Finite Group Databasebeta

← #34054877

Subgroups — #34054877

Order 19072.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23750099C211yesmaximal, characteristic, complemented
3#23749967C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749916C211yesmaximal, characteristic, complemented
6#23749906C211yesmaximal, characteristic, complemented
7#23749841C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749778C211yesmaximal, characteristic, complemented
10#23749761C211yesmaximal, characteristic
11#23749738C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13C4×#14558725C211yesmaximal, characteristic, complemented
14C4×D1192C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011911C2211yescharacteristic, complemented
22#18011906—21no—
23#18011899C2211yescharacteristic, complemented
24#18011897—21no—
25#18011893—21no—
26#18011890C2211yescharacteristic
27#18011889—21no—
28#18011885C2211yescharacteristic
29C4×Dic298C2211yescharacteristic, complemented
30C4×D596C2211yescharacteristic
31C4×D596C2211yescharacteristic
32C4×D596C2211yescharacteristic
33C4×D596C2211yescharacteristic
34C4×D596C2211yescharacteristic, complemented
35#18011873—21no—
36#18011873—21no—
37#18011870C2211yescharacteristic
38C22⋊C4×D149—21no—
39C22⋊C4×D149—21no—
40#18011845C2211yescharacteristic, complemented
41#18011845C2211yescharacteristic, complemented
42#18011843C2211yescharacteristic, complemented
43#18011843C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011836C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic, complemented
51#18011833C2211yescharacteristic, complemented
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic, complemented
54C4⋊C8×C149C2211yescharacteristic, complemented
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596—22no—
63C2×D596—22no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74#14558725—22no—
75#14558725—22no—
76D1192—22no—
77D1192—22no—
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—24no—
111C22×D149—21no—
112C22×D149—81no—
113C22×D149—81no—
114Dic298—21no—
115Dic298—21no—
116Dic298—81no—
117D596—24no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596#4112yes—
123D596#4112yes—
124C22⋊D149—81no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C4×D149—81no—
131C4×D149—81no—
132C4×D149—81no—
133C4×D149—81no—
134C4×D149—81no—
135C23×C149C2×D411yescharacteristic
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149—21no—
145C8×C149—21no—
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149C22×D411yescharacteristic
152C2×D149—22no—
153C2×D149—22no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—84no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149C2×#4111yescharacteristic
168C4×C149C2×#4111yescharacteristic
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174C2×C149—41no—
175C2×C149#52511yescharacteristic
176C2×C149#57611yescharacteristic
177C2×C149#57711yescharacteristic
178D149—42no—
179D149—42no—
180D149—81no—
181C149#311811yescharacteristic, complemented, Sylow
182#3118—1491nomaximal, Sylow
183#542—1491no—
184#518—1491no—
185#485—1491no—
186#482—1491no—
187#476—1491no—
188#474—1491no—
189#463—1491no—
190#463—1491no—
191#450—1491no—
192#447—1491no—
193#442—1491no—
194#440—1491no—
195C4×SD16—1491no—
196C4×D8—1491no—
197#433D14911yescharacteristic, complemented
198C22×D4—1491no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8—1491no—
203C4⋊Q8—1491no—
204#126—2981no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210#121—1491no—
211C4×Q8—1491no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218C4×D4—1491no—
219#117—1491no—
220#117C2×D14911yescharacteristic
221C2×C22⋊C4—2981no—
222C2×C22⋊C4—2981no—
223#107—1491no—
224#107—1491no—
225#106—1491no—
226#106—1491no—
227C4⋊C8C2×D14911yescharacteristic, complemented
228C4⋊C8C2×D14911yescharacteristic, complemented
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237C22⋊C8C2×D14911yescharacteristic
238C22⋊C8C2×D14911yescharacteristic
239#97C2×D14911yescharacteristic, complemented
240C4×C8C2×D14911yescharacteristic, complemented
241C24—2981no—
242C2×Q8—2981no—
243C2×Q8—1491no—
244C2×D4—2982no—
245C2×D4—2982no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
250C2×D4—1491no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4C22×D14911yescharacteristic
257SD16—2982no—
258SD16—2982no—
259D8—2982no—
260D8—2982no—
261C2×C8C22×D14911yescharacteristic
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C4⋊C4D59611yescharacteristic
273C4⋊C4D59611yescharacteristic
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4D59611yescharacteristic
285C22⋊C4D59611yescharacteristic
286C42—2981no—
287C42—2981no—
288C42C22×D14911yescharacteristic
289C42C22×D14911yescharacteristic
290C23—2984no—
291C23—2981no—
292C23—2981no—
293C23—2981no—
294C23—11921no—
295C23—11921no—
296C23C2×D59611yescharacteristic
297Q8—2981no—
298Q8—2981no—
299Q8—11921no—
300D4—2984no—
301D4—2981no—
302D4—2981no—
303D4—2981no—
304D4—2981no—
305D4—1492no—
306D4—1492no—
307D4—11921no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—11921no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4—11921no—
319C2×C4—11921no—
320C2×C4C2×D59611yescharacteristic
321C2×C4C2×D59611yescharacteristic
322C2×C4C2×D59611yescharacteristic
323C2×C4C2×D59611yescharacteristic
324C2×C4C2×D59611yescharacteristic
325C2×C4C23×D14911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2982no—
334C22—2982no—
335C22—5961no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22—5961no—
342C22—11924no—
343C22C22×D59611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4—5961no—
353C4—5961no—
354C4#41×D14911yescharacteristic
355C4#41×D14911yescharacteristic
356C2—41no—
357C2—5962no—
358C2—5962no—
359C2—11921no—
360C2#2375013711yescharacteristic
361C2#2375043011yescharacteristic
362C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radical#23749761C2
hypercenter#433D149
hypocenterC149#3118
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750099C2semidirect
3. #23749967C2semidirect
4. #23749950C2semidirect
5. #23749916C2semidirect
6. #23749906C2semidirect
7. #23749841C2semidirect
8. #23749841C2semidirect
9. #23749778C2semidirect
11. #23749738C2semidirect
12. #23749727C2semidirect
13. C4×#14558725C2semidirect
14. C4×D1192C2semidirect
15. #433×C149C2semidirect
21. #18011911C22semidirect
23. #18011899C22semidirect
29. C4×Dic298C22semidirect
34. C4×D596C22semidirect
40. #18011845C22semidirect
41. #18011845C22semidirect
42. #18011843C22semidirect
43. #18011843C22semidirect
44. #18011836C22semidirect
45. #18011836C22semidirect
50. #18011833C22semidirect
51. #18011833C22semidirect
53. C4⋊C8×C149C22semidirect
54. C4⋊C8×C149C22semidirect
57. #97×C149C22semidirect
58. C4×C8×C149C22semidirect
181. C149#3118semidirect
197. #433D149semidirect
227. C4⋊C8C2×D149semidirect
228. C4⋊C8C2×D149semidirect
239. #97C2×D149semidirect
240. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237500992
#237499672
#237499502
#237499162
#237499062
#237498412
#237497782
#237497612
#237497382
#237497272
C4×#145587252
C4×D11922
#433×C1492
#3118149