Finite Group Databasebeta

← #11878850

Subgroups — #11878850

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#127C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5076C211yesmaximal, characteristic, complemented
5#10591458C214yesmaximal, complemented
6#10591438C214yesmaximal, complemented
7#10590375C211yesmaximal, characteristic, complemented
8#10590273C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83169—31nomaximal
11#81766—31nomaximal
12C2×C3×D3×D4—21no—
13C2×C3×D3×D4—21no—
14C2×C3×D3×D4C2212yes—
15C32×#127C2211yescharacteristic
16#64078C2211yescharacteristic, complemented
17C3×#940—21no—
18C3×#940—21no—
19C3×#940C2212yes—
20C2×C3×#214C2214yescomplemented
21C3×#874C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23C3×#869C2211yescharacteristic, complemented
24#63869—21no—
25#63857—21no—
26#63856C2212yes—
27#63844—21no—
28Dic3×Dic6C2212yescomplemented
29#63841—21no—
30C2×#3715C2214yescomplemented
31#63659C2214yescomplemented
32C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×C4×C3⋊C8C2211yescharacteristic, complemented
34Dic3⋊(C3⋊C8)C2212yescomplemented
35#63563C2214yescomplemented
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C2×C3×#127—31no—
38#5728—31no—
39D3×#127D311yescharacteristic
40#5470—31no—
41C3×#492—31no—
42#5218—34no—
43#5169—34no—
44#5163—34no—
45#5085—31no—
46#5076—31no—
47#5076D311yescharacteristic, complemented
48#5075—34no—
49#5070—31no—
50#5070—31no—
51#5070—31no—
52#5070—61no—
53#4925—31no—
54#4694—31no—
55#4685—31no—
56C23×C3×D3—22no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×#634—21no—
61C2×C3×#67—22no—
62C2×C3×#67—22no—
63C2×C3×#67—22no—
64C3×D3×D4—44no—
65C3×D3×D4—44no—
66C3×D3×D4—44no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×#214—44no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2312yes—
85#3724—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89#3715—44no—
90#3208—91noSylow
91C22×C3×D4—32no—
92C22×C3×D4—61no—
93C22×C3×D4—61no—
94C2×D3×D4—21no—
95C2×D3×D4—21no—
96C2×D3×D4C2×D312yes—
97C2×C3×SD16—34no—
98C3×C4⋊Q8—31no—
99C3×#127—21no—
100C3×#127—32no—
101C3×#127—31no—
102C3×#127—61no—
103C3×#127—61no—
104C3×#127C2×D311yescharacteristic
105C3×#127C2×D311yescharacteristic
106C2×C3×C42—31no—
107#946—32no—
108Q8×Dic3—32no—
109C2×#215—34no—
110#940—21no—
111#940—21no—
112#940C2×D312yes—
113C2×#214—34no—
114C2×#214C2×D314yescomplemented
115#926—61no—
116#924—32no—
117#924—61no—
118#897—61no—
119#892—61no—
120#890—61no—
121#887—61no—
122#874C2×D311yescharacteristic
123C42×D3C2×D311yescharacteristic
124#870—61no—
125#869—31no—
126#869—31no—
127#869—61no—
128#869C2×D311yescharacteristic, complemented
129C4×Dic6—32no—
130C4×Dic6—61no—
131C3×C4×C8—31no—
132#832—34no—
133#832—34no—
134#832—34no—
135#832—64no—
136#830—32no—
137#821—34no—
138(C2×D3)⋊C8—32no—
139Dic3⋊C8—32no—
140C4⋊(C3⋊C8)—32no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—61no—
144C4×C3⋊C8C2×D311yescharacteristic, complemented
145C23×C32—22no—
146C22×C3×D3—22no—
147C22×C3×D3—44no—
148C22×C3×D3—44no—
149C22×C3×D3—44no—
150C22×C3×D3C2×D411yescharacteristic
151C32×D4—24no—
152C32×D4—42no—
153C32×D4—42no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158#634—42no—
159C3×#67—44no—
160C3×#67—44no—
161C3×#67—44no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D411yescharacteristic
165C2×C3×Dic3C2×D411yescharacteristic
166C3×D12—24no—
167C3×D12—42no—
168C3×D12—42no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×C4×D3SD1614yescomplemented
172C3×Dic6—24no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175#533—91no—
176C2×#127—31no—
177#492—31no—
178#492—91no—
179#486—91no—
180#486—91no—
181#460—94no—
182#450—94no—
183#431—91no—
184C24×C3—62no—
185C23×D3—22no—
186C2×C3×Q8—32no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—32no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—62no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—124no—
201C2×C3×D4—124no—
202C2×C3×D4—124no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C22×D312yes—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C2×#67—22no—
209C2×#67—22no—
210C2×#67—22no—
211D3×D4—44no—
212D3×D4—44no—
213D3×D4—44no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12C22×D312yes—
217C2×C4×D3#6711yescharacteristic
218C2×C4×D3#6711yescharacteristic
219C2×C4×D3C22×D311yescharacteristic
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6C22×D312yes—
224C3×SD16—124no—
225C2×C3×C8—32no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C42—21no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#215—124no—
236#214—44no—
237#214—124no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—121no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3#6711yescharacteristic
254C4×Dic3#6711yescharacteristic
255C4×Dic3C22×D311yescharacteristic
256C2×C3⋊C8—32no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8C22×D312yes—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—21no—
265C2×C3×D3—21no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—88no—
270C2×C3×D3C2×SD1612yes—
271C32×C4C2×SD1612yes—
272C32×C4AGL(1,ℤ/8)12yes—
273C32×C4H(5,𝔽2)12yes—
274C3⋊Dic3—42no—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3C2×SD1612yes—
279C22×D4—32no—
280C22×D4—61no—
281C22×D4—61no—
282C2×SD16—34no—
283C2×SD16—94no—
284C4⋊Q8—31no—
285C4⋊Q8—91no—
286#127—32no—
287#127—31no—
288#127—61no—
289#127—61no—
290#127D3211yescharacteristic
291#125—181no—
292C22⋊Q8—92no—
293C22⋊Q8—181no—
294C4×Q8—92no—
295C4×Q8—181no—
296#117—181no—
297C2×C42—31no—
298C4⋊C8—92no—
299#102—94no—
300#102—94no—
301C22⋊C8—92no—
302C4×C8—31no—
303C4×C8—91no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—31no—
307C23×C3—42no—
308C23×C3—62no—
309C23×C3—124no—
310C23×C3—124no—
311C23×C3—124no—
312C22×D3—22no—
313C22×D3—44no—
314C22×D3—44no—
315C22×D3—44no—
316C22×D3C2×#6711yescharacteristic
317C3×Q8—64no—
318C3×D4—24no—
319C3×D4—24no—
320C3×D4—44no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—42no—
324C3×D4—42no—
325C3×D4—64no—
326C3×D4—82no—
327C3×D4—82no—
328C3×D4—124no—
329C3×D4—124no—
330C3×D4—124no—
331C3×D4—122no—
332C3×D4—122no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—31no—
337C2×C3×C4—34no—
338C2×C3×C4—31no—
339C2×C3×C4—31no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—44no—
350#67—44no—
351#67—44no—
352C2×Dic3—22no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—122no—
356C2×Dic3C2×#6711yescharacteristic
357C2×Dic3C2×#6711yescharacteristic
358C2×Dic3C2×#6711yescharacteristic
359D12—24no—
360D12—42no—
361D12—42no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3#21414yescomplemented
365Dic6—24no—
366Dic6—122no—
367Dic6—122no—
368Dic6—242no—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32—82no—
375C2×C32#53511yescharacteristic
376C2×C32C22×SD1611yescharacteristic
377C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
378C3×D3—22no—
379C3×D3—82no—
380C24—62no—
381C2×Q8—32no—
382C2×Q8—181no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—62no—
388C2×D4—62no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—124no—
392C2×D4—124no—
393C2×D4—124no—
394C2×D4C2×D3212yes—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398SD16—124no—
399SD16—364no—
400C2×C8—32no—
401C2×C8—92no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—92no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C22⋊C4—182no—
409C42—31no—
410C42—31no—
411C42—31no—
412C42—182no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—61no—
423C22×C3—61no—
424C22×C3—82no—
425C22×C3—82no—
426C22×C3—82no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—248no—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—21no—
434C2×D3—21no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—88no—
439C2×D3C2×#21412yes—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—32no—
444C3×C4—61no—
445C3×C4—61no—
446C3×C4—122no—
447C3×C4D3×SD1612yes—
448C3×C4#91412yes—
449C3×C4#93212yes—
450C3×C4C2×#21412yes—
451C3×C4#100412yes—
452C3×C4#100412yes—
453Dic3—21no—
454Dic3—21no—
455Dic3—42no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459Dic3C2×#21412yes—
460C32#320811yescharacteristic, complemented, Sylow
461C23—22no—
462C23—31no—
463C23—62no—
464C23—124no—
465C23—124no—
466C23—124no—
467Q8—64no—
468Q8—362no—
469D4—24no—
470D4—42no—
471D4—42no—
472D4—64no—
473D4—124no—
474D4—124no—
475D4—124no—
476D4—122no—
477D4—122no—
478C2×C4—31no—
479C2×C4—34no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—182no—
486C2×C4D3×#6711yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4C22×D3211yescharacteristic
489C8—62no—
490C8—182no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—62no—
495C2×C3—82no—
496C2×C3—82no—
497C2×C3—162no—
498C2×C3—242no—
499C2×C3#571511yescharacteristic
500C2×C3C2×D3×SD1611yescharacteristic
501C2×C3C2×#91411yescharacteristic
502C2×C3C2×#93211yescharacteristic
503C2×C3C22×#21411yescharacteristic
504C2×C3#580511yescharacteristic
505D3—22no—
506D3—82no—
507C22—32no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—61no—
512C22—61no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—248no—
517C22C2×D3×#6711yescharacteristic
518C4—32no—
519C4—61no—
520C4—61no—
521C4—122no—
522C4—362no—
523C4D3×#21412yes—
524C4#6393412yes—
525C4#6431312yes—
526C3—21no—
527C3#8176611yescharacteristic, complemented
528C3#8316911yescharacteristic, complemented
529C2—62no—
530C2—82no—
531C2—242no—
532C2C2×D3×#21411yescharacteristic
533C2C2×#6393411yescharacteristic
534C2#1059523311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×D3×#127C2
hypercenter#127D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592769C2semidirect
4. C3×#5076C2semidirect
5. #10591458C2semidirect
6. #10591438C2semidirect
7. #10590375C2semidirect
8. #10590273C2semidirect
9. #10590261C2semidirect
16. #64078C22semidirect
20. C2×C3×#214C22semidirect
23. C3×#869C22semidirect
28. Dic3×Dic6C22semidirect
30. C2×#3715C22semidirect
31. #63659C22semidirect
32. C4×C3⋊(C3⋊C8)C22semidirect
33. C3×C4×C3⋊C8C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
35. #63563C22semidirect
47. #5076D3semidirect
114. C2×#214C2×D3semidirect
128. #869C2×D3semidirect
144. C4×C3⋊C8C2×D3semidirect
171. C3×C4×D3SD16semidirect
364. C4×D3#214semidirect
460. C32#3208semidirect
527. C3#81766semidirect
528. C3#83169semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1272
#105938592
#105927692
C3×#50762
#105914582
#105914382
#105903752
#105902732
#105902612
#831693
#817663