Finite Group Databasebeta

← #34054828

Subgroups — #34054828

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#23750154C211yesmaximal, characteristic, complemented
2C4×D4×D149C211yesmaximal, characteristic, complemented
3#23749954C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749926C211yesmaximal, characteristic, complemented
6#23749925C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749774C211yesmaximal, characteristic, complemented
9#23749757C211yesmaximal, characteristic
10#23749737C211yesmaximal, characteristic, complemented
11#23749734C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749726C211yesmaximal, characteristic, complemented
14#23749681C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C22×C4×D149—21no—
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20#18011904—21no—
21#18011903C2211yescharacteristic, complemented
22#18011893—21no—
23#18011887C2211yescharacteristic
24#18011882C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic, complemented
26C4×D596C2211yescharacteristic
27D4×Dic149C2211yescharacteristic
28D4×Dic149C2211yescharacteristic, complemented
29#18011873C2211yescharacteristic
30C4×C22⋊D149—21no—
31#18011871—21no—
32#18011871—21no—
33#18011867—21no—
34C4⋊C4×D149C2211yescharacteristic
35C22⋊C4×D149—21no—
36C42×D149C2211yescharacteristic
37#18011845C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51#18011821C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic, complemented
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63D4×D149—22no—
64D4×D149—22no—
65C22×Dic149—21no—
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#14558723—22no—
75#14558721—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C4×Dic149D411yescharacteristic
94C4×Dic149D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100SD16×C149—22no—
101D8×C149—22no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
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
114D596—21no—
115D596#4112yes—
116C22⋊D149—24no—
117C22⋊D149—42no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—42no—
122C2×Dic149—42no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—22no—
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—41no—
130C4×D149—42no—
131C4×D149—42no—
132C4×D149—42no—
133#11924746—21no—
134#11924746—21no—
135C23×C149—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149#4112yes—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
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#463D14911yescharacteristic, complemented
194#450—1491no—
195#447—1491no—
196#442—1491no—
197#442—1491no—
198#440—1491no—
199#440—1491no—
200#432—1491no—
201C22×D4—1491no—
202C23×C4—2981no—
203C2×SD16—1491no—
204C2×SD16C2×D14911yescharacteristic
205C2×D8—1491no—
206C2×D8C2×D14911yescharacteristic
207#126—2981no—
208#125—1491no—
209#124C2×D14911yescharacteristic, complemented
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×D4—1491no—
221C4×D4C2×D14911yescharacteristic
222#117—2981no—
223C2×C4⋊C4—1491no—
224C2×C22⋊C4—2981no—
225C2×C42—1491no—
226#107—1491no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8—1491no—
231C4⋊C8C2×D14911yescharacteristic, complemented
232#103—1491no—
233#103C2×D14911yescharacteristic, complemented
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic, complemented
240C22⋊C8—1491no—
241C22⋊C8—1491no—
242#97—1491no—
243#97—1491no—
244C24—2981no—
245C2×Q8C22×D14911yescharacteristic
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—2981no—
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—22no—
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⋊C4—1491no—
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
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—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2984no—
307D4—2981no—
308D4—5962no—
309D4—1492no—
310D4#1455873512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—2982no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—5961no—
321C2×C4—5962no—
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×#1455873511yescharacteristic
362C2—42no—
363C2—81no—
364C2—2982no—
365C2—5962no—
366C2#2375013511yescharacteristic
367C2AGL(1,ℤ/8)×D14911yescharacteristic
368C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
prime radical#23749757C2
hypercenter#463D149
hypocenterC149#3114
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750154C2semidirect
2. C4×D4×D149C2semidirect
3. #23749954C2semidirect
4. #23749937C2semidirect
5. #23749926C2semidirect
6. #23749925C2semidirect
7. #23749837C2semidirect
8. #23749774C2semidirect
10. #23749737C2semidirect
11. #23749734C2semidirect
12. #23749728C2semidirect
13. #23749726C2semidirect
14. #23749681C2semidirect
15. #463×C149C2semidirect
21. #18011903C22semidirect
25. Q8×Dic149C22semidirect
28. D4×Dic149C22semidirect
37. #18011845C22semidirect
38. #18011844C22semidirect
39. #18011843C22semidirect
40. #18011842C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011835C22semidirect
47. #18011832C22semidirect
50. #18011821C22semidirect
51. #18011821C22semidirect
54. #124×C149C22semidirect
56. C4⋊C8×C149C22semidirect
57. #103×C149C22semidirect
58. #102×C149C22semidirect
184. C149#3114semidirect
193. #463D149semidirect
209. #124C2×D149semidirect
231. C4⋊C8C2×D149semidirect
233. #103C2×D149semidirect
239. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501542
C4×D4×D1492
#237499542
#237499372
#237499262
#237499252
#237498372
#237497742
#237497572
#237497372
#237497342
#237497282
#237497262
#237496812
#463×C1492
#3114149