Finite Group Databasebeta

← D4×#3701 #11902767

Subgroups — D4×#3701 #11902767

Order 1152.

2472 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3701C212yesmaximal, complemented
2D4×Q8×C9C211yesmaximal, characteristic, complemented
3#10589919C212yesmaximal, complemented
4#10589828C213yesmaximal, complemented
5#10589827C213yesmaximal, complemented
6#10589732C216yesmaximal, complemented
7#10589729C216yesmaximal, complemented
8#10589679C211yesmaximal, characteristic, complemented
9C4×#3701C211yesmaximal, characteristic, complemented
10D4×D36C213yesmaximal, complemented
11C4×D4×D9C213yesmaximal, complemented
12D4×#239—31nomaximal
13C22×Q8×C9C2212yescomplemented
14C2×#3701—216no—
15C2×#3701C2211yescharacteristic
16C2×#3701C2216yescomplemented
17C2×#3701C2216yescomplemented
18C2×#3701C2212yescomplemented
19C2×D4×D9C2213yes—
20C22×D36C2216yescomplemented
21C22×C4×D9C2216yescomplemented
22C9×C4⋊Q8C2213yescomplemented
23C9×C22⋊Q8C2216yescomplemented
24C4×Q8×C9C2211yescharacteristic, complemented
25C4×D4×C9C2213yes—
26#63509C2216yescomplemented
27#63508C2216yescomplemented
28Q8×Dic9C2211yescharacteristic, complemented
29D4×Dic9C2211yescharacteristic
30#63492C2216yescomplemented
31C4×#611C2216yescomplemented
32#63457C2216yescomplemented
33#63457C2216yescomplemented
34#63457C2216yescomplemented
35#63456C22112yescomplemented
36#63455C2216yescomplemented
37#63455C2213yescomplemented
38#63455C2213yescomplemented
39#63454C2213yescomplemented
40C4⋊C4×D9C2213yescomplemented
41#63444C22112yescomplemented
42#611⋊C4C2216yescomplemented
43C22⋊C4×D9C2216yescomplemented
44#63436C2213yescomplemented
45C4×D36C2213yescomplemented
46C4×D36C2213yescomplemented
47C42×D9C2213yescomplemented
48C22×#239—32no—
49C3×D4×Q8D311yescharacteristic
50#5817—32no—
51#5726—33no—
52#5725—33no—
53#5630—36no—
54#5627—36no—
55#5577—31no—
56C4×#239—31no—
57D4×D12—33no—
58C4×D3×D4—33no—
59C23×D9C2316yes—
60C2×Q8×C9—28no—
61C2×Q8×C9C2316yes—
62C2×Q8×C9C2311yescharacteristic
63C2×D4×C9C2311yescharacteristic
64C22×C4×C9C2316yes—
65C2×#611C2316yes—
66C22×Dic9C2312yes—
67#3701—28no—
68#3701—224no—
69#3701—224no—
70#3701D418yesdirect product factor
71D4×D9—212no—
72C2×D36—224no—
73C2×D36C2316yes—
74C2×D36C2313yes—
75C2×D36C23112yes—
76C2×D36C2316yes—
77C2×D36C2313yes—
78C2×C4×D9—224no—
79C2×C4×D9C2316yes—
80C2×C4×D9C2313yes—
81C2×C4×D9C2316yes—
82C2×C4×D9C2316yes—
83C2×C4×D9C2313yes—
84C2×C4×D9C2313yes—
85C9×C4⋊C4C2313yes—
86C9×C4⋊C4C2313yes—
87C9×C4⋊C4C2316yes—
88C9×C22⋊C4C2316yes—
89C42×C9C2313yes—
90#3676C2312yes—
91(C2×D9)⋊C4C2316yes—
92(C2×D9)⋊C4C23112yes—
93(C2×D9)⋊C4C2316yes—
94(C2×D9)⋊C4C2316yes—
95C4⋊Dic9C2313yes—
96C4⋊Dic9C2311yescharacteristic
97Dic9⋊C4C2316yes—
98C4×Dic9C2313yes—
99C4×Dic9C2311yescharacteristic
100C4×Dic9C2313yes—
101D4×#41—91noSylow
102C22×C3×Q8C2×D312yes—
103C2×#239—31no—
104C2×#239—36no—
105C2×#239—36no—
106C2×#239—32no—
107C2×#239—616no—
108C2×D3×D4—33no—
109C22×D12—36no—
110C22×C4×D3—36no—
111C3×C4⋊Q8C2×D313yes—
112C3×C22⋊Q8C2×D316yes—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4C2×D313yes—
115#947—36no—
116#946—36no—
117Q8×Dic3—31no—
118D4×Dic3—31no—
119#930—36no—
120C4×#67—36no—
121#895—36no—
122#895—36no—
123#895—36no—
124#894—312no—
125#893—33no—
126#893—36no—
127#893—33no—
128#892—33no—
129D3×C4⋊C4—33no—
130#882—312no—
131#67⋊C4—36no—
132D3×C22⋊C4—36no—
133#874—33no—
134C4×D12—33no—
135C4×D12—33no—
136C42×D3—33no—
137C23×C9C2412yes—
138C22×D9—212no—
139C22×D9—212no—
140C22×D9—46no—
141C22×D9C2416yes—
142C22×D9C2413yes—
143Q8×C9—212no—
144Q8×C9C2×D414yescomplemented
145D4×C9#4114yescomplemented
146C2×C4×C9—212no—
147C2×C4×C9C2413yes—
148C2×C4×C9C2416yes—
149C2×C4×C9C2413yes—
150C2×C4×C9C2411yescharacteristic
151#611—212no—
152C2×Dic9—24no—
153C2×Dic9C2411yescharacteristic
154C2×Dic9C2413yes—
155C2×Dic9C2412yes—
156C2×Dic9C2411yescharacteristic
157D36—224no—
158D36—212no—
159D36—26no—
160D36—46no—
161D36C2×D4112yescomplemented
162C4×D9—212no—
163C4×D9—212no—
164C4×D9—26no—
165C4×D9—212no—
166C4×D9—43no—
167C4×D9C2×D4112yescomplemented
168C22×#41—92no—
169#550—91no—
170D4×Q8D911yescharacteristic, complemented
171#548—92no—
172#547—93no—
173#546—96no—
174D42—93no—
175#532—93no—
176#525—96no—
177C4×#41—91no—
178C2×C4×D4—93no—
179C23×D3—36no—
180C2×C3×Q8—28no—
181C2×C3×Q8C22×D316yes—
182C2×C3×Q8C22×D311yescharacteristic
183C2×C3×D4C22×D311yescharacteristic
184C22×C3×C4C22×D316yes—
185C2×#67—36no—
186C22×Dic3—32no—
187#239—38no—
188#239—624no—
189#239—624no—
190#239—68no—
191D3×D4—612no—
192C2×D12—33no—
193C2×D12—33no—
194C2×D12—36no—
195C2×D12—312no—
196C2×D12—36no—
197C2×D12—624no—
198C2×C4×D3—33no—
199C2×C4×D3—33no—
200C2×C4×D3—36no—
201C2×C4×D3—36no—
202C2×C4×D3—36no—
203C2×C4×D3—33no—
204C2×C4×D3—624no—
205C3×C4⋊C4C22×D313yes—
206C3×C4⋊C4C22×D313yes—
207C3×C4⋊C4C22×D316yes—
208C3×C22⋊C4C22×D316yes—
209C3×C42C22×D313yes—
210#217—32no—
211(C2×D3)⋊C4—36no—
212(C2×D3)⋊C4—36no—
213(C2×D3)⋊C4—36no—
214(C2×D3)⋊C4—312no—
215C4⋊Dic3—31no—
216C4⋊Dic3—33no—
217Dic3⋊C4—36no—
218C4×Dic3—31no—
219C4×Dic3—33no—
220C4×Dic3—33no—
221C22×C9—22no—
222C22×C9—22no—
223C22×C9C2×#4114yescomplemented
224C22×C9C2511yescharacteristic
225C2×D9—23no—
226C2×D9—23no—
227C2×D9—26no—
228C2×D9—26no—
229C2×D9—26no—
230C2×D9—424no—
231C2×D9C22×D416yes—
232C4×C9—26no—
233C4×C9—23no—
234C4×C9C22×D416yes—
235C4×C9C2×#4112yescomplemented
236Dic9—22no—
237Dic9—23no—
238Dic9—21no—
239Dic9C22×D412yes—
240C2×#41—91no—
241C2×#41—96no—
242C2×#41—96no—
243C2×#41—92no—
244C2×#41—1816no—
245C22×Q8C2×D912yescomplemented
246C22×D4—93no—
247C22×D4—96no—
248C23×C4—96no—
249C4⋊Q8C2×D913yescomplemented
250#127—93no—
251#124—96no—
252#123—912no—
253C22⋊Q8—96no—
254C22⋊Q8C2×D916yescomplemented
255#121—96no—
256#121—96no—
257#121—96no—
258#121—96no—
259#120—912no—
260C4×Q8—91no—
261C4×Q8C2×D911yescharacteristic, complemented
262C4×D4—91no—
263C4×D4—96no—
264C4×D4—93no—
265C4×D4—93no—
266C4×D4—96no—
267C4×D4—96no—
268C4×D4—93no—
269C4×D4—93no—
270C4×D4C2×D913yes—
271#117—93no—
272C2×C4⋊C4—93no—
273C2×C22⋊C4—96no—
274C2×C42—93no—
275C23×C3C23×D312yes—
276C22×D3—33no—
277C22×D3—36no—
278C22×D3—612no—
279C22×D3—612no—
280C22×D3—126no—
281C3×Q8—212no—
282C3×Q8D3×D414yes—
283C3×D4#23914yes—
284C2×C3×C4—212no—
285C2×C3×C4C23×D313yes—
286C2×C3×C4C23×D316yes—
287C2×C3×C4C23×D313yes—
288C2×C3×C4C23×D311yescharacteristic
289#67—612no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—33no—
293C2×Dic3—32no—
294C2×Dic3—64no—
295D12—312no—
296D12—624no—
297D12—612no—
298D12—66no—
299D12—126no—
300C4×D3—312no—
301C4×D3—612no—
302C4×D3—612no—
303C4×D3—612no—
304C4×D3—66no—
305C4×D3—123no—
306C2×C9—24no—
307C2×C9C23×D411yescharacteristic
308C2×C9C22×#4111yescharacteristic
309C2×C9#58511yescharacteristic
310D9—26no—
311D9—46no—
312C24—96no—
313#41—98no—
314#41—1824no—
315#41—1824no—
316#41—188no—
317C2×Q8—28no—
318C2×Q8C22×D916yes—
319C2×Q8C22×D911yescharacteristic
320C2×D4—96no—
321C2×D4—93no—
322C2×D4—93no—
323C2×D4—912no—
324C2×D4—96no—
325C2×D4—96no—
326C2×D4—1824no—
327C2×D4—1812no—
328C2×D4C22×D911yescharacteristic
329C22×C4—93no—
330C22×C4—92no—
331C22×C4—93no—
332C22×C4—96no—
333C22×C4—96no—
334C22×C4—96no—
335C22×C4—93no—
336C22×C4—1824no—
337C22×C4C22×D916yes—
338C4⋊C4—91no—
339C4⋊C4—96no—
340C4⋊C4—93no—
341C4⋊C4C22×D913yes—
342C4⋊C4C22×D913yes—
343C4⋊C4C22×D916yes—
344C22⋊C4—92no—
345C22⋊C4—96no—
346C22⋊C4—96no—
347C22⋊C4—96no—
348C22⋊C4—912no—
349C22⋊C4C22×D916yes—
350C42—91no—
351C42—93no—
352C42—93no—
353C42C22×D913yes—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3C2×#23914yes—
357C22×C3C24×D311yescharacteristic
358C2×D3—36no—
359C2×D3—63no—
360C2×D3—63no—
361C2×D3—66no—
362C2×D3—66no—
363C2×D3—66no—
364C2×D3—1224no—
365C3×C4—26no—
366C3×C4—23no—
367C3×C4C2×D3×D416yes—
368C3×C4C2×#23912yes—
369Dic3—32no—
370Dic3—62no—
371Dic3—63no—
372Dic3—61no—
373C9D4×#4111yescharacteristic, complemented, Sylow
374C23—93no—
375C23—96no—
376C23—1812no—
377C23—1812no—
378C23—366no—
379C23C23×D912yes—
380Q8—212no—
381Q8D4×D914yescomplemented
382D4—912no—
383D4—1824no—
384D4—1812no—
385D4—1812no—
386D4—186no—
387D4—366no—
388D4#370114yesdirect product factor
389C2×C4—212no—
390C2×C4—91no—
391C2×C4—912no—
392C2×C4—91no—
393C2×C4—93no—
394C2×C4—92no—
395C2×C4—1812no—
396C2×C4—1812no—
397C2×C4—184no—
398C2×C4—1812no—
399C2×C4—186no—
400C2×C4—363no—
401C2×C4C23×D913yes—
402C2×C4C23×D916yes—
403C2×C4C23×D913yes—
404C2×C4C23×D911yescharacteristic
405C2×C3—24no—
406C2×C3C22×D3×D411yescharacteristic
407C2×C3C22×#23911yescharacteristic
408C2×C3#596811yescharacteristic
409D3—66no—
410D3—126no—
411C22—22no—
412C22—22no—
413C22—96no—
414C22—183no—
415C22—183no—
416C22—186no—
417C22—186no—
418C22—186no—
419C22—3624no—
420C22C2×#370114yescomplemented
421C22C24×D911yescharacteristic
422C4—26no—
423C4—23no—
424C4—92no—
425C4—182no—
426C4—183no—
427C4—181no—
428C4C2×D4×D916yes—
429C4C2×#370112yescomplemented
430C3D4×#23911yescharacteristic
431C2—24no—
432C2—186no—
433C2—366no—
434C2C22×D4×D911yescharacteristic
435C2C22×#370111yescharacteristic
436C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingD4×Q8×C9C2
hypercenterD4×Q8D9
hypocenterC9D4×#41
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3701C2semidirect
2. D4×Q8×C9C2semidirect
3. #10589919C2semidirect
4. #10589828C2semidirect
5. #10589827C2semidirect
6. #10589732C2semidirect
7. #10589729C2semidirect
8. #10589679C2semidirect
9. C4×#3701C2semidirect
10. D4×D36C2semidirect
11. C4×D4×D9C2semidirect
13. C22×Q8×C9C22semidirect
16. C2×#3701C22semidirect
17. C2×#3701C22semidirect
18. C2×#3701C22semidirect
20. C22×D36C22semidirect
21. C22×C4×D9C22semidirect
22. C9×C4⋊Q8C22semidirect
23. C9×C22⋊Q8C22semidirect
24. C4×Q8×C9C22semidirect
26. #63509C22semidirect
27. #63508C22semidirect
28. Q8×Dic9C22semidirect
30. #63492C22semidirect
31. C4×#611C22semidirect
32. #63457C22semidirect
33. #63457C22semidirect
34. #63457C22semidirect
35. #63456C22semidirect
36. #63455C22semidirect
37. #63455C22semidirect
38. #63455C22semidirect
39. #63454C22semidirect
40. C4⋊C4×D9C22semidirect
41. #63444C22semidirect
42. #611⋊C4C22semidirect
43. C22⋊C4×D9C22semidirect
44. #63436C22semidirect
45. C4×D36C22semidirect
46. C4×D36C22semidirect
47. C42×D9C22semidirect
70. #3701D4direct (N × H)
144. Q8×C9C2×D4semidirect
145. D4×C9#41semidirect
161. D36C2×D4semidirect
167. C4×D9C2×D4semidirect
170. D4×Q8D9semidirect
223. C22×C9C2×#41semidirect
235. C4×C9C2×#41semidirect
245. C22×Q8C2×D9semidirect
249. C4⋊Q8C2×D9semidirect
254. C22⋊Q8C2×D9semidirect
261. C4×Q8C2×D9semidirect
373. C9D4×#41semidirect
381. Q8D4×D9semidirect
388. D4#3701direct (N × H)
420. C22C2×#3701semidirect
429. C4C2×#3701semidirect

Maximal subgroups

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

subgroupindex
C22×#37012
D4×Q8×C92
#105899192
#105898282
#105898272
#105897322
#105897292
#105896792
C4×#37012
D4×D362
C4×D4×D92
D4×#2393