Finite Group Databasebeta

← #34055530

Subgroups — #34055530

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#23750135C211yesmaximal, characteristic, complemented
2#23750132C211yesmaximal, characteristic, complemented
3#23749967C211yesmaximal, characteristic, complemented
4#23749964C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749946C211yesmaximal, characteristic, complemented
7#23749882C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749870C211yesmaximal, characteristic, complemented
10#23749868C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749784C211yesmaximal, characteristic, complemented
13#23749767C211yesmaximal, characteristic, complemented
14#23749587C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C2×#14558726C2211yescharacteristic, complemented
19C2×#14558724C2211yescharacteristic, complemented
20C2×#14558719C2211yescharacteristic
21C2×#14558719C2211yescharacteristic
22#18011893—21no—
23#18011892—21no—
24#18011891C2211yescharacteristic
25#18011890C2211yescharacteristic
26#18011887C2211yescharacteristic
27#18011887C2211yescharacteristic
28#18011882C2211yescharacteristic
29#18011882C2211yescharacteristic
30#18011882C2211yescharacteristic
31#18011879—21no—
32#18011879—21no—
33D4×Dic149—21no—
34C4×C22⋊D149—21no—
35C4×C22⋊D149—21no—
36#18011871—21no—
37#18011870C2211yescharacteristic
38#18011869C2211yescharacteristic
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic, complemented
54C2×D8×C149C2211yescharacteristic, complemented
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149D411yescharacteristic
60#14558735—41no—
61#14558735—41no—
62C2×Dic298C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C22×Dic149D411yescharacteristic
69C2×C4×D149—41no—
70C2×C4×D149—41no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74C2×C4×D149C2311yescharacteristic
75#14558726—41no—
76#14558724—41no—
77#14558719—41no—
78#14558719—41no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149—21no—
107C22×C4×C149C2311yescharacteristic
108SD16×C149—41no—
109D8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—41no—
115C22×D149—41no—
116C22×D149—41no—
117C22×D149C2×D411yescharacteristic
118C22×D149C2×D411yescharacteristic
119Dic298—21no—
120Dic298—21no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—41no—
130C2×Dic149—42no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—41no—
138C4×D149—41no—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142C23×C149—21no—
143C23×C149C2×D411yescharacteristic
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—42no—
151D4×C149—42no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—42no—
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×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149C22×D411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—44no—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—41no—
190C2×C149—81no—
191C2×C149—81no—
192C2×C149#53411yescharacteristic
193C2×C149#57511yescharacteristic
194C2×C149#57511yescharacteristic
195D149—41no—
196D149—41no—
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#468—1491no—
209#452—1491no—
210#452—1491no—
211#449—1491no—
212#449D14911yescharacteristic, complemented
213#407—1491no—
214C2×#41—1491no—
215C2×#41C2×D14911yescharacteristic
216C23×C4—1491no—
217C2×Q16—1491no—
218C2×SD16—1491no—
219C2×SD16C2×D14911yescharacteristic, complemented
220C2×D8C2×D14911yescharacteristic, complemented
221C2×M16—1491no—
222C2×M16—1491no—
223#123—2981no—
224#123—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228C22⋊Q8—1491no—
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#107—1491no—
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⋊C8C2×D14911yescharacteristic
257C24—1491no—
258#41—41no—
259#41—41no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8C22×D14911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4C22×D14911yescharacteristic
271C2×D4C22×D14911yescharacteristic
272C22×C4—21no—
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—41no—
286M16—5961no—
287M16—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2981no—
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—21no—
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—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—5961no—
348C2×C4—5961no—
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—41no—
366C22—41no—
367C22—41no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22—2981no—
374C22—5964no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4—5961no—
384C4—5961no—
385C4#1801195611yescharacteristic
386C4#1801195611yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—5961no—
391C2—5961no—
392C2#2375018511yescharacteristic
393C2#2375042111yescharacteristic
394C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3197
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750135C2semidirect
2. #23750132C2semidirect
3. #23749967C2semidirect
4. #23749964C2semidirect
5. #23749947C2semidirect
6. #23749946C2semidirect
7. #23749882C2semidirect
8. #23749875C2semidirect
9. #23749870C2semidirect
10. #23749868C2semidirect
11. #23749787C2semidirect
12. #23749784C2semidirect
13. #23749767C2semidirect
14. #23749587C2semidirect
15. #449×C149C2semidirect
18. C2×#14558726C22semidirect
19. C2×#14558724C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011832C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
53. C2×SD16×C149C22semidirect
54. C2×D8×C149C22semidirect
56. #103×C149C22semidirect
57. #102×C149C22semidirect
197. C149#3197semidirect
212. #449D149semidirect
219. C2×SD16C2×D149semidirect
220. C2×D8C2×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
#237501352
#237501322
#237499672
#237499642
#237499472
#237499462
#237498822
#237498752
#237498702
#237498682
#237497872
#237497842
#237497672
#237495872
#449×C1492
#3197149