Finite Group Databasebeta

← #34053716

Subgroups — #34053716

Order 19072.

456 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
1C4×D4×D149C211yesmaximal, characteristic
2#23749699C211yesmaximal, characteristic, complemented
3#23749698C211yesmaximal, characteristic, complemented
4#23749697C211yesmaximal, characteristic, complemented
5#23749696C211yesmaximal, characteristic, complemented
6#23749695C211yesmaximal, characteristic, complemented
7#23749694C211yesmaximal, characteristic, complemented
8#23749693C211yesmaximal, characteristic, complemented
9#23749681C211yesmaximal, characteristic, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#23749588C211yesmaximal, characteristic, complemented
12#23749587C211yesmaximal, characteristic, complemented
13C2×#18011823C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C411yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C2×#14558720C2211yescharacteristic, complemented
20C2×#14558719C2211yescharacteristic, complemented
21C2×#14558719C2211yescharacteristic, complemented
22C22×#11924746C2211yescharacteristic, complemented
23C2×C8×D149C2211yescharacteristic, complemented
24C2×C8×D149C2211yescharacteristic, complemented
25C4×D596C2211yescharacteristic
26D4×Dic149C411yescharacteristic
27#18011873C411yescharacteristic
28C4×C22⋊D149C2211yescharacteristic
29C4×C22⋊D149C2211yescharacteristic
30#18011871C411yescharacteristic
31#18011871C411yescharacteristic
32C4⋊C4×D149C411yescharacteristic
33C22⋊C4×D149C411yescharacteristic
34C22⋊C4×D149C411yescharacteristic
35C42×D149C2211yescharacteristic
36C4⋊#11924746C2211yescharacteristic, complemented
37#18011840C2211yescharacteristic, complemented
38#18011840C2211yescharacteristic, complemented
39C22⋊#11924746C2211yescharacteristic, complemented
40C22⋊#11924746C2211yescharacteristic, complemented
41#18011823C2211yescharacteristic
42#18011823C2211yescharacteristic
43#18011823C2211yescharacteristic
44#18011823C2211yescharacteristic
45#18011823C2211yescharacteristic, complemented
46#18011823C2211yescharacteristic, complemented
47#18011823C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic, complemented
49#18011822C2211yescharacteristic, complemented
50#18011821C2211yescharacteristic, complemented
51#18011821C2211yescharacteristic, complemented
52C2×M16×C149C2211yescharacteristic, complemented
53C22×C8×C149C2211yescharacteristic, complemented
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic, complemented
56C22⋊C8×C149C2211yescharacteristic, complemented
57C22⋊C8×C149C2211yescharacteristic, complemented
58#97×C149C2211yescharacteristic, complemented
59C23×D149C2×C411yescharacteristic
60C23×D149C2×C411yescharacteristic
61C2×D596C2×C411yescharacteristic
62C2×C22⋊D149C2×C411yescharacteristic
63C2×C22⋊D149C2×C411yescharacteristic
64D4×D149—24no—
65C22×Dic149C2×C411yescharacteristic
66C22×Dic149C2×C411yescharacteristic
67C2×C4×D149—41no—
68C2×C4×D149—41no—
69C2×C4×D149—41no—
70C2×C4×D149—41no—
71C2×C4×D149C2×C411yescharacteristic
72C2×C4×D149C2×C411yescharacteristic
73C2×C4×D149C2×C411yescharacteristic
74C2×C4×D149C2×C411yescharacteristic
75C2×C4×D149C2×C411yescharacteristic
76C2×C4×D149C2×C411yescharacteristic
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79C2×C4×D149C2311yescharacteristic
80#14558720—41no—
81#14558719—41no—
82#14558719—41no—
83C2×#11924746—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C8×D149—41no—
89C8×D149—41no—
90C4⋊Dic149C2×C411yescharacteristic
91#14558715C2×C411yescharacteristic
92#14558715C2×C411yescharacteristic
93C22⋊Dic149C2×C411yescharacteristic
94C22⋊Dic149C2×C411yescharacteristic
95#14558713C2×C411yescharacteristic
96#14558713C2×C411yescharacteristic
97#14558713C2×C411yescharacteristic
98#14558713C2×C411yescharacteristic
99C4×Dic149C2×C411yescharacteristic
100C4×Dic149C2×C411yescharacteristic
101C4×Dic149C2311yescharacteristic
102C2×D4×C149C2×C411yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105M16×C149—41no—
106C2×C8×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149C2×C411yescharacteristic
112C22⋊C4×C149C2×C411yescharacteristic
113C22⋊C4×C149C2×C411yescharacteristic
114C42×C149C2311yescharacteristic
115C22×D149—22no—
116C22×D149—41no—
117C22×D149—41no—
118C22×D149—41no—
119C22×D149—41no—
120C22×D149M1614yescomplemented
121C22×D149C22×C411yescharacteristic
122C22×D149C22×C411yescharacteristic
123C22×D149C22×C411yescharacteristic
124D596—22no—
125C22⋊D149—22no—
126C22⋊D149—22no—
127C2×Dic149—41no—
128C2×Dic149—41no—
129C2×Dic149C22×C411yescharacteristic
130C2×Dic149C22×C411yescharacteristic
131C2×Dic149C22×C411yescharacteristic
132C2×Dic149C22×C411yescharacteristic
133C2×Dic149C22×C411yescharacteristic
134C4×D149—22no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—41no—
142C4×D149—41no—
143C4×D149—41no—
144C4×D149—41no—
145C4×D149—41no—
146#11924746—21no—
147#11924746—21no—
148#11924746—21no—
149#11924746—21no—
150C23×C149C22×C411yescharacteristic
151C23×C149C22×C411yescharacteristic
152D4×C149—22no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C22×C411yescharacteristic
158C2×C4×C149C22×C411yescharacteristic
159C2×C4×C149C22×C411yescharacteristic
160C2×C4×C149C22×C411yescharacteristic
161C2×C4×C149C2411yescharacteristic
162C8×C149—21no—
163C8×C149—21no—
164C8×C149—21no—
165C8×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149C2×M1612yes—
172C22×C149C23×C411yescharacteristic
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—44no—
181C2×D149—44no—
182C2×D149C2×M1612yes—
183C2×D149C2×M1612yes—
184C4×C149—21no—
185C4×C149—21no—
186C4×C149—21no—
187C4×C149—21no—
188C4×C149H(5,𝔽2)11yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—21no—
192Dic149—21no—
193Dic149—21no—
194Dic149—21no—
195C2×C149—22no—
196C2×C149—41no—
197C2×C149#51811yescharacteristic
198C2×C149C22×M1611yescharacteristic
199C2×C149#56811yescharacteristic
200D149—22no—
201D149—22no—
202D149—41no—
203C149#297311yescharacteristic, complemented, Sylow
204#2973—1491nomaximal, Sylow
205C2×C4×D4—1491no—
206#435—1491no—
207#435—1491no—
208#435—1491no—
209#435—1491no—
210#435—1491no—
211#435—1491no—
212#435—1491no—
213#435D14911yescharacteristic, complemented
214#432—1491no—
215#432—1491no—
216#407—1491no—
217#407—1491no—
218C2×C22⋊C8—1491no—
219C2×C22⋊C8—1491no—
220C22×D4—1491no—
221C23×C4—1491no—
222C23×C4—1491no—
223C2×M16—1491no—
224C2×M16—1491no—
225C2×M16—1491no—
226C2×M16C2×D14911yescharacteristic, complemented
227C22×C8—1491no—
228C22×C8—1491no—
229C22×C8—1491no—
230C22×C8C2×D14911yescharacteristic, complemented
231C4×D4—1491no—
232C4×D4—1491no—
233C4×D4—1491no—
234C4×D4—1491no—
235C4×D4—1491no—
236C4×D4—1491no—
237C4×D4—1491no—
238C4×D4C2×D14911yescharacteristic
239C2×C4⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4—1491no—
242C2×C42—1491no—
243C4⋊C8—1491no—
244C4⋊C8—1491no—
245C4⋊C8—1491no—
246C4⋊C8C2×D14911yescharacteristic, complemented
247C22⋊C8—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8—1491no—
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8—1491no—
257C22⋊C8C2×D14911yescharacteristic, complemented
258C22⋊C8C2×D14911yescharacteristic, complemented
259#97—1491no—
260#97—1491no—
261#97—1491no—
262#97C2×D14911yescharacteristic, complemented
263C24—1491no—
264C24—1491no—
265C2×D4—2984no—
266C2×D4—1491no—
267C2×D4—1491no—
268C2×D4—1491no—
269C2×D4C4×D14911yescharacteristic
270C22×C4—5961no—
271C22×C4—5961no—
272C22×C4—5961no—
273C22×C4—5961no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4—1491no—
282C22×C4—1491no—
283C22×C4—1491no—
284C22×C4—1491no—
285C22×C4C22×D14911yescharacteristic
286C22×C4C22×D14911yescharacteristic
287M16—41no—
288M16—5961no—
289M16—5961no—
290M16—5961no—
291C2×C8—41no—
292C2×C8—5961no—
293C2×C8—5961no—
294C2×C8—5961no—
295C2×C8—1491no—
296C2×C8—1491no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C2×C8C22×D14911yescharacteristic
302C2×C8C22×D14911yescharacteristic
303C4⋊C4—1491no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4C4×D14911yescharacteristic
307C22⋊C4—1491no—
308C22⋊C4—1491no—
309C22⋊C4—1491no—
310C22⋊C4—1491no—
311C22⋊C4—1491no—
312C22⋊C4—1491no—
313C22⋊C4C4×D14911yescharacteristic
314C22⋊C4C4×D14911yescharacteristic
315C42—1491no—
316C42—1491no—
317C42—1491no—
318C42C22×D14911yescharacteristic
319C23—2982no—
320C23—5961no—
321C23—5961no—
322C23—5961no—
323C23—5961no—
324C23—1491no—
325C23—1491no—
326C23—1491no—
327C23—1494no—
328C23C2×C4×D14911yescharacteristic
329C23C2×C4×D14911yescharacteristic
330D4—22no—
331D4—2982no—
332D4—2982no—
333D4—2982no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2982no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—5961no—
346C2×C4—5961no—
347C2×C4—5961no—
348C2×C4—5961no—
349C2×C4—5961no—
350C2×C4—5961no—
351C2×C4—5961no—
352C2×C4—1491no—
353C2×C4—1491no—
354C2×C4—1491no—
355C2×C4—1491no—
356C2×C4—1491no—
357C2×C4C2×C4×D14911yescharacteristic
358C2×C4C2×C4×D14911yescharacteristic
359C2×C4C2×C4×D14911yescharacteristic
360C2×C4C2×C4×D14911yescharacteristic
361C2×C4C23×D14911yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—2981no—
367C8—2981no—
368C8—2981no—
369C8—2981no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—2981no—
376C22—2981no—
377C22—2981no—
378C22—2981no—
379C22—2981no—
380C22—2981no—
381C22—2981no—
382C22—5964no—
383C22—5964no—
384C22—1492no—
385C22—1492no—
386C22M16×D14912yes—
387C22C22×C4×D14911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—2981no—
393C4—2981no—
394C4—2981no—
395C4—2981no—
396C4—2981no—
397C4#1801195611yescharacteristic
398C4#1801195711yescharacteristic
399C2—22no—
400C2—41no—
401C2—2982no—
402C2—2982no—
403C2—5961no—
404C2#2375009711yescharacteristic
405C2C2×M16×D14911yescharacteristic
406C2#2375039011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D149
commutator, socleC22×C149C23×C4
Fitting#435×C149C2
prime radicalC2×D4×D149C4
cosocleC2×C4×C149C24
hypercenter#435D149
hypocenterC149#2973
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #23749699C2semidirect
3. #23749698C2semidirect
4. #23749697C2semidirect
5. #23749696C2semidirect
6. #23749695C2semidirect
7. #23749694C2semidirect
8. #23749693C2semidirect
9. #23749681C2semidirect
10. #23749680C2semidirect
11. #23749588C2semidirect
12. #23749587C2semidirect
13. C2×#18011823C2semidirect
14. C22⋊C8×D149C2semidirect
15. #435×C149C2semidirect
19. C2×#14558720C22semidirect
20. C2×#14558719C22semidirect
21. C2×#14558719C22semidirect
22. C22×#11924746C22semidirect
23. C2×C8×D149C22semidirect
24. C2×C8×D149C22semidirect
36. C4⋊#11924746C22semidirect
37. #18011840C22semidirect
38. #18011840C22semidirect
39. C22⋊#11924746C22semidirect
40. C22⋊#11924746C22semidirect
45. #18011823C22semidirect
46. #18011823C22semidirect
47. #18011823C22semidirect
48. #18011823C22semidirect
49. #18011822C22semidirect
50. #18011821C22semidirect
51. #18011821C22semidirect
52. C2×M16×C149C22semidirect
53. C22×C8×C149C22semidirect
55. C4⋊C8×C149C22semidirect
56. C22⋊C8×C149C22semidirect
57. C22⋊C8×C149C22semidirect
58. #97×C149C22semidirect
120. C22×D149M16semidirect
203. C149#2973semidirect
213. #435D149semidirect
226. C2×M16C2×D149semidirect
230. C22×C8C2×D149semidirect
246. C4⋊C8C2×D149semidirect
257. C22⋊C8C2×D149semidirect
258. C22⋊C8C2×D149semidirect
262. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1492
#237496992
#237496982
#237496972
#237496962
#237496952
#237496942
#237496932
#237496812
#237496802
#237495882
#237495872
C2×#180118232
C22⋊C8×D1492
#435×C1492
#2973149