Finite Group Databasebeta

← #11868992

Subgroups — #11868992

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2#10595051C211yesmaximal, characteristic, complemented
3#10592697C211yesmaximal, characteristic, complemented
4C3×#4995C211yesmaximal, characteristic, complemented
5#10591117C211yesmaximal, characteristic, complemented
6#10591086C211yesmaximal, characteristic
7C2×#63562C211yesmaximal, characteristic
8#10590558C212yesmaximal, complemented
9#10590555C212yesmaximal, complemented
10#10590545C212yesmaximal, complemented
11#10590542C212yesmaximal, complemented
12#82539—31nomaximal
13#79242—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#893C2212yes—
22C3×#893C2212yes—
23C3×D3×C22⋊C4—22no—
24C3×C4×D12—21no—
25C3×C4×D12—21no—
26#63964—22no—
27#63919—21no—
28#63918C2212yescomplemented
29#63872—21no—
30#63869C2212yescomplemented
31#63635C2211yescharacteristic, complemented
32#63635C2211yescharacteristic, complemented
33#63634C2211yescharacteristic, complemented
34#63634C2211yescharacteristic, complemented
35C3×#808C2212yescomplemented
36C3×#807C2212yescomplemented
37Dic3⋊(C3⋊C8)C2212yescomplemented
38Dic3⋊(C3⋊C8)C2212yescomplemented
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42#63562C2212yes—
43C3×#518—31no—
44#5521D311yescharacteristic
45#5519—31no—
46#5500—31no—
47C3×#428—31no—
48#5215—31no—
49C2×#832—31no—
50#5131—31no—
51#5119—31no—
52#5009—32no—
53#5009—32no—
54#5008—32no—
55#5007—32no—
56#4999—31no—
57#4998—31no—
58#4998—31no—
59#4998—61no—
60#4995D311yescharacteristic, complemented
61C2×#809—31no—
62#4891—32no—
63#4890—32no—
64#4871—32no—
65#4870—32no—
66C23×C3×D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12Q814yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×#627—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42—21no—
80#3757—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4×C3⋊Dic3—21no—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#217D412yes—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×C4×Dic3C2312yes—
95C3×#208—22no—
96C2×C3×C3⋊C8C2312yes—
97#3724—22no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C2×C3×M16—31no—
104C3×C4×D4—32no—
105C3×C4×D4—32no—
106C3×C4×D4—61no—
107C3×C4×D4—61no—
108C3×#117—21no—
109C3×#117—31no—
110C3×#117C2×D311yescharacteristic
111C3×#117C2×D311yescharacteristic
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—62no—
114#926—31no—
115#926—31no—
116#926—61no—
117#926C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119#924—62no—
120C2×#208C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124#893C2×D312yes—
125#893C2×D312yes—
126#890—32no—
127#890—61no—
128#890—61no—
129#888—32no—
130#888—61no—
131#888—61no—
132D3×C22⋊C4—22no—
133#878—62no—
134C4×D12—21no—
135C4×D12—21no—
136#870—32no—
137#869—32no—
138C3×#107—32no—
139C3×#106—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#821—32no—
145#821—32no—
146Dic3⋊C8—32no—
147Dic3⋊C8—32no—
148#809—32no—
149#809—32no—
150#808—31no—
151#808—31no—
152#808—31no—
153#808—31no—
154#808—61no—
155#808—61no—
156#808C2×D312yescomplemented
157#807—31no—
158#807—31no—
159#807—31no—
160#807—31no—
161#807—61no—
162#807—61no—
163#807C2×D312yescomplemented
164C4⋊(C3⋊C8)—32no—
165C4⋊(C3⋊C8)—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—24no—
169C22×C3×D3—81no—
170C22×C3×D3—81no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×Q812yes—
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—81no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—24no—
184C3×D12—22no—
185C3×D12C2×Q814yes—
186C3×C4×D3—82no—
187C3×C4×D3—82no—
188#627—82no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
191C3×C3⋊C8—22no—
192#544—91no—
193#518—31no—
194#478—92no—
195#478—92no—
196#476—92no—
197#474—92no—
198#428—31no—
199#427—91no—
200#424—91no—
201#418—91no—
202C2×#102—91no—
203C24×C3—61no—
204C23×D3—21no—
205C2×C3×D4—34no—
206C2×C3×D4—32no—
207C2×C3×D4—62no—
208C2×C3×D4—61no—
209C22×C3×C4—21no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—21no—
216C2×D12—22no—
217C2×D12—21no—
218C2×D12Dic614yescomplemented
219C2×D12C22×D312yes—
220C2×C4×D3—22no—
221C2×C4×D3—22no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C3×M16—62no—
225C2×C3×C8—32no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—32no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42—41no—
246#217—61no—
247#217—61no—
248#217—121no—
249#217#6712yes—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3#6711yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—121no—
271C4×Dic3C22×D312yes—
272#208—22no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—64no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8C22×D312yes—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32C22⋊Q812yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—24no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—84no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4C22⋊Q812yes—
294C32×C4C22×Q811yescharacteristic
295C32×C4C2×#4111yescharacteristic
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3×Dic3—22no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C22×D4—31no—
302C2×M16—31no—
303C22×C8—91no—
304C4⋊Q8—92no—
305C4⋊Q8—181no—
306#125—92no—
307#125—181no—
308C22⋊Q8—182no—
309C4×D4—32no—
310C4×D4—32no—
311C4×D4—61no—
312C4×D4—61no—
313#117—31no—
314#117—91no—
315#117D3211yescharacteristic
316C2×C4⋊C4—31no—
317C2×C22⋊C4—62no—
318#107—32no—
319#107—91no—
320#107—91no—
321#106—32no—
322#106—91no—
323#106—91no—
324C4⋊C8—92no—
325C4⋊C8—92no—
326#102—92no—
327#102—92no—
328#102—92no—
329#102—92no—
330C23×C3—21no—
331C23×C3—62no—
332C23×C3—64no—
333C23×C3—241no—
334C23×C3—241no—
335C23×C3D3×D411yescharacteristic
336C23×C3C2×#6711yescharacteristic
337C22×D3—22no—
338C22×D3—24no—
339C22×D3—81no—
340C22×D3—81no—
341C3×D4—34no—
342C3×D4—64no—
343C3×D4—62no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4—242no—
358C2×C3×C4—242no—
359C2×C3×C4—241no—
360C2×C3×C4C2×Dic612yes—
361C2×C3×C4#23512yes—
362C2×C3×C4#23512yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×Q812yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×Dic3—22no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—81no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3C2×#6712yes—
377C2×Dic3C2×#6712yes—
378D12—24no—
379D12—22no—
380D12C2×Dic614yes—
381C4×D3—82no—
382C4×D3—82no—
383Dic6—242no—
384Dic6—242no—
385C3×C8—62no—
386C3⋊C8—22no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—61no—
393C2×C32—22no—
394C2×C32C2×C22⋊Q811yescharacteristic
395C2×C32#57611yescharacteristic
396C2×C32#57711yescharacteristic
397C3×D3—44no—
398C24—61no—
399C2×Q8—182no—
400C2×D4—32no—
401C2×D4—34no—
402C2×D4—62no—
403C2×D4—61no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—61no—
407C22×C4C2×D3211yescharacteristic
408M16—62no—
409C2×C8—32no—
410C2×C8—91no—
411C2×C8—91no—
412C2×C8—182no—
413C4⋊C4—31no—
414C4⋊C4—31no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4C2×D3211yescharacteristic
423C4⋊C4C2×D3211yescharacteristic
424C22⋊C4—21no—
425C22⋊C4—32no—
426C22⋊C4—62no—
427C22⋊C4—62no—
428C22⋊C4—181no—
429C42—21no—
430C42—32no—
431C42—181no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—64no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—244no—
444C22×C3#89612yes—
445C22×C3#92412yes—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—24no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—84no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—81no—
462C3×C4—81no—
463C3×C4—122no—
464C3×C4#89612yes—
465C3×C4#92412yes—
466C3×C4C22×Dic611yescharacteristic
467C3×C4C2×#23511yescharacteristic
468C3×C4C2×#23511yescharacteristic
469C3×C4C2×D3×Q811yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—42no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478Dic3—241no—
479C32#308111yescharacteristic, complemented, Sylow
480C23—62no—
481C23—64no—
482C23—241no—
483C23—241no—
484C23D3×#6711yescharacteristic
485Q8—722no—
486D4—34no—
487D4—62no—
488D4—64no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—242no—
497C2×C4—242no—
498C2×C4—241no—
499C2×C4D3×Dic612yes—
500C2×C4#379812yes—
501C2×C4D3×#6711yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—62no—
504C8—181no—
505C8—181no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—42no—
512C2×C3—124no—
513C2×C3C2×#89611yescharacteristic
514C2×C3#577411yescharacteristic
515C2×C3#577811yescharacteristic
516C2×C3C2×#92411yescharacteristic
517C2×C3#583511yescharacteristic
518C2×C3#583611yescharacteristic
519D3—44no—
520C22—21no—
521C22—21no—
522C22—64no—
523C22—122no—
524C22—122no—
525C22—244no—
526C22#6385112yes—
527C22C2×D3×#6711yescharacteristic
528C4—41no—
529C4—41no—
530C4—62no—
531C4—62no—
532C4—122no—
533C4—361no—
534C4—361no—
535C4#6385112yes—
536C4C2×D3×Dic611yescharacteristic
537C4C2×#379811yescharacteristic
538C3—21no—
539C3#7924211yescharacteristic, complemented
540C3#8253911yescharacteristic, complemented
541C2—22no—
542C2—124no—
543C2C2×#6385111yescharacteristic
544C2#1059545411yescharacteristic
545C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595051C2semidirect
3. #10592697C2semidirect
4. C3×#4995C2semidirect
5. #10591117C2semidirect
8. #10590558C2semidirect
9. #10590555C2semidirect
10. #10590545C2semidirect
11. #10590542C2semidirect
28. #63918C22semidirect
30. #63869C22semidirect
31. #63635C22semidirect
32. #63635C22semidirect
33. #63634C22semidirect
34. #63634C22semidirect
35. C3×#808C22semidirect
36. C3×#807C22semidirect
37. Dic3⋊(C3⋊C8)C22semidirect
38. Dic3⋊(C3⋊C8)C22semidirect
60. #4995D3semidirect
71. C2×C3×D12Q8semidirect
156. #808C2×D3semidirect
163. #807C2×D3semidirect
218. C2×D12Dic6semidirect
479. C32#3081semidirect
539. C3#79242semidirect
540. C3#82539semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105950512
#105926972
C3×#49952
#105911172
#105910862
C2×#635622
#105905582
#105905552
#105905452
#105905422
#825393
#792423