Finite Group Databasebeta

← #11786511

Subgroups — #11786511

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10589163C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71576—31nomaximal
9#69506—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C3×#926—22no—
16C3×#926—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22#63657C414yescomplemented
23C3×C3⋊#95—21no—
24#63576—22no—
25#63574—22no—
26C2×C3×#117—31no—
27C2×#926D311yescharacteristic
28C3×#380—31no—
29#5212D311yescharacteristic
30C2×#830—31no—
31C2×#830—31no—
32C2×#830—61no—
33C2×#808—31no—
34C2×#808—31no—
35C2×#807—31no—
36C2×#807—31no—
37#4529—31no—
38#4529—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—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C2×C3⋊(C3⋊C8)C2×C412yes—
60C3×#217—24no—
61C3×#217—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×C4⋊Dic3D412yes—
70C3×C4×Dic3—24no—
71#1854—91noSylow
72C23×C3×C4—21no—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C2×D311yescharacteristic
75C3×#117—62no—
76C3×#117—62no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—61no—
82C2×C3×C22⋊C4—61no—
83C2×C3×C42—61no—
84C2×#217—21no—
85C2×#217—21no—
86#926—22no—
87#926—22no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—21no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8—61no—
99C3×#95—61no—
100C3⋊#95—21no—
101#830—34no—
102#830—34no—
103#830—64no—
104#808—62no—
105#808—62no—
106#807—62no—
107#807—62no—
108C23×C32—21no—
109C23×C32—21no—
110C23×C32—21no—
111C23×C32—21no—
112C23×C32—21no—
113C23×C32—21no—
114C23×C32C4⋊C412yes—
115C23×C32C2×D411yescharacteristic
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C4⋊C412yes—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3⋊(C3⋊C8)—22no—
142C3⋊(C3⋊C8)—22no—
143C2×#117—31no—
144C2×#107—91no—
145C2×#106—91no—
146C2×C22⋊C8—91no—
147#380—31no—
148#340—91no—
149#340—91no—
150C24×C3—21no—
151C24×C3#6711yescharacteristic
152C24×C3#6711yescharacteristic
153C22×C3×C4—21no—
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—22no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—41no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4Dic612yes—
174C22×C3×C4Dic612yes—
175C22×C3×C4C4×D312yes—
176C22×C3×C4C4×D312yes—
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4#6711yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—32no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—64no—
194C3×C22⋊C4—122no—
195C3×C42—64no—
196#217—24no—
197#217—42no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3#6712yes—
205C4⋊Dic3#6712yes—
206C4×Dic3—24no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—32no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222C2×C3⋊C8—121no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8—121no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—22no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C22×C32#13711yescharacteristic
239C32×C4—22no—
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C3×Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C3×Dic3—81no—
248C23×C4D3211yescharacteristic
249C22×C8—91no—
250C22×C8—91no—
251#117—62no—
252#117—62no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C22⋊C4—61no—
258C2×C22⋊C4—61no—
259C2×C42—61no—
260#107—182no—
261#106—182no—
262C22⋊C8—94no—
263#95—61no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—21no—
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—22no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3Dic3⋊C412yes—
285C23×C3Dic3⋊C412yes—
286C23×C3C2×#6711yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
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—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4Dic3⋊C412yes—
326C2×C3×C4Dic3⋊C412yes—
327C2×C3×C4C2×Dic611yescharacteristic
328C2×C3×C4C2×Dic611yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C3⋊C8—122no—
357C2×C32—42no—
358C2×C32#38511yescharacteristic
359C2×C32#42711yescharacteristic
360C2×C32#42811yescharacteristic
361C2×C32#44911yescharacteristic
362C2×C32#45211yescharacteristic
363C2×C32#48211yescharacteristic
364C2×C32#48511yescharacteristic
365C24#62511yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4#62412yes—
375C22×C4#62511yescharacteristic
376C22×C4#62712yes—
377C22×C4C2×D3211yescharacteristic
378C2×C8—92no—
379C2×C8—92no—
380C2×C8—181no—
381C2×C8—181no—
382C2×C8—181no—
383C2×C8—181no—
384C4⋊C4—32no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C22⋊C4—64no—
393C22⋊C4—122no—
394C42—64no—
395C22×C3—24no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3C2×Dic3⋊C411yescharacteristic
424C22×C3C2×Dic3⋊C411yescharacteristic
425C22×C3#92911yescharacteristic
426C22×C3#93211yescharacteristic
427C22×C3#93511yescharacteristic
428C22×C3#93711yescharacteristic
429C22×C3#94211yescharacteristic
430C22×C3#94911yescharacteristic
431C22×C3#95011yescharacteristic
432C22×C3#95011yescharacteristic
433C22×C3#95011yescharacteristic
434C22×C3#95011yescharacteristic
435C22×C3#95111yescharacteristic
436C22×C3#95311yescharacteristic
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4—241no—
447C3×C4—241no—
448C3×C4#87811yescharacteristic
449C3×C4#87811yescharacteristic
450C3×C4#67⋊C411yescharacteristic
451C3×C4#67⋊C411yescharacteristic
452C3×C4#92411yescharacteristic
453C3×C4#92411yescharacteristic
454C3×C4C4×#6711yescharacteristic
455C3×C4C4×#6711yescharacteristic
456Dic3—42no—
457Dic3—42no—
458Dic3—81no—
459Dic3—81no—
460C32#185411yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23#372412yes—
468C23C2×#62511yescharacteristic
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4#372412yes—
488C2×C4#380411yescharacteristic
489C2×C4#380411yescharacteristic
490C2×C4C2×#62411yescharacteristic
491C2×C4C2×#62711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—182no—
495C8—182no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—44no—
504C2×C3—42no—
505C2×C3—42no—
506C2×C3#494611yescharacteristic
507C2×C3#496411yescharacteristic
508C2×C3#499511yescharacteristic
509C2×C3#499611yescharacteristic
510C2×C3#499811yescharacteristic
511C2×C3#499811yescharacteristic
512C2×C3#500311yescharacteristic
513C2×C3#503511yescharacteristic
514C2×C3#503711yescharacteristic
515C2×C3#504511yescharacteristic
516C2×C3#504711yescharacteristic
517C2×C3#521011yescharacteristic
518C2×C3#523811yescharacteristic
519C2×C3#523911yescharacteristic
520C22—22no—
521C22—22no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22#6382211yescharacteristic
528C22#6382211yescharacteristic
529C22#6382311yescharacteristic
530C22#6382711yescharacteristic
531C22#6396111yescharacteristic
532C22C2×#372411yescharacteristic
533C22#6397611yescharacteristic
534C4—22no—
535C4—122no—
536C4—122no—
537C4—241no—
538C4—241no—
539C4#6395211yescharacteristic
540C4#6395211yescharacteristic
541C4#6396411yescharacteristic
542C4#6396411yescharacteristic
543C3—21no—
544C3#6950611yescharacteristic, complemented
545C3#7157611yescharacteristic, complemented
546C2—42no—
547C2#1059109011yescharacteristic
548C2#1059110211yescharacteristic
549C2#1059113811yescharacteristic
550C2#1059113911yescharacteristic
551C2#1059116111yescharacteristic
552C2#1059117011yescharacteristic
553C2#1059169311yescharacteristic
subgroupG/H
centerC23C2×#625
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×#63576C2semidirect
5. C2×#63574C2semidirect
6. #10589163C2semidirect
7. #10589163C2semidirect
22. #63657C4semidirect
460. C32#1854semidirect
544. C3#69506semidirect
545. 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
C2×#636572
C3×#52122
C2×#635762
C2×#635742
#105891632
#715763
#695063