Finite Group Databasebeta

← #11878649

Subgroups — #11878649

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2D3×#874C211yesmaximal, characteristic, complemented
3#10592772C211yesmaximal, characteristic, complemented
4C3×#5073C211yesmaximal, characteristic, complemented
5#10591515C214yesmaximal, complemented
6#10591481C214yesmaximal, complemented
7#10590281C211yesmaximal, characteristic, complemented
8#10590277C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83302—31nomaximal
11#81785—31nomaximal
12C2×C3×#237—21no—
13C2×D3×D12—21no—
14C2×D3×D12—21no—
15C2×D3×D12C2212yes—
16C32×#127C2211yescharacteristic, complemented
17C2×#3753C2214yescomplemented
18#64083C2211yescharacteristic
19C3×#938—21no—
20C3×#938C2212yes—
21C3×#936—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3C2212yescomplemented
24C2×C3×#213C2214yescomplemented
25C3×#874C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63911—21no—
29#63911—21no—
30#63911C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
32C3×C4×C3⋊C8C2211yescharacteristic, complemented
33Dic3⋊(C3⋊C8)C2212yescomplemented
34#63564C2214yescomplemented
35#63562C2214yescomplemented
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C3×#532—31no—
38#5716D311yescharacteristic, complemented
39D3×#127—31no—
40C2×#874—31no—
41C3×#493—31no—
42#5156—34no—
43#5150—34no—
44#5088—31no—
45#5088—31no—
46#5073—31no—
47#5073—31no—
48#5073—61no—
49#5073D311yescharacteristic, complemented
50#5070—31no—
51#5036—34no—
52#5015—34no—
53#4925—31no—
54#4694—31no—
55#4685—31no—
56C22×D32—22no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C3×#67—22no—
64C22×C3×Dic3—22no—
65C3×#237—44no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6—21no—
73C2×#626—22no—
74C2×#626—22no—
75C2×#626—22no—
76D3×D12—44no—
77D3×D12—44no—
78D3×D12—44no—
79C32×C42C2311yescharacteristic
80#3753—44no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#217—22no—
83C3×#217—22no—
84C3×#213—44no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4×Dic3D411yescharacteristic
88C3×C4×Dic3D411yescharacteristic
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2312yes—
91#3205—91noSylow
92C2×C3×#41—61no—
93C2×#237—21no—
94C2×D3×D4—32no—
95C2×D3×D4—61no—
96C2×D3×D4—61no—
97C22×D12—32no—
98C22×D12—61no—
99C22×D12—61no—
100C2×C3×D8—34no—
101C3×C4⋊Q8—31no—
102C3×#127—21no—
103C3×#127—31no—
104C3×#127C2×D311yescharacteristic, complemented
105C3×#127C2×D311yescharacteristic, complemented
106C3×#124—61no—
107C3×#121—32no—
108C3×#121—61no—
109C3×C4×D4—32no—
110C3×C4×D4—61no—
111C2×C3×C42—31no—
112#940—32no—
113#940—61no—
114#940—61no—
115#938—21no—
116#938C2×D312yes—
117#936—21no—
118D4×Dic3—21no—
119D4×Dic3C2×D312yescomplemented
120C2×#213—34no—
121C2×#213—34no—
122C2×#213—64no—
123C2×#213C2×D314yescomplemented
124#874—32no—
125#874—31no—
126#874—31no—
127#874—61no—
128#874—61no—
129#874—61no—
130#874C2×D311yescharacteristic
131C42×D3C2×D311yescharacteristic
132#869C2×D311yescharacteristic, complemented
133C3×C4×C8—31no—
134#832—34no—
135#830—32no—
136#821—34no—
137(C2×D3)⋊C8—32no—
138Dic3⋊C8—32no—
139#809—34no—
140#809—34no—
141C4⋊(C3⋊C8)—32no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—31no—
144C4×C3⋊C8—61no—
145C4×C3⋊C8C2×D311yescharacteristic, complemented
146C23×C32—22no—
147C22×C3⋊D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3C2×D411yescharacteristic
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—44no—
153C32×D4—24no—
154C32×D4—42no—
155C32×D4—42no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2411yescharacteristic
159C4⋊(C3⋊D3)—24no—
160C4⋊(C3⋊D3)—42no—
161C4⋊(C3⋊D3)—42no—
162C3×#67—44no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—44no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D411yescharacteristic
167C2×C3×Dic3C2×D411yescharacteristic
168C3×D12—24no—
169C3×D12—42no—
170C3×D12—42no—
171C3×C4×D3—22no—
172C3×C4×D3—22no—
173C3×C4×D3D814yescomplemented
174C3×Dic6—42no—
175#626—44no—
176#626—44no—
177#626—44no—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180#532—31no—
181C2×#127—91no—
182#493—31no—
183#493—91no—
184#486—91no—
185#486—91no—
186#459—94no—
187#447—94no—
188#431—91no—
189C23×D3—62no—
190C23×D3—62no—
191C3×#41—124no—
192C2×C3×Q8—61no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—22no—
198C2×C3×D4—32no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—62no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C2×C3×D4C22×D312yes—
205C2×C3×D4C22×D312yes—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—62no—
210C2×#67—22no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C22×Dic3—22no—
215#237—44no—
216D3×D4—124no—
217D3×D4—124no—
218D3×D4—124no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—62no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—121no—
232C2×D12—121no—
233C2×D12—124no—
234C2×D12—124no—
235C2×D12—124no—
236C2×D12C22×D312yes—
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3#6711yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—21no—
241C3×D8—124no—
242C2×C3×C8—32no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247C3×C42—21no—
248C3×C42—31no—
249C3×C42—31no—
250C3×C42—31no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—22no—
254#217—22no—
255#213—44no—
256#213—124no—
257#213—124no—
258#213—128no—
259C4⋊Dic3—21no—
260C4⋊Dic3C22×D312yes—
261C4×Dic3#6711yescharacteristic
262C4×Dic3#6711yescharacteristic
263C4×Dic3C22×D311yescharacteristic
264C2×C3⋊C8—32no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8C22×D312yes—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3C2×D812yes—
281D32—88no—
282C32×C4C2×D812yes—
283C32×C4AGL(1,ℤ/8)12yes—
284C32×C4H(5,𝔽2)12yes—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3—42no—
288C3×Dic3C2×D812yes—
289C2×#41—61no—
290C22×D4—92no—
291C22×D4—181no—
292C22×D4—181no—
293C2×D8—34no—
294C2×D8—94no—
295C4⋊Q8—31no—
296#127—31no—
297#127—92no—
298#127—91no—
299#127—181no—
300#127—181no—
301#127D3211yescharacteristic, complemented
302#124—61no—
303#121—32no—
304#121—61no—
305C4×D4—32no—
306C4×D4—61no—
307C2×C42—31no—
308C4⋊C8—92no—
309#102—94no—
310#102—94no—
311C22⋊C8—92no—
312C4×C8—31no—
313C4×C8—91no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—31no—
317C23×C3—42no—
318C23×C3—62no—
319C22×D3—22no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—122no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3C2×#6711yescharacteristic
330C3×Q8—122no—
331C3×D4—24no—
332C3×D4—24no—
333C3×D4—44no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—64no—
339C3×D4—82no—
340C3×D4—82no—
341C3×D4—124no—
342C3×D4—122no—
343C3×D4—122no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—31no—
348C2×C3×C4—34no—
349C2×C3×C4—31no—
350C2×C3×C4—31no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—124no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—44no—
362#67—124no—
363#67—124no—
364#67—124no—
365C2×Dic3—22no—
366C2×Dic3—44no—
367C2×Dic3C2×#6711yescharacteristic
368C2×Dic3C2×#6711yescharacteristic
369C2×Dic3C2×#6711yescharacteristic
370D12—24no—
371D12—42no—
372D12—42no—
373D12—64no—
374D12—64no—
375D12—124no—
376D12—124no—
377D12—124no—
378D12—124no—
379D12—122no—
380D12—122no—
381D12—122no—
382D12—122no—
383D12—242no—
384D12—242no—
385C4×D3—22no—
386C4×D3—22no—
387C4×D3#21314yescomplemented
388Dic6—42no—
389C3×C8—62no—
390C3⋊C8—22no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—82no—
395C2×C32#53511yescharacteristic
396C2×C32C22×D811yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C3⋊D3—82no—
399C3×D3—22no—
400C3×D3—82no—
401C24—182no—
402#41—124no—
403C2×Q8—61no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—32no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—92no—
411C2×D4—182no—
412C2×D4—182no—
413C2×D4—182no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—364no—
417C2×D4—364no—
418C2×D4—364no—
419C2×D4C2×D3212yes—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—62no—
424D8—124no—
425D8—364no—
426C2×C8—32no—
427C2×C8—92no—
428C4⋊C4—32no—
429C4⋊C4—61no—
430C22⋊C4—62no—
431C22⋊C4—62no—
432C42—31no—
433C42—31no—
434C42—31no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—32no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—61no—
445C22×C3—61no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C22×#6711yescharacteristic
454C2×D3—21no—
455C2×D3—21no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—248no—
469C2×D3—248no—
470C2×D3C2×#21312yes—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—32no—
475C3×C4—61no—
476C3×C4—61no—
477C3×C4—122no—
478C3×C4D3×D812yes—
479C3×C4#91112yes—
480C3×C4C2×#21312yes—
481C3×C4#94912yes—
482C3×C4#100412yes—
483C3×C4#100912yes—
484Dic3—21no—
485Dic3—21no—
486Dic3—42no—
487Dic3C2×#21312yes—
488C32#320511yescharacteristic, complemented, Sylow
489C23—22no—
490C23—31no—
491C23—62no—
492C23—182no—
493C23—364no—
494C23—364no—
495C23—364no—
496Q8—122no—
497D4—24no—
498D4—42no—
499D4—42no—
500D4—64no—
501D4—124no—
502D4—122no—
503D4—122no—
504D4—184no—
505D4—364no—
506D4—364no—
507D4—364no—
508D4—362no—
509D4—362no—
510C2×C4—31no—
511C2×C4—34no—
512C2×C4—31no—
513C2×C4—31no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—124no—
518C2×C4D3×#6711yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—62no—
522C8—182no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—62no—
527C2×C3—82no—
528C2×C3—82no—
529C2×C3—162no—
530C2×C3—242no—
531C2×C3#571511yescharacteristic
532C2×C3C2×D3×D811yescharacteristic
533C2×C3C2×#91111yescharacteristic
534C2×C3C22×#21311yescharacteristic
535C2×C3C2×#94911yescharacteristic
536C2×C3#583011yescharacteristic
537D3—22no—
538D3—82no—
539D3—242no—
540D3—242no—
541D3—482no—
542C22—32no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—61no—
547C22—61no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—362no—
552C22—362no—
553C22—362no—
554C22—728no—
555C22C2×D3×#6711yescharacteristic
556C4—32no—
557C4—61no—
558C4—61no—
559C4—122no—
560C4D3×#21312yes—
561C4#6392512yes—
562C4#6431412yes—
563C3—21no—
564C3#8178511yescharacteristic, complemented
565C3#8330211yescharacteristic, complemented
566C2—62no—
567C2—82no—
568C2—242no—
569C2—722no—
570C2C2×D3×#21311yescharacteristic
571C2C2×#6392511yescharacteristic
572C2#1059530311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3205
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
1. C3×#5716C2semidirect
2. D3×#874C2semidirect
3. #10592772C2semidirect
4. C3×#5073C2semidirect
5. #10591515C2semidirect
6. #10591481C2semidirect
7. #10590281C2semidirect
8. #10590277C2semidirect
9. #10590261C2semidirect
16. C32×#127C22semidirect
17. C2×#3753C22semidirect
23. C3×D4×Dic3C22semidirect
24. C2×C3×#213C22semidirect
27. C3×#869C22semidirect
31. C4×C3⋊(C3⋊C8)C22semidirect
32. C3×C4×C3⋊C8C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63564C22semidirect
35. #63562C22semidirect
38. #5716D3semidirect
49. #5073D3semidirect
104. C3×#127C2×D3semidirect
105. C3×#127C2×D3semidirect
119. D4×Dic3C2×D3semidirect
123. C2×#213C2×D3semidirect
132. #869C2×D3semidirect
145. C4×C3⋊C8C2×D3semidirect
173. C3×C4×D3D8semidirect
301. #127D32semidirect
387. C4×D3#213semidirect
488. C32#3205semidirect
564. C3#81785semidirect
565. C3#83302semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
D3×#8742
#105927722
C3×#50732
#105915152
#105914812
#105902812
#105902772
#105902612
#833023
#817853