Finite Group Databasebeta

← #11878651

Subgroups — #11878651

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
1D3×#874C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10592394C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590947C214yesmaximal, complemented
7#10590765C214yesmaximal, complemented
8#10590350C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#81566—31nomaximal
11#79303—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15C2×#3799—21no—
16C2×#3745C2214yescomplemented
17#64083C2211yescharacteristic
18#64083C2211yescharacteristic, complemented
19C3×#874C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic, complemented
22#63911—21no—
23#63911—21no—
24#63911C2212yes—
25#63909—21no—
26#63909C2212yes—
27#63894—21no—
28#63894C2212yescomplemented
29#63864—21no—
30C2×#3714C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32C3×#821C2214yescomplemented
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yescomplemented
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63564C2214yescomplemented
37#5725—31no—
38D3×#127—31no—
39#5477—31no—
40C2×#874—31no—
41C3×#486—31no—
42C3×#431—31no—
43#5088—31no—
44#5073—31no—
45#4843—34no—
46#4786—34no—
47#4773—34no—
48#4732—34no—
49#4695—31no—
50#4695—31no—
51#4695—31no—
52#4695—61no—
53#4694—31no—
54#4694D311yescharacteristic, complemented
55#4685D311yescharacteristic, complemented
56C22×D32—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×#626—22no—
74C2×#624—22no—
75D3×D12—44no—
76D3×D12—44no—
77D3×D12—44no—
78#3799—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81#3745—44no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88#3722—22no—
89#3722—22no—
90#3714—44no—
91#3205—91noSylow
92C2×#239—61no—
93C2×D3×D4—32no—
94C2×D3×D4—61no—
95C2×D3×D4—61no—
96C2×#235—61no—
97C22×D12—32no—
98C22×D12—61no—
99C22×D12—61no—
100C3×C4⋊Q8—31no—
101C3×#127—31no—
102C2×C3×C42—31no—
103#947—61no—
104#940—32no—
105#940—61no—
106#940—61no—
107C2×#213—34no—
108#930—32no—
109#930—61no—
110C2×D24—34no—
111C2×D24—34no—
112C2×D24—34no—
113C2×D24—64no—
114#895—32no—
115#895—61no—
116#893—32no—
117#893—61no—
118#875—61no—
119#874—32no—
120#874—31no—
121#874—31no—
122#874—31no—
123#874—31no—
124#874—61no—
125#874—61no—
126#874—61no—
127#874—61no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×D12—61no—
131C42×D3C2×D311yescharacteristic
132#869C2×D311yescharacteristic, complemented
133C3×C4⋊C8—32no—
134C3×#102—34no—
135C3×C22⋊C8—32no—
136C3×C4×C8—21no—
137C3×C4×C8—31no—
138C3×C4×C8C2×D311yescharacteristic, complemented
139C3×C4×C8C2×D311yescharacteristic, complemented
140#821—34no—
141#821C2×D314yescomplemented
142(C2×D3)⋊C8C2×D312yes—
143Dic3⋊C8C2×D312yescomplemented
144#809—34no—
145C4×C3⋊C8C2×D311yescharacteristic, complemented
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3C2×D411yescharacteristic
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—44no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C4⋊(C3⋊D3)—24no—
157C4⋊(C3⋊D3)—24no—
158C4⋊(C3⋊D3)—42no—
159C4⋊(C3⋊D3)—42no—
160C4⋊(C3⋊D3)—42no—
161C4⋊(C3⋊D3)—42no—
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×D3D814yescomplemented
172C3×Dic6—42no—
173#626—44no—
174#626—44no—
175#626—44no—
176#626—44no—
177#624—44no—
178C32×C8—22no—
179C3×C3⋊C8—22no—
180#532—91no—
181C2×#127—91no—
182#493—91no—
183#493—91no—
184#486—31no—
185#486—91no—
186#459—94no—
187#447—94no—
188#431—31no—
189C23×D3—62no—
190C23×D3—62no—
191C2×C3×Q8—61no—
192C2×C3×D4—32no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—62no—
201C2×#67—62no—
202#239—124no—
203D3×D4—124no—
204D3×D4—124no—
205D3×D4—124no—
206#235—124no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—61no—
227C2×D12—121no—
228C2×D12—121no—
229C2×D12—121no—
230C2×D12—121no—
231C2×D12—124no—
232C2×D12—124no—
233C2×D12—124no—
234C2×D12C22×D312yes—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3D1211yescharacteristic
238C2×C4×D3D1211yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—21no—
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8C22×D312yes—
244C2×C3×C8C22×D312yes—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—61no—
247C3×C42—21no—
248C3×C42—31no—
249C3×C42—31no—
250C3×C42—31no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#213—124no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—21no—
259C4⋊Dic3C22×D312yes—
260C4×Dic3D1211yescharacteristic
261C4×Dic3D1211yescharacteristic
262C4×Dic3C22×D311yescharacteristic
263C2×C3⋊C8C22×D312yes—
264D24—124no—
265D24—124no—
266D24—128no—
267D24—124no—
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—42no—
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—181no—
290C22×D4—92no—
291C22×D4—181no—
292C22×D4—181no—
293C2×D8—94no—
294C2×D8—94no—
295C4⋊Q8—31no—
296#127—31no—
297#127—92no—
298#127—91no—
299#127—91no—
300#127—181no—
301#127—181no—
302#124—181no—
303#121—92no—
304#121—181no—
305C4×D4—92no—
306C4×D4—181no—
307C2×C42—31no—
308C4⋊C8—32no—
309#102—34no—
310#102—94no—
311C22⋊C8—32no—
312C4×C8—31no—
313C4×C8D3211yescharacteristic, complemented
314C23×C3—31no—
315C23×C3—62no—
316C22×D3—22no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3C2×D1211yescharacteristic
330C3×Q8—122no—
331C3×D4—64no—
332C3×D4—122no—
333C3×D4—122no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—31no—
338C2×C3×C4—34no—
339C2×C3×C4—31no—
340C2×C3×C4—31no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—124no—
351#67—124no—
352#67—124no—
353#67—124no—
354C2×Dic3—22no—
355C2×Dic3C2×D1211yescharacteristic
356C2×Dic3C2×D1211yescharacteristic
357C2×Dic3C2×D1211yescharacteristic
358D12—24no—
359D12—42no—
360D12—42no—
361D12—64no—
362D12—64no—
363D12—64no—
364D12—64no—
365D12—124no—
366D12—124no—
367D12—124no—
368D12—124no—
369D12—124no—
370D12—124no—
371D12—122no—
372D12—122no—
373D12—122no—
374D12—122no—
375D12—122no—
376D12—122no—
377D12—122no—
378D12—122no—
379D12—242no—
380D12—242no—
381D12—242no—
382D12—242no—
383C4×D3—22no—
384C4×D3—22no—
385C4×D3—124no—
386C4×D3—124no—
387C4×D3D2414yescomplemented
388Dic6—42no—
389C3×C8—24no—
390C3×C8—22no—
391C3×C8—22no—
392C3×C8—62no—
393C3⋊C8—22no—
394C2×C32#53511yescharacteristic
395C2×C32C22×D811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C3⋊D3—82no—
398C3⋊D3—82no—
399C3×D3—22no—
400C3×D3—82no—
401C24—182no—
402#41—364no—
403C2×Q8—61no—
404C2×D4—32no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—92no—
408C2×D4—92no—
409C2×D4—182no—
410C2×D4—182no—
411C2×D4—182no—
412C2×D4—182no—
413C2×D4—181no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—364no—
418C2×D4—364no—
419C2×D4—364no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—182no—
424D8—364no—
425D8—364no—
426C2×C8—32no—
427C2×C8C2×D3212yes—
428C4⋊C4—32no—
429C4⋊C4—61no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C42—31no—
433C42—31no—
434C42—31no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—32no—
438C22×C3—61no—
439C22×C3—61no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3C22×D1211yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—242no—
463C2×D3—242no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—248no—
469C2×D3—248no—
470C2×D3C2×D2412yes—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—32no—
475C3×C4—61no—
476C3×C4—61no—
477C3×C4—122no—
478C3×C4C2×D2412yes—
479C3×C4#90812yes—
480C3×C4D3×D812yes—
481C3×C4#91412yes—
482C3×C4#100912yes—
483C3×C4#100912yes—
484Dic3—21no—
485Dic3—21no—
486Dic3—42no—
487Dic3C2×D2412yes—
488C32#320511yescharacteristic, complemented, Sylow
489C23—31no—
490C23—62no—
491C23—182no—
492C23—182no—
493C23—364no—
494C23—364no—
495C23—364no—
496Q8—122no—
497D4—64no—
498D4—122no—
499D4—122no—
500D4—184no—
501D4—184no—
502D4—364no—
503D4—364no—
504D4—364no—
505D4—364no—
506D4—362no—
507D4—362no—
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—364no—
518C2×C4D3×D1211yescharacteristic
519C2×C4D3×D1211yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—22no—
522C8—62no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—62no—
527C2×C3—242no—
528C2×C3#552511yescharacteristic
529C2×C3#567411yescharacteristic
530C2×C3C22×D2411yescharacteristic
531C2×C3C2×#90811yescharacteristic
532C2×C3C2×D3×D811yescharacteristic
533C2×C3C2×#91411yescharacteristic
534D3—22no—
535D3—82no—
536D3—242no—
537D3—242no—
538D3—242no—
539D3—242no—
540D3—482no—
541D3—482no—
542C22—32no—
543C22—61no—
544C22—61no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—362no—
549C22—362no—
550C22—362no—
551C22—362no—
552C22—362no—
553C22—362no—
554C22—728no—
555C22C2×D3×D1211yescharacteristic
556C4—32no—
557C4—61no—
558C4—61no—
559C4—122no—
560C4D3×D2412yes—
561C4#6379412yes—
562C4#6430812yes—
563C3—21no—
564C3#7930311yescharacteristic, complemented
565C3#8156611yescharacteristic, complemented
566C2—62no—
567C2—242no—
568C2—722no—
569C2—722no—
570C2#1059400111yescharacteristic
571C2C2×D3×D2411yescharacteristic
572C2C2×#6379411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. D3×#874C2semidirect
2. #10593970C2semidirect
3. #10592394C2semidirect
4. C3×#4694C2semidirect
5. C3×#4685C2semidirect
6. #10590947C2semidirect
7. #10590765C2semidirect
8. #10590350C2semidirect
9. #10590281C2semidirect
16. C2×#3745C22semidirect
18. #64083C22semidirect
21. C3×#869C22semidirect
28. #63894C22semidirect
30. C2×#3714C22semidirect
31. C32×C4×C8C22semidirect
32. C3×#821C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63564C22semidirect
54. #4694D3semidirect
55. #4685D3semidirect
132. #869C2×D3semidirect
138. C3×C4×C8C2×D3semidirect
139. C3×C4×C8C2×D3semidirect
141. #821C2×D3semidirect
143. Dic3⋊C8C2×D3semidirect
145. C4×C3⋊C8C2×D3semidirect
171. C3×C4×D3D8semidirect
313. C4×C8D32semidirect
387. C4×D3D24semidirect
488. C32#3205semidirect
564. C3#79303semidirect
565. C3#81566semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
#105939702
#105923942
C3×#46942
C3×#46852
#105909472
#105907652
#105903502
#105902812
#815663
#793033