Finite Group Databasebeta

← #34056915

Subgroups — #34056915

Order 19072.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750346C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749948C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749873C211yesmaximal, characteristic, complemented
8#23749868C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11SD16×Dic149C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749630C211yesmaximal, characteristic, complemented
14#23749628C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149—21no—
17C2×D4×D149C2211yescharacteristic
18C2×#14558723C2211yescharacteristic, complemented
19C2×#14558720C2211yescharacteristic, complemented
20C2×#14558719C2211yescharacteristic, complemented
21#18011910C2211yescharacteristic, complemented
22#18011907C2211yescharacteristic
23#18011906—21no—
24#18011904—21no—
25#18011897—21no—
26#18011887C2211yescharacteristic, complemented
27#18011885C2211yescharacteristic
28#18011883—21no—
29#18011882C2211yescharacteristic
30#18011880—21no—
31#18011879—21no—
32Q8×Dic149C2211yescharacteristic, complemented
33#18011876—21no—
34D4×Dic149C2211yescharacteristic
35C4×C22⋊D149C2211yescharacteristic
36#18011870C2211yescharacteristic, complemented
37#18011869C2211yescharacteristic, complemented
38#18011845C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic, complemented
55C22⋊Q8×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—44no—
68C2×C22⋊D149D411yescharacteristic
69D4×D149—22no—
70D4×D149—41no—
71C22×Dic149—21no—
72C2×C4×D149C2311yescharacteristic
73#14558723—41no—
74#14558720—41no—
75#14558719—41no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C24×C149—21no—
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149—22no—
100C2×D4×C149—21no—
101C2×D4×C149—41no—
102C2×D4×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105SD16×C149—22no—
106SD16×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117Dic298—42no—
118D596—21no—
119D596—21no—
120C22⋊D149—22no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—42no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138C23×C149—21no—
139C23×C149—42no—
140C23×C149—42no—
141C23×C149—81no—
142C23×C149C2×D411yescharacteristic
143Q8×C149—21no—
144Q8×C149—21no—
145D4×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—42no—
149D4×C149#4112yes—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2411yescharacteristic
156C8×C149—21no—
157C8×C149—21no—
158C22×C149—21no—
159C22×C149—22no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—84no—
168C22×C149C22×D411yescharacteristic
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—84no—
176C4×C149—21no—
177C4×C149—41no—
178C4×C149—41no—
179C4×C149C2×#4111yescharacteristic
180C4×C149H(5,𝔽2)11yescharacteristic
181Dic149—21no—
182Dic149—21no—
183Dic149—41no—
184Dic149—41no—
185Dic149—41no—
186Dic149AGL(1,ℤ/8)12yes—
187C2×C149—42no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149#54611yescharacteristic
191C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C149#57711yescharacteristic
193D149—41no—
194D149—81no—
195C149#332411yescharacteristic, complemented, Sylow
196#3324—1491nomaximal, Sylow
197#556—1491no—
198D42—1491no—
199#486—1491no—
200#482—1491no—
201#482—1491no—
202#474—1491no—
203#468—1491no—
204#468—1491no—
205#460—1491no—
206#450—1491no—
207#450D14911yescharacteristic, complemented
208C4×SD16—1491no—
209#436—1491no—
210#418—1491no—
211#418—1491no—
212C22×D4—2981no—
213C22×D4—1491no—
214C22×D4C2×D14911yescharacteristic
215C2×SD16—1491no—
216C2×SD16C2×D14911yescharacteristic
217C2×SD16C2×D14911yescharacteristic, complemented
218C2×M16—1491no—
219C2×M16—1491no—
220C4⋊Q8—1491no—
221#127—1491no—
222#126—2981no—
223#126—2981no—
224#124—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8C2×D14911yescharacteristic, complemented
227#121—2981no—
228#121—1491no—
229#121—1491no—
230#120—2981no—
231#120—2981no—
232C4×Q8—2981no—
233C4×Q8—1491no—
234C4×D4—1491no—
235C4×D4—1491no—
236#117—1491no—
237#117—1491no—
238#107—1491no—
239#107—1491no—
240#106—1491no—
241C4⋊C8—1491no—
242#103—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102C2×D14911yescharacteristic
251#102C2×D14911yescharacteristic, complemented
252C22⋊C8—1491no—
253C22⋊C8C2×D14911yescharacteristic, complemented
254C4×C8—1491no—
255C24—21no—
256C24—2981no—
257C2×Q8—2981no—
258C2×Q8C22×D14911yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—2982no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—5961no—
269C2×D4—5964no—
270C2×D4—1491no—
271C2×D4—1491no—
272C2×D4C22×D14911yescharacteristic
273C2×D4C22×D14911yescharacteristic
274C22×C4—2981no—
275C22×C4—1491no—
276C22×C4C22×D14911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—5961no—
280M16—5961no—
281M16—5961no—
282C2×C8—1491no—
283C2×C8—1491no—
284C2×C8C22×D14911yescharacteristic
285C2×C8C22×D14911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—2981no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—1491no—
291C4⋊C4—1491no—
292C4⋊C4—1491no—
293C4⋊C4—1491no—
294C4⋊C4C22×D14911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C42—2981no—
305C42—2981no—
306C42—2981no—
307C42—1491no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2981no—
314C23—5962no—
315C23—5962no—
316C23—1491no—
317C23—11921no—
318C23D4×D14911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—5962no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—2982no—
327D4—2981no—
328D4—2981no—
329D4—5962no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—11921no—
334D4#1455873512yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—5962no—
345C2×C4—1491no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4D4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—2981no—
353C8—2981no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—11924no—
371C22C2×D4×D14911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—2981no—
376C4—2981no—
377C4—5961no—
378C4—5961no—
379C4—5961no—
380C4—1492no—
381C4C2×#1455873511yescharacteristic
382C4#1801195611yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—5961no—
387C2—11921no—
388C2#2375026211yescharacteristic
389C2AGL(1,ℤ/8)×D14911yescharacteristic
390C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
prime radicalD4×C22⋊D149C2
hypercenter#450D149
hypocenterC149#3324
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23750346C2semidirect
3. #23749970C2semidirect
4. #23749950C2semidirect
5. #23749948C2semidirect
6. #23749903C2semidirect
7. #23749873C2semidirect
8. #23749868C2semidirect
9. #23749823C2semidirect
10. #23749774C2semidirect
11. SD16×Dic149C2semidirect
12. #23749700C2semidirect
13. #23749630C2semidirect
14. #23749628C2semidirect
15. #450×C149C2semidirect
18. C2×#14558723C22semidirect
19. C2×#14558720C22semidirect
20. C2×#14558719C22semidirect
21. #18011910C22semidirect
26. #18011887C22semidirect
32. Q8×Dic149C22semidirect
36. #18011870C22semidirect
37. #18011869C22semidirect
38. #18011845C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011840C22semidirect
42. #18011835C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
54. C2×SD16×C149C22semidirect
55. C22⋊Q8×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
195. C149#3324semidirect
207. #450D149semidirect
217. C2×SD16C2×D149semidirect
226. C22⋊Q8C2×D149semidirect
251. #102C2×D149semidirect
253. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503462
D4×C22⋊D1492
#237499702
#237499502
#237499482
#237499032
#237498732
#237498682
#237498232
#237497742
SD16×Dic1492
#237497002
#237496302
#237496282
#450×C1492
#3324149