Finite Group Databasebeta

← #11867113

Subgroups — #11867113

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C22×#3748C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10592741C212yesmaximal, complemented
7#10592740C212yesmaximal, complemented
8#10592738C212yesmaximal, complemented
9#10592737C212yesmaximal, complemented
10#10592665C211yesmaximal, characteristic, complemented
11#10592663C211yesmaximal, characteristic, complemented
12#82621—34nomaximal
13C22×C32×D4—21no—
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C2×#3828C2211yescharacteristic
17C32×#121—21no—
18C32×#121—21no—
19C32×#121C2212yes—
20C32×#121C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4—21no—
23#64162—21no—
24C2×#3754C2212yescomplemented
25#64141—24no—
26C2×#3753C2212yescomplemented
27#64139C2211yescharacteristic, complemented
28#64139C2211yescharacteristic, complemented
29#64138—21no—
30C4×#638—21no—
31C4×#638—21no—
32#64135C2211yescharacteristic
33#64133C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×#3748—24no—
36C2×#3748C2211yescharacteristic
37C2×#3748C2211yescharacteristic
38C2×#3748C2212yescomplemented
39C22×C3⋊(C3⋊C8)C2212yescomplemented
40#63659C2212yescomplemented
41#63659C2212yescomplemented
42#63637C2212yescomplemented
43#63636C2212yescomplemented
44#63635C2212yescomplemented
45#63634C2212yescomplemented
46C2×C3×#121D314yescomplemented
47C2×#932—34no—
48#5791—34no—
49C22×#208—34no—
50#5215—34no—
51#5042—38no—
52#5041—38no—
53#5039—38no—
54#5038—38no—
55#4966—34no—
56#4964—34no—
57C24×C32—21no—
58C24×C32D411yescharacteristic
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4—22no—
62C2×C32×D4—21no—
63C2×C32×D4—22no—
64C2×C32×D4—44no—
65C2×C32×D4C2312yes—
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4—21no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4D411yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76C2×#638—21no—
77C2×#638—21no—
78#3828—22no—
79#3828—22no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×#634C2311yescharacteristic
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2312yes—
85C32×C22⋊C4—22no—
86C32×C22⋊C4—22no—
87#3757—21no—
88#3757—21no—
89#3757—21no—
90#3754—24no—
91#3753—24no—
92#3752—21no—
93#3752—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96#3750—21no—
97#3750—21no—
98C4×C3⋊Dic3—21no—
99#3748—22no—
100#3748—24no—
101#3748D414yescomplemented
102C2×C3⋊(C3⋊C8)—24no—
103C2×C3⋊(C3⋊C8)C2312yes—
104C2×C3⋊(C3⋊C8)C2312yes—
105#3055—91noSylow
106C22×C3×D4—24no—
107C22×C3×D4C2×D314yes—
108C23×C3×C4C2×D314yes—
109C2×#235—34no—
110C3×#121—24no—
111C3×#121—24no—
112C3×#121C2×D318yes—
113C3×#121C2×D318yes—
114C2×C3×C4⋊C4C2×D314yes—
115C2×C3×C22⋊C4—24no—
116#953—64no—
117C2×#214—38no—
118#932—616no—
119C2×#213—38no—
120#930—34no—
121#930—34no—
122#929—64no—
123C4×#67—64no—
124C4×#67—64no—
125#926—34no—
126#924—34no—
127#924—34no—
128C2×#208—34no—
129C2×#208—34no—
130C2×#208—38no—
131C2×#208—616no—
132C22×C3⋊C8—38no—
133#832—38no—
134#832—38no—
135#810—38no—
136#809—38no—
137#808—38no—
138#807—38no—
139C23×C32—22no—
140C23×C32—22no—
141C23×C32—22no—
142C23×C32—41no—
143C23×C32—42no—
144C23×C32—42no—
145C23×C32—42no—
146C23×C32C2×D411yescharacteristic
147C23×C32C2×D411yescharacteristic
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—21no—
150C32×D4—22no—
151C32×D4—22no—
152C32×D4—44no—
153C32×D4—44no—
154C32×D4—42no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4—42no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4#4112yes—
169C2×C32×C4C2411yescharacteristic
170#638—42no—
171#638—42no—
172#638—42no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—21no—
178C4×C3⋊D3—42no—
179#634—21no—
180#634—21no—
181C3⋊(C3⋊C8)—22no—
182C3⋊(C3⋊C8)C2×D414yescomplemented
183C2×AGL(1,ℤ/8)—91no—
184C22×M16—91no—
185#525—91no—
186C2×#121C3⋊D311yescharacteristic, complemented
187#469—92no—
188#468—92no—
189#466—92no—
190#465—92no—
191#428—91no—
192#418—91no—
193#417—91no—
194C24×C3—24no—
195C24×C3#6714yes—
196C2×C3×D4—28no—
197C2×C3×D4—28no—
198C2×C3×D4—28no—
199C2×C3×D4—28no—
200C2×C3×D4—24no—
201C2×C3×D4—416no—
202C2×C3×D4C22×D318yes—
203C22×C3×C4—28no—
204C22×C3×C4—28no—
205C22×C3×C4—24no—
206C22×C3×C4#6714yes—
207C22×C3×C4#6714yes—
208C22×C3×C4#6714yes—
209C22×C3×C4C22×D314yes—
210C22×C3×C4C22×D314yes—
211C22×C3×C4C22×D314yes—
212C2×#67—64no—
213C2×#67—64no—
214C2×#67—64no—
215#235—68no—
216#235—68no—
217C2×D12—34no—
218C2×C4×D3—64no—
219C2×Dic6—34no—
220C3×C4⋊C4—24no—
221C3×C4⋊C4C22×D318yes—
222C3×C22⋊C4—28no—
223C3×C22⋊C4—28no—
224#217—64no—
225#217—64no—
226#217—64no—
227#214—616no—
228#213—616no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—34no—
232C4⋊Dic3—34no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235C4×Dic3—64no—
236#208—316no—
237#208—616no—
238#208—68no—
239C2×C3⋊C8—38no—
240C2×C3⋊C8—38no—
241C2×C3⋊C8—616no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—44no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—84no—
254C22×C32#12112yes—
255C22×C32AGL(1,ℤ/8)12yescomplemented
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—41no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3—41no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—42no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—41no—
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C2×#41—91no—
270C22×D4—21no—
271C22×D4C2×C3⋊D311yescharacteristic
272C23×C4C2×C3⋊D311yescharacteristic
273AGL(1,ℤ/8)—184no—
274C2×SD16—92no—
275C2×D8—92no—
276C2×M16—91no—
277C2×M16—91no—
278C2×M16—92no—
279C2×M16—184no—
280C22×C8—92no—
281#123—181no—
282C22⋊Q8—91no—
283C22⋊Q8—91no—
284#121—21no—
285#121—21no—
286#121—91no—
287#121—91no—
288#121C2×C3⋊D312yes—
289#121C2×C3⋊D312yes—
290#120—181no—
291C4×D4—181no—
292C4×D4—181no—
293#117—91no—
294C2×C4⋊C4C2×C3⋊D311yescharacteristic
295C2×C22⋊C4—21no—
296#107—92no—
297#106—92no—
298#103—92no—
299#102—92no—
300#102—92no—
301#102—92no—
302C23×C3—28no—
303C23×C3—28no—
304C23×C3—28no—
305C23×C3—44no—
306C23×C3—48no—
307C23×C3—48no—
308C23×C3—48no—
309C23×C3C2×#6714yes—
310C23×C3C2×#6714yes—
311C23×C3C2×#6714yes—
312C22×D3—64no—
313C3×D4—28no—
314C3×D4—28no—
315C3×D4—416no—
316C3×D4—416no—
317C3×D4—48no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—28no—
321C2×C3×C4—24no—
322C2×C3×C4—24no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—28no—
326C2×C3×C4—48no—
327C2×C3×C4D3×D418yes—
328C2×C3×C4#23718yes—
329C2×C3×C4C2×#6714yes—
330C2×C3×C4C2×#6714yes—
331C2×C3×C4C2×#6714yes—
332C2×C3×C4C23×D314yes—
333#67—128no—
334#67—128no—
335#67—128no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339D12—64no—
340D12—64no—
341C4×D3—128no—
342Dic6—64no—
343Dic6—64no—
344C3⋊C8—316no—
345C3⋊C8—68no—
346C2×C32—22no—
347C2×C32—22no—
348C2×C32—41no—
349C2×C32—82no—
350C2×C32C2×#12111yescharacteristic
351C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
352C2×C32#57511yescharacteristic
353C3⋊D3—81no—
354C24—21no—
355C24#63811yescharacteristic
356#41—182no—
357#41—182no—
358C2×Q8—91no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—44no—
365C2×D4—91no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4C22×C3⋊D312yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—181no—
374C22×C4#63811yescharacteristic
375C22×C4#63811yescharacteristic
376C22×C4#63811yescharacteristic
377C22×C4C22×C3⋊D311yescharacteristic
378C22×C4C22×C3⋊D311yescharacteristic
379C22×C4C22×C3⋊D311yescharacteristic
380SD16—184no—
381D8—184no—
382M16—94no—
383M16—184no—
384M16—182no—
385C2×C8—92no—
386C2×C8—92no—
387C2×C8—184no—
388C4⋊C4—21no—
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4C22×C3⋊D312yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C42—181no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3—24no—
406C22×C3—24no—
407C22×C3—24no—
408C22×C3—24no—
409C22×C3—416no—
410C22×C3—48no—
411C22×C3—48no—
412C22×C3—48no—
413C22×C3—816no—
414C22×C3#93218yescomplemented
415C22×C3#93918yes—
416C22×C3C22×#6714yes—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—124no—
420C3×C4—24no—
421C3×C4—24no—
422C3×C4—48no—
423C3×C4#93918yes—
424C3×C4C2×D3×D414yes—
425C3×C4C2×#23714yes—
426Dic3—124no—
427Dic3—124no—
428Dic3—124no—
429C32#305511yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—181no—
438C23C2×#63811yescharacteristic
439C23C2×#63811yescharacteristic
440C23C2×#63811yescharacteristic
441Q8—181no—
442Q8—181no—
443D4—22no—
444D4—22no—
445D4—44no—
446D4—44no—
447D4—42no—
448D4—181no—
449D4—181no—
450D4—362no—
451D4—362no—
452D4—362no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—362no—
466C2×C4D4×C3⋊D312yes—
467C2×C4#383012yes—
468C2×C4C2×#63811yescharacteristic
469C2×C4C2×#63811yescharacteristic
470C2×C4C2×#63811yescharacteristic
471C2×C4C23×C3⋊D311yescharacteristic
472C8—94no—
473C8—182no—
474C2×C3—28no—
475C2×C3—28no—
476C2×C3—44no—
477C2×C3—88no—
478C2×C3C2×#93214yes—
479C2×C3C2×#93914yes—
480C2×C3#582214yes—
481D3—244no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—44no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—84no—
494C22—361no—
495C22—361no—
496C22—361no—
497C22#6414112yescomplemented
498C22#6414812yes—
499C22C22×#63811yescharacteristic
500C4—21no—
501C4—21no—
502C4—42no—
503C4—361no—
504C4—361no—
505C4—361no—
506C4#6414812yes—
507C4C2×D4×C3⋊D311yescharacteristic
508C4C2×#383011yescharacteristic
509C3#8262114yescomplemented
510C2—22no—
511C2—22no—
512C2—41no—
513C2—82no—
514C2—721no—
515C2C2×#6414111yescharacteristic
516C2C2×#6414811yescharacteristic
517C2#1059629311yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#121C2
socleC22×C32C22×D4
hypercenterC2×#121C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×#64141C2semidirect
3. #10596262C2semidirect
4. C22×#3748C2semidirect
5. #10592914C2semidirect
6. #10592741C2semidirect
7. #10592740C2semidirect
8. #10592738C2semidirect
9. #10592737C2semidirect
10. #10592665C2semidirect
11. #10592663C2semidirect
24. C2×#3754C22semidirect
26. C2×#3753C22semidirect
27. #64139C22semidirect
28. #64139C22semidirect
33. #64133C22semidirect
34. #64133C22semidirect
38. C2×#3748C22semidirect
39. C22×C3⋊(C3⋊C8)C22semidirect
40. #63659C22semidirect
41. #63659C22semidirect
42. #63637C22semidirect
43. #63636C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
46. C2×C3×#121D3semidirect
101. #3748D4semidirect
182. C3⋊(C3⋊C8)C2×D4semidirect
186. C2×#121C3⋊D3semidirect
255. C22×C32AGL(1,ℤ/8)semidirect
414. C22×C3#932semidirect
429. C32#3055semidirect
497. C22#64141semidirect
509. C3#82621semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#641412
#105962622
C22×#37482
#105929142
#105927412
#105927402
#105927382
#105927372
#105926652
#105926632
#826213