Finite Group Databasebeta

← #34056321

Subgroups — #34056321

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×#18011935C211yesmaximal, characteristic, complemented
3#23750283C211yesmaximal, characteristic, complemented
4#23750268C211yesmaximal, characteristic, complemented
5#23749880C211yesmaximal, characteristic, complemented
6#23749875C211yesmaximal, characteristic, complemented
7#23749844C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749784C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11#23749769C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13C4×#14558725C211yesmaximal, characteristic, complemented
14#23749704C211yesmaximal, characteristic, complemented
15#495×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic, complemented
19C2×D4×D149C2211yescharacteristic
20#18011943—24no—
21#18011935—24no—
22C2×#14558726C2211yescharacteristic, complemented
23C2×#14558725C2211yescharacteristic
24C2×#14558724C2211yescharacteristic
25C2×#14558723C2211yescharacteristic
26C2×#14558721C2211yescharacteristic
27C2×#14558719C2211yescharacteristic
28C2×#14558719C2211yescharacteristic, complemented
29#18011897—21no—
30#18011893—21no—
31#18011888—21no—
32#18011887C2211yescharacteristic
33#18011887C2211yescharacteristic
34#18011884—21no—
35#18011884—21no—
36#18011882C2211yescharacteristic
37#18011882C2211yescharacteristic, complemented
38#18011881—21no—
39C4×Dic298C2211yescharacteristic, complemented
40C4×D596C2211yescharacteristic
41C4×D596C2211yescharacteristic
42#18011871—21no—
43C22⋊C4×D149—21no—
44#18011843C2211yescharacteristic, complemented
45C4⋊#11924746C2211yescharacteristic, complemented
46#18011836C2211yescharacteristic, complemented
47#18011835C2211yescharacteristic, complemented
48#18011835C2211yescharacteristic, complemented
49#18011833C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011832C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic
53#18011823C2211yescharacteristic, complemented
54C2×Q16×C149C2211yescharacteristic, complemented
55C2×SD16×C149C2211yescharacteristic
56C2×SD16×C149C2211yescharacteristic, complemented
57C2×D8×C149C2211yescharacteristic
58#124×C149C2211yescharacteristic
59#124×C149C2211yescharacteristic, complemented
60C4×C8×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558737—22no—
63#14558737—41no—
64#14558735—22no—
65#14558735—41no—
66C2×Dic298—21no—
67C2×Dic298C2311yescharacteristic
68Q8×D149—22no—
69Q8×D149—41no—
70C2×D596—21no—
71C2×D596D411yescharacteristic
72C2×D596C2311yescharacteristic
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77D4×D149—22no—
78D4×D149—41no—
79C22×Dic149—21no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85#14558726—22no—
86#14558725D414yescomplemented
87#14558724—22no—
88#14558723—22no—
89#14558721—22no—
90#14558719—22no—
91#14558719—22no—
92C2×#11924746C2311yescharacteristic
93C2×#11924746C2311yescharacteristic
94C4⋊Dic149D411yescharacteristic
95C4⋊Dic149C2311yescharacteristic
96C4⋊Dic149C2311yescharacteristic
97#14558715—21no—
98#14558715—21no—
99#14558715—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149—21no—
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713D411yescharacteristic
106#14558713D411yescharacteristic
107C4×Dic149—21no—
108C2×Q8×C149C2311yescharacteristic
109C2×Q8×C149C2311yescharacteristic
110C2×D4×C149C2311yescharacteristic
111C2×D4×C149C2311yescharacteristic
112Q16×C149—22no—
113SD16×C149—41no—
114SD16×C149—41no—
115D8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C22⋊C4×C149—21no—
119C22⋊C4×C149—21no—
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—42no—
125C22×D149—42no—
126C22×D149—81no—
127C22×D149C2×D411yescharacteristic
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—42no—
131Dic298C2×D412yes—
132D596—21no—
133D596—41no—
134D596—42no—
135D596C2×D412yes—
136C22⋊D149—42no—
137C22⋊D149—42no—
138C22⋊D149—42no—
139C22⋊D149—81no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—42no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—42no—
151C4×D149—42no—
152C4×D149—81no—
153#11924746—21no—
154#11924746—21no—
155C23×C149—21no—
156C23×C149—21no—
157Q8×C149—21no—
158Q8×C149—21no—
159Q8×C149—21no—
160Q8×C149—21no—
161D4×C149—21no—
162D4×C149—21no—
163D4×C149—21no—
164D4×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×C149C2×D412yes—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—22no—
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—21no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—21no—
190C4×C149—21no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149C22×D411yescharacteristic
194C4×C149H(5,𝔽2)11yescharacteristic
195Dic149—21no—
196Dic149—21no—
197Dic149—22no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—81no—
201C2×C149—81no—
202C2×C149D4211yescharacteristic
203C2×C149#57511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—41no—
206D149—41no—
207D149—42no—
208C149#327511yescharacteristic, complemented, Sylow
209#3275—1491nomaximal, Sylow
210C2×#137—1491no—
211C2×AGL(1,ℤ/8)—1491no—
212#548—1491no—
213#546—1491no—
214#495D14911yescharacteristic, complemented
215#470—1491no—
216#469—1491no—
217#464—1491no—
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×SD16C2×D14911yescharacteristic
237C2×SD16C2×D14911yescharacteristic, complemented
238C2×D8—1491no—
239C2×D8C2×D14911yescharacteristic
240C2×M16—1491no—
241C2×M16—1491no—
242#124—2981no—
243#124C2×D14911yescharacteristic
244#124C2×D14911yescharacteristic, complemented
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×Q8—1491no—
255C4×D4—2981no—
256C4×D4—1491no—
257C4×D4—1491no—
258C2×C22⋊C4—2981no—
259#106—1491no—
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103—1491no—
264#102—1491no—
265#102—1491no—
266#102—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C4×C8C2×D14911yescharacteristic, complemented
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—2982no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4C22×D14911yescharacteristic
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—41no—
301SD16—41no—
302SD16—2982no—
303SD16—2982no—
304SD16—1494no—
305D8—22no—
306D8—2982no—
307M16—2982no—
308M16—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4—1491no—
318C4⋊C4—1491no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—1491no—
329C22⋊C4—1491no—
330C42—2981no—
331C42C22×D14911yescharacteristic
332C23—21no—
333C23—21no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—1491no—
339C23—11921no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2981no—
345Q8—5962no—
346Q8—1492no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—2981no—
352D4—5961no—
353D4—5962no—
354D4—5962no—
355D4—5962no—
356D4—5962no—
357D4—1492no—
358D4—11921no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—2981no—
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—2981no—
379C8—2981no—
380C8D4×D14912yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—2981no—
388C22—2981no—
389C22—2981no—
390C22—2981no—
391C22—2981no—
392C22—2981no—
393C22—2982no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2981no—
403C4—2981no—
404C4—2982no—
405C4—5961no—
406C4—5961no—
407C4C2×D4×D14911yescharacteristic
408C4#1801195611yescharacteristic
409C2—81no—
410C2—81no—
411C2—5961no—
412C2—5961no—
413C2—5962no—
414C2#2375026011yescharacteristic
415C2#2375042211yescharacteristic
416C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3275
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. C2×#18011935C2semidirect
3. #23750283C2semidirect
4. #23750268C2semidirect
5. #23749880C2semidirect
6. #23749875C2semidirect
7. #23749844C2semidirect
8. #23749837C2semidirect
9. #23749784C2semidirect
10. #23749774C2semidirect
11. #23749769C2semidirect
12. #23749762C2semidirect
13. C4×#14558725C2semidirect
14. #23749704C2semidirect
15. #495×C149C2semidirect
18. C2×Q8×D149C22semidirect
22. C2×#14558726C22semidirect
28. C2×#14558719C22semidirect
37. #18011882C22semidirect
39. C4×Dic298C22semidirect
44. #18011843C22semidirect
45. C4⋊#11924746C22semidirect
46. #18011836C22semidirect
47. #18011835C22semidirect
48. #18011835C22semidirect
51. #18011832C22semidirect
53. #18011823C22semidirect
54. C2×Q16×C149C22semidirect
56. C2×SD16×C149C22semidirect
59. #124×C149C22semidirect
60. C4×C8×C149C22semidirect
86. #14558725D4semidirect
208. C149#3275semidirect
214. #495D149semidirect
232. C2×Q16C2×D149semidirect
237. C2×SD16C2×D149semidirect
244. #124C2×D149semidirect
269. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×#180119352
#237502832
#237502682
#237498802
#237498752
#237498442
#237498372
#237497842
#237497742
#237497692
#237497622
C4×#145587252
#237497042
#495×C1492
#3275149