Finite Group Databasebeta

← #11864552

Subgroups — #11864552

Order 1152.

2292 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×C32×#135C211yesmaximal, characteristic, complemented
3#10596304C211yesmaximal, characteristic, complemented
4C2×#64158C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10592886C212yesmaximal, complemented
7#10592871C212yesmaximal, complemented
8#10592868C212yesmaximal, complemented
9#10592855C212yesmaximal, complemented
10C2×#63648C211yesmaximal, characteristic, complemented
11#10592809C211yesmaximal, characteristic, complemented
12#83912—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×C32×#41C2211yescharacteristic, complemented
15#64366—24no—
16#64366—24no—
17C2×#3832C2212yes—
18C2×D4×C3⋊D3—22no—
19C2×D4×C3⋊D3C2212yes—
20C2×#3828—21no—
21C2×#3828C2211yescharacteristic
22C22×C4⋊(C3⋊D3)—21no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C32×#135—24no—
25C2×C32×Q16C2211yescharacteristic, complemented
26C2×C32×SD16C2211yescharacteristic, complemented
27C2×C32×SD16C2211yescharacteristic, complemented
28C2×C32×D8C2211yescharacteristic, complemented
29C22×C32×C8C2211yescharacteristic, complemented
30#64158—24no—
31#64155C2212yescomplemented
32C2×#3755C2212yescomplemented
33#64148—22no—
34#64147C2212yescomplemented
35C2×#3753C2212yescomplemented
36#64139—21no—
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38#64133—21no—
39C2×#3748C2211yescharacteristic, complemented
40#63662C2212yescomplemented
41#63659C2212yescomplemented
42#63648C2212yescomplemented
43#63648C2212yescomplemented
44#63647C2212yescomplemented
45#63647C2212yescomplemented
46C2×#1009—34no—
47C2×C3×#135D314yescomplemented
48#5833—34no—
49C2×#949—34no—
50#5232—34no—
51#5187—38no—
52#5172—38no—
53#5169—38no—
54#5156—38no—
55C2×#821—34no—
56#5110—34no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3—22no—
59C32×#41—22no—
60C32×#41—22no—
61C32×#41—22no—
62C32×#41D414yescomplemented
63C2×C32×Q8C2311yescharacteristic
64C2×C32×Q8C2311yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4C2311yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×#638—22no—
73C2×#638—22no—
74C2×#638D412yes—
75C22×C3⋊Dic3—21no—
76#3832—24no—
77#3832—24no—
78D4×C3⋊D3—216no—
79D4×C3⋊D3—24no—
80D4×C3⋊D3—24no—
81#3828—28no—
82#3828—22no—
83#3828—22no—
84C2×C4⋊(C3⋊D3)—28no—
85C2×C4⋊(C3⋊D3)—22no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)—22no—
88C2×C4⋊(C3⋊D3)D411yescharacteristic
89C2×C4⋊(C3⋊D3)D414yescomplemented
90C2×C4⋊(C3⋊D3)C2312yes—
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3C2312yes—
93C2×#634D411yescharacteristic
94C32×Q16—22no—
95C32×SD16—22no—
96C32×SD16—22no—
97C32×D8—22no—
98C2×C32×C8—22no—
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101#3757—22no—
102#3755—24no—
103#3753—24no—
104#3752—22no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2312yes—
107#3750—22no—
108#3748—22no—
109C2×C3⋊(C3⋊C8)C2312yes—
110#3012—91noSylow
111C2×C3×#41C2×D314yes—
112C2×C3×#41C2×D314yescomplemented
113#1009—616no—
114#1009—616no—
115C2×#239—38no—
116C2×D3×D4—38no—
117C2×D3×D4—68no—
118C2×#235—34no—
119C2×#235—64no—
120C22×D12—34no—
121C22×D12—64no—
122C3×#135—216no—
123C2×C3×Q16C2×D314yescomplemented
124C2×C3×SD16C2×D314yescomplemented
125C2×C3×SD16C2×D314yescomplemented
126C2×C3×D8C2×D314yescomplemented
127C22×C3×C8C2×D314yescomplemented
128#949—616no—
129#946—38no—
130C2×#215—38no—
131#939—68no—
132#938—38no—
133C2×#213—38no—
134#930—64no—
135C2×C4⋊Dic3—34no—
136#924—64no—
137C2×#208—34no—
138#835—38no—
139#832—38no—
140#821—38no—
141#821—38no—
142(C2×D3)⋊C8—38no—
143(C2×D3)⋊C8—38no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—28no—
149C22×C3⋊D3—24no—
150C22×C3⋊D3—82no—
151C22×C3⋊D3—82no—
152C22×C3⋊D3—81no—
153C22×C3⋊D3—81no—
154C22×C3⋊D3C2×D412yes—
155C32×Q8—21no—
156C32×Q8—21no—
157C32×Q8—21no—
158C32×Q8C2×D412yes—
159C32×D4—24no—
160C32×D4—21no—
161C32×D4—21no—
162C32×D4—21no—
163C32×D4—42no—
164C32×D4C2×D412yes—
165C2×C32×C4—21no—
166C2×C32×C4—24no—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2411yescharacteristic
173#638—28no—
174#638—24no—
175#638—82no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—81no—
178C2×C3⋊Dic3C2×D412yes—
179C4⋊(C3⋊D3)—28no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—24no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)C2×D414yes—
184C4×C3⋊D3—28no—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—22no—
187#634—22no—
188C32×C8—21no—
189C32×C8—21no—
190C3⋊(C3⋊C8)—22no—
191C2×H(5,𝔽2)—91no—
192C2×AGL(1,ℤ/8)—91no—
193C2×#135C3⋊D311yescharacteristic, complemented
194#537—91no—
195#452—92no—
196#450—92no—
197#449—92no—
198#447—92no—
199#417—91no—
200C2×#102—91no—
201#408—91no—
202C23×D3—68no—
203C23×D3—64no—
204C3×#41—28no—
205C3×#41—28no—
206C3×#41—28no—
207C3×#41#67116yescomplemented
208C2×C3×Q8C22×D314yes—
209C2×C3×Q8C22×D314yes—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4C22×D314yes—
213C2×C3×D4C22×D314yes—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4C22×D314yes—
217C2×#67—38no—
218C2×#67—68no—
219C2×#67—68no—
220C22×Dic3—64no—
221#239—616no—
222#239—616no—
223D3×D4—616no—
224D3×D4—664no—
225D3×D4—616no—
226#235—632no—
227#235—68no—
228#235—68no—
229C2×D12—316no—
230C2×D12—38no—
231C2×D12—34no—
232C2×D12—68no—
233C2×D12—632no—
234C2×D12—64no—
235C2×D12—68no—
236C2×C4×D3—38no—
237C2×C4×D3—68no—
238C2×Dic6—34no—
239C3×Q16—28no—
240C3×SD16—28no—
241C3×SD16—28no—
242C3×D8—28no—
243C2×C3×C8—28no—
244C2×C3×C8C22×D314yes—
245C2×C3×C8C22×D314yes—
246#217—68no—
247#215—616no—
248#213—616no—
249(C2×D3)⋊C4—68no—
250C4⋊Dic3—38no—
251C4⋊Dic3—64no—
252Dic3⋊C4—68no—
253#208—68no—
254C2×C3⋊C8—38no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—22no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32#12012yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—22no—
266C2×C3⋊D3—24no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—84no—
272C2×C3⋊D3—88no—
273C32×C4—22no—
274C32×C4—41no—
275C32×C4#12012yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C22×D411yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280H(5,𝔽2)—184no—
281H(5,𝔽2)—184no—
282C2×#41—91no—
283C2×#41—92no—
284C2×#41—181no—
285C2×#41C2×C3⋊D311yescharacteristic
286C2×#41C2×C3⋊D311yescharacteristic, complemented
287C22×D4—92no—
288C22×D4—91no—
289C22×D4—181no—
290C22×D4—182no—
291AGL(1,ℤ/8)—184no—
292#135—24no—
293C2×Q16C2×C3⋊D311yescharacteristic, complemented
294C2×SD16—92no—
295C2×SD16C2×C3⋊D311yescharacteristic, complemented
296C2×SD16C2×C3⋊D311yescharacteristic, complemented
297C2×D8—92no—
298C2×D8C2×C3⋊D311yescharacteristic, complemented
299C2×M16—91no—
300C22×C8C2×C3⋊D311yescharacteristic, complemented
301C22⋊Q8—92no—
302C22⋊Q8—181no—
303#121—92no—
304#121—181no—
305#121—182no—
306C2×C4⋊C4—91no—
307#103—92no—
308#102—92no—
309#102—92no—
310#102—92no—
311C22⋊C8—92no—
312C22⋊C8—92no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3D3×D414yes—
316C22×D3—38no—
317C22×D3—68no—
318C22×D3—632no—
319C22×D3—616no—
320C22×D3—248no—
321C22×D3—248no—
322C22×D3—244no—
323C22×D3—244no—
324C3×Q8—24no—
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8C2×#6718yes—
328C3×D4—216no—
329C3×D4—24no—
330C3×D4—24no—
331C3×D4—24no—
332C3×D4—48no—
333C3×D4C2×#6718yes—
334C2×C3×C4—24no—
335C2×C3×C4—216no—
336C2×C3×C4—24no—
337C2×C3×C4—48no—
338C2×C3×C4D3×D414yes—
339C2×C3×C4D3×D418yes—
340C2×C3×C4C2×#6718yes—
341C2×C3×C4C23×D314yes—
342#67—632no—
343#67—616no—
344#67—248no—
345C2×Dic3—38no—
346C2×Dic3—68no—
347C2×Dic3—244no—
348D12—316no—
349D12—632no—
350D12—616no—
351D12—68no—
352D12—68no—
353C4×D3—632no—
354C4×D3—68no—
355C4×D3—68no—
356Dic6—68no—
357C3×C8—24no—
358C3×C8—24no—
359C3⋊C8—68no—
360C2×C32—22no—
361C2×C32—42no—
362C2×C32—81no—
363C2×C32C2×#12011yescharacteristic
364C2×C32#57611yescharacteristic
365C2×C32#57711yescharacteristic
366C3⋊D3—42no—
367C3⋊D3—44no—
368C24—182no—
369C24—181no—
370#41—22no—
371#41—22no—
372#41—22no—
373#41—188no—
374#41—184no—
375#41—184no—
376#41—182no—
377#41—182no—
378#41#63814yescomplemented
379C2×Q8—91no—
380C2×Q8C22×C3⋊D311yescharacteristic
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—92no—
385C2×D4—92no—
386C2×D4—94no—
387C2×D4—91no—
388C2×D4—182no—
389C2×D4—188no—
390C2×D4—182no—
391C2×D4—184no—
392C2×D4—1816no—
393C2×D4—184no—
394C2×D4—182no—
395C2×D4—181no—
396C2×D4—182no—
397C2×D4C22×C3⋊D311yescharacteristic
398C2×D4C22×C3⋊D311yescharacteristic
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—92no—
402C22×C4—182no—
403C22×C4—181no—
404C22×C4C22×C3⋊D311yescharacteristic
405Q16—22no—
406SD16—22no—
407SD16—22no—
408SD16—184no—
409D8—22no—
410D8—184no—
411M16—182no—
412C2×C8—22no—
413C2×C8—92no—
414C2×C8C22×C3⋊D311yescharacteristic
415C2×C8C22×C3⋊D311yescharacteristic
416C4⋊C4—92no—
417C4⋊C4—182no—
418C4⋊C4—181no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22×C3—24no—
422C22×C3—24no—
423C22×C3—28no—
424C22×C3—44no—
425C22×C3—44no—
426C22×C3—44no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3#93718yes—
430C22×C3C2×D3×D414yes—
431C2×D3—68no—
432C2×D3—68no—
433C2×D3—616no—
434C2×D3—68no—
435C2×D3—128no—
436C2×D3—128no—
437C2×D3—2416no—
438C2×D3—2432no—
439C3×C4—28no—
440C3×C4—44no—
441C3×C4#93718yes—
442C3×C4C2×D3×D414yes—
443C3×C4C22×#6714yes—
444Dic3—68no—
445Dic3—128no—
446C32#301211yescharacteristic, complemented, Sylow
447C23—21no—
448C23—21no—
449C23—92no—
450C23—188no—
451C23—182no—
452C23—184no—
453C23—721no—
454C23—721no—
455C23—722no—
456C23—722no—
457C23D4×C3⋊D311yescharacteristic
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8—182no—
462Q8C2×#63812yes—
463D4—24no—
464D4—21no—
465D4—21no—
466D4—21no—
467D4—42no—
468D4—94no—
469D4—188no—
470D4—188no—
471D4—184no—
472D4—182no—
473D4—184no—
474D4—182no—
475D4—722no—
476D4C2×#63812yes—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—92no—
482C2×C4—188no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—721no—
487C2×C4D4×C3⋊D312yes—
488C2×C4D4×C3⋊D311yescharacteristic
489C2×C4C2×#63812yes—
490C2×C4C23×C3⋊D311yescharacteristic
491C8—21no—
492C8—21no—
493C8—182no—
494C2×C3—28no—
495C2×C3—48no—
496C2×C3—84no—
497C2×C3#576914yes—
498C2×C3#577014yes—
499C2×C3C2×#93714yes—
500D3—128no—
501D3—1216no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—182no—
511C22—182no—
512C22—184no—
513C22—182no—
514C22—362no—
515C22—362no—
516C22—724no—
517C22—728no—
518C22#6414612yes—
519C22C2×D4×C3⋊D311yescharacteristic
520C4—22no—
521C4—41no—
522C4—182no—
523C4—362no—
524C4#6414612yes—
525C4C2×D4×C3⋊D311yescharacteristic
526C4C22×#63811yescharacteristic
527C3#8391214yescomplemented
528C2—22no—
529C2—42no—
530C2—81no—
531C2—362no—
532C2—364no—
533C2#1059624011yescharacteristic
534C2#1059624111yescharacteristic
535C2C2×#6414611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×#135C3⋊D3
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×C32×#135C2semidirect
3. #10596304C2semidirect
4. C2×#64158C2semidirect
5. #10592931C2semidirect
6. #10592886C2semidirect
7. #10592871C2semidirect
8. #10592868C2semidirect
9. #10592855C2semidirect
10. C2×#63648C2semidirect
11. #10592809C2semidirect
14. C2×C32×#41C22semidirect
25. C2×C32×Q16C22semidirect
26. C2×C32×SD16C22semidirect
27. C2×C32×SD16C22semidirect
28. C2×C32×D8C22semidirect
29. C22×C32×C8C22semidirect
31. #64155C22semidirect
32. C2×#3755C22semidirect
34. #64147C22semidirect
35. C2×#3753C22semidirect
37. C2×C4⋊(C3⋊Dic3)C22semidirect
39. C2×#3748C22semidirect
40. #63662C22semidirect
41. #63659C22semidirect
42. #63648C22semidirect
43. #63648C22semidirect
44. #63647C22semidirect
45. #63647C22semidirect
47. C2×C3×#135D3semidirect
62. C32×#41D4semidirect
89. C2×C4⋊(C3⋊D3)D4semidirect
112. C2×C3×#41C2×D3semidirect
123. C2×C3×Q16C2×D3semidirect
124. C2×C3×SD16C2×D3semidirect
125. C2×C3×SD16C2×D3semidirect
126. C2×C3×D8C2×D3semidirect
127. C22×C3×C8C2×D3semidirect
193. C2×#135C3⋊D3semidirect
207. C3×#41#67semidirect
286. C2×#41C2×C3⋊D3semidirect
293. C2×Q16C2×C3⋊D3semidirect
295. C2×SD16C2×C3⋊D3semidirect
296. C2×SD16C2×C3⋊D3semidirect
298. C2×D8C2×C3⋊D3semidirect
300. C22×C8C2×C3⋊D3semidirect
378. #41#638semidirect
446. C32#3012semidirect
527. C3#83912semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×C32×#1352
#105963042
C2×#641582
#105929312
#105928862
#105928712
#105928682
#105928552
C2×#636482
#105928092
#839123