Finite Group Databasebeta

← #13155540

Subgroups — #13155540

Order 1728.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723437C211yesmaximal, characteristic
2#11722072C211yesmaximal, characteristic
3#11722050C211yesmaximal, characteristic, complemented
4#11722050C211yesmaximal, characteristic, complemented
5C3×#63557C211yesmaximal, characteristic
6C3×#63554C211yesmaximal, characteristic, complemented
7C3×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590697—31nomaximal
9#10590696—31nomaximal
10#10590298—31nomaximal
11C2×C3×C4×C3⋊D3C2211yescharacteristic
12C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
15C32×C4×Dic3C2211yescharacteristic
16C2×C32×C3⋊C8C2211yescharacteristic
17C2×C32×C3⋊C8C2211yescharacteristic
18#88807C411yescharacteristic
19#88807C411yescharacteristic
20#88803C411yescharacteristic
21#88803C411yescharacteristic
22#64081—31no—
23#63855—31no—
24#63855—31no—
25#63855—61no—
26#63641—31no—
27#63641—31no—
28C3×(C2×D3)⋊C8—31no—
29C3×(C2×D3)⋊C8—31no—
30C3×#815—31no—
31C3×C8×Dic3—31no—
32C3×#803—31no—
33C3×C4×C3⋊C8—31no—
34#63572—31no—
35#63572—31no—
36#63572—31no—
37#63572—31no—
38#63572—61no—
39#63572—61no—
40#63557—31no—
41#63557D311yescharacteristic
42(C2×D3)⋊(C3⋊C8)—31no—
43(C2×D3)⋊(C3⋊C8)—31no—
44#63554D311yescharacteristic, complemented
45Dic3×C3⋊C8D311yescharacteristic, complemented
46C22×C3×C3⋊D3C2×C411yescharacteristic
47C2×C33×C4C2311yescharacteristic
48C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
49C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
50C2×C3×C3⋊Dic3C2×C411yescharacteristic
51C3×C4×C3⋊D3—21no—
52C3×C4×C3⋊D3—21no—
53C2×C32×Dic3C2×C411yescharacteristic
54C2×C32×Dic3C2×C411yescharacteristic
55C3×C3⋊(C3⋊C8)—21no—
56C3×C3⋊(C3⋊C8)—21no—
57C32×C3⋊C8—21no—
58C32×C3⋊C8—21no—
59#4720—91no—
60#4709—91no—
61#4690—91no—
62C2×C4×C3⋊D3C2×D311yescharacteristic
63C2×C3×C4×D3—31no—
64C2×C3×C4×D3—31no—
65C2×C3×C4×D3—61no—
66C2×C32×C8—31no—
67C2×C32×C8—31no—
68C32×C42—31no—
69#3752—31no—
70#3752—31no—
71#3750—31no—
72#3750—31no—
73C4×C3⋊Dic3—31no—
74C4×C3⋊Dic3—31no—
75C4×C3⋊Dic3—31no—
76C4×C3⋊Dic3—61no—
77C4×C3⋊Dic3—61no—
78C4×C3⋊Dic3—61no—
79C4×C3⋊Dic3—121no—
80C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
81C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
82C3×C4×Dic3—21no—
83C3×C4×Dic3C2×D311yescharacteristic
84C3×C4×Dic3C2×D311yescharacteristic
85C2×C3×C3⋊C8—21no—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8—31no—
88C2×C3×C3⋊C8—31no—
89C2×C3×C3⋊C8—31no—
90C2×C3×C3⋊C8—31no—
91C2×C3×C3⋊C8—61no—
92C2×C3×C3⋊C8—61no—
93C2×C3×C3⋊C8C2×D311yescharacteristic
94C2×C3×C3⋊C8C2×D311yescharacteristic
95C2×C3×C3⋊C8C2×D311yescharacteristic
96C2×C3×C3⋊C8C2×D311yescharacteristic
97Dic3⋊Dic3—31no—
98Dic3⋊Dic3—31no—
99Dic3⋊Dic3—31no—
100Dic3⋊Dic3—31no—
101Dic3⋊Dic3—61no—
102Dic3⋊Dic3—61no—
103(C2×D3)⋊Dic3—31no—
104(C2×D3)⋊Dic3—31no—
105(C2×D3)⋊Dic3—31no—
106(C2×D3)⋊Dic3—31no—
107(C2×D3)⋊Dic3—61no—
108(C2×D3)⋊Dic3—61no—
109C22×C33C22×C411yescharacteristic
110C2×C3×C3⋊D3—21no—
111C2×C3×C3⋊D3—21no—
112C2×C3×C3⋊D3—21no—
113C33×C4#4111yescharacteristic
114C33×C4#4111yescharacteristic
115C3⋊(C3⋊Dic3)—21no—
116C3⋊(C3⋊Dic3)—21no—
117C3×C3⋊Dic3—21no—
118C32×Dic3—21no—
119C32×Dic3—21no—
120#926—91no—
121#872—91no—
122#872—91no—
123#872—181no—
124C3×C22⋊C8—91no—
125C3×#97—91no—
126C3×C4×C8—91no—
127#830—91no—
128(C2×D3)⋊C8—31no—
129(C2×D3)⋊C8—31no—
130(C2×D3)⋊C8—91no—
131(C2×D3)⋊C8—91no—
132#815—31no—
133Dic3⋊C8—91no—
134Dic3⋊C8—91no—
135Dic3⋊C8—91no—
136Dic3⋊C8—91no—
137Dic3⋊C8—91no—
138Dic3⋊C8—91no—
139Dic3⋊C8—181no—
140Dic3⋊C8—181no—
141C8×Dic3—31no—
142#803—31no—
143C4×C3⋊C8—31no—
144C22×C3⋊D3C4×D311yescharacteristic
145C22×C3×D3—31no—
146C22×C3×D3—31no—
147C22×C3×D3—61no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—31no—
152C2×C32×C4—31no—
153C2×C32×C4—41no—
154C2×C32×C4C22×D311yescharacteristic
155C2×C32×C4C22×D311yescharacteristic
156C2×C32×C4C22×D311yescharacteristic
157C2×C3⋊Dic3—31no—
158C2×C3⋊Dic3—31no—
159C2×C3⋊Dic3—31no—
160C2×C3⋊Dic3—31no—
161C2×C3⋊Dic3—31no—
162C2×C3⋊Dic3—31no—
163C2×C3⋊Dic3—61no—
164C2×C3⋊Dic3—61no—
165C2×C3⋊Dic3—61no—
166C2×C3⋊Dic3—61no—
167C2×C3⋊Dic3—61no—
168C2×C3⋊Dic3—61no—
169C2×C3⋊Dic3—121no—
170C2×C3⋊Dic3—121no—
171C2×C3⋊Dic3C4×D311yescharacteristic
172C4×C3⋊D3—21no—
173C4×C3⋊D3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—31no—
177C2×C3×Dic3—31no—
178C2×C3×Dic3—61no—
179C2×C3×Dic3C4×D311yescharacteristic
180C2×C3×Dic3C4×D311yescharacteristic
181C2×C3×Dic3C4×D311yescharacteristic
182C2×C3×Dic3C4×D311yescharacteristic
183C3×C4×D3—62no—
184C3×C4×D3—62no—
185C3×C4×D3—61no—
186C3×C4×D3—61no—
187C3×C4×D3—61no—
188C3×C4×D3—61no—
189C32×C8—61no—
190C32×C8—61no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—21no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—41no—
198C3×C3⋊C8—41no—
199C3×C3⋊C8—61no—
200C3×C3⋊C8—61no—
201C3×C3⋊C8—61no—
202C3×C3⋊C8—61no—
203C3×C3⋊C8—121no—
204C3×C3⋊C8—121no—
205#433—271noSylow
206C2×C33#11711yescharacteristic
207C2×C33#13111yescharacteristic
208C2×C33#13111yescharacteristic
209C3×C3⋊D3—41no—
210C22×C3×C4—91no—
211C2×C4×D3—31no—
212C2×C4×D3—31no—
213C2×C4×D3—61no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—91no—
221C2×C3×C8—91no—
222C3×C42—31no—
223C3×C42—31no—
224C3×C42—61no—
225#217—91no—
226#217—91no—
227(C2×D3)⋊C4—91no—
228(C2×D3)⋊C4—91no—
229(C2×D3)⋊C4—91no—
230(C2×D3)⋊C4—91no—
231(C2×D3)⋊C4—181no—
232(C2×D3)⋊C4—181no—
233C4⋊Dic3—91no—
234C4⋊Dic3—91no—
235Dic3⋊C4—91no—
236Dic3⋊C4—91no—
237Dic3⋊C4—91no—
238Dic3⋊C4—91no—
239Dic3⋊C4—181no—
240Dic3⋊C4—181no—
241C4×Dic3—91no—
242C4×Dic3—91no—
243C4×Dic3—91no—
244C4×Dic3—181no—
245C4×Dic3—181no—
246C4×Dic3—181no—
247C4×Dic3—361no—
248C4×Dic3D3211yescharacteristic
249C2×C3⋊C8—31no—
250C2×C3⋊C8—31no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—31no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8D3211yescharacteristic
256C2×C3⋊C8D3211yescharacteristic
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—41no—
261C22×C32C2×C4×D311yescharacteristic
262C22×C32C2×C4×D311yescharacteristic
263C22×C32C2×C4×D311yescharacteristic
264C2×C3⋊D3—21no—
265C2×C3⋊D3—21no—
266C2×C3⋊D3—21no—
267C2×C3×D3—62no—
268C2×C3×D3—61no—
269C2×C3×D3—61no—
270C2×C3×D3—61no—
271C2×C3×D3—61no—
272C2×C3×D3—61no—
273C2×C3×D3—61no—
274C2×C3×D3—121no—
275C2×C3×D3—121no—
276C32×C4—21no—
277C32×C4—21no—
278C32×C4—21no—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—61no—
285C32×C4—61no—
286C32×C4#23511yescharacteristic
287C32×C4#23511yescharacteristic
288C32×C4#23511yescharacteristic
289C32×C4#23511yescharacteristic
290C32×C4#23711yescharacteristic
291C32×C4#23711yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—61no—
294C3⋊Dic3—61no—
295C3⋊Dic3—62no—
296C3⋊Dic3—62no—
297C3⋊Dic3—61no—
298C3⋊Dic3—61no—
299C3⋊Dic3—61no—
300C3⋊Dic3—61no—
301C3⋊Dic3—121no—
302C3⋊Dic3—121no—
303C3⋊Dic3—121no—
304C3⋊Dic3—121no—
305C3⋊Dic3—122no—
306C3⋊Dic3—122no—
307C3×Dic3—21no—
308C3×Dic3—21no—
309C3×Dic3—21no—
310C3×Dic3—21no—
311C3×Dic3—41no—
312C3×Dic3—41no—
313C3×Dic3—62no—
314C3×Dic3—61no—
315C3×Dic3—61no—
316#117—271no—
317C4⋊C8—271no—
318C4⋊C8—271no—
319C22⋊C8—91no—
320C22⋊C8—271no—
321#97—91no—
322C4×C8—91no—
323C33#43311yescharacteristic, complemented, Sylow
324C23×C3—91no—
325C22×D3—31no—
326C22×D3—31no—
327C22×D3—61no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—31no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—41no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—91no—
339C2×C3×C4—181no—
340C2×C3×C4—181no—
341C2×C3×C4C2×D3211yescharacteristic
342C2×C3×C4C2×D3211yescharacteristic
343C2×C3×C4C2×D3211yescharacteristic
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—61no—
347C2×Dic3—91no—
348C2×Dic3—91no—
349C2×Dic3—91no—
350C2×Dic3—91no—
351C2×Dic3—91no—
352C2×Dic3—91no—
353C2×Dic3—181no—
354C2×Dic3—181no—
355C2×Dic3—181no—
356C2×Dic3—181no—
357C2×Dic3—181no—
358C2×Dic3—181no—
359C2×Dic3—361no—
360C2×Dic3—361no—
361C2×Dic3#62411yescharacteristic
362C2×Dic3#62411yescharacteristic
363C4×D3—62no—
364C4×D3—62no—
365C4×D3—61no—
366C4×D3—61no—
367C4×D3—61no—
368C4×D3—61no—
369C3×C8—61no—
370C3×C8—61no—
371C3×C8—61no—
372C3×C8—61no—
373C3×C8—121no—
374C3×C8—121no—
375C3×C8—181no—
376C3×C8—181no—
377C3⋊C8—21no—
378C3⋊C8—21no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32—41no—
395C2×C32—41no—
396C2×C32—41no—
397C2×C32#87211yescharacteristic
398C2×C32#87211yescharacteristic
399C2×C32#87711yescharacteristic
400C2×C32#90111yescharacteristic
401C2×C32#90111yescharacteristic
402C2×C32#90111yescharacteristic
403C2×C32#90711yescharacteristic
404C2×C32#90711yescharacteristic
405C2×C32#90711yescharacteristic
406C3⋊D3—41no—
407C3×D3—122no—
408C3×D3—121no—
409C3×D3—121no—
410C22×C4—91no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—91no—
414C2×C8—91no—
415C4⋊C4—271no—
416C4⋊C4—271no—
417C22⋊C4—271no—
418C22⋊C4—271no—
419C42—31no—
420C42—271no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—41no—
425C22×C3—181no—
426C22×C3—181no—
427C22×C3—181no—
428C22×C3C4×D3211yescharacteristic
429C22×C3C4×D3211yescharacteristic
430C22×C3C2×#62411yescharacteristic
431C2×D3—62no—
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—61no—
435C2×D3—61no—
436C2×D3—61no—
437C2×D3—61no—
438C2×D3—121no—
439C2×D3—121no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—61no—
449C3×C4—61no—
450C3×C4—61no—
451C3×C4—61no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4—181no—
455C3×C4#379511yescharacteristic
456C3×C4#379511yescharacteristic
457C3×C4#379811yescharacteristic
458C3×C4#379811yescharacteristic
459C3×C4#380411yescharacteristic
460C3×C4#380411yescharacteristic
461Dic3—21no—
462Dic3—21no—
463Dic3—62no—
464Dic3—61no—
465Dic3—61no—
466Dic3—182no—
467Dic3—182no—
468Dic3—181no—
469Dic3—181no—
470Dic3—181no—
471Dic3—181no—
472Dic3—181no—
473Dic3—181no—
474Dic3—361no—
475Dic3—361no—
476Dic3—361no—
477Dic3—361no—
478Dic3—362no—
479Dic3—362no—
480C32—21no—
481C32—21no—
482C32—21no—
483C32—41no—
484C32#469011yescharacteristic, complemented
485C32#470911yescharacteristic, complemented
486C32#472011yescharacteristic, complemented
487C23—91no—
488C2×C4—31no—
489C2×C4—31no—
490C2×C4—91no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—271no—
494C2×C4—271no—
495C2×C4D3311yescharacteristic
496C8—61no—
497C8—61no—
498C8—181no—
499C8—181no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—41no—
512C2×C3—361no—
513C2×C3#6380311yescharacteristic
514C2×C3#6380411yescharacteristic
515C2×C3#6380411yescharacteristic
516C2×C3#6380511yescharacteristic
517C2×C3#6381711yescharacteristic
518C2×C3#6381711yescharacteristic
519C2×C3#6387411yescharacteristic
520C2×C3#6387711yescharacteristic
521C2×C3#6387711yescharacteristic
522D3—122no—
523D3—121no—
524D3—121no—
525C22—181no—
526C22—181no—
527C22—181no—
528C22D3×#62411yescharacteristic
529C4—61no—
530C4—61no—
531C4—181no—
532C4—541no—
533C4—541no—
534C4#8896011yescharacteristic
535C4#8896011yescharacteristic
536C3—21no—
537C3—21no—
538C3—21no—
539C3—41no—
540C3#1059029811yescharacteristic, complemented
541C3#1059069611yescharacteristic, complemented
542C3#1059069711yescharacteristic, complemented
543C2—361no—
544C2#1172282411yescharacteristic
545C2#1172282511yescharacteristic
546C2#1172291911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D33
commutator, socleC22×C33C22×C4
Fitting, cosocleC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C2×C4
hypocenterC33#433
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11722050C2semidirect
4. #11722050C2semidirect
6. C3×#63554C2semidirect
7. C3×Dic3×C3⋊C8C2semidirect
44. #63554D3semidirect
45. Dic3×C3⋊C8D3semidirect
323. C33#433semidirect
484. C32#4690semidirect
485. C32#4709semidirect
486. C32#4720semidirect
540. C3#10590298semidirect
541. C3#10590696semidirect
542. C3#10590697semidirect

Maximal subgroups

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

subgroupindex
#117234372
#117220722
#117220502
C3×#635572
C3×#635542
C3×Dic3×C3⋊C82
#105906973
#105906963
#105902983