Finite Group Databasebeta

← #34055451

Subgroups — #34055451

Order 19072.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750135C211yesmaximal, characteristic, complemented
2#121×D149C211yesmaximal, characteristic, complemented
3#23749962C211yesmaximal, characteristic, complemented
4#23749952C211yesmaximal, characteristic, complemented
5#23749948C211yesmaximal, characteristic, complemented
6#23749942C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749771C211yesmaximal, characteristic, complemented
12#23749767C211yesmaximal, characteristic, complemented
13#23749757C211yesmaximal, characteristic, complemented
14C2×#18011823C211yesmaximal, characteristic, complemented
15#466×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic, complemented
17C2×D4×D149—21no—
18C2×D4×D149C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic, complemented
22C2×#14558721C2211yescharacteristic, complemented
23C22×#11924746C2211yescharacteristic, complemented
24#18011893—21no—
25#18011891C2211yescharacteristic
26#18011890C2211yescharacteristic, complemented
27#18011886C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011884—21no—
30#18011883—21no—
31#18011882C2211yescharacteristic
32#18011882C2211yescharacteristic
33#18011879—21no—
34D4×Dic149—21no—
35#18011871—21no—
36#18011869C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic
38C22⋊C4×D149—21no—
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C2×D8×C149C2211yescharacteristic, complemented
53C22×C8×C149C2211yescharacteristic, complemented
54#121×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic, complemented
56#107×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149D411yescharacteristic
61#14558735—41no—
62#14558735—41no—
63C2×Dic298C2311yescharacteristic
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71D4×D149—41no—
72D4×D149—41no—
73D4×D149—44no—
74C22×Dic149—21no—
75C22×Dic149D411yescharacteristic
76C2×C4×D149—21no—
77C2×C4×D149—41no—
78C2×C4×D149—41no—
79C2×C4×D149D411yescharacteristic
80C2×C4×D149D411yescharacteristic
81C2×C4×D149C2311yescharacteristic
82C2×C4×D149C2311yescharacteristic
83#14558725—41no—
84#14558724—41no—
85#14558721—41no—
86C2×#11924746—41no—
87C2×#11924746C2311yescharacteristic
88C2×#11924746C2311yescharacteristic
89C4⋊Dic149—21no—
90C4⋊Dic149C2311yescharacteristic
91C4⋊Dic149C2311yescharacteristic
92#14558715—21no—
93#14558715—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101C4×Dic149—21no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107D8×C149—41no—
108C2×C8×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22⋊C4×C149—21no—
115C22×D149—22no—
116C22×D149—22no—
117C22×D149—21no—
118C22×D149—41no—
119C22×D149—42no—
120C22×D149—42no—
121C22×D149—42no—
122C22×D149C2×D411yescharacteristic
123C22×D149C2×D411yescharacteristic
124Dic298—21no—
125Dic298—21no—
126D596—21no—
127D596—21no—
128D596—42no—
129C22⋊D149—42no—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C22⋊D149—42no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—41no—
138C2×Dic149—42no—
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—21no—
144C4×D149—21no—
145C4×D149—41no—
146C4×D149—41no—
147C4×D149—42no—
148#11924746—21no—
149#11924746—21no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149C2×D411yescharacteristic
153D4×C149—21no—
154D4×C149—21no—
155D4×C149—21no—
156D4×C149—21no—
157D4×C149—42no—
158D4×C149—42no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2411yescharacteristic
165C8×C149—21no—
166C8×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149AGL(1,ℤ/8)12yes—
176C22×C149C22×D411yescharacteristic
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C2×D149—44no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—84no—
187C2×D149#13512yes—
188C4×C149—21no—
189C4×C149—41no—
190C4×C149—41no—
191C4×C149H(5,𝔽2)11yescharacteristic
192C4×C149H(5,𝔽2)11yescharacteristic
193Dic149—21no—
194Dic149—21no—
195Dic149—41no—
196Dic149—41no—
197Dic149—41no—
198C2×C149—22no—
199C2×C149—81no—
200C2×C149—81no—
201C2×C149#53411yescharacteristic
202C2×C149C2×#13511yescharacteristic
203C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
204D149—22no—
205D149—41no—
206D149—81no—
207C149#318811yescharacteristic, complemented, Sylow
208#3188—1491nomaximal, Sylow
209#525—1491no—
210C2×#121—1491no—
211#484—1491no—
212#482—1491no—
213#482—1491no—
214#481—1491no—
215#466—1491no—
216#466D14911yescharacteristic, complemented
217#465—1491no—
218#465—1491no—
219#450—1491no—
220#449—1491no—
221#449—1491no—
222#447—1491no—
223C2×C22⋊C8—1491no—
224C2×#41—1491no—
225C22×D4—2981no—
226C22×D4—1491no—
227C23×C4—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×D8—1491no—
231C2×D8C2×D14911yescharacteristic, complemented
232C22×C8—1491no—
233C22×C8C2×D14911yescharacteristic, complemented
234#123—2981no—
235C22⋊Q8—1491no—
236C22⋊Q8—1491no—
237#121—2981no—
238#121—2981no—
239#121—1491no—
240#121—1491no—
241#121—1491no—
242#121—1491no—
243#121C2×D14911yescharacteristic
244#121C2×D14911yescharacteristic, complemented
245#120—2981no—
246C4×D4—2981no—
247C4×D4—2981no—
248#117—1491no—
249C2×C4⋊C4—1491no—
250C2×C22⋊C4—2981no—
251#107—1491no—
252#107C2×D14911yescharacteristic, complemented
253#106—1491no—
254#106—1491no—
255#103—1491no—
256#103—1491no—
257#102—1491no—
258#102—1491no—
259#102—1491no—
260#102—1491no—
261#102C2×D14911yescharacteristic, complemented
262#102C2×D14911yescharacteristic, complemented
263C22⋊C8—1491no—
264C22⋊C8—1491no—
265C22⋊C8—1491no—
266C22⋊C8—1491no—
267C24—2981no—
268C24—1491no—
269#41—5961no—
270#41—5961no—
271C2×Q8—1491no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—5961no—
281C2×D4—5961no—
282C2×D4—5964no—
283C2×D4—1491no—
284C2×D4C22×D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—5961no—
289C22×C4—5961no—
290C22×C4—1491no—
291C22×C4—1491no—
292C22×C4—1491no—
293C22×C4—1491no—
294C22×C4—1491no—
295C22×C4C22×D14911yescharacteristic
296SD16—5961no—
297SD16—5961no—
298D8—41no—
299D8—5961no—
300C2×C8—41no—
301C2×C8—5961no—
302C2×C8—1491no—
303C2×C8—1491no—
304C2×C8C22×D14911yescharacteristic
305C2×C8C22×D14911yescharacteristic
306C4⋊C4—2981no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4—1491no—
311C4⋊C4C22×D14911yescharacteristic
312C4⋊C4C22×D14911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C42—2981no—
323C23—21no—
324C23—21no—
325C23—2982no—
326C23—2982no—
327C23—2981no—
328C23—5961no—
329C23—5962no—
330C23—5962no—
331C23—5962no—
332C23—1491no—
333C23—1491no—
334C23D4×D14911yescharacteristic
335Q8—2981no—
336Q8—2981no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—2981no—
344D4—2981no—
345D4—5962no—
346D4—5962no—
347D4—5962no—
348D4—5962no—
349D4—5962no—
350D4—5962no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—5961no—
363C2×C4—5961no—
364C2×C4—5962no—
365C2×C4—5961no—
366C2×C4—5962no—
367C2×C4—1491no—
368C2×C4—1491no—
369C2×C4D4×D14911yescharacteristic
370C2×C4C23×D14911yescharacteristic
371C8—21no—
372C8—21no—
373C8—2981no—
374C8—2981no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—2981no—
384C22—2981no—
385C22—2981no—
386C22—2981no—
387C22—2981no—
388C22—5964no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22—1492no—
393C22—11924no—
394C22#1801193512yes—
395C22C2×D4×D14911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—2981no—
400C4—2981no—
401C4—5961no—
402C4—5961no—
403C4—5961no—
404C4#1801195611yescharacteristic
405C4#1801195711yescharacteristic
406C2—22no—
407C2—81no—
408C2—81no—
409C2—2982no—
410C2—5961no—
411C2—11921no—
412C2#2375018311yescharacteristic
413C2#135×D14911yescharacteristic
414C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3188
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23750135C2semidirect
2. #121×D149C2semidirect
3. #23749962C2semidirect
4. #23749952C2semidirect
5. #23749948C2semidirect
6. #23749942C2semidirect
7. #23749859C2semidirect
8. #23749854C2semidirect
9. #23749852C2semidirect
10. #23749777C2semidirect
11. #23749771C2semidirect
12. #23749767C2semidirect
13. #23749757C2semidirect
14. C2×#18011823C2semidirect
15. #466×C149C2semidirect
16. C2×#14558735C22semidirect
20. C2×#14558725C22semidirect
21. C2×#14558724C22semidirect
22. C2×#14558721C22semidirect
23. C22×#11924746C22semidirect
26. #18011890C22semidirect
36. #18011869C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011842C22semidirect
42. #18011836C22semidirect
43. #18011834C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
47. #18011831C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
52. C2×D8×C149C22semidirect
53. C22×C8×C149C22semidirect
55. #121×C149C22semidirect
56. #107×C149C22semidirect
57. #102×C149C22semidirect
58. #102×C149C22semidirect
207. C149#3188semidirect
216. #466D149semidirect
231. C2×D8C2×D149semidirect
233. C22×C8C2×D149semidirect
244. #121C2×D149semidirect
252. #107C2×D149semidirect
261. #102C2×D149semidirect
262. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501352
#121×D1492
#237499622
#237499522
#237499482
#237499422
#237498592
#237498542
#237498522
#237497772
#237497712
#237497672
#237497572
C2×#180118232
#466×C1492
#3188149