Finite Group Databasebeta

← #11786472

Subgroups — #11786472

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
3C2×C3×#817C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic
5C2×#63573C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70579—31nomaximal
9#69928—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20D3×C4⋊Dic3—22no—
21D3×C4⋊Dic3—22no—
22C3×(C2×D3)⋊C8C414yescomplemented
23C3×#817—22no—
24#63579—21no—
25#63573—22no—
26C22×C4⋊Dic3—31no—
27C2×D3×C4⋊C4—31no—
28C2×C3×#106—31no—
29C2×C3×C22⋊C8—31no—
30#5212—31no—
31C2×(C2×D3)⋊C8D311yescharacteristic
32C2×#817—31no—
33C2×#817D311yescharacteristic, complemented
34#4987—31no—
35C2×#808—31no—
36#4551—31no—
37#4551—31no—
38#4551—31no—
39#4551—61no—
40#4529—31no—
41C23×C3×D3D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D412yes—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yescomplemented
71Dic3⋊Dic3—24no—
72(C2×D3)⋊Dic3—42no—
73#1853—91noSylow
74C23×C3×C4—31no—
75C23×Dic3—61no—
76C22×C4×D3—61no—
77C22×C4×D3C2×D311yescharacteristic
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×#217—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—62no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—62no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101C3×#106—62no—
102C3×C22⋊C8—34no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105(C2×D3)⋊C8Dic314yescomplemented
106#817—22no—
107#817—62no—
108#808—62no—
109C23×C32C2×D411yescharacteristic
110C22×C3×D3—21no—
111C22×C3×D3—21no—
112C22×C3×D3—21no—
113C22×C3×D3—21no—
114C22×C3×D3C4⋊C412yes—
115C22×C3×D3SD1612yes—
116C22×C3×D3SD1612yes—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3C4⋊C412yes—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142D3×Dic3—48no—
143C32×C8—22no—
144C3×C3⋊C8—22no—
145C22×C4⋊C4—91no—
146C2×#106—31no—
147C2×#106—91no—
148C2×C22⋊C8—31no—
149#380—91no—
150#340—91no—
151#340—91no—
152C24×C3—31no—
153C23×D3D1211yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—64no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—121no—
174C22×Dic3—121no—
175C22×Dic3—122no—
176C22×Dic3—122no—
177C22×Dic3D1211yescharacteristic
178C2×C4×D3—21no—
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—64no—
183C2×C4×D3—122no—
184C2×C4×D3—122no—
185C2×C4×D3Dic612yes—
186C2×C4×D3C2×Dic312yes—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—22no—
192C2×C3×C8—32no—
193C2×C3×C8—41no—
194C2×C3×C8—41no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8C4×D312yescomplemented
198C2×C3×C8C2×Dic312yescomplemented
199C3×C4⋊C4—32no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203#217—122no—
204(C2×D3)⋊C4—122no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—62no—
211C4⋊Dic3—64no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—62no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3—121no—
221C4⋊Dic3#6712yes—
222Dic3⋊C4—64no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C2×Dic312yescomplemented
226C22×C32C2×C4⋊C411yescharacteristic
227C22×C32#12011yescharacteristic
228C22×C32#12311yescharacteristic
229C22×C32C2×SD1611yescharacteristic
230C22×C32C2×SD1611yescharacteristic
231C22×C32AGL(1,ℤ/8)11yescharacteristic
232C22×C32#13711yescharacteristic
233C2×C3×D3—22no—
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—22no—
237C2×C3×D3—22no—
238C2×C3×D3—22no—
239C2×C3×D3#10614yescomplemented
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C3⋊Dic3—42no—
245C3⋊Dic3—81no—
246C3×Dic3—22no—
247C3×Dic3—42no—
248C3×Dic3—81no—
249C23×C4—31no—
250C23×C4—181no—
251C22×C8—31no—
252C22×C8D3211yescharacteristic
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—182no—
258C2×C4⋊C4—182no—
259C2×C4⋊C4—181no—
260C2×C22⋊C4—181no—
261#106—62no—
262#106—182no—
263C22⋊C8—34no—
264#95—181no—
265C23×C3—21no—
266C23×C3—32no—
267C23×C3—32no—
268C23×C3—32no—
269C23×C3—61no—
270C23×C3—61no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3C2×D1211yescharacteristic
274C23×C3D3×D411yescharacteristic
275C22×D3—21no—
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3#20412yes—
280C22×D3#20412yes—
281C22×D3C4⋊Dic312yes—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—32no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4C2×Dic611yescharacteristic
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23711yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4D3×Q811yescharacteristic
310C2×C3×C4#23911yescharacteristic
311C2×C3×C4C22×Dic311yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—22no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3—128no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—122no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339C2×Dic3—241no—
340C2×Dic3C4⋊Dic312yes—
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—128no—
346C3×C8—22no—
347C3×C8—22no—
348C3×C8—42no—
349C3×C8—62no—
350C3⋊C8—22no—
351C2×C32#38511yescharacteristic
352C2×C32C2×#10611yescharacteristic
353C2×C32#42811yescharacteristic
354C2×C32#44811yescharacteristic
355C2×C32#45011yescharacteristic
356C2×C32#48111yescharacteristic
357C2×C32#48311yescharacteristic
358C3×D3—24no—
359C24—31no—
360C22×C4—31no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—61no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—184no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—362no—
373C22×C4—362no—
374C22×C4C2×D3211yescharacteristic
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—32no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8D3×Dic312yescomplemented
381C4⋊C4—32no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4—61no—
385C4⋊C4—92no—
386C4⋊C4—184no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C22⋊C4—362no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—34no—
399C22×C3—62no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3—62no—
405C22×C3#88211yescharacteristic
406C22×C3#88611yescharacteristic
407C22×C3D3×C4⋊C411yescharacteristic
408C22×C3#89411yescharacteristic
409C22×C3C2×#20411yescharacteristic
410C22×C3C2×#20411yescharacteristic
411C22×C3#90811yescharacteristic
412C22×C3#90911yescharacteristic
413C22×C3D3×SD1611yescharacteristic
414C22×C3D3×SD1611yescharacteristic
415C22×C3#91411yescharacteristic
416C22×C3#91511yescharacteristic
417C22×C3C2×C4⋊Dic311yescharacteristic
418C22×C3#93711yescharacteristic
419C2×D3—22no—
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—22no—
424C2×D3—22no—
425C2×D3#81714yescomplemented
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—62no—
431C3×C4—122no—
432C3×C4—241no—
433C3×C4#87811yescharacteristic
434C3×C4#87811yescharacteristic
435C3×C4#89311yescharacteristic
436C3×C4#89611yescharacteristic
437C3×C4C4×#6711yescharacteristic
438C3×C4D4×Dic311yescharacteristic
439C3×C4D4×Dic311yescharacteristic
440C3×C4#94611yescharacteristic
441Dic3—22no—
442Dic3—42no—
443Dic3—81no—
444Dic3—122no—
445Dic3—122no—
446Dic3—242no—
447Dic3—242no—
448Dic3—241no—
449Dic3—241no—
450C32#185311yescharacteristic, complemented, Sylow
451C23—32no—
452C23—32no—
453C23—32no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23D3×D1211yescharacteristic
459C2×C4—32no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—182no—
473C2×C4—368no—
474C2×C4—361no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4D3×Dic611yescharacteristic
480C2×C4#379611yescharacteristic
481C2×C4#380211yescharacteristic
482C2×C4C2×D3×Dic311yescharacteristic
483C2×C4#380411yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C8—22no—
486C8—62no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—64no—
495C2×C3#472111yescharacteristic
496C2×C3#473111yescharacteristic
497C2×C3#473511yescharacteristic
498C2×C3#473811yescharacteristic
499C2×C3D3×#10611yescharacteristic
500C2×C3#486111yescharacteristic
501C2×C3#486211yescharacteristic
502C2×C3#486311yescharacteristic
503C2×C3#495011yescharacteristic
504C2×C3#498911yescharacteristic
505C2×C3C2×#81711yescharacteristic
506C2×C3#512111yescharacteristic
507C2×C3#516911yescharacteristic
508C2×C3#517011yescharacteristic
509D3—24no—
510C22—34no—
511C22—62no—
512C22—62no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22D3×#20411yescharacteristic
518C22D3×#20411yescharacteristic
519C22#6379411yescharacteristic
520C22#6380011yescharacteristic
521C22D3×C4⋊Dic311yescharacteristic
522C22#6389011yescharacteristic
523C22#6392211yescharacteristic
524C4—62no—
525C4—122no—
526C4—241no—
527C4—362no—
528C4—721no—
529C4#6388711yescharacteristic
530C4#6389811yescharacteristic
531C4#6389911yescharacteristic
532C4Dic3×#6711yescharacteristic
533C3—21no—
534C3#6992811yescharacteristic, complemented
535C3#7057911yescharacteristic, complemented
536C2—64no—
537C2D3×#81711yescharacteristic
538C2#1059067411yescharacteristic
539C2#1059067711yescharacteristic
540C2#1059068111yescharacteristic
541C2#1059082211yescharacteristic
542C2#1059094211yescharacteristic
543C2#1059137711yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1853
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
3. C2×C3×#817C2semidirect
5. C2×#63573C2semidirect
6. #10589417C2semidirect
7. #10589164C2semidirect
22. C3×(C2×D3)⋊C8C4semidirect
33. C2×#817D3semidirect
59. C2×C32×C8C2×C4semidirect
70. C2×C3×C3⋊C8C2×C4semidirect
105. (C2×D3)⋊C8Dic3semidirect
197. C2×C3×C8C4×D3semidirect
198. C2×C3×C8C2×Dic3semidirect
225. C2×C3⋊C8C2×Dic3semidirect
239. C2×C3×D3#106semidirect
380. C2×C8D3×Dic3semidirect
425. C2×D3#817semidirect
450. C32#1853semidirect
534. C3#69928semidirect
535. C3#70579semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×C3×(C2×D3)⋊C82
C2×C3×#8172
#105913132
C2×#635732
#105894172
#105891642
#705793
#699283