Finite Group Databasebeta

← #11787601

Subgroups — #11787601

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3#10591318C211yesmaximal, characteristic
4C2×#63566C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6#10589417C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#68686—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204C414yescomplemented
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24Dic3×Dic6—22no—
25Dic3×Dic6—22no—
26#63566—22no—
27#63563—22no—
28C22×C3×SD16—31no—
29C2×Q8×Dic3—31no—
30C22×#204D311yescharacteristic
31C2×C4×Dic6—31no—
32C2×#835—31no—
33#5221—31no—
34C2×#832—31no—
35C2×#821—31no—
36C2×#816—31no—
37#4939—31no—
38C3×#336—31no—
39#4551—31no—
40#4551—31no—
41#4551—61no—
42#4550D311yescharacteristic, complemented
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8C2×C412yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yes—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C3×#204—28no—
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3—42no—
78Dic32—24no—
79#1880—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C22×D12C2×D311yescharacteristic
83C22×Dic6C2×D311yescharacteristic
84C2×C3×SD16—34no—
85C2×C3×SD16—62no—
86C2×C3×SD16—62no—
87C22×C3×C8—21no—
88C22×C3×C8—31no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C42—31no—
92C2×#217—61no—
93C2×#217—61no—
94Q8×Dic3—62no—
95Q8×Dic3—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3—61no—
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—22no—
111C2×#204—22no—
112C2×#204Dic314yescomplemented
113C4×Dic6—62no—
114C4×Dic6—62no—
115#835—62no—
116#832—62no—
117#821—62no—
118#816—62no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6C22⋊C414yescomplemented
156C32×C8—22no—
157C3×C3⋊C8—41no—
158C22×SD16—31no—
159C2×C4×Q8—91no—
160C2×#103—91no—
161C2×#102—91no—
162#390—91no—
163#340—91no—
164#336—31no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—32no—
168C2×C3×Q8—32no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—121no—
191C22×Dic3—121no—
192C22×Dic3D1211yescharacteristic
193C22×Dic3D1211yescharacteristic
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C2×Dic312yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6C2×Dic312yes—
204C2×Dic6#6712yes—
205C2×Dic6#6712yes—
206C3×SD16—68no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—22no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8C4×D312yes—
218C2×C3×C8C2×Dic312yes—
219C3×C42—61no—
220C3×C42—61no—
221#217—122no—
222#217—122no—
223(C2×D3)⋊C4—122no—
224(C2×D3)⋊C4—122no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—64no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—62no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—121no—
237C4⋊Dic3—121no—
238Dic3⋊C4—64no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246#204—28no—
247C22×C32C4×D411yescharacteristic
248C22×C32#12011yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32C2×SD1611yescharacteristic
251C22×C32#13511yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C22×C32#13711yescharacteristic
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4C2×C22⋊C411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12111yescharacteristic
264C32×C4#12311yescharacteristic
265C3⋊Dic3—42no—
266C3⋊Dic3—81no—
267C3×Dic3—24no—
268C3×Dic3—22no—
269C3×Dic3—41no—
270C22×Q8—31no—
271C22×D4—31no—
272C2×SD16—34no—
273C2×SD16—62no—
274C2×SD16—62no—
275C22×C8—31no—
276C22×C8D3211yescharacteristic
277C4×Q8—182no—
278C4×Q8—182no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—181no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C2×C42—181no—
286#103—182no—
287#102—182no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3C2×D1211yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C3×Q8—34no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—32no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23911yescharacteristic
337C2×C3×C4C22×Dic311yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—122no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—241no—
363C2×Dic3—241no—
364C2×Dic3—241no—
365C2×Dic3—241no—
366C2×Dic3#20412yescomplemented
367D12—22no—
368D12—22no—
369D12—41no—
370D12—41no—
371Dic6—22no—
372Dic6—22no—
373Dic6—22no—
374Dic6#21714yescomplemented
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—42no—
378C3×C8—121no—
379C3⋊C8—41no—
380C2×C32#38611yescharacteristic
381C2×C32C4×SD1611yescharacteristic
382C2×C32#44011yescharacteristic
383C2×C32#44811yescharacteristic
384C2×C32#44911yescharacteristic
385C2×C32#46011yescharacteristic
386C2×C32#46411yescharacteristic
387C3×D3—82no—
388C24—61no—
389C2×Q8—32no—
390C2×Q8—32no—
391C2×Q8—32no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4C2×D3211yescharacteristic
407SD16—68no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8D3×Dic312yes—
414C4⋊C4—92no—
415C4⋊C4—184no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C22⋊C4—362no—
420C22⋊C4—362no—
421C42—61no—
422C42—61no—
423C42—184no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—241no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3C4×D1211yescharacteristic
439C22×C3#88211yescharacteristic
440C22×C3#89511yescharacteristic
441C22×C3C2×#20411yescharacteristic
442C22×C3#90411yescharacteristic
443C22×C3#90811yescharacteristic
444C22×C3#90911yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91411yescharacteristic
447C22×C3#91511yescharacteristic
448C22×C3#91611yescharacteristic
449C22×C3D4×Dic311yescharacteristic
450C22×C3#93711yescharacteristic
451C22×C3#93911yescharacteristic
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—81no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—62no—
464C3×C4—64no—
465C3×C4—121no—
466C3×C4D3×C22⋊C411yescharacteristic
467C3×C4#88411yescharacteristic
468C3×C4#89311yescharacteristic
469C3×C4#89411yescharacteristic
470C3×C4D4×Dic311yescharacteristic
471C3×C4#93511yescharacteristic
472C3×C4#93911yescharacteristic
473C3×C4C2×#21711yescharacteristic
474Dic3—24no—
475Dic3—22no—
476Dic3—41no—
477Dic3—122no—
478Dic3—122no—
479Dic3—242no—
480Dic3—242no—
481Dic3—241no—
482Dic3—241no—
483C32#188011yescharacteristic, complemented, Sylow
484C23—62no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23D3×D1211yescharacteristic
492Q8—34no—
493Q8—62no—
494Q8—62no—
495Q8—62no—
496D4—62no—
497D4—62no—
498D4—121no—
499D4—121no—
500C2×C4—32no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—61no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—182no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4—361no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4#379511yescharacteristic
516C2×C4#379611yescharacteristic
517C2×C4#380211yescharacteristic
518C2×C4C2×D3×Dic311yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4D3×#6711yescharacteristic
521C8—22no—
522C8—121no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—242no—
531C2×C3#466511yescharacteristic
532C2×C3C4×#20411yescharacteristic
533C2×C3#471011yescharacteristic
534C2×C3#473411yescharacteristic
535C2×C3#473811yescharacteristic
536C2×C3#484511yescharacteristic
537C2×C3#484811yescharacteristic
538C2×C3Dic3×SD1611yescharacteristic
539C2×C3#516311yescharacteristic
540C2×C3#516411yescharacteristic
541C2×C3#516611yescharacteristic
542C2×C3#517011yescharacteristic
543C2×C3#517211yescharacteristic
544C2×C3#522011yescharacteristic
545D3—82no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22—241no—
550C22—241no—
551C22—241no—
552C22—241no—
553C22D3×#20411yescharacteristic
554C22#6379411yescharacteristic
555C22#6380011yescharacteristic
556C22#6380611yescharacteristic
557C22#6388611yescharacteristic
558C22Dic3×D1211yescharacteristic
559C22#6392211yescharacteristic
560C4—62no—
561C4—64no—
562C4—121no—
563C4—362no—
564C4—721no—
565C4#6388411yescharacteristic
566C4#6388511yescharacteristic
567C4#6389811yescharacteristic
568C4D3×#21711yescharacteristic
569C3—21no—
570C3#6868611yescharacteristic, complemented
571C3#7204811yescharacteristic, complemented
572C2—242no—
573C2Dic3×#20411yescharacteristic
574C2#1059076611yescharacteristic
575C2#1059079911yescharacteristic
576C2#1059082211yescharacteristic
577C2#1059082311yescharacteristic
578C2#1059085911yescharacteristic
579C2#1059137611yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic6C2semidirect
4. C2×#63566C2semidirect
6. #10589417C2semidirect
7. C3×#4550C2semidirect
19. C2×C3×#204C4semidirect
42. #4550D3semidirect
112. C2×#204Dic3semidirect
147. C2×C3×Dic3SD16semidirect
155. C3×Dic6C22⋊C4semidirect
366. C2×Dic3#204semidirect
374. Dic6#217semidirect
483. C32#1880semidirect
570. C3#68686semidirect
571. C3#72048semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×Dic3×Dic62
#105913182
C2×#635662
C2×#635632
#105894172
C3×#45502
#720483
#686863