Finite Group Databasebeta

← #34056317

Subgroups — #34056317

Order 19072.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic, complemented
2C2×#18011938C211yesmaximal, characteristic, complemented
3#23750287C211yesmaximal, characteristic, complemented
4#23750268C211yesmaximal, characteristic, complemented
5#23750007C211yesmaximal, characteristic, complemented
6#23749882C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749786C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749773C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13C4×#14558723C211yesmaximal, characteristic, complemented
14#23749702C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558737C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic, complemented
19C2×D4×D149C2211yescharacteristic
20#18011943—24no—
21#18011938—24no—
22C2×#14558726C2211yescharacteristic, complemented
23C2×#14558725C2211yescharacteristic
24C2×#14558724C2211yescharacteristic
25C2×#14558723C2211yescharacteristic
26C2×#14558723C2211yescharacteristic, complemented
27C2×D1192C2211yescharacteristic
28C2×#14558721C2211yescharacteristic
29C2×#14558719C2211yescharacteristic
30C2×#14558719C2211yescharacteristic, complemented
31#18011899—21no—
32#18011899C2211yescharacteristic, complemented
33#18011893—21no—
34#18011891—21no—
35#18011891C2211yescharacteristic
36#18011887C2211yescharacteristic
37#18011886—21no—
38#18011886C2211yescharacteristic, complemented
39#18011884—21no—
40#18011882C2211yescharacteristic
41#18011881—21no—
42C4×D596—21no—
43C4×D596C2211yescharacteristic
44C4×D596C2211yescharacteristic
45C22⋊C4×D149—21no—
46#18011842C2211yescharacteristic, complemented
47#18011836C2211yescharacteristic, complemented
48#18011835C2211yescharacteristic, complemented
49#18011833C2211yescharacteristic, complemented
50#18011831C2211yescharacteristic
51#18011823C2211yescharacteristic
52#18011823C2211yescharacteristic, complemented
53C4×#11924746C2211yescharacteristic, complemented
54C2×Q16×C149C2211yescharacteristic, complemented
55C2×SD16×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#103×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic
61C23×D149—21no—
62#14558737—22no—
63#14558737—22no—
64#14558737—41no—
65#14558737—41no—
66C2×Dic298—21no—
67C2×Dic298C2311yescharacteristic
68Q8×D149—22no—
69Q8×D149—41no—
70C2×D596—21no—
71C2×D596—21no—
72C2×D596—21no—
73C2×D596D411yescharacteristic
74C2×D596C2311yescharacteristic
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78D4×D149—22no—
79D4×D149—41no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149—21no—
84C2×C4×D149C2311yescharacteristic
85C2×C4×D149C2311yescharacteristic
86#14558726—22no—
87#14558725—22no—
88#14558724—41no—
89#14558723—41no—
90#14558723D414yescomplemented
91D1192—22no—
92#14558721—22no—
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×Q8×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113Q16×C149—22no—
114SD16×C149—22no—
115C2×C8×C149C2311yescharacteristic
116C2×C8×C149C2311yescharacteristic
117C4⋊C4×C149—21no—
118C4⋊C4×C149C2311yescharacteristic
119C22⋊C4×C149—21no—
120C22⋊C4×C149—21no—
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129C22×D149C2×D411yescharacteristic
130Dic298—21no—
131Dic298—21no—
132Dic298—42no—
133D596—21no—
134D596—21no—
135D596—21no—
136D596—41no—
137D596—42no—
138D596—42no—
139D596—42no—
140D596C2×D412yes—
141C22⋊D149—42no—
142C22⋊D149—81no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—21no—
151C4×D149—42no—
152C4×D149—42no—
153C4×D149—42no—
154C4×D149—81no—
155#11924746—21no—
156#11924746C2×D412yes—
157C23×C149—21no—
158Q8×C149—21no—
159Q8×C149—21no—
160Q8×C149—21no—
161Q8×C149C2×D412yes—
162D4×C149—21no—
163D4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149—21no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149C22×D411yescharacteristic
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—22no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—22no—
190C4×C149—21no—
191C4×C149—21no—
192C4×C149—41no—
193C4×C149—41no—
194C4×C149C22×D411yescharacteristic
195C4×C149H(5,𝔽2)11yescharacteristic
196Dic149—21no—
197Dic149—21no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—81no—
201C2×C149D4211yescharacteristic
202C2×C149#57511yescharacteristic
203C2×C149#57711yescharacteristic
204D149—41no—
205D149—41no—
206D149—42no—
207D149—81no—
208C149#327511yescharacteristic, complemented, Sylow
209#3275—1491nomaximal, Sylow
210C2×#137—1491no—
211C2×AGL(1,ℤ/8)—1491no—
212#548—1491no—
213#546—1491no—
214#495—1491no—
215#470—1491no—
216#469—1491no—
217#464D14911yescharacteristic, complemented
218#463—1491no—
219#452—1491no—
220#450—1491no—
221#449—1491no—
222#448—1491no—
223C4×SD16—1491no—
224#436—1491no—
225C2×#41—1491no—
226C2×#41—1491no—
227C22×Q8—1491no—
228C22×D4—1491no—
229#137—2984no—
230AGL(1,ℤ/8)—2984no—
231C2×Q16—1491no—
232C2×Q16C2×D14911yescharacteristic, complemented
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16—1491no—
237C2×SD16C2×D14911yescharacteristic
238C2×D8—1491no—
239C2×D8—1491no—
240C2×M16—1491no—
241C2×M16—1491no—
242#124—2981no—
243#124—1491no—
244#124C2×D14911yescharacteristic
245#123—2981no—
246C22⋊Q8—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8—1491no—
249#121—2981no—
250#121—2981no—
251#121—1491no—
252#121—1491no—
253#120—2981no—
254C4×Q8C2×D14911yescharacteristic, complemented
255C4×D4—2981no—
256C4×D4—1491no—
257C4×D4—1491no—
258C2×C22⋊C4—2981no—
259#106—1491no—
260C4⋊C8C2×D14911yescharacteristic, complemented
261#103—1491no—
262#103—1491no—
263#103C2×D14911yescharacteristic, complemented
264#102—1491no—
265#102—1491no—
266#102C2×D14911yescharacteristic
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C4×C8—1491no—
270C24—2981no—
271#41—2982no—
272#41—2982no—
273#41—5961no—
274#41—5961no—
275C2×Q8—2981no—
276C2×Q8—2982no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8C22×D14911yescharacteristic
280C2×Q8C22×D14911yescharacteristic
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2982no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4C22×D14911yescharacteristic
292C22×C4—2981no—
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4—1491no—
298Q16—22no—
299Q16—2982no—
300SD16—22no—
301SD16—2982no—
302SD16—5961no—
303SD16—5961no—
304SD16—1494no—
305D8—2982no—
306D8—2982no—
307M16—2982no—
308M16—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4—1491no—
318C4⋊C4C22×D14911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—1491no—
329C22⋊C4—1491no—
330C42—21no—
331C42C22×D14911yescharacteristic
332C23—21no—
333C23—2981no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—1491no—
339C23—11921no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—2981no—
344Q8—2981no—
345Q8—5962no—
346Q8D4×D14912yes—
347D4—21no—
348D4—21no—
349D4—2981no—
350D4—2981no—
351D4—2981no—
352D4—5961no—
353D4—5962no—
354D4—5962no—
355D4—5962no—
356D4—5962no—
357D4—1492no—
358D4—11921no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—2981no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—5962no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4—1491no—
372C2×C4—1491no—
373C2×C4—11921no—
374C2×C4D4×D14911yescharacteristic
375C2×C4D4×D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—21no—
378C8—21no—
379C8—2981no—
380C8—1492no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—2981no—
385C22—2981no—
386C22—2981no—
387C22—2981no—
388C22—2981no—
389C22—2981no—
390C22—2982no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—2981no—
404C4—2981no—
405C4—5961no—
406C4—5961no—
407C4C2×D4×D14911yescharacteristic
408C4#1801195711yescharacteristic
409C2—81no—
410C2—5961no—
411C2—5961no—
412C2—5962no—
413C2—11921no—
414C2#2375025911yescharacteristic
415C2#2375042211yescharacteristic
416C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
hypercenter#464D149
hypocenterC149#3275
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. C2×#18011938C2semidirect
3. #23750287C2semidirect
4. #23750268C2semidirect
5. #23750007C2semidirect
6. #23749882C2semidirect
7. #23749877C2semidirect
8. #23749841C2semidirect
9. #23749786C2semidirect
10. #23749777C2semidirect
11. #23749773C2semidirect
12. #23749762C2semidirect
13. C4×#14558723C2semidirect
14. #23749702C2semidirect
15. #464×C149C2semidirect
18. C2×Q8×D149C22semidirect
22. C2×#14558726C22semidirect
26. C2×#14558723C22semidirect
30. C2×#14558719C22semidirect
32. #18011899C22semidirect
38. #18011886C22semidirect
46. #18011842C22semidirect
47. #18011836C22semidirect
48. #18011835C22semidirect
49. #18011833C22semidirect
52. #18011823C22semidirect
53. C4×#11924746C22semidirect
54. C2×Q16×C149C22semidirect
57. C4×Q8×C149C22semidirect
58. C4⋊C8×C149C22semidirect
59. #103×C149C22semidirect
90. #14558723D4semidirect
208. C149#3275semidirect
217. #464D149semidirect
232. C2×Q16C2×D149semidirect
254. C4×Q8C2×D149semidirect
260. C4⋊C8C2×D149semidirect
263. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×#180119382
#237502872
#237502682
#237500072
#237498822
#237498772
#237498412
#237497862
#237497772
#237497732
#237497622
C4×#145587232
#237497022
#464×C1492
#3275149