Finite Group Databasebeta

← #34058329

Subgroups — #34058329

Order 19072.

1560 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011956C211yesmaximal, characteristic, complemented
2C22×#14558736C211yesmaximal, characteristic, complemented
3#23750276C214yesmaximal, complemented
4#23750273C214yesmaximal, complemented
5#23750267C214yesmaximal, complemented
6#23750265C214yesmaximal, complemented
7#23750197C212yesmaximal, complemented
8#23750187C211yesmaximal, characteristic, complemented
9#23750186C212yesmaximal, complemented
10#23750184C211yesmaximal, characteristic, complemented
11#23750133C212yesmaximal, complemented
12C2×#18011894C211yesmaximal, characteristic, complemented
13#123×D149C212yesmaximal, complemented
14#23750098C211yesmaximal, characteristic, complemented
15C2×#123×C149C211yesmaximal, characteristic, complemented
16#18011956—28no—
17C2×#14558736—28no—
18C2×#14558736C2214yescomplemented
19C2×#14558736C2214yescomplemented
20C2×#14558736C2212yescomplemented
21C2×#14558735C2212yes—
22C2×#14558735C2212yescomplemented
23C22×Dic298C2211yescharacteristic, complemented
24C22×D596C2211yescharacteristic, complemented
25C22×C22⋊D149C2211yescharacteristic
26C22×C22⋊D149C2211yescharacteristic
27C22×C22⋊D149C2211yescharacteristic, complemented
28C22×C22⋊D149C2212yescomplemented
29C2×D4×D149C2212yes—
30C2×D4×D149C2212yescomplemented
31C22×C4×D149C2211yescharacteristic, complemented
32C22×C4×D149C2211yescharacteristic, complemented
33#18011910C2214yescomplemented
34#18011897C2214yescomplemented
35#18011896C2214yescomplemented
36#18011896C2214yescomplemented
37#18011895C2212yescomplemented
38#18011895C2212yescomplemented
39#18011894C2212yescomplemented
40#18011894C2212yescomplemented
41#18011894C2214yescomplemented
42#18011894C2212yescomplemented
43#18011893C2214yescomplemented
44#18011892C2212yescomplemented
45#18011889C2214yescomplemented
46#18011889C2214yescomplemented
47#18011888C2214yescomplemented
48#18011886C2214yescomplemented
49#18011885C2214yescomplemented
50#18011884C2214yescomplemented
51#18011884C2214yescomplemented
52#18011883C2214yescomplemented
53#18011881C2212yescomplemented
54#18011881C2214yescomplemented
55#18011881C2212yescomplemented
56#18011880C2212yescomplemented
57#18011879C2212yescomplemented
58#18011873C2214yescomplemented
59C4×C22⋊D149C2214yescomplemented
60#18011871C2214yescomplemented
61#18011871C2214yescomplemented
62#18011867C2212yescomplemented
63C2×#14558715C2212yescomplemented
64C4⋊C4×D149C2214yescomplemented
65C2×C22⋊Dic149C2211yescharacteristic, complemented
66C2×#14558713C2212yescomplemented
67C22⋊C4×D149C2212yescomplemented
68C22⋊C4×D149C2214yescomplemented
69C22×D4×C149C2211yescharacteristic
70C23×C4×C149C2211yescharacteristic, complemented
71#123×C149C2212yescomplemented
72#123×C149C2214yescomplemented
73#123×C149C2212yescomplemented
74C2×C4⋊C4×C149C2212yescomplemented
75C2×C22⋊C4×C149C2211yescharacteristic, complemented
76C2×C22⋊C4×C149C2212yescomplemented
77C23×D149C2311yescharacteristic
78C23×D149C2312yes—
79C23×D149C2311yescharacteristic
80C23×D149C2311yescharacteristic
81#14558736—216no—
82#14558736—216no—
83#14558736—28no—
84#14558735—28no—
85#14558735—28no—
86C2×Dic298—24no—
87C2×Dic298C2312yes—
88C2×Dic298C2314yes—
89C2×D596—24no—
90C2×D596C2312yes—
91C2×D596C2314yes—
92C2×D596C2314yes—
93C2×C22⋊D149—28no—
94C2×C22⋊D149—24no—
95C2×C22⋊D149—24no—
96C2×C22⋊D149D418yescomplemented
97C2×C22⋊D149C2312yes—
98C2×C22⋊D149C2312yes—
99C2×C22⋊D149C2312yes—
100C2×C22⋊D149C2312yes—
101C2×C22⋊D149C2312yes—
102C2×C22⋊D149C2312yes—
103C2×C22⋊D149C2314yes—
104C2×C22⋊D149C2312yes—
105C2×C22⋊D149C2312yes—
106D4×D149—28no—
107D4×D149—28no—
108C22×Dic149C2311yescharacteristic
109C22×Dic149C2311yescharacteristic
110C22×Dic149C2312yes—
111C22×Dic149C2312yes—
112C22×Dic149C2311yescharacteristic
113C2×C4×D149—24no—
114C2×C4×D149—24no—
115C2×C4×D149C2314yes—
116C2×C4×D149C2314yes—
117C2×C4×D149C2312yes—
118C2×C4×D149C2312yes—
119C2×C4×D149C2314yes—
120C4⋊Dic149C2314yes—
121#14558715C2314yes—
122#14558715C2314yes—
123#14558715C2314yes—
124#14558715C2314yes—
125C22⋊Dic149C2312yes—
126C22⋊Dic149C2314yes—
127C22⋊Dic149C2312yes—
128#14558713C2314yes—
129#14558713C2314yes—
130#14558713C2314yes—
131#14558713C2314yes—
132#14558713C2314yes—
133#14558713C2314yes—
134C4×Dic149C2314yes—
135C24×C149C2311yescharacteristic
136C24×C149C2311yescharacteristic
137C2×D4×C149—24no—
138C2×D4×C149C2312yes—
139C2×D4×C149C2312yes—
140C22×C4×C149—24no—
141C22×C4×C149C2311yescharacteristic
142C22×C4×C149C2311yescharacteristic
143C22×C4×C149C2312yes—
144C22×C4×C149C2311yescharacteristic
145C22×C4×C149C2312yes—
146C22×C4×C149C2312yes—
147C4⋊C4×C149C2314yes—
148C4⋊C4×C149C2314yes—
149C22⋊C4×C149C2312yes—
150C22⋊C4×C149C2314yes—
151C22⋊C4×C149C2312yes—
152C22⋊C4×C149C2314yes—
153C22×D149—22no—
154C22×D149—22no—
155C22×D149—24no—
156C22×D149—42no—
157C22×D149—42no—
158C22×D149—44no—
159C22×D149—42no—
160C22×D149C2×D414yes—
161C22×D149C2412yes—
162C22×D149C2412yes—
163C22×D149C2412yes—
164Dic298—28no—
165Dic298—24no—
166D596—24no—
167D596—28no—
168D596—44no—
169C22⋊D149—24no—
170C22⋊D149—24no—
171C22⋊D149—24no—
172C22⋊D149—24no—
173C22⋊D149—24no—
174C22⋊D149—24no—
175C22⋊D149—44no—
176C22⋊D149C2×D418yes—
177C22⋊D149C2×D418yes—
178C2×Dic149—22no—
179C2×Dic149—22no—
180C2×Dic149—24no—
181C2×Dic149—42no—
182C2×Dic149C2×D414yes—
183C2×Dic149C2412yes—
184C2×Dic149C2412yes—
185C2×Dic149C2414yes—
186C2×Dic149C2412yes—
187C4×D149—28no—
188C4×D149—24no—
189C4×D149—28no—
190C4×D149—24no—
191C4×D149—44no—
192C23×C149—22no—
193C23×C149—42no—
194C23×C149—42no—
195C23×C149C2×D414yes—
196C23×C149C2412yes—
197C23×C149C2411yescharacteristic
198C23×C149C2411yescharacteristic
199C23×C149C2411yescharacteristic
200D4×C149—24no—
201D4×C149—24no—
202C2×C4×C149—22no—
203C2×C4×C149—22no—
204C2×C4×C149—24no—
205C2×C4×C149—24no—
206C2×C4×C149—22no—
207C2×C4×C149—42no—
208C2×C4×C149C2412yes—
209C2×C4×C149C2412yes—
210C2×C4×C149C2414yes—
211C2×C4×C149C2412yes—
212C22×C149—22no—
213C22×C149—22no—
214C22×C149—22no—
215C22×C149—22no—
216C22×C149—24no—
217C22×C149—44no—
218C22×C149—82no—
219C22×C149C22×D412yes—
220C22×C149C22×D412yes—
221C22×C149C22×D412yes—
222C22×C149C2511yescharacteristic
223C2×D149—24no—
224C2×D149—22no—
225C2×D149—22no—
226C2×D149—24no—
227C2×D149—24no—
228C2×D149—44no—
229C2×D149—44no—
230C2×D149—84no—
231C2×D149—82no—
232C2×D149C22×D414yes—
233C4×C149—22no—
234C4×C149—22no—
235C4×C149—22no—
236C4×C149—24no—
237Dic149—22no—
238Dic149—22no—
239Dic149—24no—
240Dic149C22×D414yes—
241C2×C149—22no—
242C2×C149—22no—
243C2×C149—22no—
244C2×C149—42no—
245C2×C149C23×D411yescharacteristic
246C2×C149#58512yes—
247D149—24no—
248D149—42no—
249D149—42no—
250C149#348511yescharacteristic, complemented, Sylow
251#3485—1491nomaximal, Sylow
252C2×H(5,𝔽2)—1491no—
253C22×#41—1491no—
254#547—1494no—
255#547—1494no—
256#546—1494no—
257#546—1494no—
258#536—1492no—
259#534—1491no—
260#534—1492no—
261#534—1491no—
262#525—1492no—
263C2×#123—1491no—
264C2×#123—1492no—
265C2×#123D14911yescharacteristic, complemented
266#518—1491no—
267H(5,𝔽2)—2988no—
268C2×#41—2988no—
269C2×#41—1492no—
270C2×#41—1492no—
271C2×#41—1494no—
272C2×#41—1494no—
273C2×#41—1492no—
274C22×Q8—1491no—
275C22×D4—1491no—
276C22×D4—1491no—
277C22×D4—1492no—
278C22×D4—1492no—
279C22×D4—1492no—
280C22×D4—1491no—
281C22×D4—1491no—
282C22×D4C2×D14911yescharacteristic
283C23×C4—1491no—
284C23×C4—1491no—
285C23×C4C2×D14911yescharacteristic, complemented
286C4⋊Q8—1494no—
287#124—1494no—
288#123—1492no—
289#123—1492no—
290#123—1492no—
291#123—1494no—
292#123—1492no—
293#123—1494no—
294#123—1494no—
295#123—1492no—
296#123—1494no—
297#123—1492no—
298#123C2×D14912yescomplemented
299#123C2×D14912yescomplemented
300#123C2×D14914yescomplemented
301C22⋊Q8—1494no—
302C22⋊Q8—1494no—
303C22⋊Q8—1494no—
304#121—1494no—
305#121—1494no—
306#121—1494no—
307#121—1494no—
308#121—1494no—
309#120—1492no—
310#120—1492no—
311#120—1492no—
312#120—1494no—
313#120—1492no—
314C4×D4—1494no—
315C4×D4—1494no—
316C4×D4—1494no—
317C4×D4—1494no—
318#117—1492no—
319C2×C4⋊C4—1492no—
320C2×C4⋊C4—1494no—
321C2×C4⋊C4C2×D14912yescomplemented
322C2×C22⋊C4—1491no—
323C2×C22⋊C4—1492no—
324C2×C22⋊C4—1492no—
325C2×C22⋊C4—1494no—
326C2×C22⋊C4C2×D14911yescharacteristic, complemented
327C2×C22⋊C4C2×D14912yescomplemented
328C24—1492no—
329C24—1491no—
330C24—1491no—
331C24—1491no—
332C24C22×D14911yescharacteristic
333C24C22×D14911yescharacteristic
334#41—29816no—
335#41—29816no—
336#41—2988no—
337#41—2988no—
338#41—2988no—
339C2×Q8—2984no—
340C2×Q8—1494no—
341C2×Q8—1492no—
342C2×D4—24no—
343C2×D4—2984no—
344C2×D4—2988no—
345C2×D4—2988no—
346C2×D4—2984no—
347C2×D4—2984no—
348C2×D4—2988no—
349C2×D4—1492no—
350C2×D4—1492no—
351C2×D4—1492no—
352C2×D4—1492no—
353C2×D4—1492no—
354C2×D4—1492no—
355C2×D4—1494no—
356C2×D4—1498no—
357C2×D4—1492no—
358C2×D4—1492no—
359C2×D4—1494no—
360C2×D4—1492no—
361C2×D4—1494no—
362C2×D4C22×D14912yes—
363C2×D4C22×D14912yes—
364C22×C4—24no—
365C22×C4—2984no—
366C22×C4—2984no—
367C22×C4—1491no—
368C22×C4—1492no—
369C22×C4—1491no—
370C22×C4—1494no—
371C22×C4—1492no—
372C22×C4—1494no—
373C22×C4—1492no—
374C22×C4—1492no—
375C22×C4—1494no—
376C22×C4—1491no—
377C22×C4C22×D14912yes—
378C22×C4C22×D14912yes—
379C22×C4C22×D14911yescharacteristic
380C22×C4C22×D14911yescharacteristic
381C22×C4C22×D14911yescharacteristic
382C22×C4C22×D14912yes—
383C4⋊C4—1494no—
384C4⋊C4—1494no—
385C4⋊C4—1494no—
386C4⋊C4—1494no—
387C4⋊C4—1494no—
388C4⋊C4C22×D14914yes—
389C4⋊C4C22×D14914yes—
390C22⋊C4—1492no—
391C22⋊C4—1492no—
392C22⋊C4—1494no—
393C22⋊C4—1494no—
394C22⋊C4—1494no—
395C22⋊C4—1494no—
396C22⋊C4—1494no—
397C22⋊C4—1494no—
398C22⋊C4—1494no—
399C22⋊C4C22×D14912yes—
400C22⋊C4C22×D14914yes—
401C22⋊C4C22×D14912yes—
402C22⋊C4C22×D14914yes—
403C42—1494no—
404C23—22no—
405C23—42no—
406C23—42no—
407C23—2984no—
408C23—2982no—
409C23—2982no—
410C23—5962no—
411C23—5962no—
412C23—5962no—
413C23—5964no—
414C23—1492no—
415C23—1492no—
416C23—1492no—
417C23—1494no—
418C23D4×D14914yes—
419C23C23×D14912yes—
420C23C23×D14911yescharacteristic
421C23C23×D14911yescharacteristic
422C23C23×D14911yescharacteristic
423Q8—2988no—
424Q8—2984no—
425D4—24no—
426D4—24no—
427D4—2984no—
428D4—2988no—
429D4—2984no—
430D4—2984no—
431D4—2984no—
432D4—2984no—
433D4—2984no—
434D4—2984no—
435D4—5964no—
436D4—5964no—
437D4—1498no—
438D4—1498no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—2988no—
446C2×C4—2984no—
447C2×C4—2988no—
448C2×C4—2984no—
449C2×C4—2982no—
450C2×C4—2982no—
451C2×C4—2984no—
452C2×C4—5964no—
453C2×C4—5962no—
454C2×C4—1494no—
455C2×C4—1492no—
456C2×C4—1492no—
457C2×C4—1494no—
458C2×C4—1492no—
459C2×C4C23×D14914yes—
460C2×C4C23×D14912yes—
461C2×C4C23×D14912yes—
462C2×C4C23×D14912yes—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—24no—
468C22—44no—
469C22—82no—
470C22—2984no—
471C22—2982no—
472C22—2982no—
473C22—2984no—
474C22—2984no—
475C22—5964no—
476C22—5964no—
477C22—1494no—
478C22—11922no—
479C22—11924no—
480C22C2×D4×D14912yes—
481C22C2×D4×D14912yes—
482C22C2×D4×D14912yes—
483C22C24×D14911yescharacteristic
484C4—22no—
485C4—22no—
486C4—22no—
487C4—24no—
488C4—2982no—
489C4—2982no—
490C4—2984no—
491C4—1494no—
492C2—22no—
493C2—22no—
494C2—22no—
495C2—42no—
496C2—2984no—
497C2—5962no—
498C2—5962no—
499C2C22×D4×D14911yescharacteristic
500C2#2375046112yes—
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
FittingC2×#123×C149C2
hypercenterC2×#123D149
hypocenterC149#3485
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#18011956C2semidirect
2. C22×#14558736C2semidirect
3. #23750276C2semidirect
4. #23750273C2semidirect
5. #23750267C2semidirect
6. #23750265C2semidirect
7. #23750197C2semidirect
8. #23750187C2semidirect
9. #23750186C2semidirect
10. #23750184C2semidirect
11. #23750133C2semidirect
12. C2×#18011894C2semidirect
13. #123×D149C2semidirect
14. #23750098C2semidirect
15. C2×#123×C149C2semidirect
18. C2×#14558736C22semidirect
19. C2×#14558736C22semidirect
20. C2×#14558736C22semidirect
22. C2×#14558735C22semidirect
23. C22×Dic298C22semidirect
24. C22×D596C22semidirect
27. C22×C22⋊D149C22semidirect
28. C22×C22⋊D149C22semidirect
30. C2×D4×D149C22semidirect
31. C22×C4×D149C22semidirect
32. C22×C4×D149C22semidirect
33. #18011910C22semidirect
34. #18011897C22semidirect
35. #18011896C22semidirect
36. #18011896C22semidirect
37. #18011895C22semidirect
38. #18011895C22semidirect
39. #18011894C22semidirect
40. #18011894C22semidirect
41. #18011894C22semidirect
42. #18011894C22semidirect
43. #18011893C22semidirect
44. #18011892C22semidirect
45. #18011889C22semidirect
46. #18011889C22semidirect
47. #18011888C22semidirect
48. #18011886C22semidirect
49. #18011885C22semidirect
50. #18011884C22semidirect
51. #18011884C22semidirect
52. #18011883C22semidirect
53. #18011881C22semidirect
54. #18011881C22semidirect
55. #18011881C22semidirect
56. #18011880C22semidirect
57. #18011879C22semidirect
58. #18011873C22semidirect
59. C4×C22⋊D149C22semidirect
60. #18011871C22semidirect
61. #18011871C22semidirect
62. #18011867C22semidirect
63. C2×#14558715C22semidirect
64. C4⋊C4×D149C22semidirect
65. C2×C22⋊Dic149C22semidirect
66. C2×#14558713C22semidirect
67. C22⋊C4×D149C22semidirect
68. C22⋊C4×D149C22semidirect
70. C23×C4×C149C22semidirect
71. #123×C149C22semidirect
72. #123×C149C22semidirect
73. #123×C149C22semidirect
74. C2×C4⋊C4×C149C22semidirect
75. C2×C22⋊C4×C149C22semidirect
76. C2×C22⋊C4×C149C22semidirect
96. C2×C22⋊D149D4semidirect
250. C149#3485semidirect
265. C2×#123D149semidirect
285. C23×C4C2×D149semidirect
298. #123C2×D149semidirect
299. #123C2×D149semidirect
300. #123C2×D149semidirect
321. C2×C4⋊C4C2×D149semidirect
326. C2×C22⋊C4C2×D149semidirect
327. C2×C22⋊C4C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119562
C22×#145587362
#237502762
#237502732
#237502672
#237502652
#237501972
#237501872
#237501862
#237501842
#237501332
C2×#180118942
#123×D1492
#237500982
C2×#123×C1492
#3485149