Finite Group Databasebeta

← #34054827

Subgroups — #34054827

Order 19072.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750157C211yesmaximal, characteristic, complemented
2C4×D4×D149C211yesmaximal, characteristic, complemented
3#23749957C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749924C211yesmaximal, characteristic, complemented
6#23749923C211yesmaximal, characteristic, complemented
7#23749839C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749777C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic
11#23749735C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13#23749725C211yesmaximal, characteristic, complemented
14#23749680C211yesmaximal, characteristic, complemented
15#442×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C22×C4×D149—21no—
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011904—21no—
22#18011902C2211yescharacteristic, complemented
23#18011898C2211yescharacteristic, complemented
24#18011893—21no—
25#18011891C2211yescharacteristic
26#18011882C2211yescharacteristic
27C4×Dic298C2211yescharacteristic, complemented
28C4×D596C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30#18011873C2211yescharacteristic
31C4×C22⋊D149—21no—
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011870—21no—
35C4⋊C4×D149C2211yescharacteristic
36C22⋊C4×D149—21no—
37C42×D149C2211yescharacteristic
38#18011845C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic, complemented
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58#97×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64D4×D149—22no—
65D4×D149—22no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—44no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74#14558725—22no—
75#14558724—22no—
76#14558721—22no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100C22×C4×C149—21no—
101D8×C149—22no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—24no—
110C22×D149—21no—
111C22×D149—42no—
112C22×D149—42no—
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—21no—
116D596—21no—
117D596#4112yes—
118C22⋊D149—24no—
119C22⋊D149—42no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—22no—
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—41no—
131C4×D149—42no—
132C4×D149—42no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137C23×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149#4112yes—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—42no—
145C2×C4×C149—42no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—22no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—22no—
161C2×D149—48no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149AGL(1,ℤ/8)12yes—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149C2×#4111yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—42no—
178C2×C149—81no—
179C2×C149#52511yescharacteristic
180C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C149#57511yescharacteristic
182D149—22no—
183D149—42no—
184C149#311411yescharacteristic, complemented, Sylow
185#3114—1491nomaximal, Sylow
186#529—1491no—
187C2×C4×D4—1491no—
188#483—1491no—
189#480—1491no—
190#478—1491no—
191#478—1491no—
192#463—1491no—
193#463—1491no—
194#450—1491no—
195#447—1491no—
196#442—1491no—
197#442D14911yescharacteristic, complemented
198#440—1491no—
199#440—1491no—
200#432—1491no—
201C22×D4—1491no—
202C23×C4—2981no—
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C2×D8C2×D14911yescharacteristic
207#126—2981no—
208#125—1491no—
209#124—1491no—
210#123—2981no—
211C22⋊Q8—1491no—
212#121—1491no—
213C4×Q8—1491no—
214C4×D4—2981no—
215C4×D4—2981no—
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4C2×D14911yescharacteristic
221C4×D4C2×D14911yescharacteristic, complemented
222#117—2981no—
223C2×C4⋊C4—1491no—
224C2×C22⋊C4—2981no—
225C2×C42—1491no—
226#107—1491no—
227#107—1491no—
228#106—1491no—
229#106C2×D14911yescharacteristic, complemented
230C4⋊C8—1491no—
231C4⋊C8—1491no—
232#103—1491no—
233#103—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102C2×D14911yescharacteristic
239#102C2×D14911yescharacteristic, complemented
240C22⋊C8—1491no—
241C22⋊C8—1491no—
242#97—1491no—
243#97C2×D14911yescharacteristic, complemented
244C24—2981no—
245C2×Q8—1491no—
246C2×D4—2982no—
247C2×D4—2982no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4C22×D14911yescharacteristic
252C2×D4C22×D14911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—5964no—
260C22×C4—1491no—
261C22×C4—1491no—
262C22×C4—1491no—
263SD16—2982no—
264SD16—2982no—
265D8—22no—
266D8—2982no—
267C2×C8—1491no—
268C2×C8—1491no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4C22×D14911yescharacteristic
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C42—2981no—
290C42—1491no—
291C42—1491no—
292C42—1491no—
293C42C22×D14911yescharacteristic
294C23—21no—
295C23—21no—
296C23—2984no—
297C23—2981no—
298C23—5962no—
299C23—5962no—
300C23—1491no—
301Q8—2981no—
302Q8—2981no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2984no—
307D4—2981no—
308D4—5962no—
309D4—1492no—
310D4#1455873612yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2982no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—5961no—
322C2×C4—5962no—
323C2×C4—5962no—
324C2×C4—5962no—
325C2×C4—5962no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4D4×D14911yescharacteristic
330C2×C4D4×D14911yescharacteristic
331C2×C4C23×D14911yescharacteristic
332C8—21no—
333C8—21no—
334C8—2981no—
335C8—2981no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—2981no—
343C22—2981no—
344C22—2982no—
345C22—5968no—
346C22—5961no—
347C22—5961no—
348C22—1492no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—2981no—
355C4—2981no—
356C4—2981no—
357C4—5961no—
358C4—5961no—
359C4—5961no—
360C4#41×D14911yescharacteristic
361C4C2×#1455873611yescharacteristic
362C2—42no—
363C2—81no—
364C2—2982no—
365C2—5962no—
366C2#2375013411yescharacteristic
367C2AGL(1,ℤ/8)×D14911yescharacteristic
368C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
prime radical#23749757C2
hypercenter#442D149
hypocenterC149#3114
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23750157C2semidirect
2. C4×D4×D149C2semidirect
3. #23749957C2semidirect
4. #23749937C2semidirect
5. #23749924C2semidirect
6. #23749923C2semidirect
7. #23749839C2semidirect
8. #23749838C2semidirect
9. #23749777C2semidirect
11. #23749735C2semidirect
12. #23749727C2semidirect
13. #23749725C2semidirect
14. #23749680C2semidirect
15. #442×C149C2semidirect
22. #18011902C22semidirect
23. #18011898C22semidirect
27. C4×Dic298C22semidirect
38. #18011845C22semidirect
39. #18011844C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
47. #18011832C22semidirect
51. #18011822C22semidirect
54. C4×D4×C149C22semidirect
55. #106×C149C22semidirect
57. #102×C149C22semidirect
58. #97×C149C22semidirect
184. C149#3114semidirect
197. #442D149semidirect
221. C4×D4C2×D149semidirect
229. #106C2×D149semidirect
239. #102C2×D149semidirect
243. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501572
C4×D4×D1492
#237499572
#237499372
#237499242
#237499232
#237498392
#237498382
#237497772
#237497572
#237497352
#237497272
#237497252
#237496802
#442×C1492
#3114149