Finite Group Databasebeta

← #11786509

Subgroups — #11786509

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71576—31nomaximal
9#69929—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C2×#3757—21no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#217—21no—
15C3×#926—22no—
16C3×#926—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63658—21no—
23C3×#830C414yescomplemented
24#63575—22no—
25#63573—22no—
26C2×C3×#117—31no—
27C2×#926D311yescharacteristic
28C2×C3×C22⋊C8—31no—
29#5212—31no—
30#5212—31no—
31#5212—61no—
32C2×#830D311yescharacteristic
33C2×#818—31no—
34C2×#817—31no—
35C2×#808—31no—
36C2×#807—31no—
37#4551—31no—
38#4551—31no—
39#4529—31no—
40#4529—31no—
41C24×C32D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2×C412yes—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4Q812yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54#3757—42no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C3×#217—24no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C3×C4⋊Dic3D412yes—
64C3×C4×Dic3—24no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8C2×C412yes—
71#1854—91noSylow
72C23×C3×C4—21no—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C2×D311yescharacteristic
75C22×C3×C8—31no—
76C22×C3×C8—31no—
77C3×#117—62no—
78C3×#117—62no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—61no—
82C2×C3×C42—61no—
83C2×#217—21no—
84C2×#217—62no—
85C2×#217—61no—
86C2×#217—61no—
87#926—22no—
88#926—22no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4×Dic3—21no—
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C3×C22⋊C8—34no—
101C3⋊#95—62no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104#830Dic314yescomplemented
105#818—62no—
106#817—62no—
107#808—62no—
108#807—62no—
109C23×C32—21no—
110C23×C32—21no—
111C23×C32—21no—
112C23×C32—21no—
113C23×C32—21no—
114C23×C32—21no—
115C23×C32C4⋊C412yes—
116C23×C32C2×D411yescharacteristic
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4C4⋊C412yes—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C2×#117—31no—
145C2×#107—91no—
146C2×#106—91no—
147C2×C22⋊C8—31no—
148#380—91no—
149#340—91no—
150#340—91no—
151C24×C3—21no—
152C24×C3D1211yescharacteristic
153C24×C3#6711yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—22no—
165C22×C3×C4—21no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4Dic612yes—
173C22×C3×C4Dic612yes—
174C22×C3×C4C4×D312yes—
175C22×C3×C4D1211yescharacteristic
176C22×C3×C4C2×Dic312yes—
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C2×C3×C8—32no—
189C2×C3×C8—32no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—64no—
199C3×C42—64no—
200#217—24no—
201#217—124no—
202#217—122no—
203#217—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217C4⋊Dic3—121no—
218C4⋊Dic3#6712yes—
219C4⋊Dic3#6712yes—
220C4×Dic3—24no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C2×Dic312yes—
226C2×C3⋊C8C2×Dic312yes—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32C2×C4⋊C411yescharacteristic
235C22×C32#12011yescharacteristic
236C22×C32#12311yescharacteristic
237C22×C32#13511yescharacteristic
238C22×C32#13511yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C22×C32#13711yescharacteristic
241C32×C4—22no—
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—81no—
247C3⋊Dic3—81no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C23×C4D3211yescharacteristic
251C22×C8—31no—
252C22×C8—31no—
253#117—62no—
254#117—62no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C22⋊C4—61no—
260C2×C22⋊C4—181no—
261C2×C42—61no—
262#107—182no—
263#106—182no—
264C22⋊C8—34no—
265#95—181no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3Dic3⋊C412yes—
287C23×C3C4⋊Dic312yes—
288C23×C3C2×D1211yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4Dic3⋊C412yes—
322C2×C3×C4C4⋊Dic312yes—
323C2×C3×C4C2×Dic611yescharacteristic
324C2×C3×C4C2×Dic611yescharacteristic
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4#23711yescharacteristic
332C2×C3×C4C22×Dic311yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C3×C8—62no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—22no—
363C2×C32—42no—
364C2×C32#38511yescharacteristic
365C2×C32#42711yescharacteristic
366C2×C32#42811yescharacteristic
367C2×C32#44911yescharacteristic
368C2×C32#45211yescharacteristic
369C2×C32#48211yescharacteristic
370C2×C32#48511yescharacteristic
371C24#62611yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4D3×Dic312yes—
381C22×C4#62611yescharacteristic
382C22×C4#62712yes—
383C22×C4C2×D3211yescharacteristic
384C2×C8—32no—
385C2×C8—32no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—32no—
391C4⋊C4—32no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—64no—
399C22⋊C4—362no—
400C42—64no—
401C22×C3—24no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3#88211yescharacteristic
430C22×C3#88611yescharacteristic
431C22×C3#90411yescharacteristic
432C22×C3#90411yescharacteristic
433C22×C3#90811yescharacteristic
434C22×C3#90911yescharacteristic
435C22×C3C2×Dic3⋊C411yescharacteristic
436C22×C3C2×C4⋊Dic311yescharacteristic
437C22×C3#92911yescharacteristic
438C22×C3#94911yescharacteristic
439C22×C3#95011yescharacteristic
440C22×C3#95011yescharacteristic
441C22×C3#95111yescharacteristic
442C22×C3#95311yescharacteristic
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—122no—
451C3×C4—122no—
452C3×C4#87811yescharacteristic
453C3×C4#87811yescharacteristic
454C3×C4#92411yescharacteristic
455C3×C4#92411yescharacteristic
456C3×C4C4×#6711yescharacteristic
457C3×C4C4×#6711yescharacteristic
458C3×C4D4×Dic311yescharacteristic
459C3×C4D4×Dic311yescharacteristic
460Dic3—42no—
461Dic3—42no—
462Dic3—242no—
463Dic3—242no—
464Dic3—241no—
465Dic3—241no—
466Dic3—241no—
467Dic3—241no—
468C32#185411yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23Dic3⋊Dic312yes—
476C23C2×#62611yescharacteristic
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4—361no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4Dic3⋊Dic312yes—
496C2×C4C2×D3×Dic311yescharacteristic
497C2×C4#380411yescharacteristic
498C2×C4#380411yescharacteristic
499C2×C4C2×#62711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C8—62no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—44no—
512C2×C3—42no—
513C2×C3—42no—
514C2×C3#472311yescharacteristic
515C2×C3#473311yescharacteristic
516C2×C3#473411yescharacteristic
517C2×C3#473711yescharacteristic
518C2×C3#495011yescharacteristic
519C2×C3#499511yescharacteristic
520C2×C3#499611yescharacteristic
521C2×C3#499811yescharacteristic
522C2×C3#500311yescharacteristic
523C2×C3#510611yescharacteristic
524C2×C3#512111yescharacteristic
525C2×C3#521011yescharacteristic
526C2×C3#523811yescharacteristic
527C2×C3#523911yescharacteristic
528C22—22no—
529C22—22no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22#6382511yescharacteristic
536C22#6382911yescharacteristic
537C22#6382911yescharacteristic
538C22#6383111yescharacteristic
539C22C2×Dic3⋊Dic311yescharacteristic
540C22#6396611yescharacteristic
541C22#6397711yescharacteristic
542C4—22no—
543C4—122no—
544C4—122no—
545C4—721no—
546C4—721no—
547C4#6396411yescharacteristic
548C4#6396411yescharacteristic
549C4Dic3×#6711yescharacteristic
550C4Dic3×#6711yescharacteristic
551C3—21no—
552C3#6992911yescharacteristic, complemented
553C3#7157611yescharacteristic, complemented
554C2—42no—
555C2#1059112211yescharacteristic
556C2#1059113111yescharacteristic
557C2#1059113411yescharacteristic
558C2#1059113611yescharacteristic
559C2#1059116311yescharacteristic
560C2#1059117311yescharacteristic
561C2#1059171811yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1854
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63575C2semidirect
5. C2×#63573C2semidirect
6. #10589164C2semidirect
7. #10589164C2semidirect
23. C3×#830C4semidirect
104. #830Dic3semidirect
468. C32#1854semidirect
552. C3#69929semidirect
553. C3#71576semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
#105929112
C2×C3×#8302
C2×#635752
C2×#635732
#105891642
#715763
#699293