Finite Group Databasebeta

← #11860640

Subgroups — #11860640

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4#10592820C211yesmaximal, characteristic, complemented
5C3×#5122C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic
8#10590812C212yesmaximal, complemented
9Dic3×Dic12C212yesmaximal, complemented
10#10590766C212yesmaximal, complemented
11Dic3×#204C212yesmaximal, complemented
12#83965—31nomaximal
13#78571—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#909C418yescomplemented
22C2×C3×Dic12C2212yes—
23C2×C3×#204C2212yes—
24#67⋊Dic3—22no—
25#63955—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63843—21no—
29#63843—21no—
30Dic3×Dic6C2212yes—
31Dic3×Dic6C2212yes—
32Dic3×Dic6C2212yes—
33#63841—21no—
34#63645C2212yes—
35#63644C2212yes—
36C3×#815C2212yes—
37C3×C8×Dic3C2212yes—
38#63566C2212yes—
39#63566C2212yes—
40#63566C2211yescharacteristic
41#63566C2211yescharacteristic
42#63563C2211yescharacteristic
43#63563C2211yescharacteristic
44C2×C3×#137—31no—
45#5827—31no—
46#5812—31no—
47C2×#909D311yescharacteristic
48#5523—31no—
49#5516—31no—
50C3×#405—31no—
51#5233—31no—
52C2×#835—31no—
53#5184—32no—
54Dic3×Q16—32no—
55#5164—32no—
56Dic3×SD16—32no—
57#5122D311yescharacteristic, complemented
58#5121—31no—
59#5121—31no—
60#5121—61no—
61#5113—31no—
62C2×#816—31no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C3×#67—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C32×M16C2×C414yescomplemented
82C2×C32×C8C2312yes—
83#3757—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88C4×C3⋊Dic3—21no—
89C3×#217D412yes—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×Dic12C2×C418yescomplemented
97C3×#204C2×C418yescomplemented
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103Dic32—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C3×#137—38no—
111C2×C3×Q16—32no—
112C2×C3×SD16—32no—
113C2×C3×M16—21no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C2×D311yescharacteristic
116C22×C3×C8—31no—
117C3×#117—31no—
118Q8×Dic3—32no—
119Q8×Dic3—32no—
120Q8×Dic3—32no—
121Q8×Dic3—61no—
122Q8×Dic3—61no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125#926—31no—
126#926—31no—
127#926—61no—
128#926—62no—
129#926—61no—
130#926C2×D311yescharacteristic
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136#909Dic318yescomplemented
137C2×Dic12C2×D312yes—
138C2×#204C2×D312yes—
139#892—61no—
140D3×C4⋊C4—61no—
141#887—61no—
142#887—61no—
143#67⋊C4—62no—
144#877—62no—
145C4×D12—32no—
146C4×Dic6—32no—
147C4×Dic6—32no—
148C4×Dic6—32no—
149C3×#97—32no—
150C3×C4×C8—32no—
151#835—32no—
152#835—32no—
153#835—31no—
154#835—31no—
155#832—31no—
156#832—31no—
157#821—31no—
158#821—31no—
159#818—32no—
160#818—32no—
161#818—62no—
162#817—32no—
163#817—32no—
164#817—62no—
165#816—32no—
166#816—31no—
167#816—32no—
168#816—31no—
169#815C2×D312yes—
170C8×Dic3C2×D312yes—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—81no—
181C3×#67—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6C22×C414yes—
194C3×Dic6C22×C412yes—
195D3×Dic3—82no—
196C32×C8C22×C414yes—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C2×#137—31no—
200#520—91no—
201#519—91no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—91no—
208C2×#103—91no—
209#405—31no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C22×Dic3—21no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—62no—
229C22×Dic3—121no—
230#235—22no—
231#235C2×Dic314yes—
232C2×D12C22×D311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—62no—
235C2×Dic6—21no—
236C2×Dic6—22no—
237C2×Dic6C2×Dic314yescomplemented
238C2×Dic6C22×D312yes—
239C2×Dic6C22×D311yescharacteristic
240C3×Q16—38no—
241C3×SD16—38no—
242C3×M16—24no—
243C3×M16C4×D314yescomplemented
244C3×M16C2×Dic314yescomplemented
245C2×C3×C8—22no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C2×C3×C8—62no—
249C2×C3×C8C22×D312yes—
250C2×C3×C8C22×D312yes—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C22⋊C4—32no—
254C3×C42—32no—
255#217—61no—
256#217—61no—
257#217—62no—
258#217—121no—
259#217D1212yes—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—32no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—32no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—121no—
276C4⋊Dic3D1211yescharacteristic
277C4⋊Dic3D1211yescharacteristic
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—121no—
290C4×Dic3C22×D312yes—
291C2×C3⋊C8—22no—
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D311yescharacteristic
294Dic12C2×Dic318yescomplemented
295#204C2×Dic318yescomplemented
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4C4×D412yes—
304C32×C4C23×C411yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—42no—
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3×Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—38no—
316C2×Q16—32no—
317C2×SD16—32no—
318C2×M16D3211yescharacteristic
319C22×C8—31no—
320C4×Q8—92no—
321C4×Q8—92no—
322C4×Q8—92no—
323C4×Q8—181no—
324C4×Q8—181no—
325C4×D4—92no—
326C4×D4—182no—
327#117—31no—
328#117—91no—
329#117—182no—
330#117—181no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—181no—
333#107—92no—
334#106—92no—
335#103—92no—
336#103—92no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#97—32no—
342C4×C8—32no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3C2×D1211yescharacteristic
346C23×C3D3×D411yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—62no—
352C3×Q8—61no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—64no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—64no—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23512yes—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23712yes—
371C2×C3×C4C22×Dic312yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—24no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—62no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—122no—
387C2×Dic3—242no—
388C2×Dic3—241no—
389C2×Dic3—241no—
390C2×Dic3—242no—
391C2×Dic3C2×D1212yes—
392C2×Dic3C2×D1212yes—
393D12—21no—
394D12C22×Dic312yes—
395C4×D3—24no—
396C4×D3—242no—
397Dic6—24no—
398Dic6—22no—
399Dic6—21no—
400Dic6C22×Dic314yes—
401Dic6C22×Dic312yes—
402C3×C8—24no—
403C3×C8—61no—
404C3×C8—61no—
405C3×C8C2×C4×D314yes—
406C3×C8C22×Dic314yes—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—32no—
417C2×Q8—31no—
418C2×Q8—34no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—182no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—38no—
429SD16—38no—
430M16D3×Dic314yescomplemented
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—62no—
434C2×C8C2×D3212yes—
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—91no—
438C4⋊C4—91no—
439C4⋊C4—92no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4—181no—
444C22⋊C4—32no—
445C22⋊C4—182no—
446C22⋊C4—181no—
447C42—32no—
448C42—182no—
449C42—182no—
450C42—182no—
451C42—181no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3C4×D1212yes—
464C22×C3D4×Dic312yes—
465C22×C3C22×D1211yescharacteristic
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—62no—
474C3×C4—64no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4C4×D1212yes—
478C3×C4D4×Dic312yes—
479C3×C4C22×C4×D311yescharacteristic
480C3×C4C2×#23511yescharacteristic
481C3×C4C2×#23711yescharacteristic
482C3×C4C23×Dic311yescharacteristic
483Dic3—22no—
484Dic3—22no—
485Dic3—24no—
486Dic3—22no—
487Dic3—122no—
488Dic3—121no—
489Dic3—121no—
490Dic3—122no—
491Dic3—121no—
492Dic3—121no—
493Dic3—242no—
494Dic3—241no—
495Dic3—241no—
496C32#294711yescharacteristic, complemented, Sylow
497C23—61no—
498C23D3×D1211yescharacteristic
499Q8—34no—
500Q8—32no—
501Q8—62no—
502Q8—61no—
503Q8—64no—
504D4—32no—
505D4—64no—
506D4—61no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—182no—
516C2×C4—722no—
517C2×C4—721no—
518C2×C4#379512yes—
519C2×C4D3×D1211yescharacteristic
520C2×C4C2×D3×Dic312yes—
521C2×C4C22×D3211yescharacteristic
522C8—61no—
523C8—61no—
524C8C2×D3×Dic314yes—
525C2×C3—22no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—42no—
531C2×C3—122no—
532C2×C3C2×C4×D1211yescharacteristic
533C2×C3#575111yescharacteristic
534C2×C3#575311yescharacteristic
535C2×C3#577811yescharacteristic
536C2×C3#577911yescharacteristic
537C2×C3C2×D4×Dic311yescharacteristic
538D3—42no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—121no—
543C22—121no—
544C22Dic3×D1212yes—
545C22C2×D3×D1211yescharacteristic
546C4—62no—
547C4—64no—
548C4—62no—
549C4—62no—
550C4—362no—
551C4—361no—
552C4—361no—
553C4Dic3×D1212yes—
554C4C2×#379511yescharacteristic
555C4C22×D3×Dic311yescharacteristic
556C3—21no—
557C3#7857111yescharacteristic, complemented
558C3#8396511yescharacteristic, complemented
559C2—22no—
560C2—122no—
561C2#1059471511yescharacteristic
562C2#1059472111yescharacteristic
563C2C2×Dic3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
4. #10592820C2semidirect
5. C3×#5122C2semidirect
6. C2×#63566C2semidirect
8. #10590812C2semidirect
9. Dic3×Dic12C2semidirect
10. #10590766C2semidirect
11. Dic3×#204C2semidirect
21. C3×#909C4semidirect
57. #5122D3semidirect
77. C2×C3×Dic6C2×C4semidirect
81. C32×M16C2×C4semidirect
96. C3×Dic12C2×C4semidirect
97. C3×#204C2×C4semidirect
136. #909Dic3semidirect
237. C2×Dic6C2×Dic3semidirect
243. C3×M16C4×D3semidirect
244. C3×M16C2×Dic3semidirect
294. Dic12C2×Dic3semidirect
295. #204C2×Dic3semidirect
430. M16D3×Dic3semidirect
496. C32#2947semidirect
557. C3#78571semidirect
558. C3#83965semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105949922
#105948182
#105928202
C3×#51222
C2×#635662
#105910842
#105908122
Dic3×Dic122
#105907662
Dic3×#2042
#839653
#785713