492no—
324C2×C4—1492no—
325C2×C4—11921no—
326C2×C4—11921no—
327C2×C4—11921no—
328C2×C4D4×D14911yescharacteristic
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—2981no—
333C8—1492no—
334C8C2×C4×D14912yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—2981no—
339C22—2981no—
340C22—2982no—
341C22—5961no—
342C22—5961no—
343C22—1492no—
344C22—11924no—
345C22C2×D4×D14911yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—2981no—
352C4—2981no—
353C4—2982no—
354C4—5961no—
355C4—5961no—
356C4—1492no—
357C4C22×C4×D14911yescharacteristic
358C4#41×D14911yescharacteristic
359C2—42no—
360C2—2982no—
361C2—5962no—
362C2C4×D4×D14911yescharacteristic
363C2#2375043111yescharacteristic
364C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
cosocleC2×C4×C149C24
hypercenterC4×SD16D149
hypocenterC149#2949
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #23750101C2semidirect
4. #23749728C2semidirect
5. #23749725C2semidirect
6. #23749723C2semidirect
7. #23749722C2semidirect
8. C4×#14558725C2semidirect
9. SD16×Dic149C2semidirect
10. #23749712C2semidirect
11. #23749660C2semidirect
12. #23749632C2semidirect
14. #23749579C2semidirect
15. C4×SD16×C149C2semidirect
21. SD16×D149C4semidirect
24. Q8×Dic149C22semidirect
26. C4×Dic298C22semidirect
28. #18011876C22semidirect
41. #18011844C22semidirect
42. #18011844C22semidirect
43. #18011843C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011834C22semidirect
50. #18011822C22semidirect
51. #18011821C22semidirect
52. C8×Dic149C22semidirect
54. C4×Q8×C149C22semidirect
56. #106×C149C22semidirect
57. #103×C149C22semidirect
59. C4×C8×C149C22semidirect
64. Q8×D149C2×C4semidirect
74. #14558725C2×C4semidirect
75. #14558724C2×C4semidirect
76. #14558723C2×C4semidirect
80. C8×D149C2×C4semidirect
104. SD16×C149C2×C4semidirect
182. C149#2949semidirect
194. C4×SD16D149semidirect
213. C4×Q8C2×D149semidirect
230. #106C2×D149semidirect
234. #103C2×D149semidirect
242. C4×C8C2×D149semidirect
263. SD16C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1492
#237501012
#237500972
#237497282
#237497252
#237497232
#237497222
C4×#145587252
SD16×Dic1492
#237497122
#237496602
#237496322
#237496282
#237495792
C4×SD16×C1492
#2949149