Finite Group Databasebeta

← C4×#64224 #11860349

Subgroups — C4×#64224 #11860349

Order 1152.

916 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 916 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64224C211yesmaximal, characteristic
2C4×#3802C211yesmaximal, characteristic, complemented
3C4×#3798C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5#10593432C212yesmaximal, complemented
6C4×#3775C212yesmaximal, complemented
7#10593419C212yesmaximal, complemented
8C4×#3774C212yesmaximal, complemented
9#10593394C211yesmaximal, characteristic, complemented
10#10593363C211yesmaximal, characteristic, complemented
11#10593360C211yesmaximal, characteristic, complemented
12C2×#3802C2211yescharacteristic
13C2×C4×D32—21no—
14C2×#3798C2211yescharacteristic
15C2×#3788C2211yescharacteristic
16C2×#3788C2211yescharacteristic
17C2×#3775C2212yes—
18C2×#3774C2212yes—
19#64224C418yesdirect product factor
20C42×C3⋊D3C2211yescharacteristic
21C3×C4×D12—21no—
22C3×C42×D3—21no—
23#63921—21no—
24C4×#627C2211yescharacteristic, complemented
25C4×#627C2211yescharacteristic, complemented
26C4×#626—21no—
27C4×#626—21no—
28#63902C2212yes—
29C4×#625C2212yes—
30C4×#625C2211yescharacteristic, complemented
31C4×#625C2211yescharacteristic, complemented
32#63900C2211yescharacteristic
33#63898—21no—
34#63874C2211yescharacteristic
35#63855—21no—
36#63777C2212yescomplemented
37C4×#622C2212yescomplemented
38#63743C2212yescomplemented
39#63742C2212yescomplemented
40#63740C2212yescomplemented
41#63739C2212yes—
42#63739C2212yes—
43#63739C2212yescomplemented
44C4×D3×D4—61no—
45C4×#235—61no—
46C22×D32—21no—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×C3×D12—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—22no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×#627C2311yescharacteristic
56C2×#626—21no—
57C2×#625C2312yes—
58C2×#625C2311yescharacteristic
59C2×#624—21no—
60C2×D3×Dic3—22no—
61#3802—22no—
62#3802C2×C414yescomplemented
63C4×D32—44no—
64#3798—22no—
65#3798C2×C414yescomplemented
66C2×#622C2312yes—
67C2×#622C2312yes—
68#3788—22no—
69#3788C2×C414yescomplemented
70#3775C2×C418yescomplemented
71#3774C2×C418yescomplemented
72C32×C42D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81#3724C2311yescharacteristic
82#3724C2311yescharacteristic
83#3724C2312yes—
84Dic3⋊Dic3—21no—
85Dic3⋊Dic3—21no—
86#3722—21no—
87(C2×D3)⋊Dic3—21no—
88(C2×D3)⋊Dic3—21no—
89(C2×D3)⋊Dic3—22no—
90C4×AGL(1,ℤ/8)—91nomaximal, Sylow
91C2×D3×D4—61no—
92C2×#235—61no—
93C22×C4×D3—62no—
94C3×C4×D4—61no—
95C2×C3×C42—61no—
96D4×Dic3—61no—
97C4×#67—61no—
98C4×#67—61no—
99C4×#67—62no—
100C4×#67—61no—
101C4×#67—61no—
102#926—61no—
103#893—61no—
104D3×C4⋊C4—61no—
105#67⋊C4—62no—
106D3×C22⋊C4—62no—
107C4×D12—21no—
108C4×D12—61no—
109C4×D12—61no—
110#872—61no—
111#872—61no—
112C42×D3—21no—
113C42×D3—61no—
114C42×D3—61no—
115C4×Dic6—61no—
116C4×Dic6—61no—
117C22×C3⋊D3C2×D411yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—21no—
120C2×D32—24no—
121C2×D32—42no—
122C2×D32—42no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2411yescharacteristic
129C4×C3⋊D3—22no—
130C4×C3⋊D3—41no—
131C4×C3⋊D3C22×C412yes—
132C4×C3⋊D3#4112yes—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—22no—
137C3×D12—24no—
138C3×C4×D3—24no—
139C3×C4×D3—42no—
140C3×C4×D3—44no—
141C3×C4×D3—42no—
142#627—21no—
143#627C22×C412yescomplemented
144#626—24no—
145#625—21no—
146#625—22no—
147#625C22×C414yes—
148#625C22×C412yescomplemented
149#624—42no—
150D3×Dic3—44no—
151#622—22no—
152#622C22×C414yescomplemented
153C2×AGL(1,ℤ/8)—91no—
154C4×#41—91no—
155C2×C4×D4—91no—
156#442—92no—
157#440—92no—
158C4×SD16—92no—
159C4×D8—92no—
160#428—91no—
161#418—91no—
162#417—91no—
163C4×M16—91no—
164C23×D3—62no—
165C2×C3×D4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—62no—
170C2×#67—62no—
171C2×#67—61no—
172C2×#67—61no—
173C22×Dic3—62no—
174D3×D4—64no—
175D3×D4—64no—
176#235—64no—
177#235—64no—
178C2×D12—21no—
179C2×D12—61no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—22no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—128no—
193C2×Dic6—61no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—62no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—61no—
199C3×C42—61no—
200C3×C42—61no—
201#217—62no—
202#217—61no—
203#217—61no—
204(C2×D3)⋊C4—22no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—62no—
210C4⋊Dic3—21no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—62no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218C4×Dic3—21no—
219C4×Dic3—21no—
220C4×Dic3—21no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C22×C32C22×D411yescharacteristic
228C2×C3⋊D3—21no—
229C2×C3⋊D3—21no—
230C2×C3⋊D3C4×D412yes—
231C2×C3×D3—24no—
232C2×C3×D3—22no—
233C2×C3×D3—42no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—42no—
237D32—48no—
238C32×C4—21no—
239C32×C4C4×D412yes—
240C32×C4AGL(1,ℤ/8)12yescomplemented
241C3⋊Dic3—21no—
242C3⋊Dic3—21no—
243C3⋊Dic3C23×C411yescharacteristic
244C3⋊Dic3C2×#4111yescharacteristic
245C3×Dic3—22no—
246C3×Dic3—42no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C2×#41—91no—
250C22×D4—91no—
251C23×C4—181no—
252AGL(1,ℤ/8)—98no—
253C2×SD16—92no—
254C2×D8—92no—
255C2×M16—91no—
256C2×M16—91no—
257C4×Q8—91no—
258C4×Q8—91no—
259C4×D4—61no—
260C4×D4—92no—
261C4×D4—92no—
262C4×D4—91no—
263C4×D4—91no—
264C4×D4—181no—
265C4×D4—181no—
266C4×D4—181no—
267#117—91no—
268#117—181no—
269C2×C4⋊C4—91no—
270C2×C22⋊C4—181no—
271C2×C42—61no—
272C2×C42—91no—
273#107—92no—
274#106—92no—
275#103—92no—
276#102—92no—
277#102—92no—
278#102—92no—
279#97—92no—
280C4×C8—92no—
281C23×C3—61no—
282C23×C3—62no—
283C22×D3—22no—
284C22×D3—21no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—68no—
288C22×D3—124no—
289C22×D3—124no—
290C3×D4—64no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—64no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—62no—
302C2×C3×C4—124no—
303C2×C3×C4—122no—
304C2×C3×C4—122no—
305#67—64no—
306#67—62no—
307#67—64no—
308#67—62no—
309#67—64no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—22no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—124no—
321D12—24no—
322D12—64no—
323C4×D3—24no—
324C4×D3—42no—
325C4×D3—42no—
326C4×D3—44no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—64no—
332C4×D3—122no—
333C4×D3—124no—
334C4×D3—124no—
335C4×D3—122no—
336C4×D3—122no—
337Dic6—62no—
338Dic6—62no—
339C2×C32C2×C4×D411yescharacteristic
340C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C32#57511yescharacteristic
342C3⋊D3—22no—
343C3×D3—44no—
344C3×D3—42no—
345C24—181no—
346#41—94no—
347#41—182no—
348C2×Q8—91no—
349C2×D4—61no—
350C2×D4—94no—
351C2×D4—91no—
352C2×D4—92no—
353C2×D4—181no—
354C2×D4—182no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—62no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—181no—
363C22×C4—182no—
364C22×C4—364no—
365SD16—98no—
366D8—98no—
367M16—94no—
368M16—182no—
369C2×C8—92no—
370C2×C8—92no—
371C4⋊C4—61no—
372C4⋊C4—91no—
373C4⋊C4—91no—
374C4⋊C4—92no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C22⋊C4—62no—
378C22⋊C4—181no—
379C22⋊C4—182no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C42—61no—
383C42—61no—
384C42—61no—
385C42—91no—
386C42—91no—
387C42—91no—
388C42GO+(4,𝔽2)11yescharacteristic
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—62no—
392C22×C3—64no—
393C22×C3—122no—
394C22×C3—121no—
395C22×C3—121no—
396C22×C3—122no—
397C2×D3—22no—
398C2×D3—24no—
399C2×D3—42no—
400C2×D3—41no—
401C2×D3—41no—
402C2×D3—42no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—62no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—1216no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—41no—
416C3×C4—62no—
417C3×C4—122no—
418C3×C4—121no—
419C3×C4—121no—
420Dic3—22no—
421Dic3—42no—
422Dic3—41no—
423Dic3—41no—
424Dic3—61no—
425Dic3—61no—
426Dic3—61no—
427Dic3—61no—
428Dic3—62no—
429Dic3—121no—
430Dic3—121no—
431Dic3—121no—
432C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
433C23—62no—
434C23—61no—
435C23—91no—
436C23—184no—
437C23—362no—
438C23—362no—
439Q8—92no—
440Q8—181no—
441D4—64no—
442D4—92no—
443D4—94no—
444D4—184no—
445D4—182no—
446D4—181no—
447C2×C4—61no—
448C2×C4—64no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—62no—
452C2×C4—91no—
453C2×C4—92no—
454C2×C4—92no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—122no—
458C2×C4—124no—
459C2×C4—122no—
460C2×C4—182no—
461C2×C4—361no—
462C2×C4—362no—
463C2×C4—364no—
464C2×C4C2×GO+(4,𝔽2)11yescharacteristic
465C2×C4C2×GO+(4,𝔽2)11yescharacteristic
466C2×C4C2×GO+(4,𝔽2)11yescharacteristic
467C8—94no—
468C8—182no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—124no—
476C2×C3—122no—
477D3—44no—
478D3—42no—
479D3—64no—
480D3—122no—
481C22—62no—
482C22—64no—
483C22—92no—
484C22—122no—
485C22—121no—
486C22—121no—
487C22—122no—
488C22—181no—
489C22—181no—
490C22—368no—
491C22C22×GO+(4,𝔽2)11yescharacteristic
492C4—21no—
493C4—62no—
494C4—91no—
495C4—91no—
496C4—122no—
497C4—121no—
498C4—121no—
499C4—181no—
500C4—181no—
501C4#6422412yesdirect product factor
502C4C4×GO+(4,𝔽2)12yes—
503C3—21no—
504C3—21no—
505C2—124no—
506C2—122no—
507C2—182no—
508C2C2×#6422411yescharacteristic
509C2#1059649911yescharacteristic
510C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#64224C2
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3802C2semidirect
3. C4×#3798C2semidirect
4. C4×#3788C2semidirect
5. #10593432C2semidirect
6. C4×#3775C2semidirect
7. #10593419C2semidirect
8. C4×#3774C2semidirect
9. #10593394C2semidirect
10. #10593363C2semidirect
11. #10593360C2semidirect
19. #64224C4direct (N × H)
24. C4×#627C22semidirect
25. C4×#627C22semidirect
30. C4×#625C22semidirect
31. C4×#625C22semidirect
36. #63777C22semidirect
37. C4×#622C22semidirect
38. #63743C22semidirect
39. #63742C22semidirect
40. #63740C22semidirect
43. #63739C22semidirect
62. #3802C2×C4semidirect
65. #3798C2×C4semidirect
69. #3788C2×C4semidirect
70. #3775C2×C4semidirect
71. #3774C2×C4semidirect
143. #627C22×C4semidirect
148. #625C22×C4semidirect
152. #622C22×C4semidirect
240. C32×C4AGL(1,ℤ/8)semidirect
432. C32C4×AGL(1,ℤ/8)semidirect
501. C4#64224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642242
C4×#38022
C4×#37982
C4×#37882
#105934322
C4×#37752
#105934192
C4×#37742
#105933942
#105933632
#105933602
C4×AGL(1,ℤ/8)9