Finite Group Databasebeta

← #11878849

Subgroups — #11878849

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#127C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3C3×#5076C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591467C214yesmaximal, complemented
6#10591444C214yesmaximal, complemented
7#10590373C211yesmaximal, characteristic, complemented
8#10590297C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#81766—31nomaximal
11#81568—31nomaximal
12C2×D4×C3⋊D3—21no—
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3C2212yes—
15C32×#127C2211yescharacteristic
16#64149—21no—
17#64149—21no—
18#64149C2212yes—
19#64083C2211yescharacteristic
20C42×C3⋊D3C2211yescharacteristic
21C2×C3×#214C2214yescomplemented
22C3×#869C2211yescharacteristic, complemented
23C3×#869C2211yescharacteristic, complemented
24#63872—21no—
25#63871—21no—
26#63871C2212yes—
27#63849—21no—
28#63843—21no—
29#63843C2212yescomplemented
30C2×#3717C2214yescomplemented
31C3×#832C2214yescomplemented
32C3×C4×C3⋊C8C2211yescharacteristic, complemented
33C3×C4×C3⋊C8C2211yescharacteristic, complemented
34#63572C2212yescomplemented
35#63564C2214yescomplemented
36#63557C2212yes—
37#5728—31no—
38#5728—31no—
39D3×#127—31no—
40D3×#127—31no—
41D3×#127—61no—
42C3×#492—31no—
43C3×#486—31no—
44#5169—34no—
45#5163—34no—
46#5088—31no—
47#5085—31no—
48#5076D311yescharacteristic, complemented
49#5070D311yescharacteristic, complemented
50#4776—34no—
51#4762—34no—
52#4694—31no—
53#4693—31no—
54#4685—31no—
55#4685—31no—
56C23×C3⋊D3—22no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×#638—22no—
61C2×#638—22no—
62C2×#638—22no—
63D4×C3⋊D3—44no—
64D4×C3⋊D3—44no—
65D4×C3⋊D3—44no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2312yes—
74C32×C42C2311yescharacteristic
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3C2311yescharacteristic
78C3×#214—44no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88Dic32—22no—
89#3717—44no—
90#3208—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—32no—
93C2×D3×D4—62no—
94C2×D3×D4—61no—
95C2×D3×D4—61no—
96C2×D3×D4—61no—
97C2×D3×D4—61no—
98C2×D3×D4—62no—
99C2×D3×D4—62no—
100C2×C3×SD16—34no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—31no—
103C3×#127—21no—
104C3×#127C2×D311yescharacteristic
105C3×#127C2×D311yescharacteristic
106#946—32no—
107#946—61no—
108Q8×Dic3—32no—
109Q8×Dic3—61no—
110C2×#215—34no—
111#940—32no—
112#940—32no—
113#940—62no—
114#940—61no—
115#940—61no—
116#940—61no—
117#940—61no—
118#940—62no—
119#940—62no—
120C2×#214C2×D314yescomplemented
121C2×#204—34no—
122#897—32no—
123#897—61no—
124#892—61no—
125#892—61no—
126#890—61no—
127#890—61no—
128#887—32no—
129#887—61no—
130#874—31no—
131#874—31no—
132#874—61no—
133C42×D3—31no—
134C42×D3—31no—
135C42×D3—61no—
136#869C2×D311yescharacteristic, complemented
137#869C2×D311yescharacteristic, complemented
138C3×#102—34no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141#832C2×D314yescomplemented
142#821—34no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145Dic3⋊C8—32no—
146Dic3⋊C8—32no—
147#809—34no—
148C4×C3⋊C8C2×D311yescharacteristic, complemented
149C4×C3⋊C8C2×D311yescharacteristic, complemented
150C23×C32—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—44no—
153C22×C3⋊D3—44no—
154C22×C3⋊D3—44no—
155C22×C3⋊D3C2×D411yescharacteristic
156C32×D4—24no—
157C32×D4—42no—
158C32×D4—42no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2411yescharacteristic
162#638—44no—
163#638—44no—
164#638—44no—
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C2×C3⋊Dic3C2×D411yescharacteristic
168C4⋊(C3⋊D3)—24no—
169C4⋊(C3⋊D3)—42no—
170C4⋊(C3⋊D3)—42no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C4×C3⋊D3SD1614yescomplemented
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C3×Dic6—24no—
177C3×Dic6—42no—
178C3×C3⋊C8—22no—
179C3×C3⋊C8—22no—
180#533—91no—
181C2×#127—91no—
182#492—31no—
183#492—91no—
184#486—31no—
185#486—91no—
186#460—94no—
187#450—94no—
188#431—91no—
189C23×D3—62no—
190C23×D3—62no—
191C23×D3—64no—
192C2×C3×Q8—32no—
193C2×C3×Q8—61no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—22no—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C2×#67—62no—
204C2×#67—62no—
205C2×#67—62no—
206C2×#67—62no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67—64no—
210C2×#67—64no—
211C2×#67—64no—
212D3×D4—124no—
213D3×D4—124no—
214D3×D4—124no—
215D3×D4—124no—
216D3×D4—128no—
217D3×D4—128no—
218D3×D4—128no—
219D3×D4—124no—
220D3×D4—124no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—61no—
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×Dic6—21no—
240C2×Dic6C22×D312yes—
241C3×SD16—124no—
242C2×C3×C8—32no—
243C2×C3×C8—32no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C42—21no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#215—124no—
252#214—44no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263C4×Dic3—31no—
264C4×Dic3—31no—
265C4×Dic3—31no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—31no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C2×C3⋊C8C22×D312yes—
275C2×C3⋊C8C22×D312yes—
276#204—124no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—88no—
287C2×C3⋊D3C2×SD1612yes—
288C32×C4C2×SD1612yes—
289C32×C4AGL(1,ℤ/8)12yes—
290C32×C4H(5,𝔽2)12yes—
291C3⋊Dic3—21no—
292C3⋊Dic3—21no—
293C3⋊Dic3C2×SD1612yes—
294C3×Dic3—42no—
295C3×Dic3—42no—
296C22×D4—92no—
297C22×D4—181no—
298C22×D4—181no—
299C2×SD16—34no—
300C2×SD16—94no—
301C4⋊Q8—31no—
302C4⋊Q8—31no—
303#127—92no—
304#127—91no—
305#127—181no—
306#127—181no—
307#127D3211yescharacteristic
308#125—181no—
309C22⋊Q8—92no—
310C22⋊Q8—181no—
311C4×Q8—92no—
312C4×Q8—181no—
313#117—181no—
314C2×C42—91no—
315C4⋊C8—92no—
316#102—34no—
317#102—94no—
318C22⋊C8—92no—
319C4×C8—31no—
320C4×C8—31no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C22×D3—31no—
325C22×D3—31no—
326C22×D3—61no—
327C22×D3—64no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—124no—
331C22×D3—124no—
332C22×D3—128no—
333C22×D3—128no—
334C22×D3—128no—
335C22×D3—124no—
336C22×D3—124no—
337C22×D3—124no—
338C22×D3—124no—
339C3×Q8—64no—
340C3×Q8—122no—
341C3×D4—24no—
342C3×D4—24no—
343C3×D4—44no—
344C3×D4—44no—
345C3×D4—44no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—42no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—124no—
362#67—124no—
363#67—128no—
364#67—128no—
365#67—128no—
366#67—124no—
367#67—124no—
368#67—124no—
369#67—124no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—31no—
373C2×Dic3—31no—
374C2×Dic3—31no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—31no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381D12—64no—
382D12—64no—
383D12—124no—
384D12—124no—
385D12—124no—
386D12—122no—
387D12—122no—
388D12—122no—
389D12—122no—
390C4×D3—34no—
391C4×D3—34no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—64no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399Dic6—24no—
400Dic6—42no—
401C3×C8—62no—
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—22no—
405C2×C32—82no—
406C2×C32#53511yescharacteristic
407C2×C32C22×SD1611yescharacteristic
408C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
409C3⋊D3—22no—
410C3⋊D3—82no—
411C24—182no—
412C2×Q8—32no—
413C2×Q8—61no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—92no—
417C2×D4—182no—
418C2×D4—182no—
419C2×D4—182no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—364no—
423C2×D4—364no—
424C2×D4—364no—
425C2×D4C2×D3212yes—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—91no—
429SD16—124no—
430SD16—364no—
431C2×C8—32no—
432C2×C8—32no—
433C4⋊C4—32no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C22⋊C4—182no—
440C42—91no—
441C42—91no—
442C42—91no—
443C42—182no—
444C42C2×D3211yescharacteristic
445C22×C3—21no—
446C22×C3—44no—
447C22×C3—44no—
448C22×C3—44no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3C2×D3×D411yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C2×D3—32no—
458C2×D3—32no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—61no—
463C2×D3—61no—
464C2×D3—61no—
465C2×D3—61no—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—2416no—
476C2×D3—248no—
477C2×D3—248no—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4—122no—
482C3×C4—122no—
483C3×C4#91112yes—
484C3×C4D3×SD1612yes—
485C3×C4D3×SD1612yes—
486C3×C4#91412yes—
487C3×C4#100412yes—
488C3×C4#100912yes—
489Dic3—32no—
490Dic3—32no—
491Dic3—42no—
492Dic3—42no—
493Dic3—62no—
494Dic3—62no—
495Dic3—62no—
496Dic3—61no—
497Dic3—61no—
498Dic3—61no—
499Dic3—61no—
500C32#320811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—91no—
503C23—182no—
504C23—364no—
505C23—364no—
506C23—364no—
507Q8—64no—
508Q8—122no—
509D4—24no—
510D4—42no—
511D4—42no—
512D4—184no—
513D4—364no—
514D4—364no—
515D4—364no—
516D4—362no—
517D4—362no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—91no—
521C2×C4—94no—
522C2×C4—91no—
523C2×C4—91no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4#381111yescharacteristic
527C2×C4#381111yescharacteristic
528C2×C4C22×D3211yescharacteristic
529C8—62no—
530C8—62no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—84no—
535C2×C3—82no—
536C2×C3—82no—
537C2×C3#567411yescharacteristic
538C2×C3#571511yescharacteristic
539C2×C3C2×#91111yescharacteristic
540C2×C3C2×D3×SD1611yescharacteristic
541C2×C3C2×D3×SD1611yescharacteristic
542C2×C3C2×#91411yescharacteristic
543D3—64no—
544D3—62no—
545D3—62no—
546D3—244no—
547D3—242no—
548D3—242no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—92no—
553C22—181no—
554C22—181no—
555C22—362no—
556C22—362no—
557C22—362no—
558C22—728no—
559C22C2×#381111yescharacteristic
560C4—92no—
561C4—122no—
562C4—122no—
563C4—181no—
564C4—181no—
565C4#6393012yes—
566C4#6393712yes—
567C4#6431412yes—
568C3—21no—
569C3#8156811yescharacteristic, complemented
570C3#8176611yescharacteristic, complemented
571C2—82no—
572C2—182no—
573C2—722no—
574C2C2×#6393011yescharacteristic
575C2C2×#6393711yescharacteristic
576C2#1059516811yescharacteristic
subgroupG/H
centerC22C2×#3811
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. #10593866C2semidirect
3. C3×#5076C2semidirect
4. C3×#5070C2semidirect
5. #10591467C2semidirect
6. #10591444C2semidirect
7. #10590373C2semidirect
8. #10590297C2semidirect
9. #10590281C2semidirect
21. C2×C3×#214C22semidirect
22. C3×#869C22semidirect
23. C3×#869C22semidirect
29. #63843C22semidirect
30. C2×#3717C22semidirect
31. C3×#832C22semidirect
32. C3×C4×C3⋊C8C22semidirect
33. C3×C4×C3⋊C8C22semidirect
34. #63572C22semidirect
35. #63564C22semidirect
48. #5076D3semidirect
49. #5070D3semidirect
120. C2×#214C2×D3semidirect
136. #869C2×D3semidirect
137. #869C2×D3semidirect
141. #832C2×D3semidirect
148. C4×C3⋊C8C2×D3semidirect
149. C4×C3⋊C8C2×D3semidirect
173. C4×C3⋊D3SD16semidirect
500. C32#3208semidirect
569. C3#81568semidirect
570. C3#81766semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
#105938662
C3×#50762
C3×#50702
#105914672
#105914442
#105903732
#105902972
#105902812
#817663
#815683