Finite Group Databasebeta

← #34056190

Subgroups — #34056190

Order 19072.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011935C211yesmaximal, characteristic, complemented
2C22×#14558724C211yesmaximal, characteristic, complemented
3#23750281C211yesmaximal, characteristic, complemented
4D4×C22⋊D149C211yesmaximal, characteristic, complemented
5#23750013C211yesmaximal, characteristic, complemented
6#23749870C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749767C211yesmaximal, characteristic, complemented
12#23749766C211yesmaximal, characteristic, complemented
13#23749722C211yesmaximal, characteristic, complemented
14#23749693C211yesmaximal, characteristic, complemented
15#447×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic, complemented
17C22×Dic298C2211yescharacteristic, complemented
18C22×C22⋊D149—21no—
19C2×D4×D149C2211yescharacteristic
20#18011935—24no—
21C2×#14558725C2211yescharacteristic, complemented
22C2×#14558725C2211yescharacteristic, complemented
23C2×#14558724—24no—
24C2×#14558724C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558724C2211yescharacteristic, complemented
27C2×#14558724C2211yescharacteristic, complemented
28C2×#14558721C2211yescharacteristic, complemented
29C2×#14558719C2211yescharacteristic, complemented
30C22×#11924746C2211yescharacteristic, complemented
31#18011907C2211yescharacteristic
32#18011898C2211yescharacteristic, complemented
33#18011897—21no—
34#18011891C2211yescharacteristic, complemented
35#18011888—21no—
36#18011885C2211yescharacteristic
37#18011883—21no—
38#18011883—21no—
39#18011882C2211yescharacteristic
40#18011880—21no—
41#18011879—21no—
42#18011876C2211yescharacteristic, complemented
43D4×Dic149—21no—
44D4×Dic149C2211yescharacteristic
45C4×C22⋊D149C2211yescharacteristic
46#18011844C2211yescharacteristic, complemented
47#18011840C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011836C2211yescharacteristic, complemented
50#18011832C2211yescharacteristic, complemented
51#18011831C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic, complemented
53#18011821C2211yescharacteristic, complemented
54C22×D4×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic
56C2×D8×C149C2211yescharacteristic, complemented
57#121×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic
59#102×C149C2211yescharacteristic, complemented
60C22⋊C8×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558735—22no—
63#14558735—41no—
64C2×Dic298—22no—
65C2×Dic298—21no—
66C2×Dic298—41no—
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—44no—
77C2×C22⋊D149D411yescharacteristic
78D4×D149—22no—
79D4×D149—41no—
80C22×Dic149—21no—
81C22×Dic149—21no—
82C22×Dic149—21no—
83C2×C4×D149C2311yescharacteristic
84#14558725—22no—
85#14558725—41no—
86#14558724—22no—
87#14558724—22no—
88#14558724—22no—
89#14558724D414yescomplemented
90#14558721—22no—
91#14558719—22no—
92C2×#11924746—22no—
93C2×#11924746C2311yescharacteristic
94C2×#11924746C2311yescharacteristic
95C4⋊Dic149—21no—
96C4⋊Dic149C2311yescharacteristic
97#14558715—21no—
98#14558715D411yescharacteristic
99C22⋊Dic149—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149—21no—
102C22⋊Dic149—21no—
103C22⋊Dic149D411yescharacteristic
104#14558713—21no—
105#14558713—21no—
106#14558713D411yescharacteristic
107C4×Dic149—21no—
108C4×Dic149C2311yescharacteristic
109C24×C149—21no—
110C2×D4×C149—22no—
111C2×D4×C149—21no—
112C2×D4×C149—21no—
113C2×D4×C149—41no—
114C2×D4×C149C2311yescharacteristic
115C2×D4×C149C2311yescharacteristic
116C2×D4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118D8×C149—22no—
119D8×C149—41no—
120C2×C8×C149C2311yescharacteristic
121C2×C8×C149C2311yescharacteristic
122C4⋊C4×C149C2311yescharacteristic
123C22⋊C4×C149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—42no—
133Dic298C2×D412yescomplemented
134D596—21no—
135D596—21no—
136C22⋊D149—22no—
137C22⋊D149—42no—
138C22⋊D149—42no—
139C22⋊D149—42no—
140C22⋊D149—42no—
141C22⋊D149—42no—
142C22⋊D149—81no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—21no—
146C2×Dic149—42no—
147C2×Dic149—42no—
148C2×Dic149—42no—
149C2×Dic149C2×D411yescharacteristic
150C2×Dic149C2×D411yescharacteristic
151C2×Dic149C2×D411yescharacteristic
152C4×D149—21no—
153C4×D149—21no—
154#11924746—21no—
155#11924746C2×D412yescomplemented
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—42no—
160C23×C149—42no—
161C23×C149—81no—
162C23×C149C2×D411yescharacteristic
163D4×C149—21no—
164D4×C149—21no—
165D4×C149—21no—
166D4×C149—21no—
167D4×C149—21no—
168D4×C149—42no—
169D4×C149—42no—
170D4×C149C2×D412yes—
171C2×C4×C149—21no—
172C2×C4×C149—21no—
173C2×C4×C149—21no—
174C2×C4×C149C2×D411yescharacteristic
175C2×C4×C149C2411yescharacteristic
176C8×C149—21no—
177C8×C149—21no—
178C22×C149—21no—
179C22×C149—21no—
180C22×C149—22no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149—41no—
185C22×C149—41no—
186C22×C149—41no—
187C22×C149—41no—
188C22×C149—41no—
189C22×C149—84no—
190C22×C149AGL(1,ℤ/8)12yescomplemented
191C22×C149C22×D411yescharacteristic
192C2×D149—21no—
193C2×D149—21no—
194C2×D149—21no—
195C2×D149—41no—
196C2×D149—41no—
197C2×D149—41no—
198C2×D149—84no—
199C4×C149—21no—
200C4×C149—41no—
201C4×C149C22×D411yescharacteristic
202C4×C149H(5,𝔽2)11yescharacteristic
203Dic149—21no—
204Dic149—22no—
205Dic149—21no—
206Dic149—21no—
207Dic149—41no—
208Dic149—41no—
209C2×C149—22no—
210C2×C149—42no—
211C2×C149—81no—
212C2×C149—81no—
213C2×C149D4211yescharacteristic
214C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C149#57711yescharacteristic
216D149—41no—
217D149—81no—
218C149#326511yescharacteristic, complemented, Sylow
219#3265—1491nomaximal, Sylow
220C2×AGL(1,ℤ/8)—1491no—
221C22×SD16—1491no—
222#548—1491no—
223D42—1491no—
224#496—1491no—
225#468—1491no—
226#466—1491no—
227#463—1491no—
228#460—1491no—
229#450—1491no—
230#449—1491no—
231#448—1491no—
232#447D14911yescharacteristic, complemented
233#440—1491no—
234#435—1491no—
235C2×#41—1491no—
236C22×Q8—1491no—
237C22×D4—2981no—
238C22×D4—1491no—
239C22×D4C2×D14911yescharacteristic
240AGL(1,ℤ/8)—2984no—
241C2×SD16—2984no—
242C2×SD16—1491no—
243C2×SD16—1491no—
244C2×SD16—1491no—
245C2×SD16—1491no—
246C2×SD16—1491no—
247C2×SD16—1491no—
248C2×D8—1491no—
249C2×D8C2×D14911yescharacteristic
250C2×D8C2×D14911yescharacteristic, complemented
251C2×M16—1491no—
252C22×C8—1491no—
253#127—1491no—
254#124—2981no—
255#124—1491no—
256C22⋊Q8—2981no—
257C22⋊Q8—1491no—
258#121—2981no—
259#121—2981no—
260#121—1491no—
261#121—1491no—
262#121C2×D14911yescharacteristic, complemented
263#120—2981no—
264#120—2981no—
265C4×Q8—1491no—
266C4×D4—2981no—
267C4×D4—1491no—
268C4×D4—1491no—
269#107—1491no—
270C4⋊C8—1491no—
271#103—1491no—
272#103—1491no—
273#102—1491no—
274#102—1491no—
275#102C2×D14911yescharacteristic
276#102C2×D14911yescharacteristic, complemented
277C22⋊C8—1491no—
278C22⋊C8C2×D14911yescharacteristic, complemented
279#97—1491no—
280C24—21no—
281C24—2981no—
282#41—2982no—
283#41—5961no—
284C2×Q8—2982no—
285C2×Q8—2981no—
286C2×Q8—5961no—
287C2×Q8—1491no—
288C2×Q8—1491no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—2982no—
294C2×D4—2981no—
295C2×D4—2981no—
296C2×D4—2981no—
297C2×D4—2981no—
298C2×D4—2981no—
299C2×D4—2981no—
300C2×D4—5961no—
301C2×D4—5964no—
302C2×D4—1491no—
303C2×D4—1491no—
304C2×D4C22×D14911yescharacteristic
305C2×D4C22×D14911yescharacteristic
306C2×D4C22×D14911yescharacteristic
307C22×C4—2981no—
308C22×C4—2981no—
309C22×C4—2981no—
310C22×C4—1491no—
311C22×C4C22×D14911yescharacteristic
312SD16—2982no—
313SD16—2982no—
314SD16—2982no—
315SD16—2982no—
316SD16—5961no—
317SD16—1494no—
318D8—22no—
319D8—41no—
320D8—2982no—
321M16—2982no—
322C2×C8—2982no—
323C2×C8—1491no—
324C2×C8—1491no—
325C2×C8C22×D14911yescharacteristic
326C2×C8C22×D14911yescharacteristic
327C4⋊C4—2981no—
328C4⋊C4—2981no—
329C4⋊C4—1491no—
330C4⋊C4—1491no—
331C4⋊C4C22×D14911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—2981no—
334C22⋊C4—2981no—
335C22⋊C4—2981no—
336C22⋊C4—2981no—
337C22⋊C4—2981no—
338C22⋊C4—2981no—
339C22⋊C4—1491no—
340C22⋊C4—1491no—
341C42—2981no—
342C42—1491no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—2981no—
350C23—5962no—
351C23—5962no—
352C23—1491no—
353C23—11921no—
354C23D4×D14911yescharacteristic
355Q8—2981no—
356Q8—2981no—
357Q8—2981no—
358Q8—5962no—
359Q8—1492no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—2982no—
368D4—2981no—
369D4—2981no—
370D4—5962no—
371D4—5962no—
372D4—5962no—
373D4—5962no—
374D4—5962no—
375D4—11921no—
376D4D4×D14912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—2981no—
381C2×C4—2981no—
382C2×C4—2981no—
383C2×C4—2981no—
384C2×C4—2981no—
385C2×C4—5962no—
386C2×C4—5962no—
387C2×C4—5962no—
388C2×C4—1491no—
389C2×C4—1491no—
390C2×C4—1491no—
391C2×C4D4×D14911yescharacteristic
392C2×C4C23×D14911yescharacteristic
393C8—21no—
394C8—21no—
395C8—2981no—
396C8—1492no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—84no—
409C22—2981no—
410C22—2981no—
411C22—2981no—
412C22—5961no—
413C22—5961no—
414C22—5961no—
415C22—11924no—
416C22#1801193512yescomplemented
417C22C2×D4×D14911yescharacteristic
418C4—21no—
419C4—41no—
420C4—2981no—
421C4—2981no—
422C4—2981no—
423C4—2982no—
424C4—5961no—
425C4—5961no—
426C4C2×D4×D14911yescharacteristic
427C4#1801195611yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—5961no—
433C2—11921no—
434C2#2375025711yescharacteristic
435C2C2×#1801193511yescharacteristic
436C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3265
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. C22×#14558724C2semidirect
3. #23750281C2semidirect
4. D4×C22⋊D149C2semidirect
5. #23750013C2semidirect
6. #23749870C2semidirect
7. #23749859C2semidirect
8. #23749838C2semidirect
9. #23749824C2semidirect
10. #23749777C2semidirect
11. #23749767C2semidirect
12. #23749766C2semidirect
13. #23749722C2semidirect
14. #23749693C2semidirect
15. #447×C149C2semidirect
16. C2×#14558735C22semidirect
17. C22×Dic298C22semidirect
21. C2×#14558725C22semidirect
22. C2×#14558725C22semidirect
26. C2×#14558724C22semidirect
27. C2×#14558724C22semidirect
28. C2×#14558721C22semidirect
29. C2×#14558719C22semidirect
30. C22×#11924746C22semidirect
32. #18011898C22semidirect
34. #18011891C22semidirect
42. #18011876C22semidirect
46. #18011844C22semidirect
47. #18011840C22semidirect
48. #18011836C22semidirect
49. #18011836C22semidirect
50. #18011832C22semidirect
51. #18011831C22semidirect
52. #18011823C22semidirect
53. #18011821C22semidirect
56. C2×D8×C149C22semidirect
57. #121×C149C22semidirect
59. #102×C149C22semidirect
60. C22⋊C8×C149C22semidirect
89. #14558724D4semidirect
133. Dic298C2×D4semidirect
155. #11924746C2×D4semidirect
190. C22×C149AGL(1,ℤ/8)semidirect
218. C149#3265semidirect
232. #447D149semidirect
250. C2×D8C2×D149semidirect
262. #121C2×D149semidirect
276. #102C2×D149semidirect
278. C22⋊C8C2×D149semidirect
416. C22#18011935semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
C22×#145587242
#237502812
D4×C22⋊D1492
#237500132
#237498702
#237498592
#237498382
#237498242
#237497772
#237497672
#237497662
#237497222
#237496932
#447×C1492
#3265149