Finite Group Databasebeta

← #34055529

Subgroups — #34055529

Order 19072.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750138C211yesmaximal, characteristic, complemented
2#23750135C211yesmaximal, characteristic, complemented
3#23749968C211yesmaximal, characteristic, complemented
4#23749965C211yesmaximal, characteristic, complemented
5#23749952C211yesmaximal, characteristic, complemented
6#23749947C211yesmaximal, characteristic, complemented
7#23749881C211yesmaximal, characteristic, complemented
8#23749876C211yesmaximal, characteristic, complemented
9#23749871C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749784C211yesmaximal, characteristic, complemented
12#23749771C211yesmaximal, characteristic, complemented
13#23749769C211yesmaximal, characteristic, complemented
14#23749588C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C2×#14558726C2211yescharacteristic, complemented
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558721C2211yescharacteristic, complemented
22C2×#14558720C2211yescharacteristic
23#18011896—21no—
24#18011893—21no—
25#18011891C2211yescharacteristic
26#18011890C2211yescharacteristic
27#18011887C2211yescharacteristic
28#18011886C2211yescharacteristic
29#18011885C2211yescharacteristic
30#18011882C2211yescharacteristic
31#18011881—21no—
32#18011879—21no—
33D4×Dic149—21no—
34#18011873—21no—
35#18011871—21no—
36#18011871—21no—
37#18011869C2211yescharacteristic
38#18011869C2211yescharacteristic
39#18011845C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic, complemented
53C2×M16×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#107×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149D411yescharacteristic
60#14558737—41no—
61#14558737—41no—
62#14558735—41no—
63#14558735—41no—
64C2×Dic298C2311yescharacteristic
65C2×D596—21no—
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C22×Dic149D411yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149—41no—
75C2×C4×D149—41no—
76C2×C4×D149D411yescharacteristic
77C2×C4×D149D411yescharacteristic
78C2×C4×D149C2311yescharacteristic
79C2×C4×D149C2311yescharacteristic
80#14558726—41no—
81#14558725—41no—
82#14558721—41no—
83#14558720—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C4⋊Dic149—21no—
87C4⋊Dic149C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99C4×Dic149—21no—
100C4×Dic149—21no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105SD16×C149—41no—
106M16×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—41no—
116C22×D149—41no—
117C22×D149—41no—
118C22×D149C2×D411yescharacteristic
119C22×D149C2×D411yescharacteristic
120Dic298—21no—
121Dic298—21no—
122D596—21no—
123D596—21no—
124D596—42no—
125D596—42no—
126C22⋊D149—42no—
127C22⋊D149—42no—
128C22⋊D149—42no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—41no—
133C2×Dic149—42no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—41no—
141C4×D149—41no—
142C4×D149—42no—
143#11924746—21no—
144#11924746—21no—
145C23×C149—21no—
146C23×C149C2×D411yescharacteristic
147Q8×C149—21no—
148Q8×C149—21no—
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—42no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149C22×D411yescharacteristic
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—44no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149H(5,𝔽2)11yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—41no—
190C2×C149—81no—
191C2×C149#53411yescharacteristic
192C2×C149#57511yescharacteristic
193C2×C149#57511yescharacteristic
194D149—41no—
195D149—41no—
196D149—81no—
197C149#319711yescharacteristic, complemented, Sylow
198#3197—1491nomaximal, Sylow
199#525—1491no—
200#525—1491no—
201#485—1491no—
202#485—1491no—
203#482—1491no—
204#482—1491no—
205#470—1491no—
206#469—1491no—
207#468—1491no—
208#468D14911yescharacteristic, complemented
209#452—1491no—
210#452—1491no—
211#449—1491no—
212#449—1491no—
213#407—1491no—
214C2×#41—1491no—
215C2×#41—1491no—
216C23×C4—1491no—
217C2×Q16—1491no—
218C2×SD16—1491no—
219C2×SD16C2×D14911yescharacteristic, complemented
220C2×D8—1491no—
221C2×M16—1491no—
222C2×M16C2×D14911yescharacteristic
223#123—2981no—
224#123—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228C22⋊Q8C2×D14911yescharacteristic
229#121—1491no—
230#121—1491no—
231#121—1491no—
232#121C2×D14911yescharacteristic
233#120—2981no—
234#120—2981no—
235C4×D4—2981no—
236C4×D4—2981no—
237C4×D4—2981no—
238C4×D4—2981no—
239#117—1491no—
240#117—1491no—
241#107—1491no—
242#107C2×D14911yescharacteristic, complemented
243#106—1491no—
244#106—1491no—
245#103—1491no—
246#103—1491no—
247#103—1491no—
248#103C2×D14911yescharacteristic, complemented
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102C2×D14911yescharacteristic, complemented
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8—1491no—
257C24—1491no—
258#41—5961no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8C22×D14911yescharacteristic
264C2×D4—21no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—1491no—
271C2×D4C22×D14911yescharacteristic
272C22×C4—2981no—
273C22×C4—2981no—
274C22×C4—5961no—
275C22×C4—5961no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4C22×D14911yescharacteristic
282Q16—5961no—
283SD16—41no—
284SD16—5961no—
285D8—5961no—
286M16—41no—
287M16—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C42—2981no—
311C42—2981no—
312C23—21no—
313C23—2981no—
314C23—5961no—
315C23—5961no—
316C23—5961no—
317C23—1491no—
318C23—1491no—
319C23D4×D14911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2981no—
323Q8—2981no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2981no—
328D4—2981no—
329D4—5962no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5961no—
347C2×C4—5961no—
348C2×C4—5962no—
349C2×C4—5961no—
350C2×C4—5962no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4D4×D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C8—21no—
356C8—21no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—5964no—
372C22—5961no—
373C22—5961no—
374C22—5961no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2981no—
381C4—2981no—
382C4—5961no—
383C4—5961no—
384C4—5961no—
385C4#1801195611yescharacteristic
386C4#1801195711yescharacteristic
387C2—41no—
388C2—81no—
389C2—5961no—
390C2—5961no—
391C2—11921no—
392C2#2375018311yescharacteristic
393C2#2375042111yescharacteristic
394C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
hypercenter#468D149
hypocenterC149#3197
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #23750138C2semidirect
2. #23750135C2semidirect
3. #23749968C2semidirect
4. #23749965C2semidirect
5. #23749952C2semidirect
6. #23749947C2semidirect
7. #23749881C2semidirect
8. #23749876C2semidirect
9. #23749871C2semidirect
10. #23749790C2semidirect
11. #23749784C2semidirect
12. #23749771C2semidirect
13. #23749769C2semidirect
14. #23749588C2semidirect
15. #468×C149C2semidirect
19. C2×#14558726C22semidirect
20. C2×#14558725C22semidirect
21. C2×#14558721C22semidirect
39. #18011845C22semidirect
40. #18011842C22semidirect
41. #18011842C22semidirect
42. #18011836C22semidirect
43. #18011835C22semidirect
44. #18011834C22semidirect
45. #18011833C22semidirect
46. #18011832C22semidirect
47. #18011831C22semidirect
52. C2×SD16×C149C22semidirect
56. #107×C149C22semidirect
57. #103×C149C22semidirect
58. #102×C149C22semidirect
197. C149#3197semidirect
208. #468D149semidirect
219. C2×SD16C2×D149semidirect
242. #107C2×D149semidirect
248. #103C2×D149semidirect
252. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501382
#237501352
#237499682
#237499652
#237499522
#237499472
#237498812
#237498762
#237498712
#237497902
#237497842
#237497712
#237497692
#237495882
#468×C1492
#3197149