Finite Group Databasebeta

← #34053956

Subgroups — #34053956

Order 19072.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011957C211yesmaximal, characteristic, complemented
2C2×#18011938C211yesmaximal, characteristic, complemented
3C2×D8×D149C211yesmaximal, characteristic, complemented
4#23750191C211yesmaximal, characteristic, complemented
5#23749773C211yesmaximal, characteristic, complemented
6#23749770C211yesmaximal, characteristic, complemented
7#23749769C211yesmaximal, characteristic, complemented
8#23749761C211yesmaximal, characteristic, complemented
9#23749760C211yesmaximal, characteristic, complemented
10#23749758C211yesmaximal, characteristic, complemented
11#23749757C211yesmaximal, characteristic, complemented
12#23749628C211yesmaximal, characteristic, complemented
13#23749620C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16#18011957—24no—
17#18011957—24no—
18C2×#14558737C2211yescharacteristic
19C2×#14558737C2211yescharacteristic, complemented
20C2×#14558736—21no—
21C2×#14558736C2211yescharacteristic
22C22×D596—21no—
23C22×D596C2211yescharacteristic, complemented
24C2×D4×D149—21no—
25C2×D4×D149—21no—
26C2×D4×D149C2211yescharacteristic
27C2×D4×D149C2211yescharacteristic, complemented
28C2×D4×D149C2211yescharacteristic, complemented
29#18011938—24no—
30C2×#14558723C2211yescharacteristic, complemented
31C2×D1192C2211yescharacteristic, complemented
32C2×D1192C2211yescharacteristic, complemented
33C2×#14558721C2211yescharacteristic, complemented
34C2×#14558721C2211yescharacteristic, complemented
35C2×#14558721C2211yescharacteristic, complemented
36D8×D149—24no—
37C2×#14558719C2211yescharacteristic, complemented
38C2×C8×D149C2211yescharacteristic, complemented
39#18011907—21no—
40#18011897—21no—
41#18011886C2211yescharacteristic, complemented
42#18011885C2211yescharacteristic, complemented
43#18011882C2211yescharacteristic, complemented
44#18011881—21no—
45#18011879—21no—
46#18011869C2211yescharacteristic, complemented
47#18011835C2211yescharacteristic, complemented
48#18011833C2211yescharacteristic, complemented
49#18011833C2211yescharacteristic, complemented
50#18011832C2211yescharacteristic, complemented
51#18011831C2211yescharacteristic, complemented
52#18011831C2211yescharacteristic, complemented
53C22⋊#11924746C2211yescharacteristic, complemented
54#18011823C2211yescharacteristic, complemented
55#18011823C2211yescharacteristic, complemented
56C2×#41×C149C2211yescharacteristic, complemented
57C2×SD16×C149C2211yescharacteristic, complemented
58C2×D8×C149C2211yescharacteristic, complemented
59#121×C149C2211yescharacteristic, complemented
60#103×C149C2211yescharacteristic, complemented
61#102×C149C2211yescharacteristic, complemented
62C22⋊C8×C149C2211yescharacteristic, complemented
63C23×D149—21no—
64C23×D149—21no—
65C23×D149—21no—
66C23×D149—21no—
67#14558737—22no—
68#14558737—22no—
69#14558737—22no—
70#14558737D414yescomplemented
71#14558736—28no—
72#14558736—22no—
73#14558736—22no—
74C2×Dic298D411yescharacteristic
75C2×D596—28no—
76C2×D596—21no—
77C2×D596—21no—
78C2×D596—22no—
79C2×D596—22no—
80C2×D596—21no—
81C2×D596—21no—
82C2×D596D411yescharacteristic
83C2×D596C2311yescharacteristic
84C2×D596C2311yescharacteristic
85C2×D596C2311yescharacteristic
86C2×C22⋊D149—21no—
87C2×C22⋊D149—21no—
88C2×C22⋊D149—21no—
89C2×C22⋊D149—21no—
90C2×C22⋊D149—21no—
91C2×C22⋊D149D411yescharacteristic
92C2×C22⋊D149D411yescharacteristic
93D4×D149—28no—
94D4×D149—28no—
95D4×D149—22no—
96D4×D149—22no—
97D4×D149—22no—
98D4×D149—22no—
99D4×D149—22no—
100D4×D149D414yescomplemented
101C2×C4×D149—21no—
102C2×C4×D149—21no—
103C2×C4×D149C2311yescharacteristic
104C2×C4×D149C2311yescharacteristic
105#14558723—22no—
106D1192—22no—
107D1192—22no—
108#14558721—22no—
109#14558721—22no—
110#14558721—22no—
111#14558719—22no—
112C2×#11924746C2311yescharacteristic
113C2×#11924746C2311yescharacteristic
114C8×D149—22no—
115C4⋊Dic149C2311yescharacteristic
116C22⋊Dic149—21no—
117#14558713—21no—
118#14558713—21no—
119#14558713—21no—
120C4×Dic149—21no—
121#41×C149—22no—
122#41×C149—22no—
123C2×Q8×C149C2311yescharacteristic
124C2×D4×C149—21no—
125C2×D4×C149—21no—
126C2×D4×C149C2311yescharacteristic
127C2×D4×C149C2311yescharacteristic
128C22×C4×C149—21no—
129C22×C4×C149C2311yescharacteristic
130SD16×C149—22no—
131D8×C149—22no—
132C2×C8×C149C2311yescharacteristic
133C2×C8×C149C2311yescharacteristic
134C4⋊C4×C149C2311yescharacteristic
135C22⋊C4×C149—21no—
136C22×D149—21no—
137C22×D149—21no—
138C22×D149—24no—
139C22×D149—24no—
140C22×D149—24no—
141C22×D149—21no—
142C22×D149—42no—
143C22×D149—81no—
144C22×D149—81no—
145C22×D149—81no—
146C22×D149—81no—
147C22×D149—81no—
148C22×D149—81no—
149C22×D149—81no—
150C22×D149—81no—
151C22×D149C2×D411yescharacteristic
152C22×D149C2×D411yescharacteristic
153Dic298—22no—
154D596—24no—
155D596—24no—
156D596—24no—
157D596—22no—
158D596—21no—
159D596—21no—
160D596—21no—
161D596—21no—
162D596—81no—
163D596C2×D412yes—
164D596C2×D412yes—
165C22⋊D149—24no—
166C22⋊D149—22no—
167C22⋊D149—22no—
168C22⋊D149—24no—
169C22⋊D149—42no—
170C22⋊D149—81no—
171C22⋊D149—81no—
172C2×Dic149—21no—
173C2×Dic149C2×D411yescharacteristic
174C2×Dic149C2×D411yescharacteristic
175C4×D149—24no—
176C4×D149—21no—
177C4×D149—21no—
178C4×D149—24no—
179C4×D149C2×D412yes—
180C4×D149C2×D412yes—
181#11924746—21no—
182#11924746—21no—
183C23×C149—21no—
184C23×C149—21no—
185C23×C149C2×D411yescharacteristic
186Q8×C149—21no—
187Q8×C149C2×D412yes—
188D4×C149—24no—
189D4×C149—21no—
190D4×C149—21no—
191D4×C149—21no—
192D4×C149—81no—
193D4×C149C2×D412yes—
194C2×C4×C149—24no—
195C2×C4×C149—21no—
196C2×C4×C149—21no—
197C2×C4×C149—21no—
198C2×C4×C149—21no—
199C2×C4×C149C2×D411yescharacteristic
200C2×C4×C149C2411yescharacteristic
201C8×C149—21no—
202C8×C149—21no—
203C22×C149—21no—
204C22×C149—22no—
205C22×C149—21no—
206C22×C149—21no—
207C22×C149—41no—
208C22×C149—41no—
209C22×C149—41no—
210C22×C149—41no—
211C22×C149—41no—
212C22×C149C22×D411yescharacteristic
213C2×D149—21no—
214C2×D149—21no—
215C2×D149—21no—
216C2×D149—22no—
217C2×D149—22no—
218C2×D149—21no—
219C2×D149—21no—
220C2×D149—41no—
221C2×D149—41no—
222C2×D149—41no—
223C2×D149—41no—
224C2×D149—41no—
225C2×D149—41no—
226C2×D149—41no—
227C2×D149—84no—
228C2×D149—84no—
229C2×D149—84no—
230C2×D149—84no—
231C2×D149#12012yes—
232C4×C149—21no—
233C4×C149—22no—
234C4×C149—41no—
235C4×C149C22×D411yescharacteristic
236C4×C149C22×D411yescharacteristic
237Dic149—21no—
238Dic149—41no—
239Dic149#12012yes—
240C2×C149—41no—
241C2×C149—42no—
242C2×C149—81no—
243C2×C149C2×#12011yescharacteristic
244C2×C149#57611yescharacteristic
245C2×C149#57611yescharacteristic
246D149—22no—
247D149—41no—
248D149—42no—
249D149—42no—
250D149—81no—
251C149#300811yescharacteristic, complemented, Sylow
252#3008—1491nomaximal, Sylow
253C2×H(5,𝔽2)—1491no—
254C2×AGL(1,ℤ/8)—1491no—
255C22×D8—1491no—
256#535—1491no—
257#449—1491no—
258#449—1491no—
259#449—1491no—
260#449D14911yescharacteristic, complemented
261#447—1491no—
262#447—1491no—
263#447—1491no—
264#447—1491no—
265#418—1491no—
266#416—1491no—
267#408—1491no—
268H(5,𝔽2)—2984no—
269H(5,𝔽2)—2984no—
270C2×#41—2981no—
271C2×#41—1491no—
272C2×#41—1491no—
273C2×#41—1491no—
274C2×#41C2×D14911yescharacteristic, complemented
275C22×D4—2981no—
276C22×D4—2981no—
277C22×D4—2981no—
278C22×D4—1491no—
279C22×D4—1491no—
280C22×D4—1491no—
281C22×D4—1491no—
282AGL(1,ℤ/8)—2984no—
283C2×SD16—1491no—
284C2×SD16C2×D14911yescharacteristic, complemented
285C2×D8—2984no—
286C2×D8—1491no—
287C2×D8—1491no—
288C2×D8—1491no—
289C2×D8—1491no—
290C2×D8—1491no—
291C2×D8C2×D14911yescharacteristic, complemented
292C2×M16—1491no—
293C22×C8—1491no—
294#127—2981no—
295#124—2981no—
296#121—1491no—
297#121—1491no—
298#121—1491no—
299#121C2×D14911yescharacteristic, complemented
300#120—2981no—
301#120—2981no—
302#117—1491no—
303#103—1491no—
304#103C2×D14911yescharacteristic, complemented
305#102—1491no—
306#102—1491no—
307#102—1491no—
308#102—1491no—
309#102—1491no—
310#102C2×D14911yescharacteristic, complemented
311C22⋊C8—1491no—
312C22⋊C8—1491no—
313C22⋊C8—1491no—
314C22⋊C8C2×D14911yescharacteristic, complemented
315C24—2981no—
316C24—2981no—
317C24—2981no—
318C24—2981no—
319#41—22no—
320#41—22no—
321#41—2988no—
322#41—2982no—
323#41—2982no—
324#41—2982no—
325#41—2982no—
326#41—2982no—
327#41—1494no—
328C2×Q8—1491no—
329C2×Q8C22×D14911yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—2988no—
333C2×D4—2981no—
334C2×D4—2981no—
335C2×D4—2982no—
336C2×D4—2982no—
337C2×D4—2981no—
338C2×D4—2988no—
339C2×D4—2988no—
340C2×D4—2982no—
341C2×D4—2982no—
342C2×D4—2981no—
343C2×D4—2981no—
344C2×D4—2982no—
345C2×D4—2982no—
346C2×D4—2982no—
347C2×D4—2981no—
348C2×D4—2981no—
349C2×D4—2981no—
350C2×D4—2981no—
351C2×D4—1491no—
352C2×D4—1491no—
353C2×D4—1494no—
354C2×D4—1491no—
355C2×D4—1491no—
356C2×D4—1491no—
357C2×D4—1491no—
358C2×D4C22×D14911yescharacteristic
359C2×D4C22×D14911yescharacteristic
360C22×C4—21no—
361C22×C4—2981no—
362C22×C4—2981no—
363C22×C4—1491no—
364C22×C4—1491no—
365C22×C4C22×D14911yescharacteristic
366SD16—22no—
367SD16—2982no—
368D8—22no—
369D8—2982no—
370D8—2982no—
371D8—2982no—
372D8—2982no—
373D8—2982no—
374M16—2982no—
375C2×C8—2982no—
376C2×C8—1491no—
377C2×C8—1491no—
378C2×C8C22×D14911yescharacteristic
379C2×C8C22×D14911yescharacteristic
380C4⋊C4—1491no—
381C4⋊C4C22×D14911yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—2981no—
384C22⋊C4—2981no—
385C22⋊C4—2981no—
386C22⋊C4—2981no—
387C42—2981no—
388C23—21no—
389C23—21no—
390C23—2984no—
391C23—2984no—
392C23—2984no—
393C23—2981no—
394C23—2981no—
395C23—2981no—
396C23—5962no—
397C23—1491no—
398C23—1491no—
399C23—11921no—
400C23—11921no—
401C23—11921no—
402C23—11921no—
403C23—11921no—
404C23—11921no—
405C23—11921no—
406C23—11921no—
407C23D4×D14911yescharacteristic
408Q8—21no—
409Q8—2982no—
410Q8D4×D14912yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—2984no—
417D4—2984no—
418D4—2984no—
419D4—2982no—
420D4—2984no—
421D4—2982no—
422D4—2982no—
423D4—2984no—
424D4—2981no—
425D4—2981no—
426D4—2981no—
427D4—2981no—
428D4—5962no—
429D4—1492no—
430D4—1492no—
431D4—11921no—
432D4—11921no—
433D4—11921no—
434D4D4×D14912yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—2984no—
441C2×C4—2984no—
442C2×C4—2981no—
443C2×C4—2981no—
444C2×C4—2981no—
445C2×C4—1491no—
446C2×C4—1491no—
447C2×C4—1492no—
448C2×C4—1492no—
449C2×C4D4×D14911yescharacteristic
450C2×C4C23×D14911yescharacteristic
451C8—21no—
452C8—21no—
453C8—2981no—
454C8—2981no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2981no—
465C22—2981no—
466C22—2981no—
467C22—2981no—
468C22—2981no—
469C22—2982no—
470C22—2982no—
471C22—5961no—
472C22—5961no—
473C22—5961no—
474C22—5961no—
475C22—5961no—
476C22—5961no—
477C22—5961no—
478C22—1492no—
479C22—11924no—
480C22—11924no—
481C22—11924no—
482C22—11924no—
483C22C2×D4×D14911yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—2981no—
488C4—5961no—
489C4—1492no—
490C4C2×D4×D14911yescharacteristic
491C4C2×D4×D14911yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—2982no—
496C2—5961no—
497C2—5962no—
498C2—5962no—
499C2—11921no—
500C2#120×D14911yescharacteristic
501C2#2375042711yescharacteristic
502C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3008
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#18011957C2semidirect
2. C2×#18011938C2semidirect
3. C2×D8×D149C2semidirect
4. #23750191C2semidirect
5. #23749773C2semidirect
6. #23749770C2semidirect
7. #23749769C2semidirect
8. #23749761C2semidirect
9. #23749760C2semidirect
10. #23749758C2semidirect
11. #23749757C2semidirect
12. #23749628C2semidirect
13. #23749620C2semidirect
14. #23749590C2semidirect
15. #449×C149C2semidirect
19. C2×#14558737C22semidirect
23. C22×D596C22semidirect
27. C2×D4×D149C22semidirect
28. C2×D4×D149C22semidirect
30. C2×#14558723C22semidirect
31. C2×D1192C22semidirect
32. C2×D1192C22semidirect
33. C2×#14558721C22semidirect
34. C2×#14558721C22semidirect
35. C2×#14558721C22semidirect
37. C2×#14558719C22semidirect
38. C2×C8×D149C22semidirect
41. #18011886C22semidirect
42. #18011885C22semidirect
43. #18011882C22semidirect
46. #18011869C22semidirect
47. #18011835C22semidirect
48. #18011833C22semidirect
49. #18011833C22semidirect
50. #18011832C22semidirect
51. #18011831C22semidirect
52. #18011831C22semidirect
53. C22⋊#11924746C22semidirect
54. #18011823C22semidirect
55. #18011823C22semidirect
56. C2×#41×C149C22semidirect
57. C2×SD16×C149C22semidirect
58. C2×D8×C149C22semidirect
59. #121×C149C22semidirect
60. #103×C149C22semidirect
61. #102×C149C22semidirect
62. C22⋊C8×C149C22semidirect
70. #14558737D4semidirect
100. D4×D149D4semidirect
251. C149#3008semidirect
260. #449D149semidirect
274. C2×#41C2×D149semidirect
284. C2×SD16C2×D149semidirect
291. C2×D8C2×D149semidirect
299. #121C2×D149semidirect
304. #103C2×D149semidirect
310. #102C2×D149semidirect
314. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119572
C2×#180119382
C2×D8×D1492
#237501912
#237497732
#237497702
#237497692
#237497612
#237497602
#237497582
#237497572
#237496282
#237496202
#237495902
#449×C1492
#3008149