Finite Group Databasebeta

← #34056297

Subgroups — #34056297

Order 19072.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011938C211yesmaximal, characteristic, complemented
2C2×#18011935C211yesmaximal, characteristic, complemented
3#23750270C211yesmaximal, characteristic, complemented
4#23750268C211yesmaximal, characteristic, complemented
5#23750007C211yesmaximal, characteristic, complemented
6#23749874C211yesmaximal, characteristic, complemented
7#23749870C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749790C211yesmaximal, characteristic, complemented
10#23749784C211yesmaximal, characteristic, complemented
11#23749760C211yesmaximal, characteristic, complemented
12#23749757C211yesmaximal, characteristic, complemented
13C4×#14558721C211yesmaximal, characteristic, complemented
14#23749702C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic, complemented
19C2×D4×D149C2211yescharacteristic, complemented
20#18011938—24no—
21#18011935—24no—
22C2×#14558726C2211yescharacteristic, complemented
23C2×#14558725C2211yescharacteristic, complemented
24C2×#14558724C2211yescharacteristic, complemented
25C2×#14558723C2211yescharacteristic, complemented
26C2×D1192C2211yescharacteristic
27C2×#14558721C2211yescharacteristic
28C2×#14558721C2211yescharacteristic
29C2×#14558719C2211yescharacteristic, complemented
30C2×#14558719C2211yescharacteristic, complemented
31#18011899C2211yescharacteristic, complemented
32#18011895—21no—
33#18011893—21no—
34#18011891C2211yescharacteristic, complemented
35#18011887C2211yescharacteristic, complemented
36#18011886C2211yescharacteristic
37#18011885—21no—
38#18011884—21no—
39#18011882C2211yescharacteristic
40#18011881—21no—
41#18011881—21no—
42C4×D596C2211yescharacteristic
43C4×D596C2211yescharacteristic, complemented
44C2×#14558713—21no—
45C22⋊C4×D149—21no—
46#18011844C2211yescharacteristic, complemented
47#18011836C2211yescharacteristic, complemented
48#18011833C2211yescharacteristic, complemented
49#18011832C2211yescharacteristic, complemented
50#18011831C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic, complemented
53C4×#11924746C2211yescharacteristic, complemented
54C2×SD16×C149C2211yescharacteristic, complemented
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic, complemented
57C4×D4×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#103×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62C23×D149—21no—
63#14558737—22no—
64#14558737—41no—
65#14558735—22no—
66#14558735—41no—
67C2×Dic298C2311yescharacteristic
68C2×D596—21no—
69C2×D596—21no—
70C2×D596D411yescharacteristic
71C2×D596C2311yescharacteristic
72C2×D596C2311yescharacteristic
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77D4×D149—22no—
78D4×D149—22no—
79D4×D149—41no—
80D4×D149—41no—
81C22×Dic149—21no—
82C2×C4×D149—21no—
83C2×C4×D149—21no—
84C2×C4×D149C2311yescharacteristic
85C2×C4×D149C2311yescharacteristic
86#14558726—41no—
87#14558725—22no—
88#14558724—22no—
89#14558723—22no—
90D1192—22no—
91#14558721—41no—
92#14558721D414yescomplemented
93#14558719—22no—
94#14558719—22no—
95C2×#11924746C2311yescharacteristic
96C2×#11924746C2311yescharacteristic
97C4⋊Dic149—21no—
98C4⋊Dic149D411yescharacteristic
99C4⋊Dic149C2311yescharacteristic
100#14558715—21no—
101C22⋊Dic149—21no—
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713D411yescharacteristic
109#14558713D411yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114SD16×C149—22no—
115D8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149C2311yescharacteristic
119C22⋊C4×C149—21no—
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—42no—
128C22×D149—42no—
129C22×D149—81no—
130C22×D149—81no—
131C22×D149C2×D411yescharacteristic
132C22×D149C2×D411yescharacteristic
133Dic298—21no—
134Dic298—21no—
135D596—21no—
136D596—21no—
137D596—21no—
138D596—41no—
139D596—42no—
140D596—81no—
141D596C2×D412yes—
142C22⋊D149—42no—
143C22⋊D149—42no—
144C22⋊D149—42no—
145C22⋊D149—81no—
146C2×Dic149—21no—
147C2×Dic149—21no—
148C2×Dic149—42no—
149C2×Dic149C2×D411yescharacteristic
150C2×Dic149C2×D411yescharacteristic
151C4×D149—21no—
152C4×D149—21no—
153C4×D149—21no—
154C4×D149—21no—
155C4×D149—42no—
156C4×D149—81no—
157#11924746—21no—
158#11924746C2×D412yes—
159C23×C149—21no—
160C23×C149—21no—
161Q8×C149—21no—
162Q8×C149—21no—
163D4×C149—21no—
164D4×C149—21no—
165D4×C149—21no—
166D4×C149C2×D412yes—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—81no—
170C2×C4×C149C2×D411yescharacteristic
171C2×C4×C149C2×D411yescharacteristic
172C2×C4×C149C2411yescharacteristic
173C8×C149—21no—
174C8×C149—21no—
175C22×C149—22no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149C22×D411yescharacteristic
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—22no—
185C2×D149—21no—
186C2×D149—21no—
187C2×D149—21no—
188C2×D149—21no—
189C2×D149—41no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—41no—
194C2×D149—84no—
195C2×D149—84no—
196C4×C149—21no—
197C4×C149—21no—
198C4×C149—41no—
199C4×C149—41no—
200C4×C149C22×D411yescharacteristic
201C4×C149H(5,𝔽2)11yescharacteristic
202Dic149—21no—
203Dic149—21no—
204Dic149—41no—
205Dic149—41no—
206C2×C149—42no—
207C2×C149—81no—
208C2×C149D4211yescharacteristic
209C2×C149#57511yescharacteristic
210C2×C149#57611yescharacteristic
211D149—41no—
212D149—41no—
213D149—42no—
214D149—81no—
215C149#327311yescharacteristic, complemented, Sylow
216#3273—1491nomaximal, Sylow
217C2×AGL(1,ℤ/8)—1491no—
218C2×AGL(1,ℤ/8)—1491no—
219#546—1491no—
220#546—1491no—
221#495—1491no—
222#468—1491no—
223#468—1491no—
224#463—1491no—
225#463D14911yescharacteristic, complemented
226#452—1491no—
227#452—1491no—
228#447—1491no—
229#447—1491no—
230C4×D8—1491no—
231#436—1491no—
232C2×#41—1491no—
233C2×#41—1491no—
234C22×D4—1491no—
235C22×D4—1491no—
236AGL(1,ℤ/8)—2984no—
237AGL(1,ℤ/8)—2984no—
238C2×Q16—1491no—
239C2×SD16—1491no—
240C2×SD16—1491no—
241C2×SD16—1491no—
242C2×SD16C2×D14911yescharacteristic, complemented
243C2×D8—1491no—
244C2×D8—1491no—
245C2×D8—1491no—
246C2×D8C2×D14911yescharacteristic
247C2×M16—1491no—
248C2×M16—1491no—
249#124—1491no—
250#124C2×D14911yescharacteristic, complemented
251#123—2981no—
252#123—2981no—
253C22⋊Q8—1491no—
254C22⋊Q8—1491no—
255#121—2981no—
256#121—2981no—
257#121—1491no—
258#121—1491no—
259#120—2981no—
260#120—2981no—
261C4×D4—1491no—
262C4×D4—1491no—
263C4×D4C2×D14911yescharacteristic, complemented
264C2×C22⋊C4—2981no—
265C2×C22⋊C4—2981no—
266#107—1491no—
267C4⋊C8C2×D14911yescharacteristic, complemented
268#103—1491no—
269#103C2×D14911yescharacteristic, complemented
270#102—1491no—
271#102—1491no—
272#102—1491no—
273#102C2×D14911yescharacteristic, complemented
274C22⋊C8—1491no—
275C22⋊C8—1491no—
276C4×C8—1491no—
277C24—2981no—
278C24—2981no—
279#41—2982no—
280#41—2982no—
281#41—5961no—
282#41—5961no—
283C2×Q8—1491no—
284C2×Q8C22×D14911yescharacteristic
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2982no—
288C2×D4—2982no—
289C2×D4—2981no—
290C2×D4—2981no—
291C2×D4—2981no—
292C2×D4—2981no—
293C2×D4—5961no—
294C2×D4—5961no—
295C2×D4—1491no—
296C2×D4—1491no—
297C2×D4—1491no—
298C2×D4C22×D14911yescharacteristic
299C2×D4C22×D14911yescharacteristic
300C22×C4—21no—
301C22×C4—2981no—
302C22×C4—2981no—
303C22×C4—2981no—
304C22×C4—1491no—
305C22×C4—1491no—
306Q16—5961no—
307SD16—22no—
308SD16—2982no—
309SD16—2982no—
310SD16—2982no—
311D8—22no—
312D8—2982no—
313D8—5961no—
314D8—1494no—
315M16—2982no—
316M16—2982no—
317C2×C8—1491no—
318C2×C8—1491no—
319C2×C8C22×D14911yescharacteristic
320C2×C8C22×D14911yescharacteristic
321C4⋊C4—2981no—
322C4⋊C4—2981no—
323C4⋊C4—1491no—
324C4⋊C4—1491no—
325C4⋊C4C22×D14911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—2981no—
330C22⋊C4—2981no—
331C22⋊C4—2981no—
332C22⋊C4—2981no—
333C22⋊C4—2981no—
334C22⋊C4—2981no—
335C22⋊C4—2981no—
336C22⋊C4—1491no—
337C22⋊C4—1491no—
338C42C22×D14911yescharacteristic
339C23—21no—
340C23—21no—
341C23—2981no—
342C23—2981no—
343C23—5962no—
344C23—5962no—
345C23—5962no—
346C23—5962no—
347C23—1491no—
348C23—1491no—
349C23—11921no—
350C23—11921no—
351Q8—21no—
352Q8—21no—
353Q8—2981no—
354Q8—2981no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—2981no—
359D4—2981no—
360D4—2981no—
361D4—5961no—
362D4—5962no—
363D4—5962no—
364D4—5962no—
365D4—5962no—
366D4—1492no—
367D4—11921no—
368D4—11921no—
369D4D4×D14912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2981no—
374C2×C4—2981no—
375C2×C4—2981no—
376C2×C4—2981no—
377C2×C4—2981no—
378C2×C4—2981no—
379C2×C4—5962no—
380C2×C4—5962no—
381C2×C4—1491no—
382C2×C4—1491no—
383C2×C4—11921no—
384C2×C4D4×D14911yescharacteristic
385C2×C4D4×D14911yescharacteristic
386C2×C4C23×D14911yescharacteristic
387C8—21no—
388C8—21no—
389C8—2981no—
390C8—1492no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—2981no—
398C22—2981no—
399C22—2981no—
400C22—2981no—
401C22—2981no—
402C22—2981no—
403C22—2982no—
404C22—5961no—
405C22—5961no—
406C22—5961no—
407C22—5961no—
408C22—5961no—
409C22—11924no—
410C22—11924no—
411C22C2×D4×D14911yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—2981no—
417C4—2981no—
418C4—5961no—
419C4—5961no—
420C4C2×D4×D14911yescharacteristic
421C4#1801195711yescharacteristic
422C2—42no—
423C2—81no—
424C2—5961no—
425C2—5961no—
426C2—5962no—
427C2—11921no—
428C2#2375025911yescharacteristic
429C2#2375042211yescharacteristic
430C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3273
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. C2×#18011935C2semidirect
3. #23750270C2semidirect
4. #23750268C2semidirect
5. #23750007C2semidirect
6. #23749874C2semidirect
7. #23749870C2semidirect
8. #23749841C2semidirect
9. #23749790C2semidirect
10. #23749784C2semidirect
11. #23749760C2semidirect
12. #23749757C2semidirect
13. C4×#14558721C2semidirect
14. #23749702C2semidirect
15. #463×C149C2semidirect
18. C2×D4×D149C22semidirect
19. C2×D4×D149C22semidirect
22. C2×#14558726C22semidirect
23. C2×#14558725C22semidirect
24. C2×#14558724C22semidirect
25. C2×#14558723C22semidirect
29. C2×#14558719C22semidirect
30. C2×#14558719C22semidirect
31. #18011899C22semidirect
34. #18011891C22semidirect
35. #18011887C22semidirect
43. C4×D596C22semidirect
46. #18011844C22semidirect
47. #18011836C22semidirect
48. #18011833C22semidirect
49. #18011832C22semidirect
50. #18011831C22semidirect
51. #18011823C22semidirect
52. #18011823C22semidirect
53. C4×#11924746C22semidirect
54. C2×SD16×C149C22semidirect
56. #124×C149C22semidirect
57. C4×D4×C149C22semidirect
58. C4⋊C8×C149C22semidirect
59. #103×C149C22semidirect
60. #102×C149C22semidirect
92. #14558721D4semidirect
215. C149#3273semidirect
225. #463D149semidirect
242. C2×SD16C2×D149semidirect
250. #124C2×D149semidirect
263. C4×D4C2×D149semidirect
267. C4⋊C8C2×D149semidirect
269. #103C2×D149semidirect
273. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
C2×#180119352
#237502702
#237502682
#237500072
#237498742
#237498702
#237498412
#237497902
#237497842
#237497602
#237497572
C4×#145587212
#237497022
#463×C1492
#3273149