Finite Group Databasebeta

← C4×#63715 #11900166

Subgroups — C4×#63715 #11900166

Order 1152.

2490 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63715C211yesmaximal, characteristic
2C4×C9×#41C211yesmaximal, characteristic, complemented
3#10589929C211yesmaximal, characteristic, complemented
4#10589676C212yesmaximal, complemented
5C4×#3701C212yesmaximal, complemented
6#10589647C216yesmaximal, complemented
7C4×D4×D9C216yesmaximal, complemented
8#10589625C213yesmaximal, complemented
9#10589623C213yesmaximal, complemented
10C4×#3697C213yesmaximal, complemented
11C2×C4×D36C213yesmaximal, complemented
12C4×#1009—31nomaximal
13C2×C9×#41C2211yescharacteristic
14#63715C4116yesdirect product factor
15C2×#3701C2212yes—
16C2×D4×D9C2216yes—
17C2×#3697C2213yes—
18C22×D36C2213yes—
19C22×C4×D9C2216yescomplemented
20C4×Q8×C9C2211yescharacteristic, complemented
21C4×Q8×C9C2211yescharacteristic, complemented
22C4×D4×C9C2213yescomplemented
23C4×D4×C9C2213yescomplemented
24C9×#117C2213yescomplemented
25C2×C42×C9C2213yescomplemented
26Q8×Dic9C2212yescomplemented
27D4×Dic9C2216yescomplemented
28C4×#611C2216yescomplemented
29C4×#611C2216yescomplemented
30C2×(C2×D9)⋊C4C2216yescomplemented
31#63488C2213yescomplemented
32C2×C4⋊Dic9C2213yescomplemented
33#63455C2216yescomplemented
34#63455C2216yescomplemented
35#63454C2216yescomplemented
36C4⋊C4×D9C2216yescomplemented
37#611⋊C4C22112yescomplemented
38C22⋊C4×D9C22112yescomplemented
39C4×D36C2213yescomplemented
40C4×D36C2216yescomplemented
41C4×D36C2216yescomplemented
42C4×D36C2216yescomplemented
43C4×D36C2213yescomplemented
44#63434C2216yescomplemented
45C42×D9C2216yescomplemented
46C4×Dic18C2211yescharacteristic, complemented
47C4×Dic18C2213yescomplemented
48C2×#1009—31no—
49C3×C4×#41D311yescharacteristic
50#5827—31no—
51#5574—32no—
52C4×#239—32no—
53#5545—36no—
54C4×D3×D4—36no—
55#5523—33no—
56#5521—33no—
57C4×#235—33no—
58C2×C4×D12—33no—
59C23×D9C2316yes—
60C9×#41C2×C418yescomplemented
61C2×Q8×C9C2311yescharacteristic
62C2×D4×C9C2313yes—
63C22×C4×C9C2313yes—
64C22×C4×C9C2313yes—
65C22×C4×C9C2313yes—
66C2×#611C2316yes—
67C22×Dic9C2316yes—
68#3701C2×C4116yescomplemented
69D4×D9C2×C4148yescomplemented
70#3697C2×C4124yescomplemented
71C2×D36C2×C4124yescomplemented
72C2×D36C2313yes—
73C2×D36C2316yes—
74C2×C4×D9—412no—
75C2×C4×D9C2316yes—
76C2×C4×D9C2316yes—
77C2×C4×D9C23112yes—
78C2×C4×D9C2316yes—
79C2×Dic18C2311yescharacteristic
80C9×C4⋊C4C2313yes—
81C9×C4⋊C4C2313yes—
82C9×C22⋊C4C2316yes—
83C42×C9C2311yescharacteristic
84C42×C9C2313yes—
85C42×C9C2313yes—
86C42×C9C2313yes—
87#3676C2316yes—
88(C2×D9)⋊C4C2316yes—
89(C2×D9)⋊C4C23112yes—
90(C2×D9)⋊C4C2316yes—
91C4⋊Dic9C2311yescharacteristic
92C4⋊Dic9C2313yes—
93C4⋊Dic9C2316yes—
94Dic9⋊C4C2312yes—
95Dic9⋊C4C2316yes—
96C4×Dic9C2316yes—
97C4×Dic9C2312yes—
98C4×Dic9C2316yes—
99C4×H(5,𝔽2)—91noSylow
100C2×C3×#41C2×D311yescharacteristic
101#1009—316no—
102C2×#239—32no—
103C2×D3×D4—36no—
104C2×#235—33no—
105C22×D12—33no—
106C22×C4×D3—36no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4C2×D313yes—
110C3×C4×D4C2×D313yes—
111C3×#117C2×D313yes—
112C2×C3×C42C2×D313yes—
113Q8×Dic3—32no—
114D4×Dic3—36no—
115C4×#67—36no—
116C4×#67—36no—
117C2×(C2×D3)⋊C4—36no—
118#926—33no—
119C2×C4⋊Dic3—33no—
120#893—36no—
121#893—36no—
122#892—36no—
123D3×C4⋊C4—36no—
124#67⋊C4—312no—
125D3×C22⋊C4—312no—
126C4×D12—33no—
127C4×D12—36no—
128C4×D12—36no—
129C4×D12—36no—
130C4×D12—33no—
131#872—36no—
132C42×D3—36no—
133C4×Dic6—31no—
134C4×Dic6—33no—
135C23×C9C2413yes—
136C22×D9—46no—
137C22×D9—46no—
138C22×D9C22×C4124yescomplemented
139C22×D9C2416yes—
140Q8×C9C22×C414yescomplemented
141D4×C9C22×C4112yescomplemented
142C2×C4×C9—26no—
143C2×C4×C9—43no—
144C2×C4×C9C22×C4112yescomplemented
145C2×C4×C9C2413yes—
146C2×C4×C9C2411yescharacteristic
147C2×C4×C9C2413yes—
148C2×C4×C9C2413yes—
149C2×C4×C9C2411yescharacteristic
150C2×C4×C9C2411yescharacteristic
151#611C22×C4124yescomplemented
152C2×Dic9—46no—
153C2×Dic9C2412yes—
154C2×Dic9C2416yes—
155C2×Dic9C2412yes—
156D36C22×C4112yescomplemented
157D36C22×C4124yescomplemented
158C4×D9—212no—
159C4×D9—412no—
160C4×D9—46no—
161C4×D9C22×C4124yescomplemented
162Dic18C22×C414yescomplemented
163C2×H(5,𝔽2)—91no—
164#520—91no—
165#520—92no—
166#520—93no—
167#518—96no—
168#518—93no—
169C4×#41—92no—
170C4×#41—93no—
171C4×#41D911yescharacteristic, complemented
172C2×C4×D4—96no—
173C2×C4×D4—93no—
174C23×D3—36no—
175C3×#41C4×D318yes—
176C2×C3×Q8C22×D311yescharacteristic
177C2×C3×D4C22×D313yes—
178C22×C3×C4C22×D313yes—
179C22×C3×C4C22×D313yes—
180C22×C3×C4C22×D313yes—
181C2×#67—36no—
182C22×Dic3—36no—
183#239—316no—
184D3×D4—348no—
185#235—324no—
186C2×D12—324no—
187C2×D12—33no—
188C2×D12—36no—
189C2×C4×D3—36no—
190C2×C4×D3—36no—
191C2×C4×D3—36no—
192C2×C4×D3—312no—
193C2×C4×D3—1212no—
194C2×Dic6—31no—
195C3×C4⋊C4C22×D313yes—
196C3×C4⋊C4C22×D313yes—
197C3×C22⋊C4C22×D316yes—
198C3×C42C22×D311yescharacteristic
199C3×C42C22×D313yes—
200C3×C42C22×D313yes—
201C3×C42C22×D313yes—
202#217—36no—
203(C2×D3)⋊C4—36no—
204(C2×D3)⋊C4—36no—
205(C2×D3)⋊C4—312no—
206C4⋊Dic3—33no—
207C4⋊Dic3—31no—
208C4⋊Dic3—36no—
209Dic3⋊C4—32no—
210Dic3⋊C4—36no—
211C4×Dic3—32no—
212C4×Dic3—36no—
213C4×Dic3—36no—
214C22×C9—23no—
215C22×C9—23no—
216C22×C9C23×C416yes—
217C22×C9C2511yescharacteristic
218C2×D9—26no—
219C2×D9—26no—
220C2×D9—424no—
221C2×D9C23×C4112yes—
222C4×C9—23no—
223C4×C9—23no—
224C4×C9—21no—
225C4×C9C23×C412yes—
226C4×C9C23×C416yes—
227C4×C9H(5,𝔽2)12yescomplemented
228Dic9—26no—
229Dic9—22no—
230Dic9C23×C414yes—
231H(5,𝔽2)—916no—
232C2×#41—92no—
233C2×#41—93no—
234C2×#41C2×D911yescharacteristic
235C22×D4—96no—
236C22×D4—93no—
237C23×C4—96no—
238C4×Q8—92no—
239C4×Q8—91no—
240C4×Q8—93no—
241C4×Q8C2×D911yescharacteristic, complemented
242C4×Q8C2×D911yescharacteristic, complemented
243C4×D4—96no—
244C4×D4—96no—
245C4×D4—96no—
246C4×D4—96no—
247C4×D4—96no—
248C4×D4—912no—
249C4×D4—96no—
250C4×D4—93no—
251C4×D4—96no—
252C4×D4—96no—
253C4×D4—93no—
254C4×D4C2×D913yescomplemented
255C4×D4C2×D913yescomplemented
256#117—93no—
257#117—96no—
258#117—96no—
259#117C2×D913yescomplemented
260C2×C4⋊C4—93no—
261C2×C4⋊C4—96no—
262C2×C22⋊C4—96no—
263C2×C22⋊C4—912no—
264C2×C42—96no—
265C2×C42C2×D913yescomplemented
266C23×C3C23×D313yes—
267C22×D3—36no—
268C22×D3—324no—
269C22×D3—126no—
270C22×D3—126no—
271C3×Q8C2×C4×D314yes—
272C3×D4C2×C4×D3112yes—
273C2×C3×C4—26no—
274C2×C3×C4—43no—
275C2×C3×C4C2×C4×D3112yes—
276C2×C3×C4C23×D313yes—
277C2×C3×C4C23×D311yescharacteristic
278C2×C3×C4C23×D313yes—
279C2×C3×C4C23×D313yes—
280C2×C3×C4C23×D311yescharacteristic
281C2×C3×C4C23×D311yescharacteristic
282#67—324no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—36no—
286C2×Dic3—126no—
287D12—312no—
288D12—324no—
289C4×D3—324no—
290C4×D3—612no—
291C4×D3—126no—
292C4×D3—1212no—
293Dic6—34no—
294C2×C9—26no—
295C2×C9C24×C411yescharacteristic
296C2×C9C2×H(5,𝔽2)11yescharacteristic
297C2×C9#58511yescharacteristic
298D9—212no—
299C24—96no—
300#41—916no—
301#41—924no—
302#41C4×D918yescomplemented
303C2×Q8—91no—
304C2×Q8C22×D911yescharacteristic
305C2×D4—96no—
306C2×D4—948no—
307C2×D4—924no—
308C2×D4—96no—
309C2×D4—93no—
310C2×D4C22×D913yes—
311C22×C4—96no—
312C22×C4—96no—
313C22×C4—96no—
314C22×C4—96no—
315C22×C4—912no—
316C22×C4—3612no—
317C22×C4C22×D913yes—
318C22×C4C22×D913yes—
319C22×C4C22×D913yes—
320C4⋊C4—96no—
321C4⋊C4—96no—
322C4⋊C4—93no—
323C4⋊C4—92no—
324C4⋊C4—91no—
325C4⋊C4C22×D913yes—
326C4⋊C4C22×D913yes—
327C22⋊C4—96no—
328C22⋊C4—96no—
329C22⋊C4—912no—
330C22⋊C4—96no—
331C22⋊C4C22×D916yes—
332C42—96no—
333C42—96no—
334C42—92no—
335C42C22×D913yes—
336C42C22×D913yes—
337C42C22×D913yes—
338C42C22×D911yescharacteristic
339C22×C3—23no—
340C22×C3—23no—
341C22×C3C22×C4×D316yes—
342C22×C3C24×D311yescharacteristic
343C2×D3—312no—
344C2×D3—66no—
345C2×D3—66no—
346C2×D3—1224no—
347C3×C4—23no—
348C3×C4—23no—
349C3×C4—21no—
350C3×C4C22×C4×D312yes—
351C3×C4C22×C4×D316yes—
352C3×C4#100912yes—
353Dic3—34no—
354Dic3—66no—
355Dic3—62no—
356C9C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
357C23—96no—
358C23—924no—
359C23—366no—
360C23—366no—
361C23C23×D913yes—
362Q8—94no—
363Q8C2×C4×D914yescomplemented
364D4—924no—
365D4—924no—
366D4—912no—
367D4C2×C4×D9112yescomplemented
368C2×C4—26no—
369C2×C4—43no—
370C2×C4—92no—
371C2×C4—924no—
372C2×C4—92no—
373C2×C4—96no—
374C2×C4—1812no—
375C2×C4—3612no—
376C2×C4—366no—
377C2×C4—366no—
378C2×C4C2×C4×D9112yescomplemented
379C2×C4C23×D913yes—
380C2×C4C23×D911yescharacteristic
381C2×C4C23×D913yes—
382C2×C4C23×D913yes—
383C2×C4C23×D911yescharacteristic
384C2×C4C23×D911yescharacteristic
385C2×C3—26no—
386C2×C3C23×C4×D311yescharacteristic
387C2×C3C2×#100911yescharacteristic
388C2×C3#596411yescharacteristic
389D3—612no—
390C22—23no—
391C22—23no—
392C22—912no—
393C22—186no—
394C22—186no—
395C22—3624no—
396C22C22×C4×D916yes—
397C22C24×D911yescharacteristic
398C4—23no—
399C4—21no—
400C4—23no—
401C4—94no—
402C4—186no—
403C4—182no—
404C4C22×C4×D916yes—
405C4C22×C4×D912yes—
406C4#6371512yesdirect product factor
407C3C4×#100911yescharacteristic
408C2—26no—
409C2—1812no—
410C2C23×C4×D911yescharacteristic
411C2C2×#6371511yescharacteristic
412C2#1059313911yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutatorC2×C9C24×C4
Frattini, socleC22×C3C24×D3
FittingC4×C9×#41C2
prime radicalC2×#63715C2
cosocleC22×C9C25
hypercenterC4×#41D9
hypocenterC9C4×H(5,𝔽2)
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C4×C9×#41C2semidirect
3. #10589929C2semidirect
4. #10589676C2semidirect
5. C4×#3701C2semidirect
6. #10589647C2semidirect
7. C4×D4×D9C2semidirect
8. #10589625C2semidirect
9. #10589623C2semidirect
10. C4×#3697C2semidirect
11. C2×C4×D36C2semidirect
14. #63715C4direct (N × H)
19. C22×C4×D9C22semidirect
20. C4×Q8×C9C22semidirect
21. C4×Q8×C9C22semidirect
22. C4×D4×C9C22semidirect
23. C4×D4×C9C22semidirect
24. C9×#117C22semidirect
25. C2×C42×C9C22semidirect
26. Q8×Dic9C22semidirect
27. D4×Dic9C22semidirect
28. C4×#611C22semidirect
29. C4×#611C22semidirect
30. C2×(C2×D9)⋊C4C22semidirect
31. #63488C22semidirect
32. C2×C4⋊Dic9C22semidirect
33. #63455C22semidirect
34. #63455C22semidirect
35. #63454C22semidirect
36. C4⋊C4×D9C22semidirect
37. #611⋊C4C22semidirect
38. C22⋊C4×D9C22semidirect
39. C4×D36C22semidirect
40. C4×D36C22semidirect
41. C4×D36C22semidirect
42. C4×D36C22semidirect
43. C4×D36C22semidirect
44. #63434C22semidirect
45. C42×D9C22semidirect
46. C4×Dic18C22semidirect
47. C4×Dic18C22semidirect
60. C9×#41C2×C4semidirect
68. #3701C2×C4semidirect
69. D4×D9C2×C4semidirect
70. #3697C2×C4semidirect
71. C2×D36C2×C4semidirect
138. C22×D9C22×C4semidirect
140. Q8×C9C22×C4semidirect
141. D4×C9C22×C4semidirect
144. C2×C4×C9C22×C4semidirect
151. #611C22×C4semidirect
156. D36C22×C4semidirect
157. D36C22×C4semidirect
161. C4×D9C22×C4semidirect
162. Dic18C22×C4semidirect
171. C4×#41D9semidirect
227. C4×C9H(5,𝔽2)semidirect
241. C4×Q8C2×D9semidirect
242. C4×Q8C2×D9semidirect
254. C4×D4C2×D9semidirect
255. C4×D4C2×D9semidirect
259. #117C2×D9semidirect
265. C2×C42C2×D9semidirect
302. #41C4×D9semidirect
356. C9C4×H(5,𝔽2)semidirect
363. Q8C2×C4×D9semidirect
367. D4C2×C4×D9semidirect
378. C2×C4C2×C4×D9semidirect
406. C4#63715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637152
C4×C9×#412
#105899292
#105896762
C4×#37012
#105896472
C4×D4×D92
#105896252
#105896232
C4×#36972
C2×C4×D362
C4×#10093