Finite Group Databasebeta

← #11864579

Subgroups — #11864579

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×#64361C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3C2×#64113C211yesmaximal, characteristic, complemented
4#10595981C211yesmaximal, characteristic, complemented
5C2×C32×#102C211yesmaximal, characteristic, complemented
6#10592809C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592482C212yesmaximal, complemented
9#10592480C212yesmaximal, complemented
10#10592475C212yesmaximal, complemented
11#10592472C212yesmaximal, complemented
12#78747—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638—22no—
15#64361—24no—
16#64361—24no—
17C2×#3830—21no—
18C2×#3830C2212yes—
19C2×D4×C3⋊D3—21no—
20C2×D4×C3⋊D3C2212yes—
21C2×#3828C2211yescharacteristic
22C2×#3828C2211yescharacteristic
23C2×#3828C2211yescharacteristic, complemented
24C22×C32×C8C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3754C2212yescomplemented
27#64141—24no—
28C2×#3753C2212yescomplemented
29#64139—22no—
30C2×#3748C2211yescharacteristic, complemented
31C2×#3746C2211yescharacteristic, complemented
32#64113—24no—
33C2×#3745C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C2×#3744C2211yescharacteristic, complemented
36#64106—21no—
37#64106C2212yescomplemented
38#64104—21no—
39#64104C2212yescomplemented
40C32×#102C2212yescomplemented
41C32×#102C2212yescomplemented
42#63647C2212yescomplemented
43#63647C2212yescomplemented
44#63637C2212yescomplemented
45#63636C2212yescomplemented
46C2×#1004—34no—
47C2×#932—34no—
48C2×#904—34no—
49#5510—34no—
50C2×C3×#102D314yescomplemented
51#5110—34no—
52#4966—34no—
53#4783—38no—
54#4781—38no—
55#4776—38no—
56#4773—38no—
57C24×C32—21no—
58C23×C3⋊D3—22no—
59C2×C32×D4—21no—
60C2×C32×D4—22no—
61C2×C32×D4D414yescomplemented
62C2×C32×D4C2312yes—
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×#638—216no—
66C2×#638—21no—
67C2×#638—22no—
68C2×#638—21no—
69C2×#638—22no—
70C2×#638D412yes—
71C22×C3⋊Dic3—22no—
72#3830—28no—
73#3830—24no—
74#3830—24no—
75D4×C3⋊D3—28no—
76D4×C3⋊D3—24no—
77D4×C3⋊D3—24no—
78#3828—22no—
79#3828—22no—
80#3828—22no—
81#3828—22no—
82#3828—22no—
83#3828D414yescomplemented
84C2×C4⋊(C3⋊D3)—22no—
85C2×C4⋊(C3⋊D3)D411yescharacteristic
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2312yes—
91C2×#634D411yescharacteristic
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C32×C8—22no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2312yes—
99#3754—24no—
100#3753—24no—
101#3752—22no—
102#3752—22no—
103C4⋊(C3⋊Dic3)—22no—
104#3748—22no—
105C2×C3⋊(C3⋊C8)C2312yes—
106#3746—22no—
107#3745—22no—
108#3744—22no—
109#3744—22no—
110#3012—91noSylow
111C22×C3×D4C2×D314yes—
112C22×#67—68no—
113#1004—616no—
114#1004—616no—
115C2×#237—38no—
116C2×#237—64no—
117C2×D3×D4—38no—
118C2×D3×D4—64no—
119C2×#235—34no—
120C2×#235—34no—
121C2×#235—34no—
122C22×C3×C8C2×D314yescomplemented
123C2×C3×C4⋊C4C2×D314yescomplemented
124C2×#214—38no—
125#932—616no—
126C2×#213—38no—
127#930—68no—
128C2×#208—34no—
129C2×Dic12—34no—
130#904—616no—
131C2×D24—34no—
132C2×#204—34no—
133C2×#204—34no—
134#897—38no—
135#897—64no—
136#895—38no—
137#895—64no—
138C3×#102C2×D318yescomplemented
139C3×#102C2×D318yescomplemented
140(C2×D3)⋊C8—38no—
141(C2×D3)⋊C8—38no—
142#810—38no—
143#809—38no—
144C23×C32—22no—
145C23×C32—24no—
146C23×C32—81no—
147C23×C32—81no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—21no—
150C22×C3⋊D3—28no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—82no—
153C22×C3⋊D3—82no—
154C22×C3⋊D3C2×D412yes—
155C32×D4—24no—
156C32×D4—22no—
157C32×D4C2×D414yes—
158C2×C32×C4—22no—
159C2×C32×C4—81no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164#638—28no—
165#638—28no—
166#638—24no—
167#638—24no—
168#638—42no—
169C2×C3⋊Dic3—28no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C2×D412yes—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—82no—
178C4⋊(C3⋊D3)C2×D412yes—
179C4×C3⋊D3—24no—
180C4×C3⋊D3—22no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3—42no—
183#634—22no—
184#634—21no—
185#634—21no—
186#634—21no—
187#634C2×D412yes—
188C32×C8—21no—
189C32×C8—21no—
190C3⋊(C3⋊C8)—22no—
191C2×H(5,𝔽2)—91no—
192C2×AGL(1,ℤ/8)—91no—
193C2×#135—91no—
194#537—91no—
195#452—92no—
196#450—92no—
197#449—92no—
198#447—92no—
199#417—91no—
200C2×#102C3⋊D311yescharacteristic, complemented
201#408—91no—
202C24×C3—24no—
203C23×D3—68no—
204C2×C3×D4—24no—
205C2×C3×D4—28no—
206C2×C3×D4D12116yescomplemented
207C2×C3×D4C22×D318yes—
208C22×C3×C4—24no—
209C22×C3×C4C22×D314yes—
210C2×#67—38no—
211C2×#67—68no—
212C2×#67—68no—
213C2×#67—664no—
214C2×#67—64no—
215C2×#67—64no—
216C22×Dic3—68no—
217#237—616no—
218#237—632no—
219#237—616no—
220D3×D4—616no—
221D3×D4—632no—
222D3×D4—616no—
223#235—316no—
224#235—68no—
225#235—68no—
226#235—68no—
227#235—68no—
228#235—68no—
229C2×D12—34no—
230C2×D12—34no—
231C2×D12—34no—
232C2×D12—68no—
233C2×C4×D3—38no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—34no—
239C2×C3×C8—28no—
240C2×C3×C8C22×D314yes—
241C2×C3×C8C22×D314yes—
242C3×C4⋊C4—24no—
243C3×C4⋊C4C22×D318yes—
244#214—616no—
245#213—616no—
246(C2×D3)⋊C4—68no—
247(C2×D3)⋊C4—68no—
248C4⋊Dic3—68no—
249#208—68no—
250C2×C3⋊C8—38no—
251Dic12—68no—
252D24—68no—
253#204—68no—
254#204—68no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—24no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—84no—
261C22×C32#12012yes—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C2×C3⋊D3—41no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—88no—
273C32×C4—42no—
274C32×C4#12012yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C22×D411yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3⋊Dic3—41no—
280H(5,𝔽2)—184no—
281H(5,𝔽2)—184no—
282C2×#41—91no—
283C2×#41—92no—
284C2×#41—91no—
285C2×#41—91no—
286C2×#41—181no—
287C22×D4—92no—
288C22×D4—181no—
289C22×D4—182no—
290C22×D4C2×C3⋊D311yescharacteristic
291AGL(1,ℤ/8)—184no—
292#135—184no—
293C2×Q16—91no—
294C2×SD16—92no—
295C2×SD16—91no—
296C2×SD16—91no—
297C2×D8—92no—
298C2×D8—91no—
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⋊C4C2×C3⋊D311yescharacteristic, complemented
307#103—92no—
308#102—92no—
309#102C2×C3⋊D312yescomplemented
310#102C2×C3⋊D312yescomplemented
311C22⋊C8—92no—
312C22⋊C8—92no—
313C23×C3—28no—
314C23×C3—216no—
315C23×C3—84no—
316C23×C3—84no—
317C23×C3D3×D414yes—
318C22×D3—38no—
319C22×D3—64no—
320C22×D3—632no—
321C22×D3—64no—
322C22×D3—248no—
323C22×D3—248no—
324C3×D4—216no—
325C3×D4—28no—
326C3×D4C2×D12116yes—
327C2×C3×C4—28no—
328C2×C3×C4—84no—
329C2×C3×C4C2×D1218yes—
330C2×C3×C4D3×D414yes—
331C2×C3×C4D3×D418yes—
332C2×C3×C4C23×D314yes—
333#67—632no—
334#67—632no—
335#67—616no—
336#67—616no—
337#67—128no—
338C2×Dic3—38no—
339C2×Dic3—632no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342D12—38no—
343D12—68no—
344D12—64no—
345D12—64no—
346D12—64no—
347D12—248no—
348C4×D3—616no—
349C4×D3—68no—
350C4×D3—68no—
351C4×D3—128no—
352Dic6—38no—
353Dic6—68no—
354Dic6—64no—
355Dic6—64no—
356Dic6—64no—
357C3×C8—24no—
358C3×C8—24no—
359C3⋊C8—68no—
360C2×C32—22no—
361C2×C32—44no—
362C2×C32C2×#12011yescharacteristic
363C2×C32#57611yescharacteristic
364C2×C32#57711yescharacteristic
365C3⋊D3—42no—
366C3⋊D3—42no—
367C3⋊D3—81no—
368C24—21no—
369C24—182no—
370#41—94no—
371#41—184no—
372#41—188no—
373#41—184no—
374#41—182no—
375#41—182no—
376#41—182no—
377#41—182no—
378#41—182no—
379C2×Q8—91no—
380C2×Q8—91no—
381C2×Q8—91no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—92no—
385C2×D4—91no—
386C2×D4—91no—
387C2×D4—91no—
388C2×D4—182no—
389C2×D4—182no—
390C2×D4—184no—
391C2×D4—188no—
392C2×D4—182no—
393C2×D4—1816no—
394C2×D4—181no—
395C2×D4—184no—
396C2×D4—181no—
397C2×D4C4⋊(C3⋊D3)14yescomplemented
398C2×D4C22×C3⋊D312yes—
399C22×C4—21no—
400C22×C4—92no—
401C22×C4—182no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4C22×C3⋊D311yescharacteristic
405Q16—182no—
406SD16—182no—
407SD16—182no—
408SD16—184no—
409D8—182no—
410D8—184no—
411M16—182no—
412C2×C8—22no—
413C2×C8—92no—
414C2×C8C22×C3⋊D311yescharacteristic
415C2×C8C22×C3⋊D311yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—182no—
418C4⋊C4C22×C3⋊D312yes—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22×C3—24no—
422C22×C3—24no—
423C22×C3—216no—
424C22×C3—48no—
425C22×C3—48no—
426C22×C3—816no—
427C22×C3#88218yes—
428C22×C3C2×D3×D414yes—
429C2×D3—68no—
430C2×D3—68no—
431C2×D3—68no—
432C2×D3—68no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—2432no—
439C3×C4—48no—
440C3×C4#88218yes—
441C3×C4C22×D1214yes—
442C3×C4C2×D3×D414yes—
443Dic3—68no—
444Dic3—68no—
445Dic3—124no—
446C32#301211yescharacteristic, complemented, Sylow
447C23—22no—
448C23—24no—
449C23—81no—
450C23—81no—
451C23—92no—
452C23—188no—
453C23—181no—
454C23—181no—
455C23—722no—
456C23—722no—
457C23D4×C3⋊D311yescharacteristic
458Q8—92no—
459Q8—182no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463D4—24no—
464D4—22no—
465D4—92no—
466D4—188no—
467D4—188no—
468D4—184no—
469D4—184no—
470D4—182no—
471D4—181no—
472D4—181no—
473D4—181no—
474D4—362no—
475D4—722no—
476D4C2×C4⋊(C3⋊D3)14yes—
477C2×C4—22no—
478C2×C4—81no—
479C2×C4—92no—
480C2×C4—188no—
481C2×C4—181no—
482C2×C4—184no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—181no—
486C2×C4—362no—
487C2×C4C2×C4⋊(C3⋊D3)12yes—
488C2×C4D4×C3⋊D311yescharacteristic
489C2×C4D4×C3⋊D312yes—
490C2×C4C23×C3⋊D311yescharacteristic
491C8—21no—
492C8—21no—
493C8—182no—
494C2×C3—28no—
495C2×C3—416no—
496C2×C3C2×#88214yes—
497C2×C3#575714yes—
498C2×C3#576214yes—
499D3—128no—
500D3—128no—
501D3—244no—
502C22—21no—
503C22—21no—
504C22—24no—
505C22—42no—
506C22—42no—
507C22—84no—
508C22—182no—
509C22—182no—
510C22—182no—
511C22—182no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22—728no—
518C22#6409112yes—
519C22C2×D4×C3⋊D311yescharacteristic
520C4—42no—
521C4—182no—
522C4—182no—
523C4—361no—
524C4#6409112yes—
525C4C22×C4⋊(C3⋊D3)11yescharacteristic
526C4C2×D4×C3⋊D311yescharacteristic
527C3#7874714yescomplemented
528C2—22no—
529C2—44no—
530C2—362no—
531C2—362no—
532C2—721no—
533C2C2×#6409111yescharacteristic
534C2#1059622811yescharacteristic
535C2#1059623311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC22×C32C22×D4
hypercenterC2×#102C3⋊D3
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64141C2semidirect
3. C2×#64113C2semidirect
4. #10595981C2semidirect
5. C2×C32×#102C2semidirect
6. #10592809C2semidirect
7. #10592665C2semidirect
8. #10592482C2semidirect
9. #10592480C2semidirect
10. #10592475C2semidirect
11. #10592472C2semidirect
23. C2×#3828C22semidirect
24. C22×C32×C8C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×#3754C22semidirect
28. C2×#3753C22semidirect
30. C2×#3748C22semidirect
31. C2×#3746C22semidirect
33. C2×#3745C22semidirect
34. C2×#3744C22semidirect
35. C2×#3744C22semidirect
37. #64106C22semidirect
39. #64104C22semidirect
40. C32×#102C22semidirect
41. C32×#102C22semidirect
42. #63647C22semidirect
43. #63647C22semidirect
44. #63637C22semidirect
45. #63636C22semidirect
50. C2×C3×#102D3semidirect
61. C2×C32×D4D4semidirect
83. #3828D4semidirect
122. C22×C3×C8C2×D3semidirect
123. C2×C3×C4⋊C4C2×D3semidirect
138. C3×#102C2×D3semidirect
139. C3×#102C2×D3semidirect
200. C2×#102C3⋊D3semidirect
206. C2×C3×D4D12semidirect
300. C22×C8C2×C3⋊D3semidirect
306. C2×C4⋊C4C2×C3⋊D3semidirect
309. #102C2×C3⋊D3semidirect
310. #102C2×C3⋊D3semidirect
397. C2×D4C4⋊(C3⋊D3)semidirect
446. C32#3012semidirect
527. C3#78747semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#641412
C2×#641132
#105959812
C2×C32×#1022
#105928092
#105926652
#105924822
#105924802
#105924752
#105924722
#787473