Finite Group Databasebeta

← #11860624

Subgroups — #11860624

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596283C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3#10594986C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591582C212yesmaximal, complemented
6#10591581C212yesmaximal, complemented
7#10591572C212yesmaximal, complemented
8#10591571C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591084C211yesmaximal, characteristic
11#10591059C211yesmaximal, characteristic, complemented
12#83965—31nomaximal
13#78774—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16Q8×C3⋊Dic3—21no—
17Q8×C3⋊Dic3—21no—
18Q8×C3⋊Dic3C2212yes—
19Q8×C3⋊Dic3C2212yes—
20#64135—22no—
21#64135C2211yescharacteristic
22#64135C2211yescharacteristic
23C2×C3×#216C2212yes—
24C3×#942C418yescomplemented
25C2×C3×#215C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29Dic3×#67—22no—
30#63898C2212yes—
31D3×C4⋊Dic3—21no—
32#63843C2212yes—
33#63841—21no—
34C3×#835C2212yes—
35C3×#835C2212yes—
36#63575C2212yes—
37#63573C2212yes—
38#63566C2211yescharacteristic
39#63566C2211yescharacteristic
40#63563C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#63553C2212yes—
44C2×C3×#137—31no—
45#5827—31no—
46#5812—31no—
47#5812—31no—
48#5812—61no—
49C2×#942D311yescharacteristic
50#5504—31no—
51C2×C3×#103—31no—
52#5233—31no—
53C2×#835D311yescharacteristic, complemented
54#5184—32no—
55Dic3×Q16—32no—
56#5164—32no—
57Dic3×SD16—32no—
58#5122—31no—
59#5121—31no—
60#5113—31no—
61#5101—31no—
62#4964—31no—
63#4817—32no—
64#4790—32no—
65#4789—32no—
66#4788—32no—
67C2×C32×Q8—21no—
68C2×C32×Q8—22no—
69C2×C32×Q8C2×C414yescomplemented
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81#3757—21no—
82#3757D412yes—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3C2312yes—
93C3×#216C2×C418yescomplemented
94C3×#215C2×C418yescomplemented
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×#208C2×C414yescomplemented
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—21no—
108C22×C3×Q8C2×D311yescharacteristic
109C22×C3×Q8C2×D311yescharacteristic
110C2×#235C2×D311yescharacteristic
111C3×#137—38no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C2×C3×M16—31no—
115C22×C3×C8—31no—
116C2×C3×C4⋊C4—31no—
117Q8×Dic3—32no—
118Q8×Dic3—32no—
119Q8×Dic3—32no—
120Q8×Dic3—32no—
121Q8×Dic3—32no—
122Q8×Dic3—62no—
123Q8×Dic3—62no—
124Q8×Dic3—61no—
125Q8×Dic3—61no—
126Q8×Dic3—61no—
127Q8×Dic3—61no—
128Q8×Dic3—62no—
129Q8×Dic3—62no—
130C2×#216C2×D312yes—
131#942Dic318yescomplemented
132C2×#215C2×D312yes—
133D4×Dic3—32no—
134D4×Dic3—62no—
135C4×#67—62no—
136#926—31no—
137#926—31no—
138#926—31no—
139#926—31no—
140#926—61no—
141#926—61no—
142#926—61no—
143#926—62no—
144#926—62no—
145#926—64no—
146C2×C4⋊Dic3—61no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×#208C2×D311yescharacteristic
149C22×C3⋊C8C2×D311yescharacteristic
150#893—32no—
151#892—61no—
152D3×C4⋊C4—61no—
153#887—32no—
154C3×#103—32no—
155C3×#103—32no—
156#835—31no—
157#835—31no—
158#835C2×D312yes—
159#835C2×D312yes—
160#832—31no—
161#832—31no—
162#821—31no—
163#821—31no—
164#818—32no—
165#817—32no—
166#816—31no—
167#816—31no—
168#815—32no—
169#815—32no—
170C8×Dic3—32no—
171C8×Dic3—32no—
172#808—32no—
173#807—32no—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—21no—
176C32×Q8—24no—
177C32×Q8—22no—
178C32×Q8C22×C414yes—
179C2×C32×C4—24no—
180C2×C32×C4—22no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3C2×D412yes—
188C2×C3⋊Dic3C2×D412yes—
189C3×#67—24no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—81no—
193C3×D12—21no—
194C3×D12C22×C412yes—
195C3×C4×D3—24no—
196C3×Dic6—21no—
197C3×Dic6C22×C412yes—
198D3×Dic3—82no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C22×C414yes—
202C2×#137—31no—
203#520—91no—
204#519—91no—
205#441—92no—
206#440—92no—
207C4×Q16—92no—
208C4×SD16—92no—
209#428—91no—
210#416—91no—
211C2×#103—31no—
212#405—91no—
213C3×#41—34no—
214C3×#41—62no—
215C2×C3×Q8—22no—
216C2×C3×Q8—24no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C2×C3×Q8—22no—
223C2×C3×Q8—31no—
224C2×C3×Q8C4×D314yescomplemented
225C2×C3×Q8C2×Dic314yescomplemented
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C22×D312yes—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C22×Dic3—21no—
240C22×Dic3—62no—
241#235—22no—
242#235C2×Dic314yes—
243C2×D12C22×D311yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—62no—
246C2×Dic6C22×D311yescharacteristic
247C3×Q16—38no—
248C3×SD16—38no—
249C3×M16—34no—
250C2×C3×C8—32no—
251C2×C3×C8—31no—
252C2×C3×C8—31no—
253C2×C3×C8—62no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—61no—
256#217—32no—
257#217—32no—
258#217—62no—
259#217—62no—
260#217—62no—
261#217—61no—
262#217—61no—
263#216C2×Dic318yescomplemented
264#215C2×Dic318yescomplemented
265(C2×D3)⋊C4—62no—
266C4⋊Dic3—21no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—64no—
285C4⋊Dic3—64no—
286C4⋊Dic3C22×D312yes—
287Dic3⋊C4—62no—
288C4×Dic3—32no—
289C4×Dic3—32no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—64no—
298C4×Dic3—64no—
299C4×Dic3—62no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302#208C2×Dic314yescomplemented
303C2×C3⋊C8—22no—
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D312yes—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C4×D412yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C32×C4—24no—
315C32×C4C4×D412yes—
316C32×C4C23×C411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—22no—
319C3⋊Dic3—22no—
320C3⋊Dic3—41no—
321C3⋊Dic3—41no—
322C3×Dic3—22no—
323C3×Dic3—42no—
324C2×#41—31no—
325C22×Q8D3211yescharacteristic
326#137—38no—
327C2×Q16—32no—
328C2×SD16—32no—
329C2×M16—31no—
330C22×C8—31no—
331C4×Q8—92no—
332C4×Q8—92no—
333C4×Q8—92no—
334C4×Q8—181no—
335C4×Q8—181no—
336C4×D4—92no—
337C4×D4—182no—
338#117—91no—
339#117—91no—
340#117—182no—
341#117—181no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—181no—
344#107—92no—
345#106—92no—
346#103—32no—
347#103—32no—
348#103—91no—
349#103—91no—
350#102—91no—
351#102—91no—
352#97—92no—
353C4×C8—92no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3D3×D411yescharacteristic
357C23×C3D3×D411yescharacteristic
358C22×D3—21no—
359C3×Q8—24no—
360C3×Q8—28no—
361C3×Q8—24no—
362C3×Q8—24no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8—24no—
366C3×Q8—32no—
367C3×Q8—61no—
368C3×Q8C2×C4×D314yes—
369C3×Q8C22×Dic314yes—
370C3×D4—32no—
371C3×D4—64no—
372C3×D4—61no—
373C2×C3×C4—24no—
374C2×C3×C4—28no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—61no—
384C2×C3×C4—64no—
385C2×C3×C4—62no—
386C2×C3×C4—241no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4#23712yes—
391C2×C3×C4#23712yes—
392C2×C3×C4C22×Dic312yes—
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—24no—
396C2×Dic3—21no—
397C2×Dic3—22no—
398C2×Dic3—32no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—81no—
411C2×Dic3—242no—
412D12—21no—
413D12C22×Dic312yes—
414C4×D3—24no—
415C4×D3—242no—
416Dic6—21no—
417Dic6C22×Dic312yes—
418C3×C8—34no—
419C3×C8—61no—
420C3×C8—61no—
421C3⋊C8—21no—
422C3⋊C8—21no—
423C3⋊C8C22×Dic314yes—
424C2×C32—22no—
425C2×C32C2×C4×D411yescharacteristic
426C2×C32#57711yescharacteristic
427C2×C32#57811yescharacteristic
428C3×D3—42no—
429#41—34no—
430#41—62no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—31no—
434C2×Q8D3×Dic314yescomplemented
435C2×Q8C2×D3212yes—
436C2×D4—31no—
437C2×D4—61no—
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—182no—
442C22×C4C2×D3211yescharacteristic
443Q16—38no—
444SD16—38no—
445M16—34no—
446C2×C8—32no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C4⋊C4—32no—
451C4⋊C4—61no—
452C4⋊C4—91no—
453C4⋊C4—91no—
454C4⋊C4—91no—
455C4⋊C4—91no—
456C4⋊C4—182no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C22⋊C4—92no—
460C22⋊C4—182no—
461C22⋊C4—181no—
462C42—92no—
463C42—182no—
464C42—182no—
465C42—182no—
466C42—181no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—62no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3#67⋊C412yes—
479C22×C3D4×Dic312yes—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C2×D3—22no—
483C2×D3—41no—
484C2×D3—41no—
485C3×C4—28no—
486C3×C4—24no—
487C3×C4—24no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—62no—
492C3×C4—122no—
493C3×C4#67⋊C412yes—
494C3×C4D4×Dic312yes—
495C3×C4C22×C4×D311yescharacteristic
496C3×C4C2×#23711yescharacteristic
497C3×C4C2×#23711yescharacteristic
498C3×C4C23×Dic311yescharacteristic
499Dic3—22no—
500Dic3—42no—
501Dic3—62no—
502Dic3—62no—
503Dic3—62no—
504Dic3—62no—
505Dic3—122no—
506Dic3—122no—
507Dic3—122no—
508Dic3—122no—
509Dic3—121no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513C32#294711yescharacteristic, complemented, Sylow
514C23—61no—
515C23#381111yescharacteristic
516Q8—22no—
517Q8—24no—
518Q8—32no—
519Q8—61no—
520Q8C2×D3×Dic314yes—
521D4—32no—
522D4—64no—
523D4—61no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—61no—
527C2×C4—64no—
528C2×C4—62no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—241no—
534C2×C4—722no—
535C2×C4C2×D3×Dic312yes—
536C2×C4#380512yes—
537C2×C4#381111yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—34no—
540C8—61no—
541C8—61no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—122no—
549C2×C3C2×#67⋊C411yescharacteristic
550C2×C3#576211yescharacteristic
551C2×C3#576611yescharacteristic
552C2×C3#577811yescharacteristic
553C2×C3#577911yescharacteristic
554C2×C3C2×D4×Dic311yescharacteristic
555D3—42no—
556C22—21no—
557C22—21no—
558C22—62no—
559C22—121no—
560C22—121no—
561C22#67⋊Dic312yes—
562C22C2×#381111yescharacteristic
563C4—24no—
564C4—62no—
565C4—122no—
566C4—182no—
567C4—182no—
568C4—361no—
569C4—361no—
570C4#67⋊Dic312yes—
571C4C22×D3×Dic311yescharacteristic
572C4C2×#380511yescharacteristic
573C3—21no—
574C3#7877411yescharacteristic, complemented
575C3#8396511yescharacteristic, complemented
576C2—22no—
577C2—122no—
578C2#1059532411yescharacteristic
579C2#1059533711yescharacteristic
580C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596283C2semidirect
4. C2×C3×#835C2semidirect
5. #10591582C2semidirect
6. #10591581C2semidirect
7. #10591572C2semidirect
8. #10591571C2semidirect
9. #10591130C2semidirect
11. #10591059C2semidirect
24. C3×#942C4semidirect
53. C2×#835D3semidirect
69. C2×C32×Q8C2×C4semidirect
93. C3×#216C2×C4semidirect
94. C3×#215C2×C4semidirect
97. C3×#208C2×C4semidirect
131. #942Dic3semidirect
224. C2×C3×Q8C4×D3semidirect
225. C2×C3×Q8C2×Dic3semidirect
263. #216C2×Dic3semidirect
264. #215C2×Dic3semidirect
302. #208C2×Dic3semidirect
434. C2×Q8D3×Dic3semidirect
513. C32#2947semidirect
574. C3#78774semidirect
575. C3#83965semidirect

Maximal subgroups

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

subgroupindex
#105962832
C2×C3×#9422
#105949862
C2×C3×#8352
#105915822
#105915812
#105915722
#105915712
#105911302
#105910842
#105910592
#839653
#787743