Finite Group Databasebeta

← #34058100

Subgroups — #34058100

Order 19072.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750251C211yesmaximal, characteristic, complemented
2#23750222C212yesmaximal, complemented
3#23750217C214yesmaximal, complemented
4#23750213C212yesmaximal, complemented
5#23750208C214yesmaximal, complemented
6#23750187C211yesmaximal, characteristic, complemented
7#23750184C212yesmaximal, complemented
8#23750159C212yesmaximal, complemented
9#23750155C214yesmaximal, complemented
10#23750136C212yesmaximal, complemented
11#23750134C214yesmaximal, complemented
12C2×C4×C22⋊D149C212yesmaximal, complemented
13C2×C4×D4×C149C211yesmaximal, characteristic, complemented
14C2×#14558736C2212yescomplemented
15C22×C22⋊D149C2212yes—
16C22×C4×D149C2212yescomplemented
17#18011906C2214yescomplemented
18#18011905C2214yescomplemented
19#18011904C2214yescomplemented
20#18011903C2212yescomplemented
21#18011901C2214yescomplemented
22#18011899C2212yescomplemented
23#18011897C2214yescomplemented
24#18011896C2214yescomplemented
25#18011895C2214yescomplemented
26#18011894C2214yescomplemented
27#18011894C2214yescomplemented
28#18011893C2214yescomplemented
29#18011892C2214yescomplemented
30#18011890C2212yescomplemented
31#18011890C2212yescomplemented
32#18011890C2212yescomplemented
33#18011889C2214yescomplemented
34#18011888C2214yescomplemented
35#18011888C2214yescomplemented
36#18011885C2212yes—
37#18011885C2212yes—
38#18011885C2212yescomplemented
39#18011884C2214yescomplemented
40#18011883C2214yes—
41#18011883C2214yes—
42#18011881C2214yescomplemented
43#18011880C2214yescomplemented
44#18011879C2214yescomplemented
45C4×Dic298C2212yescomplemented
46C4×D596C2212yescomplemented
47C4×C22⋊D149C2214yescomplemented
48C4×C22⋊D149C2214yescomplemented
49C4×C22⋊D149C2214yescomplemented
50C4×C22⋊D149C2214yescomplemented
51C4×C22⋊D149C2214yescomplemented
52#18011870C2212yescomplemented
53#18011868C2214yescomplemented
54C2×#14558715C2212yescomplemented
55C2×C22⋊Dic149C2212yes—
56C2×#14558713C2212yescomplemented
57C2×C4×Dic149C2212yescomplemented
58C22×D4×C149C2211yescharacteristic
59C23×C4×C149C2211yescharacteristic
60C23×C4×C149C2211yescharacteristic, complemented
61C4×D4×C149C2214yescomplemented
62C4×D4×C149C2214yescomplemented
63C2×C4⋊C4×C149C2211yescharacteristic, complemented
64C2×C22⋊C4×C149C2211yescharacteristic
65C2×C22⋊C4×C149C2211yescharacteristic, complemented
66C2×C42×C149C2211yescharacteristic, complemented
67C23×D149C2312yes—
68#14558736—44no—
69C2×Dic298C2312yes—
70C2×Dic298C2312yes—
71C2×D596C2312yes—
72C2×D596C2312yes—
73C2×C22⋊D149—28no—
74C2×C22⋊D149C2314yes—
75C2×C22⋊D149C2314yes—
76C2×C22⋊D149C2314yes—
77C2×C22⋊D149C2314yes—
78C22×Dic149C2312yes—
79C22×Dic149C2312yes—
80C22×Dic149C2312yes—
81C2×C4×D149—44no—
82C2×C4×D149C2314yes—
83C2×C4×D149C2314yes—
84C4⋊Dic149C2312yes—
85C4⋊Dic149C2312yes—
86C4⋊Dic149C2312yes—
87C4⋊Dic149C2312yes—
88#14558715C2314yes—
89#14558715C2314yes—
90#14558715C2314yes—
91#14558715C2314yes—
92#14558715C2314yes—
93#14558715C2314yes—
94C22⋊Dic149C2314yes—
95C22⋊Dic149C2314yes—
96C22⋊Dic149C2314yes—
97C22⋊Dic149C2314yes—
98#14558713C2314yes—
99#14558713C2314yes—
100#14558713C2314yes—
101#14558713C2314yes—
102#14558713C2314yes—
103#14558713C2314yes—
104C4×Dic149C2314yes—
105C4×Dic149C2314yes—
106C24×C149C2311yescharacteristic
107C24×C149C2311yescharacteristic
108C2×D4×C149—24no—
109C2×D4×C149C2314yes—
110C22×C4×C149—42no—
111C22×C4×C149—42no—
112C22×C4×C149C2312yes—
113C22×C4×C149C2312yes—
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C22×C4×C149C2311yescharacteristic
119C22×C4×C149C2312yes—
120C22×C4×C149C2312yes—
121C4⋊C4×C149C2314yes—
122C22⋊C4×C149C2314yes—
123C22⋊C4×C149C2314yes—
124C42×C149C2312yes—
125C42×C149C2312yes—
126C22×D149—24no—
127C22×D149—42no—
128C22×D149—42no—
129C22×D149C2414yes—
130Dic298—42no—
131Dic298—42no—
132D596—42no—
133D596—42no—
134C22⋊D149—28no—
135C22⋊D149—28no—
136C22⋊D149—44no—
137C22⋊D149—44no—
138C2×Dic149—24no—
139C2×Dic149—42no—
140C2×Dic149—42no—
141C2×Dic149C2414yes—
142C2×Dic149C2414yes—
143C2×Dic149C2414yes—
144C4×D149—28no—
145C4×D149—44no—
146C23×C149—22no—
147C23×C149—41no—
148C23×C149—41no—
149C23×C149—41no—
150C23×C149—41no—
151C23×C149#4114yescomplemented
152C23×C149C2412yes—
153C23×C149C2412yes—
154C23×C149C2411yescharacteristic
155D4×C149—28no—
156C2×C4×C149—22no—
157C2×C4×C149—24no—
158C2×C4×C149—24no—
159C2×C4×C149—22no—
160C2×C4×C149—42no—
161C2×C4×C149—42no—
162C2×C4×C149—41no—
163C2×C4×C149—41no—
164C2×C4×C149—41no—
165C2×C4×C149C2412yes—
166C2×C4×C149C2412yes—
167C2×C4×C149C2412yes—
168C2×C4×C149C2412yes—
169C2×C4×C149C2411yescharacteristic
170C2×C4×C149C2411yescharacteristic
171C22×C149—21no—
172C22×C149—22no—
173C22×C149—21no—
174C22×C149—22no—
175C22×C149—22no—
176C22×C149—22no—
177C22×C149—22no—
178C22×C149—44no—
179C22×C149—44no—
180C22×C149C2×#4112yes—
181C22×C149C2×#4114yes—
182C22×C149C2511yescharacteristic
183C2×D149—24no—
184C2×D149—24no—
185C2×D149—24no—
186C2×D149—48no—
187C4×C149—22no—
188C4×C149—21no—
189C4×C149—22no—
190C4×C149—22no—
191C4×C149—22no—
192C4×C149H(5,𝔽2)12yes—
193Dic149—24no—
194Dic149—24no—
195Dic149—24no—
196C2×C149—24no—
197C2×C149—22no—
198C2×C149—42no—
199C2×C149C22×#4111yescharacteristic
200C2×C149C2×H(5,𝔽2)11yescharacteristic
201C2×C149#58511yescharacteristic
202D149—44no—
203C149#345911yescharacteristic, complemented, Sylow
204#3459—1491nomaximal, Sylow
205#543—1491no—
206#539—1494no—
207#539—1492no—
208#538—1494no—
209#538—1492no—
210#534—1492no—
211#534—1491no—
212#529—1494no—
213#529—1492no—
214#525—1492no—
215#525—1494no—
216C2×C4×D4—1492no—
217C2×C4×D4D14911yescharacteristic, complemented
218C2×#41—1492no—
219C22×D4—1492no—
220C22×D4C2×D14911yescharacteristic
221C23×C4—1492no—
222C23×C4C2×D14911yescharacteristic
223C23×C4C2×D14911yescharacteristic, complemented
224#126—1494no—
225#126—1494no—
226#126—1494no—
227#125—1494no—
228#125—1492no—
229#124—1494no—
230#124—1492no—
231#123—1494no—
232#123—1494no—
233#123—1494no—
234#123—1494no—
235#123—1494no—
236#123—1494no—
237C22⋊Q8—1492no—
238C22⋊Q8—1492no—
239C22⋊Q8—1492no—
240C22⋊Q8—1494no—
241C22⋊Q8—1494no—
242C22⋊Q8—1494no—
243#121—1494no—
244#121—1494no—
245#121—1492no—
246#121—1492no—
247#121—1492no—
248#121—1494no—
249#120—1494no—
250#120—1494no—
251#120—1494no—
252C4×Q8—1492no—
253C4×D4—1494no—
254C4×D4—1494no—
255C4×D4—1494no—
256C4×D4—1494no—
257C4×D4—1494no—
258C4×D4—1492no—
259C4×D4C2×D14914yescomplemented
260C4×D4C2×D14914yescomplemented
261#117—1492no—
262#117—1494no—
263C2×C4⋊C4—1492no—
264C2×C4⋊C4C2×D14911yescharacteristic, complemented
265C2×C22⋊C4—1492no—
266C2×C22⋊C4—1492no—
267C2×C22⋊C4C2×D14911yescharacteristic
268C2×C22⋊C4C2×D14911yescharacteristic, complemented
269C2×C42—1492no—
270C2×C42C2×D14911yescharacteristic, complemented
271C24—1492no—
272C24C22×D14911yescharacteristic
273C24C22×D14911yescharacteristic
274#41—5964no—
275C2×Q8—1492no—
276C2×Q8—1492no—
277C2×D4—24no—
278C2×D4—2988no—
279C2×D4—1494no—
280C2×D4—1494no—
281C2×D4—1494no—
282C2×D4—1494no—
283C2×D4—1492no—
284C2×D4—1492no—
285C2×D4C22×D14914yes—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—5964no—
289C22×C4—1492no—
290C22×C4—1494no—
291C22×C4—1492no—
292C22×C4—1492no—
293C22×C4—1494no—
294C22×C4C22×D14911yescharacteristic
295C22×C4C22×D14912yes—
296C22×C4C22×D14911yescharacteristic
297C22×C4C22×D14912yes—
298C22×C4C22×D14911yescharacteristic
299C22×C4C22×D14912yes—
300C22×C4C22×D14911yescharacteristic
301C22×C4C22×D14911yescharacteristic
302C22×C4C22×D14912yes—
303C4⋊C4—1494no—
304C4⋊C4—1494no—
305C4⋊C4—1494no—
306C4⋊C4—1492no—
307C4⋊C4—1494no—
308C4⋊C4—1492no—
309C4⋊C4—1494no—
310C4⋊C4—1492no—
311C4⋊C4—1494no—
312C4⋊C4—1492no—
313C4⋊C4C22×D14914yes—
314C22⋊C4—1494no—
315C22⋊C4—1494no—
316C22⋊C4—1494no—
317C22⋊C4—1494no—
318C22⋊C4—1494no—
319C22⋊C4—1494no—
320C22⋊C4—1494no—
321C22⋊C4—1494no—
322C22⋊C4—1494no—
323C22⋊C4—1494no—
324C22⋊C4C22×D14914yes—
325C22⋊C4C22×D14914yes—
326C42—1494no—
327C42—1494no—
328C42C22×D14912yes—
329C42C22×D14912yes—
330C23—22no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—2984no—
336C23—5962no—
337C23—5962no—
338C23—1494no—
339C23#1455873614yescomplemented
340C23C23×D14912yes—
341C23C23×D14911yescharacteristic
342C23C23×D14912yes—
343Q8—5962no—
344Q8—5962no—
345D4—28no—
346D4—2988no—
347D4—2988no—
348D4—5962no—
349D4—5962no—
350D4—5964no—
351D4—5964no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—2984no—
362C2×C4—2988no—
363C2×C4—5964no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—1494no—
367C2×C4—1494no—
368C2×C4—1494no—
369C2×C4C23×D14912yes—
370C2×C4C23×D14912yes—
371C2×C4C23×D14911yescharacteristic
372C2×C4C23×D14912yes—
373C2×C4C23×D14912yes—
374C2×C4C23×D14911yescharacteristic
375C22—21no—
376C22—22no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—44no—
383C22—44no—
384C22—2984no—
385C22—2984no—
386C22—2984no—
387C22—5968no—
388C22C2×#1455873612yes—
389C22C2×#1455873614yes—
390C22C24×D14911yescharacteristic
391C4—22no—
392C4—21no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—2984no—
397C4—2984no—
398C4—2984no—
399C4#1801195612yes—
400C2—22no—
401C2—24no—
402C2—42no—
403C2—5964no—
404C2C22×#1455873611yescharacteristic
405C2C2×#1801195611yescharacteristic
406C2#2375046111yescharacteristic
subgroupG/H
centerC2×C4C23×D149
commutator, socle, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×C4×D4×C149C2
hypercenterC2×C4×D4D149
hypocenterC149#3459
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750251C2semidirect
2. #23750222C2semidirect
3. #23750217C2semidirect
4. #23750213C2semidirect
5. #23750208C2semidirect
6. #23750187C2semidirect
7. #23750184C2semidirect
8. #23750159C2semidirect
9. #23750155C2semidirect
10. #23750136C2semidirect
11. #23750134C2semidirect
12. C2×C4×C22⋊D149C2semidirect
13. C2×C4×D4×C149C2semidirect
14. C2×#14558736C22semidirect
16. C22×C4×D149C22semidirect
17. #18011906C22semidirect
18. #18011905C22semidirect
19. #18011904C22semidirect
20. #18011903C22semidirect
21. #18011901C22semidirect
22. #18011899C22semidirect
23. #18011897C22semidirect
24. #18011896C22semidirect
25. #18011895C22semidirect
26. #18011894C22semidirect
27. #18011894C22semidirect
28. #18011893C22semidirect
29. #18011892C22semidirect
30. #18011890C22semidirect
31. #18011890C22semidirect
32. #18011890C22semidirect
33. #18011889C22semidirect
34. #18011888C22semidirect
35. #18011888C22semidirect
38. #18011885C22semidirect
39. #18011884C22semidirect
42. #18011881C22semidirect
43. #18011880C22semidirect
44. #18011879C22semidirect
45. C4×Dic298C22semidirect
46. C4×D596C22semidirect
47. C4×C22⋊D149C22semidirect
48. C4×C22⋊D149C22semidirect
49. C4×C22⋊D149C22semidirect
50. C4×C22⋊D149C22semidirect
51. C4×C22⋊D149C22semidirect
52. #18011870C22semidirect
53. #18011868C22semidirect
54. C2×#14558715C22semidirect
56. C2×#14558713C22semidirect
57. C2×C4×Dic149C22semidirect
60. C23×C4×C149C22semidirect
61. C4×D4×C149C22semidirect
62. C4×D4×C149C22semidirect
63. C2×C4⋊C4×C149C22semidirect
65. C2×C22⋊C4×C149C22semidirect
66. C2×C42×C149C22semidirect
151. C23×C149#41semidirect
203. C149#3459semidirect
217. C2×C4×D4D149semidirect
223. C23×C4C2×D149semidirect
259. C4×D4C2×D149semidirect
260. C4×D4C2×D149semidirect
264. C2×C4⋊C4C2×D149semidirect
268. C2×C22⋊C4C2×D149semidirect
270. C2×C42C2×D149semidirect
339. C23#14558736semidirect

Maximal subgroups

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

subgroupindex
#237502512
#237502222
#237502172
#237502132
#237502082
#237501872
#237501842
#237501592
#237501552
#237501362
#237501342
C2×C4×C22⋊D1492
C2×C4×D4×C1492
#3459149