Finite Group Databasebeta

← #13155712

Subgroups — #13155712

Order 1728.

734 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#63898C211yesmaximal, characteristic, complemented
3C2×C3×#3713C211yesmaximal, characteristic
4#11722071C211yesmaximal, characteristic, complemented
5#11722054C211yesmaximal, characteristic, complemented
6#11722032C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8#10591436—31nomaximal
9#10591430—31nomaximal
10#10590455—31nomaximal
11C2×C32×D12C2211yescharacteristic
12C2×C32×D12C2211yescharacteristic
13C2×D3×C3⋊Dic3—21no—
14C2×C3×D3×Dic3—21no—
15C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
16C3×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
19C32×C4⋊Dic3C2211yescharacteristic
20(C2×D3)⋊(C3⋊Dic3)—21no—
21C3×(C2×D3)⋊Dic3—21no—
22C3×#3713C414yescomplemented
23D4×C3⋊Dic3—31no—
24C3×D4×Dic3—31no—
25C2×C3×#213—31no—
26C2×C3×#213—31no—
27C3×#893—31no—
28#63898D311yescharacteristic, complemented
29Dic3×D12—31no—
30Dic3×D12—31no—
31Dic3×D12—61no—
32C2×#3713D311yescharacteristic
33#63659—31no—
34#63635—31no—
35C3×#832—31no—
36C3×#809—31no—
37#63573—31no—
38#63573—31no—
39#63573—61no—
40#63563—31no—
41#63563—31no—
42#63563—61no—
43#63562D311yescharacteristic, complemented
44#63555—31no—
45#63554—31no—
46#63554—31no—
47C22×C32×D3—21no—
48C22×C32×D3—21no—
49C2×C33×C4C2311yescharacteristic
50C2×C3⋊(C3⋊Dic3)—21no—
51C2×C3×C3⋊Dic3D411yescharacteristic
52C2×C3×C3⋊Dic3D411yescharacteristic
53C2×C32×Dic3—21no—
54C32×D12—21no—
55C32×D12—21no—
56C32×D12C2×C412yescomplemented
57C32×D12C2×C412yescomplemented
58D3×C3⋊Dic3—42no—
59C3×D3×Dic3—42no—
60C3×C3⋊(C3⋊C8)—21no—
61C3×C3⋊(C3⋊C8)C2×C412yescomplemented
62#5152—91no—
63#5014—91no—
64#4785—91no—
65C2×C32×D4—31no—
66C2×C32×D4—31no—
67C22×C3⋊Dic3—61no—
68C22×C3×Dic3—61no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2×D311yescharacteristic
72C2×C3×D12C2×D311yescharacteristic
73C2×C3×D12C2×D311yescharacteristic
74C2×C3×D12C2×D311yescharacteristic
75C2×C3×C4×D3—61no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—61no—
78C2×D3×Dic3—61no—
79C2×D3×Dic3—62no—
80C32×C4⋊C4—31no—
81#3757—61no—
82C4⋊(C3⋊Dic3)—31no—
83C4⋊(C3⋊Dic3)—31no—
84C4⋊(C3⋊Dic3)—31no—
85C4⋊(C3⋊Dic3)—61no—
86C4⋊(C3⋊Dic3)—61no—
87C4⋊(C3⋊Dic3)—61no—
88C4⋊(C3⋊Dic3)—121no—
89C4×C3⋊Dic3C2×D311yescharacteristic
90C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
91C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
92C3×#217—61no—
93C3×#213—34no—
94C3×#213—34no—
95C3×(C2×D3)⋊C4—61no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2×D311yescharacteristic
98C3×C4⋊Dic3C2×D311yescharacteristic
99C3×C4×Dic3—31no—
100C3×C4×Dic3—31no—
101C3×C4×Dic3—61no—
102C2×C3×C3⋊C8—31no—
103C2×C3×C3⋊C8—31no—
104C2×C3×C3⋊C8—31no—
105C2×C3×C3⋊C8—31no—
106C2×C3×C3⋊C8—61no—
107C2×C3×C3⋊C8—61no—
108(C2×D3)⋊Dic3—21no—
109(C2×D3)⋊Dic3—61no—
110(C2×D3)⋊Dic3—61no—
111(C2×D3)⋊Dic3—62no—
112#3713Dic314yescomplemented
113C22×C33C2×D411yescharacteristic
114C2×C32×D3—22no—
115C2×C32×D3—22no—
116C2×C32×D3—41no—
117C2×C32×D3—41no—
118C2×C32×D3—41no—
119C2×C32×D3—41no—
120C33×C4C22×C411yescharacteristic
121C33×C4#4111yescharacteristic
122C3⋊(C3⋊Dic3)—41no—
123C3×C3⋊Dic3—21no—
124C3×C3⋊Dic3—21no—
125C32×Dic3—41no—
126C2×C3×D8—91no—
127C3×C4×D4—91no—
128D4×Dic3—31no—
129D4×Dic3—91no—
130D4×Dic3—91no—
131D4×Dic3—181no—
132C2×#213—31no—
133C2×#213—31no—
134#893—31no—
135C4×D12—91no—
136C3×#102—91no—
137#832—31no—
138#832—91no—
139#832—91no—
140#832—181no—
141#821—91no—
142#817—91no—
143#815—91no—
144#815—91no—
145#809—31no—
146#808—91no—
147#808—91no—
148#808—181no—
149#803—91no—
150C23×C32—61no—
151C23×C32—61no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—41no—
158C32×D4—32no—
159C32×D4—32no—
160C32×D4—61no—
161C32×D4—61no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—41no—
166C2×C32×C4—61no—
167C2×C32×C4C22×D311yescharacteristic
168C2×C32×C4C22×D311yescharacteristic
169C2×C32×C4C22×D311yescharacteristic
170C2×C3⋊Dic3—61no—
171C2×C3⋊Dic3—62no—
172C2×C3⋊Dic3—61no—
173C2×C3⋊Dic3—61no—
174C2×C3⋊Dic3—121no—
175C2×C3⋊Dic3—121no—
176C2×C3⋊Dic3—122no—
177C2×C3⋊Dic3—122no—
178C2×C3⋊Dic3#6711yescharacteristic
179C2×C3⋊Dic3#6711yescharacteristic
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—31no—
183C2×C3×Dic3—31no—
184C2×C3×Dic3—31no—
185C2×C3×Dic3—31no—
186C2×C3×Dic3—41no—
187C2×C3×Dic3—61no—
188C2×C3×Dic3—61no—
189C2×C3×Dic3—122no—
190C3×D12—22no—
191C3×D12—21no—
192C3×D12—21no—
193C3×D12—21no—
194C3×D12—21no—
195C3×D12—22no—
196C3×D12—22no—
197C3×D12—41no—
198C3×D12C4×D312yescomplemented
199C3×D12C4×D312yescomplemented
200C3×D12C2×Dic312yescomplemented
201C3×D12C2×Dic312yescomplemented
202C3×C4×D3—122no—
203D3×Dic3—42no—
204D3×Dic3—124no—
205D3×Dic3—122no—
206D3×Dic3—122no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)C2×Dic312yescomplemented
209C3×C3⋊C8—32no—
210C3×C3⋊C8—32no—
211C3×C3⋊C8—62no—
212C3×C3⋊C8—61no—
213C3×C3⋊C8—61no—
214C3×C3⋊C8—121no—
215#442—271noSylow
216C2×C33C4×D411yescharacteristic
217C2×C33AGL(1,ℤ/8)11yescharacteristic
218C2×C33AGL(1,ℤ/8)11yescharacteristic
219C32×D3—42no—
220C32×D3—42no—
221C2×C3×D4—31no—
222C2×C3×D4—31no—
223C2×C3×D4—31no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C22×C3×C4—181no—
228C22×Dic3—61no—
229C22×Dic3—181no—
230C22×Dic3—181no—
231C22×Dic3—182no—
232C2×D12D3211yescharacteristic
233C2×D12D3211yescharacteristic
234C2×C4×D3—61no—
235C2×C4×D3—181no—
236C3×D8—94no—
237C2×C3×C8—91no—
238C2×C3×C8—91no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—181no—
243C3×C42—91no—
244#217—61no—
245#217—181no—
246#217—181no—
247#217—182no—
248#213—34no—
249#213—34no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—181no—
252C4⋊Dic3—91no—
253C4⋊Dic3—91no—
254C4⋊Dic3—91no—
255C4⋊Dic3—181no—
256C4⋊Dic3—181no—
257C4⋊Dic3—181no—
258C4⋊Dic3—361no—
259C4⋊Dic3D3211yescharacteristic
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—61no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—41no—
273C22×C32—62no—
274C22×C32—62no—
275C22×C32—121no—
276C22×C32—121no—
277C22×C32—121no—
278C22×C32—121no—
279C22×C32D3×D411yescharacteristic
280C22×C32D3×D411yescharacteristic
281C22×C32C2×#6711yescharacteristic
282C2×C3×D3—24no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C2×C3×D3—81no—
299C2×C3×D3—81no—
300C32×C4—21no—
301C32×C4—21no—
302C32×C4—21no—
303C32×C4—21no—
304C32×C4—21no—
305C32×C4—21no—
306C32×C4—41no—
307C32×C4—41no—
308C32×C4—121no—
309C32×C4C2×C4×D311yescharacteristic
310C32×C4C2×C4×D311yescharacteristic
311C32×C4#23511yescharacteristic
312C32×C4#23711yescharacteristic
313C32×C4#23711yescharacteristic
314C32×C4C22×Dic311yescharacteristic
315C3⋊Dic3—21no—
316C3⋊Dic3—21no—
317C3⋊Dic3—121no—
318C3⋊Dic3—122no—
319C3⋊Dic3—121no—
320C3⋊Dic3—121no—
321C3⋊Dic3—241no—
322C3⋊Dic3—241no—
323C3⋊Dic3—242no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3—62no—
327C3×Dic3—61no—
328C3×Dic3—61no—
329C3×Dic3—61no—
330C3×Dic3—61no—
331C3×Dic3—81no—
332C3×Dic3—121no—
333C2×D8—91no—
334C4×D4—91no—
335C4×D4—271no—
336#106—271no—
337#102—91no—
338#102—271no—
339#97—271no—
340C33#44211yescharacteristic, complemented, Sylow
341C23×C3—62no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—121no—
347C22×D3—21no—
348C22×D3—21no—
349C3×D4—32no—
350C3×D4—32no—
351C3×D4—32no—
352C3×D4—32no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—62no—
356C3×D4—61no—
357C3×D4—61no—
358C3×D4—61no—
359C3×D4—61no—
360C3×D4—121no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—41no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—91no—
368C2×C3×C4—91no—
369C2×C3×C4—121no—
370C2×C3×C4—362no—
371C2×C3×C4C2×D3211yescharacteristic
372C2×C3×C4C2×D3211yescharacteristic
373C2×C3×C4C2×D3211yescharacteristic
374C2×Dic3—21no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—122no—
382C2×Dic3—182no—
383C2×Dic3—181no—
384C2×Dic3—181no—
385C2×Dic3—181no—
386C2×Dic3—361no—
387C2×Dic3—361no—
388C2×Dic3—362no—
389C2×Dic3—364no—
390C2×Dic3—362no—
391C2×Dic3—362no—
392D12—21no—
393D12—21no—
394D12D3×Dic312yescomplemented
395D12D3×Dic312yescomplemented
396C4×D3—122no—
397C4×D3—362no—
398C3×C8—92no—
399C3×C8—181no—
400C3⋊C8—32no—
401C3⋊C8—32no—
402C3⋊C8—62no—
403C3⋊C8—61no—
404C3⋊C8—61no—
405C3⋊C8—121no—
406C2×C32—21no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—41no—
416C2×C32—41no—
417C2×C32—41no—
418C2×C32—122no—
419C2×C32—122no—
420C2×C32#67⋊C411yescharacteristic
421C2×C32#91111yescharacteristic
422C2×C32#91111yescharacteristic
423C2×C32#91111yescharacteristic
424C2×C32#91411yescharacteristic
425C2×C32C4×#6711yescharacteristic
426C2×C32#93211yescharacteristic
427C2×C32D4×Dic311yescharacteristic
428C2×C32#94911yescharacteristic
429C3×D3—44no—
430C3×D3—42no—
431C3×D3—42no—
432C3×D3—42no—
433C3×D3—42no—
434C3×D3—82no—
435C2×D4—31no—
436C2×D4—31no—
437C22×C4—181no—
438C22×C4—541no—
439D8—94no—
440C2×C8—91no—
441C2×C8—91no—
442C4⋊C4—31no—
443C4⋊C4—271no—
444C22⋊C4—181no—
445C22⋊C4—541no—
446C42—91no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—41no—
451C22×C3—64no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3—121no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3—121no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3—241no—
468C22×C3—241no—
469C22×C3D3×#6711yescharacteristic
470C22×C3D3×#6711yescharacteristic
471C22×C3#381111yescharacteristic
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—41no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—121no—
487C3×C4—121no—
488C3×C4—181no—
489C3×C4—181no—
490C3×C4—241no—
491C3×C4#379511yescharacteristic
492C3×C4C4×D3211yescharacteristic
493C3×C4C2×D3×Dic311yescharacteristic
494C3×C4C2×D3×Dic311yescharacteristic
495C3×C4#380411yescharacteristic
496C3×C4#380511yescharacteristic
497Dic3—41no—
498Dic3—62no—
499Dic3—61no—
500Dic3—61no—
501Dic3—61no—
502Dic3—61no—
503Dic3—121no—
504Dic3—362no—
505Dic3—361no—
506Dic3—361no—
507Dic3—361no—
508Dic3—721no—
509Dic3—721no—
510Dic3—722no—
511C32—21no—
512C32—21no—
513C32—21no—
514C32—41no—
515C32#478511yescharacteristic, complemented
516C32#501411yescharacteristic, complemented
517C32#515211yescharacteristic, complemented
518C23—61no—
519C23—61no—
520D4—32no—
521D4—32no—
522D4—61no—
523D4—61no—
524C2×C4—61no—
525C2×C4—91no—
526C2×C4—91no—
527C2×C4—362no—
528C2×C4—541no—
529C2×C4—1082no—
530C2×C4D3311yescharacteristic
531C8—92no—
532C8—181no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—41no—
543C2×C3—41no—
544C2×C3—41no—
545C2×C3—124no—
546C2×C3—122no—
547C2×C3—122no—
548C2×C3—122no—
549C2×C3—122no—
550C2×C3—242no—
551C2×C3#6387911yescharacteristic
552C2×C3#6392511yescharacteristic
553C2×C3#6392711yescharacteristic
554C2×C3#6393211yescharacteristic
555C2×C3#6393211yescharacteristic
556C2×C3#6393711yescharacteristic
557C2×C3#6393911yescharacteristic
558C2×C3Dic3×#6711yescharacteristic
559C2×C3#67⋊Dic311yescharacteristic
560D3—42no—
561D3—42no—
562C22—62no—
563C22—62no—
564C22—121no—
565C22—121no—
566C22—121no—
567C22—121no—
568C22#8895211yescharacteristic
569C4—121no—
570C4—181no—
571C4—181no—
572C4—1081no—
573C4D32×Dic311yescharacteristic
574C4#8896111yescharacteristic
575C3—21no—
576C3—21no—
577C3—21no—
578C3—41no—
579C3#1059045511yescharacteristic, complemented
580C3#1059143011yescharacteristic, complemented
581C3#1059143611yescharacteristic, complemented
582C2—122no—
583C2—122no—
584C2#1172287211yescharacteristic
585C2#1172287411yescharacteristic
586C2#1172292411yescharacteristic
subgroupG/H
centerC22#88952
commutatorC33×C4C22×C4
Frattini, hypercenterC2×C4D33
Fitting, cosocleC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×C3×#3713C2
hypocenterC33#442
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. D12×C3⋊Dic3C2semidirect
2. C3×#63898C2semidirect
4. #11722071C2semidirect
5. #11722054C2semidirect
6. #11722032C2semidirect
7. C3×#63562C2semidirect
22. C3×#3713C4semidirect
28. #63898D3semidirect
43. #63562D3semidirect
56. C32×D12C2×C4semidirect
57. C32×D12C2×C4semidirect
61. C3×C3⋊(C3⋊C8)C2×C4semidirect
112. #3713Dic3semidirect
198. C3×D12C4×D3semidirect
199. C3×D12C4×D3semidirect
200. C3×D12C2×Dic3semidirect
201. C3×D12C2×Dic3semidirect
208. C3⋊(C3⋊C8)C2×Dic3semidirect
340. C33#442semidirect
394. D12D3×Dic3semidirect
395. D12D3×Dic3semidirect
515. C32#4785semidirect
516. C32#5014semidirect
517. C32#5152semidirect
579. C3#10590455semidirect
580. C3#10591430semidirect
581. C3#10591436semidirect

Maximal subgroups

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

subgroupindex
D12×C3⋊Dic32
C3×#638982
C2×C3×#37132
#117220712
#117220542
#117220322
C3×#635622
#105914363
#105914303
#105904553