Finite Group Databasebeta

← #34056918

Subgroups — #34056918

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#23750343C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749949C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749871C211yesmaximal, characteristic, complemented
8#23749870C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749628C211yesmaximal, characteristic, complemented
15#418×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149—21no—
17C2×D4×D149C2211yescharacteristic
18C2×#14558725C2211yescharacteristic, complemented
19C2×#14558724C2211yescharacteristic
20C2×#14558724C2211yescharacteristic, complemented
21C2×#14558719C2211yescharacteristic, complemented
22#18011910C2211yescharacteristic, complemented
23#18011907C2211yescharacteristic
24#18011905—21no—
25#18011904—21no—
26#18011897—21no—
27#18011891C2211yescharacteristic, complemented
28#18011890C2211yescharacteristic, complemented
29#18011885C2211yescharacteristic
30#18011883—21no—
31#18011882C2211yescharacteristic
32#18011880—21no—
33#18011879—21no—
34C4×Dic298—21no—
35#18011876C2211yescharacteristic, complemented
36D4×Dic149C2211yescharacteristic
37C4×C22⋊D149C2211yescharacteristic
38#18011869C2211yescharacteristic, complemented
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic, complemented
54#117×C149C2211yescharacteristic, complemented
55#102×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—44no—
69C2×C22⋊D149D411yescharacteristic
70D4×D149—22no—
71D4×D149—41no—
72C22×Dic149—21no—
73C2×C4×D149C2311yescharacteristic
74#14558725—41no—
75#14558724—22no—
76#14558724—41no—
77#14558719—41no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715D411yescharacteristic
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C24×C149—21no—
99C2×D4×C149—22no—
100C2×D4×C149—21no—
101C2×D4×C149—41no—
102C2×D4×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105M16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C42×C149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119Dic298—42no—
120D596—21no—
121D596—21no—
122C22⋊D149—22no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—42no—
126C22⋊D149—42no—
127C22⋊D149—81no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—42no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C4×D149—21no—
136C4×D149—21no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140C23×C149—21no—
141C23×C149—42no—
142C23×C149—42no—
143C23×C149—81no—
144C23×C149C2×D411yescharacteristic
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#450—1491no—
208C4×SD16—1491no—
209#436—1491no—
210#418—1491no—
211#418D14911yescharacteristic, complemented
212C22×D4—2981no—
213C22×D4—1491no—
214C22×D4C2×D14911yescharacteristic
215C2×SD16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×M16—1491no—
219C2×M16C2×D14911yescharacteristic, complemented
220C4⋊Q8—1491no—
221#127—1491no—
222#126—2981no—
223#126—2981no—
224#124—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
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#117C2×D14911yescharacteristic, complemented
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#102C2×D14911yescharacteristic
249#102C2×D14911yescharacteristic
250#102C2×D14911yescharacteristic, complemented
251#102C2×D14911yescharacteristic, complemented
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C4×C8—1491no—
255C24—21no—
256C24—2981no—
257C2×Q8—2981no—
258C2×Q8—1491no—
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—2982no—
278SD16—5961no—
279SD16—5961no—
280M16—41no—
281M16—5961no—
282C2×C8—1491no—
283C2×C8—1491no—
284C2×C8C22×D14911yescharacteristic
285C2×C8C22×D14911yescharacteristic
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—1491no—
291C4⋊C4—1491no—
292C4⋊C4—1491no—
293C4⋊C4C22×D14911yescharacteristic
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—21no—
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—2981no—
320Q8—2981no—
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#1455873612yes—
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×#1455873611yescharacteristic
382C4#1801195611yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—5961no—
387C2—11921no—
388C2#2375026511yescharacteristic
389C2AGL(1,ℤ/8)×D14911yescharacteristic
390C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#418×C149C2
socleC22×C149C22×D4
prime radicalD4×C22⋊D149C2
hypercenter#418D149
hypocenterC149#3324
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #23750343C2semidirect
3. #23749970C2semidirect
4. #23749949C2semidirect
5. #23749947C2semidirect
6. #23749903C2semidirect
7. #23749871C2semidirect
8. #23749870C2semidirect
9. #23749824C2semidirect
10. #23749777C2semidirect
11. #23749776C2semidirect
12. #23749716C2semidirect
13. #23749701C2semidirect
14. #23749628C2semidirect
15. #418×C149C2semidirect
18. C2×#14558725C22semidirect
20. C2×#14558724C22semidirect
21. C2×#14558719C22semidirect
22. #18011910C22semidirect
27. #18011891C22semidirect
28. #18011890C22semidirect
35. #18011876C22semidirect
38. #18011869C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011842C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011833C22semidirect
46. #18011832C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
53. C2×M16×C149C22semidirect
54. #117×C149C22semidirect
57. #102×C149C22semidirect
58. #102×C149C22semidirect
195. C149#3324semidirect
211. #418D149semidirect
219. C2×M16C2×D149semidirect
237. #117C2×D149semidirect
250. #102C2×D149semidirect
251. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503432
D4×C22⋊D1492
#237499702
#237499492
#237499472
#237499032
#237498712
#237498702
#237498242
#237497772
#237497762
#237497162
#237497012
#237496282
#418×C1492
#3324149