Finite Group Databasebeta

← #34056889

Subgroups — #34056889

Order 19072.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750328C211yesmaximal, characteristic, complemented
2#23750270C211yesmaximal, characteristic, complemented
3#23749982C211yesmaximal, characteristic, complemented
4#23749969C211yesmaximal, characteristic, complemented
5#23749940C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749771C211yesmaximal, characteristic, complemented
10#23749760C211yesmaximal, characteristic, complemented
11C4×#14558721C211yesmaximal, characteristic, complemented
12#23749702C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic, complemented
14#23749623C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558725C2211yescharacteristic, complemented
19C2×D1192C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×#14558719C2211yescharacteristic
22C2×#14558719C2211yescharacteristic, complemented
23#18011906—21no—
24#18011899C2211yescharacteristic
25#18011896—21no—
26#18011895—21no—
27#18011891C2211yescharacteristic
28#18011886—21no—
29#18011886C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic, complemented
32#18011885—21no—
33#18011881—21no—
34C4×D596C2211yescharacteristic
35C4×D596C2211yescharacteristic, complemented
36#18011873—21no—
37#18011869C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic, complemented
39C2×#14558713—21no—
40#18011844C2211yescharacteristic, complemented
41#18011836C2211yescharacteristic, complemented
42#18011834C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic, complemented
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51C4×#11924746C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60#14558735—22no—
61#14558735—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596D411yescharacteristic
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71D4×D149—22no—
72D4×D149—41no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77C2×C4×D149C2311yescharacteristic
78#14558725—41no—
79D1192—41no—
80#14558721—22no—
81#14558719—41no—
82#14558719—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C4⋊Dic149—21no—
86C4⋊Dic149D411yescharacteristic
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713D411yescharacteristic
98#14558713D411yescharacteristic
99C4×Dic149—21no—
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117C22×D149C2×D411yescharacteristic
118Dic298—21no—
119Dic298—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—41no—
125D596—42no—
126D596—81no—
127D596—81no—
128C22⋊D149—42no—
129C22⋊D149—42no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—42no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—81no—
140C4×D149—81no—
141#11924746—21no—
142#11924746—21no—
143C23×C149—21no—
144D4×C149—21no—
145D4×C149#4112yes—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—81no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—22no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—21no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—84no—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149C2×#4111yescharacteristic
178C4×C149H(5,𝔽2)11yescharacteristic
179Dic149—21no—
180Dic149—21no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—42no—
184C2×C149#54611yescharacteristic
185C2×C149#57511yescharacteristic
186C2×C149#57611yescharacteristic
187D149—41no—
188D149—41no—
189D149—81no—
190D149—81no—
191C149#332211yescharacteristic, complemented, Sylow
192#3322—1491nomaximal, Sylow
193#553—1491no—
194#546—1491no—
195#488—1491no—
196#485—1491no—
197#480—1491no—
198#478D14911yescharacteristic, complemented
199#469—1491no—
200#468—1491no—
201#463—1491no—
202#449—1491no—
203#447—1491no—
204C4×D8—1491no—
205#436—1491no—
206#418—1491no—
207#417—1491no—
208C2×#41—1491no—
209C22×D4—1491no—
210C2×SD16—1491no—
211C2×D8—1491no—
212C2×D8—1491no—
213C2×M16—1491no—
214C2×M16—1491no—
215#126—2981no—
216#125C2×D14911yescharacteristic, complemented
217#124—1491no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8—1491no—
221#121—2981no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121—1491no—
226#120—2981no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4—1491no—
230C4×D4C2×D14911yescharacteristic
231#117—1491no—
232C2×C4⋊C4—1491no—
233C2×C22⋊C4—2981no—
234#107—1491no—
235#107C2×D14911yescharacteristic, complemented
236#106C2×D14911yescharacteristic, complemented
237C4⋊C8C2×D14911yescharacteristic, complemented
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102C2×D14911yescharacteristic
247#102C2×D14911yescharacteristic
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C4×C8—1491no—
251C24—2981no—
252#41—2982no—
253#41—5961no—
254C2×Q8—1491no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2982no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—5961no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—1491no—
271C22×C4—1491no—
272SD16—5961no—
273D8—2982no—
274D8—5961no—
275M16—5961no—
276M16—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4C22×D14911yescharacteristic
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C42—2981no—
302C42C22×D14911yescharacteristic
303C23—21no—
304C23—2981no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—1491no—
309C23—1491no—
310C23—11921no—
311Q8—2981no—
312Q8—2981no—
313D4—21no—
314D4—2981no—
315D4—2981no—
316D4—2981no—
317D4—2981no—
318D4—5961no—
319D4—5962no—
320D4—5962no—
321D4—5962no—
322D4—11921no—
323D4—11921no—
324D4#1455873712yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—5962no—
336C2×C4—1491no—
337C2×C4—1491no—
338C2×C4—11921no—
339C2×C4—11921no—
340C2×C4D4×D14911yescharacteristic
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—2981no—
351C22—2981no—
352C22—2981no—
353C22—2981no—
354C22—2981no—
355C22—2981no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—5961no—
362C22—11924no—
363C22C2×D4×D14911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2981no—
370C4—2981no—
371C4—5961no—
372C4—5961no—
373C4C2×#1455873711yescharacteristic
374C4#1801195711yescharacteristic
375C2—42no—
376C2—5961no—
377C2—5961no—
378C2—11921no—
379C2—11921no—
380C2#2375026611yescharacteristic
381C2#2375042211yescharacteristic
382C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
hypercenter#478D149
hypocenterC149#3322
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750328C2semidirect
2. #23750270C2semidirect
3. #23749982C2semidirect
4. #23749969C2semidirect
5. #23749940C2semidirect
6. #23749879C2semidirect
7. #23749872C2semidirect
8. #23749841C2semidirect
9. #23749771C2semidirect
10. #23749760C2semidirect
11. C4×#14558721C2semidirect
12. #23749702C2semidirect
13. #23749628C2semidirect
14. #23749623C2semidirect
15. #478×C149C2semidirect
18. C2×#14558725C22semidirect
22. C2×#14558719C22semidirect
31. #18011886C22semidirect
35. C4×D596C22semidirect
38. C4⋊C4×D149C22semidirect
40. #18011844C22semidirect
41. #18011836C22semidirect
42. #18011834C22semidirect
43. #18011834C22semidirect
48. #18011831C22semidirect
50. #18011823C22semidirect
51. C4×#11924746C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
191. C149#3322semidirect
198. #478D149semidirect
216. #125C2×D149semidirect
235. #107C2×D149semidirect
236. #106C2×D149semidirect
237. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503282
#237502702
#237499822
#237499692
#237499402
#237498792
#237498722
#237498412
#237497712
#237497602
C4×#145587212
#237497022
#237496282
#237496232
#478×C1492
#3322149