Finite Group Databasebeta

← #11868982

Subgroups — #11868982

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic
2#10595051C211yesmaximal, characteristic, complemented
3C3×#5215C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5#10591495C212yesmaximal, complemented
6#10591494C212yesmaximal, complemented
7#10591479C212yesmaximal, complemented
8#10591479C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591122C211yesmaximal, characteristic, complemented
11#10591119C211yesmaximal, characteristic, complemented
12#78918—31nomaximal
13#78731—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C2×#3757—22no—
16D4×C3⋊Dic3—21no—
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3C2212yes—
19D4×C3⋊Dic3C2212yes—
20#64135C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63964—22no—
27#63919C2212yescomplemented
28#63918—21no—
29#63872C2212yescomplemented
30#63869—21no—
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×#832C2212yes—
35#63575C2211yescharacteristic, complemented
36#63575C2212yescomplemented
37#63575C2211yescharacteristic, complemented
38#63573C2211yescharacteristic, complemented
39#63573C2212yescomplemented
40#63573C2211yescharacteristic, complemented
41#63572C2212yescomplemented
42#63572C2212yescomplemented
43#5798—31no—
44#5798—31no—
45#5798—61no—
46#5519—31no—
47#5500—31no—
48C3×#418—31no—
49C2×C3×#102—31no—
50#5215D311yescharacteristic
51C2×#832D311yescharacteristic
52#5121—31no—
53#5119—31no—
54#5106—31no—
55#5102—31no—
56#4998—31no—
57#4964—31no—
58#4766—32no—
59#4766—32no—
60#4763—32no—
61#4763—32no—
62#4761—32no—
63#4761—32no—
64#4759—32no—
65#4759—32no—
66C24×C32—21no—
67C2×C32×D4—21no—
68C2×C32×D4—22no—
69C2×C32×D4Q814yescomplemented
70C2×C32×D4C2312yes—
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3—22no—
74C22×C3×Dic3—21no—
75C2×#627—22no—
76#3757—21no—
77#3757—22no—
78#3757—22no—
79#3757D412yes—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)D411yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3C2312yes—
86C3×#217—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4×Dic3—21no—
92C3×#208—22no—
93C2×C3×C3⋊C8—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3724—22no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—21no—
102C22×C3×D4C2×D311yescharacteristic
103C22×C3×D4C2×D311yescharacteristic
104C2×C3×M16—31no—
105C22×C3×C8—31no—
106C3×#117—31no—
107C2×C3×C4⋊C4—31no—
108C2×#217—62no—
109C2×#217—62no—
110C2×#217—64no—
111D4×Dic3—32no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117D4×Dic3—61no—
118D4×Dic3—61no—
119D4×Dic3—61no—
120D4×Dic3—61no—
121D4×Dic3—62no—
122D4×Dic3—62no—
123#926—31no—
124#926—31no—
125#926—31no—
126#926—31no—
127#926—61no—
128#926—61no—
129#926C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131#924—62no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8C2×D311yescharacteristic
134#890—32no—
135#890—32no—
136#890—61no—
137#888—32no—
138#888—32no—
139#888—61no—
140#878—62no—
141#870—61no—
142#869—61no—
143C3×#102—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×#102—32no—
147#832C2×D312yes—
148#832C2×D312yes—
149#832C2×D312yes—
150#832C2×D312yes—
151#818—32no—
152#818—31no—
153#818—31no—
154#817—32no—
155#817—31no—
156#817—31no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161#808—32no—
162#808—31no—
163#808—31no—
164#807—32no—
165#807—31no—
166#807—31no—
167C23×C32—22no—
168C23×C32—24no—
169C23×C32—81no—
170C23×C32—81no—
171C23×C32C2×D411yescharacteristic
172C32×D4—24no—
173C32×D4—22no—
174C32×D4C2×Q814yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×Q812yes—
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—82no—
182C2×C3⋊Dic3—82no—
183C2×C3⋊Dic3C2×D412yes—
184C2×C3⋊Dic3C2×D412yes—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—81no—
189#627—82no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193#544—91no—
194#518—91no—
195#478—92no—
196#478—92no—
197#476—92no—
198#474—92no—
199#428—91no—
200#427—91no—
201#424—91no—
202#418—31no—
203C2×#102—31no—
204C24×C3—22no—
205C24×C3—21no—
206C24×C3—21no—
207C2×C3×D4—22no—
208C2×C3×D4—24no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—24no—
214C2×C3×D4—22no—
215C2×C3×D4Dic614yescomplemented
216C2×C3×D4Dic614yescomplemented
217C2×C3×D4C22×D312yes—
218C2×C3×D4C22×D312yes—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×Dic3—21no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—64no—
229C22×Dic3—64no—
230C2×Dic6—62no—
231C2×Dic6—62no—
232C3×M16—62no—
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C2×C3×C8—31no—
236C2×C3×C8—62no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C42—61no—
243#217—21no—
244#217—32no—
245#217—32no—
246#217—62no—
247#217—62no—
248#217—62no—
249#217—62no—
250#217—62no—
251#217—62no—
252#217—64no—
253#217—64no—
254#217—61no—
255#217—61no—
256C4⋊Dic3—21no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3C22×D311yescharacteristic
272C4⋊Dic3C22×D312yes—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—21no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285#208—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D312yes—
289C2×C3⋊C8C22×D311yescharacteristic
290C22×C32—24no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—42no—
294C22×C32—42no—
295C22×C32—84no—
296C22×C32C22⋊Q812yes—
297C22×C32C22×D411yescharacteristic
298C32×C4C22⋊Q812yes—
299C32×C4C22×Q811yescharacteristic
300C32×C4C2×#4111yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C3×Dic3—41no—
306C3×Dic3—42no—
307C3×Dic3—41no—
308C22×D4D3211yescharacteristic
309C2×M16—31no—
310C22×C8—31no—
311C4⋊Q8—92no—
312C4⋊Q8—181no—
313#125—92no—
314#125—181no—
315C22⋊Q8—182no—
316C4×D4—92no—
317C4×D4—92no—
318C4×D4—181no—
319C4×D4—181no—
320#117—31no—
321#117—91no—
322#117—91no—
323C2×C4⋊C4—31no—
324C2×C22⋊C4—182no—
325#107—91no—
326#107—91no—
327#107—92no—
328#106—91no—
329#106—91no—
330#106—92no—
331C4⋊C8—92no—
332C4⋊C8—92no—
333#102—32no—
334#102—32no—
335#102—32no—
336#102—32no—
337C23×C3—24no—
338C23×C3—28no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—21no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3—81no—
347C23×C3—81no—
348C23×C3—82no—
349C23×C3—82no—
350C23×C3D3×D411yescharacteristic
351C23×C3D3×D411yescharacteristic
352C3×D4—24no—
353C3×D4—28no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—24no—
359C3×D4C2×Dic614yes—
360C3×D4C2×Dic614yes—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—241no—
369C2×C3×C4C2×Dic612yes—
370C2×C3×C4C2×Dic612yes—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23712yes—
374C2×C3×C4#23712yes—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—81no—
393C2×Dic3—242no—
394C2×Dic3—242no—
395C2×Dic3—242no—
396C2×Dic3—242no—
397C2×Dic3—244no—
398C2×Dic3—244no—
399Dic6—242no—
400Dic6—242no—
401C3×C8—61no—
402C3×C8—61no—
403C3×C8—62no—
404C3⋊C8—21no—
405C3⋊C8—21no—
406C3⋊C8—22no—
407C2×C32—22no—
408C2×C32—44no—
409C2×C32C2×C22⋊Q811yescharacteristic
410C2×C32#57611yescharacteristic
411C2×C32#57711yescharacteristic
412C24—21no—
413C2×Q8—182no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4#62714yescomplemented
417C2×D4C2×D3212yes—
418C22×C4—61no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4C2×D3211yescharacteristic
422M16—62no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—31no—
426C2×C8—62no—
427C4⋊C4—32no—
428C4⋊C4—31no—
429C4⋊C4—31no—
430C4⋊C4—61no—
431C4⋊C4—91no—
432C4⋊C4—91no—
433C4⋊C4—91no—
434C4⋊C4—91no—
435C4⋊C4—182no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C22⋊C4—61no—
439C22⋊C4—92no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—181no—
443C42—61no—
444C42—92no—
445C42—181no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—28no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—84no—
464C22×C3—84no—
465C22×C3—88no—
466C22×C3#87812yes—
467C22×C3#87812yes—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—122no—
476C3×C4#87812yes—
477C3×C4#87812yes—
478C3×C4C22×Dic611yescharacteristic
479C3×C4C22×Dic611yescharacteristic
480C3×C4C2×#23711yescharacteristic
481C3×C4C2×#23711yescharacteristic
482Dic3—42no—
483Dic3—41no—
484Dic3—41no—
485Dic3—62no—
486Dic3—62no—
487Dic3—62no—
488Dic3—62no—
489Dic3—122no—
490Dic3—122no—
491Dic3—122no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495Dic3—121no—
496Dic3—121no—
497C32#308111yescharacteristic, complemented, Sylow
498C23—22no—
499C23—24no—
500C23—81no—
501C23—81no—
502C23#381111yescharacteristic
503Q8—722no—
504D4—22no—
505D4—24no—
506D4C2×#62714yes—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—241no—
515C2×C4—722no—
516C2×C4—722no—
517C2×C4#380512yes—
518C2×C4C2×#62712yes—
519C2×C4#381111yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—61no—
522C8—61no—
523C8—62no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—42no—
530C2×C3—48no—
531C2×C3—44no—
532C2×C3—44no—
533C2×C3C2×#87811yescharacteristic
534C2×C3C2×#87811yescharacteristic
535C2×C3#575711yescharacteristic
536C2×C3#576211yescharacteristic
537C2×C3#577411yescharacteristic
538C2×C3#577511yescharacteristic
539C22—21no—
540C22—21no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—84no—
545C22#6398212yes—
546C22C2×#381111yescharacteristic
547C4—122no—
548C4—121no—
549C4—121no—
550C4—182no—
551C4—182no—
552C4—361no—
553C4—361no—
554C4#6398212yes—
555C4C2×#380511yescharacteristic
556C4C22×#62711yescharacteristic
557C3—21no—
558C3#7873111yescharacteristic, complemented
559C3#7891811yescharacteristic, complemented
560C2—22no—
561C2—44no—
562C2#1059510211yescharacteristic
563C2#1059511511yescharacteristic
564C2C2×#6398211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10595051C2semidirect
5. #10591495C2semidirect
6. #10591494C2semidirect
7. #10591479C2semidirect
8. #10591479C2semidirect
9. #10591130C2semidirect
10. #10591122C2semidirect
11. #10591119C2semidirect
27. #63919C22semidirect
29. #63872C22semidirect
35. #63575C22semidirect
36. #63575C22semidirect
37. #63575C22semidirect
38. #63573C22semidirect
39. #63573C22semidirect
40. #63573C22semidirect
41. #63572C22semidirect
42. #63572C22semidirect
69. C2×C32×D4Q8semidirect
215. C2×C3×D4Dic6semidirect
216. C2×C3×D4Dic6semidirect
416. C2×D4#627semidirect
497. C32#3081semidirect
558. C3#78731semidirect
559. C3#78918semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105950512
C3×#52152
C2×C3×#8322
#105914952
#105914942
#105914792
#105911302
#105911222
#105911192
#789183
#787313