Finite Group Databasebeta

← #11864570

Subgroups — #11864570

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×#64159C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4#10595981C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6#10592828C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic, complemented
8#10592509C212yesmaximal, complemented
9#10592507C212yesmaximal, complemented
10#10592475C212yesmaximal, complemented
11#10592472C212yesmaximal, complemented
12#78886—34nomaximal
13C2×C32×#41C2211yescharacteristic
14#64366—24no—
15#64366—24no—
16C2×#3832C2212yes—
17C2×D4×C3⋊D3—22no—
18C2×D4×C3⋊D3C2212yes—
19C2×#3828—21no—
20C2×#3828C2211yescharacteristic
21C2×#3828C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)—21no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26#64159—24no—
27C2×#3756C2211yescharacteristic, complemented
28C2×#3755C2211yescharacteristic, complemented
29C2×#3754C2211yescharacteristic, complemented
30C2×#3753C2211yescharacteristic, complemented
31#64139—22no—
32C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33#64117—24no—
34C2×#3745C2212yescomplemented
35C2×#3744C2212yescomplemented
36#64106—21no—
37#64106C2212yescomplemented
38#64104—21no—
39#64104C2212yescomplemented
40C32×#103C2212yescomplemented
41C32×#102C2212yescomplemented
42#63647C2212yescomplemented
43#63647C2212yescomplemented
44#63636C2212yescomplemented
45#63636C2212yescomplemented
46C2×#1009—34no—
47C2×#950—34no—
48C2×#908—34no—
49#5510—34no—
50C3×#417D314yescomplemented
51#5129—34no—
52C2×#809—34no—
53#4810—38no—
54#4808—38no—
55#4776—38no—
56#4773—38no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3—22no—
59C32×#41—22no—
60C32×#41D414yescomplemented
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68C2×#638—22no—
69C2×#638D412yes—
70#3832—24no—
71#3832—24no—
72D4×C3⋊D3—216no—
73D4×C3⋊D3—24no—
74D4×C3⋊D3—24no—
75#3828—28no—
76#3828—22no—
77#3828—22no—
78#3828—22no—
79#3828—22no—
80C2×C4⋊(C3⋊D3)—28no—
81C2×C4⋊(C3⋊D3)—22no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)—22no—
84C2×C4⋊(C3⋊D3)—22no—
85C2×C4⋊(C3⋊D3)D411yescharacteristic
86C2×C4⋊(C3⋊D3)D414yescomplemented
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4⋊(C3⋊D3)C2312yes—
89C2×C4×C3⋊D3—22no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3C2312yes—
92C2×#634D411yescharacteristic
93C2×#634C2311yescharacteristic
94C32×M16—22no—
95C2×C32×C8C2312yes—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2312yes—
98#3756—22no—
99#3755—22no—
100#3754—22no—
101#3753—22no—
102#3752—22no—
103#3752—22no—
104C4⋊(C3⋊Dic3)—22no—
105C2×C3⋊(C3⋊C8)—22no—
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108#3745—24no—
109#3744—24no—
110#3012—91noSylow
111C2×C3×#41C2×D314yes—
112#1009—616no—
113#1009—616no—
114C2×#239—38no—
115C2×D3×D4—38no—
116C2×D3×D4—68no—
117C2×#235—34no—
118C2×#235—34no—
119C2×#235—64no—
120C22×D12—34no—
121C22×D12—64no—
122C2×C3×M16C2×D314yescomplemented
123C2×C3×C4⋊C4C2×D314yescomplemented
124#950—616no—
125C2×#216—34no—
126C2×#215—34no—
127C2×#214—34no—
128C2×#213—34no—
129#930—68no—
130C22×C3⋊C8—34no—
131#908—616no—
132C2×D24—38no—
133C2×#204—38no—
134#897—38no—
135#897—64no—
136#895—38no—
137#895—64no—
138C3×#103C2×D318yescomplemented
139C3×#102C2×D318yescomplemented
140(C2×D3)⋊C8—38no—
141(C2×D3)⋊C8—38no—
142#809—38no—
143#809—38no—
144C23×C32—21no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—28no—
148C22×C3⋊D3—24no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—82no—
151C22×C3⋊D3—82no—
152C22×C3⋊D3—81no—
153C22×C3⋊D3—81no—
154C22×C3⋊D3C2×D412yes—
155C32×Q8—21no—
156C32×Q8C2×D412yes—
157C32×D4—24no—
158C32×D4—21no—
159C32×D4C2×D412yes—
160C2×C32×C4—21no—
161C2×C32×C4—24no—
162C2×C32×C4—22no—
163C2×C32×C4—81no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2411yescharacteristic
168#638—28no—
169#638—24no—
170#638—42no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C2×D412yes—
173C4⋊(C3⋊D3)—28no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—24no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—82no—
180C4⋊(C3⋊D3)C2×D414yes—
181C4×C3⋊D3—28no—
182C4×C3⋊D3—22no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—42no—
185#634—22no—
186#634—21no—
187#634—21no—
188C32×C8—22no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
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#417C3⋊D311yescharacteristic, complemented
200C2×#102—91no—
201#408—91no—
202C23×D3—68no—
203C23×D3—64no—
204C3×#41—28no—
205C3×#41D12116yescomplemented
206C2×C3×Q8C22×D314yes—
207C2×C3×D4—24no—
208C2×C3×D4C22×D314yes—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4C22×D314yes—
212C2×#67—38no—
213C2×#67—68no—
214C2×#67—64no—
215#239—616no—
216#239—616no—
217D3×D4—616no—
218D3×D4—664no—
219D3×D4—616no—
220#235—632no—
221#235—68no—
222#235—68no—
223#235—68no—
224#235—68no—
225C2×D12—316no—
226C2×D12—38no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—68no—
230C2×D12—632no—
231C2×D12—68no—
232C2×D12—64no—
233C2×D12—68no—
234C2×C4×D3—38no—
235C2×C4×D3—68no—
236C2×C4×D3—64no—
237C2×Dic6—34no—
238C2×Dic6—34no—
239C3×M16—28no—
240C2×C3×C8C22×D318yes—
241C3×C4⋊C4—24no—
242C3×C4⋊C4C22×D318yes—
243#216—68no—
244#215—68no—
245#214—68no—
246#213—68no—
247(C2×D3)⋊C4—68no—
248(C2×D3)⋊C4—68no—
249C4⋊Dic3—68no—
250C2×C3⋊C8—34no—
251C2×C3⋊C8—34no—
252C2×C3⋊C8—68no—
253D24—616no—
254#204—616no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—22no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32#12012yes—
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—24no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C2×C3⋊D3—41no—
271C2×C3⋊D3—84no—
272C2×C3⋊D3—88no—
273C32×C4—22no—
274C32×C4—42no—
275C32×C4#12012yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C22×D411yescharacteristic
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—181no—
286C2×#41C2×C3⋊D311yescharacteristic
287C22×D4—92no—
288C22×D4—91no—
289C22×D4—181no—
290C22×D4—182no—
291AGL(1,ℤ/8)—184no—
292#135—184no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16—92no—
297C2×D8—91no—
298C2×D8—92no—
299C2×M16C2×C3⋊D311yescharacteristic, complemented
300C22×C8—91no—
301C22⋊Q8—92no—
302C22⋊Q8—181no—
303#121—92no—
304#121—181no—
305#121—182no—
306C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
307#103C2×C3⋊D312yescomplemented
308#102—92no—
309#102—92no—
310#102C2×C3⋊D312yescomplemented
311C22⋊C8—92no—
312C22⋊C8—92no—
313C23×C3—24no—
314C23×C3D3×D414yes—
315C22×D3—38no—
316C22×D3—68no—
317C22×D3—632no—
318C22×D3—616no—
319C22×D3—64no—
320C22×D3—248no—
321C22×D3—248no—
322C22×D3—244no—
323C22×D3—244no—
324C3×Q8—24no—
325C3×Q8C2×D1218yes—
326C3×D4—216no—
327C3×D4—24no—
328C3×D4C2×D1218yes—
329C2×C3×C4—24no—
330C2×C3×C4—216no—
331C2×C3×C4—28no—
332C2×C3×C4—84no—
333C2×C3×C4C2×D1218yes—
334C2×C3×C4D3×D414yes—
335C2×C3×C4D3×D418yes—
336C2×C3×C4C23×D314yes—
337#67—632no—
338#67—616no—
339#67—128no—
340C2×Dic3—38no—
341C2×Dic3—64no—
342D12—316no—
343D12—632no—
344D12—616no—
345D12—68no—
346D12—68no—
347D12—64no—
348D12—64no—
349D12—248no—
350C4×D3—632no—
351C4×D3—68no—
352C4×D3—68no—
353C4×D3—128no—
354Dic6—68no—
355Dic6—64no—
356Dic6—64no—
357C3×C8—28no—
358C3⋊C8—64no—
359C3⋊C8—64no—
360C2×C32—22no—
361C2×C32—42no—
362C2×C32C2×#12011yescharacteristic
363C2×C32#57611yescharacteristic
364C2×C32#57711yescharacteristic
365C3⋊D3—42no—
366C3⋊D3—44no—
367C3⋊D3—81no—
368C24—182no—
369C24—181no—
370#41—22no—
371#41—188no—
372#41—184no—
373#41—184no—
374#41—182no—
375#41—182no—
376#41—182no—
377#41—182no—
378#41C4⋊(C3⋊D3)14yescomplemented
379C2×Q8—91no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—21no—
383C2×D4—92no—
384C2×D4—92no—
385C2×D4—91no—
386C2×D4—94no—
387C2×D4—91no—
388C2×D4—182no—
389C2×D4—188no—
390C2×D4—182no—
391C2×D4—182no—
392C2×D4—184no—
393C2×D4—1816no—
394C2×D4—184no—
395C2×D4—181no—
396C2×D4—182no—
397C2×D4—181no—
398C2×D4C22×C3⋊D311yescharacteristic
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—92no—
402C22×C4—182no—
403C22×C4—181no—
404C22×C4C22×C3⋊D311yescharacteristic
405Q16—182no—
406SD16—184no—
407SD16—182no—
408SD16—182no—
409D8—184no—
410D8—182no—
411M16—22no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8—182no—
415C2×C8C22×C3⋊D312yes—
416C4⋊C4—21no—
417C4⋊C4—182no—
418C4⋊C4C22×C3⋊D312yes—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22×C3—24no—
422C22×C3—24no—
423C22×C3—28no—
424C22×C3—44no—
425C22×C3—44no—
426C22×C3#88218yes—
427C22×C3C2×D3×D414yes—
428C2×D3—616no—
429C2×D3—68no—
430C2×D3—68no—
431C2×D3—68no—
432C2×D3—128no—
433C2×D3—128no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C2×D3—2416no—
438C2×D3—2432no—
439C3×C4—28no—
440C3×C4—48no—
441C3×C4#88218yes—
442C3×C4C22×D1214yes—
443C3×C4C2×D3×D414yes—
444Dic3—68no—
445Dic3—124no—
446C32#301211yescharacteristic, complemented, Sylow
447C23—21no—
448C23—92no—
449C23—188no—
450C23—182no—
451C23—184no—
452C23—181no—
453C23—721no—
454C23—721no—
455C23—722no—
456C23—722no—
457C23D4×C3⋊D311yescharacteristic
458Q8—21no—
459Q8—182no—
460Q8—181no—
461Q8—181no—
462Q8C2×C4⋊(C3⋊D3)12yes—
463D4—24no—
464D4—21no—
465D4—94no—
466D4—188no—
467D4—188no—
468D4—184no—
469D4—184no—
470D4—182no—
471D4—182no—
472D4—181no—
473D4—181no—
474D4—362no—
475D4—722no—
476D4C2×C4⋊(C3⋊D3)12yes—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—81no—
481C2×C4—92no—
482C2×C4—188no—
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—22no—
492C8—181no—
493C8—181no—
494C2×C3—28no—
495C2×C3—48no—
496C2×C3C2×#88214yes—
497C2×C3#577414yes—
498C2×C3#577814yes—
499D3—128no—
500D3—1216no—
501D3—244no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—184no—
508C22—182no—
509C22—182no—
510C22—182no—
511C22—362no—
512C22—362no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22—724no—
517C22—728no—
518C22#6409112yes—
519C22C2×D4×C3⋊D311yescharacteristic
520C4—22no—
521C4—42no—
522C4—182no—
523C4—361no—
524C4#6409112yes—
525C4C22×C4⋊(C3⋊D3)11yescharacteristic
526C4C2×D4×C3⋊D311yescharacteristic
527C3#7888614yescomplemented
528C2—22no—
529C2—42no—
530C2—362no—
531C2—364no—
532C2—721no—
533C2C2×#6409111yescharacteristic
534C2#1059624511yescharacteristic
535C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenter#417C3⋊D3
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×#64159C2semidirect
3. C2×#64117C2semidirect
4. #10595981C2semidirect
5. C32×#417C2semidirect
6. #10592828C2semidirect
7. C2×#63636C2semidirect
8. #10592509C2semidirect
9. #10592507C2semidirect
10. #10592475C2semidirect
11. #10592472C2semidirect
21. C2×#3828C22semidirect
24. C2×C32×M16C22semidirect
25. C2×C32×C4⋊C4C22semidirect
27. C2×#3756C22semidirect
28. C2×#3755C22semidirect
29. C2×#3754C22semidirect
30. C2×#3753C22semidirect
32. C22×C3⋊(C3⋊C8)C22semidirect
34. C2×#3745C22semidirect
35. C2×#3744C22semidirect
37. #64106C22semidirect
39. #64104C22semidirect
40. C32×#103C22semidirect
41. C32×#102C22semidirect
42. #63647C22semidirect
43. #63647C22semidirect
44. #63636C22semidirect
45. #63636C22semidirect
50. C3×#417D3semidirect
60. C32×#41D4semidirect
86. C2×C4⋊(C3⋊D3)D4semidirect
122. C2×C3×M16C2×D3semidirect
123. C2×C3×C4⋊C4C2×D3semidirect
138. C3×#103C2×D3semidirect
139. C3×#102C2×D3semidirect
199. #417C3⋊D3semidirect
205. C3×#41D12semidirect
299. C2×M16C2×C3⋊D3semidirect
306. C2×C4⋊C4C2×C3⋊D3semidirect
307. #103C2×C3⋊D3semidirect
310. #102C2×C3⋊D3semidirect
378. #41C4⋊(C3⋊D3)semidirect
446. C32#3012semidirect
527. C3#78886semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#641592
C2×#641172
#105959812
C32×#4172
#105928282
C2×#636362
#105925092
#105925072
#105924752
#105924722
#788863