Finite Group Databasebeta

← #11786848

Subgroups — #11786848

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2#10592627C211yesmaximal, characteristic, complemented
3C2×#63575C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic
5C2×#63563C211yesmaximal, characteristic
6C3×#4524C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71606—31nomaximal
9#68670—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×C4×D12—22no—
21C3×C4×D12—22no—
22#63658—21no—
23#63575—22no—
24#63563—22no—
25#63563C414yescomplemented
26C2×C3×C4×D4—31no—
27C2×C4×D12D311yescharacteristic
28C2×#832—31no—
29C2×#832—31no—
30C2×#821—31no—
31C2×#821—31no—
32C2×#818—31no—
33C2×#807—31no—
34#4928—31no—
35#4928—31no—
36#4928—61no—
37C3×#336—31no—
38#4551—31no—
39#4529—31no—
40#4524D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×C3×C4×D3—24no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C32×C42—21no—
58C32×C42—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)C2×C412yescomplemented
63#3750—42no—
64C3×(C2×D3)⋊C4—24no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D412yes—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C412yescomplemented
73#1862—91noSylow
74C22×C3×D4—31no—
75C23×C3×C4—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—21no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C3×C4×D4—62no—
81C3×C4×D4—62no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C42—21no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C2×(C2×D3)⋊C4—21no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—62no—
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C4×D12—22no—
101C4×D12—22no—
102#832—34no—
103#832—62no—
104C3⋊#95—62no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#821—34no—
108#821—62no—
109#818—62no—
110#807—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4D812yes—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
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×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12C4⋊C414yescomplemented
144C3×C4×D3—48no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C2×C4×D4—31no—
148C2×#107—91no—
149C2×#102—91no—
150C2×#102—91no—
151#389—91no—
152#340—91no—
153#336—31no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—64no—
166C22×C3×C4—61no—
167C22×C3×C4—122no—
168C22×C3×C4—122no—
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4D1211yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4#6711yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—62no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—62no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12Dic612yes—
186C2×D12C4×D312yes—
187C2×D12#6712yes—
188C2×C4×D3—24no—
189C2×C4×D3—42no—
190C2×C4×D3—42no—
191C2×C3×C8—32no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C22⋊C4—64no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42—41no—
205C3×C42—41no—
206(C2×D3)⋊C4—24no—
207C4⋊Dic3—21no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—121no—
219C4⋊Dic3—121no—
220C4⋊Dic3#6712yes—
221Dic3⋊C4—124no—
222Dic3⋊C4—122no—
223Dic3⋊C4—122no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C4×D312yescomplemented
230C22×C32C4×D411yescharacteristic
231C22×C32#12011yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C22×C32C2×D811yescharacteristic
234C22×C32#13511yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3×D3—24no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C32×C4—22no—
245C32×C4—41no—
246C32×C4C2×C4⋊C411yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4#12311yescharacteristic
250C3⋊Dic3—42no—
251C3⋊Dic3—81no—
252C3×Dic3—42no—
253C22×D4—31no—
254C23×C4—61no—
255C22×C8—31no—
256C22×C8—31no—
257C4×D4—62no—
258C4×D4—62no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—181no—
263C2×C22⋊C4—61no—
264C2×C42D3211yescharacteristic
265#107—182no—
266#102—94no—
267#102—182no—
268#95—181no—
269C23×C3—21no—
270C23×C3—62no—
271C23×C3—62no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3C2×D1211yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C3×D4—34no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—62no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—62no—
313C2×C3×C4—128no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4D2412yes—
317C2×C3×C4#21312yes—
318C2×C3×C4C2×Dic611yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4D3×Q811yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351D12—22no—
352D12—22no—
353D12—22no—
354D12Dic3⋊C414yescomplemented
355C4×D3—48no—
356C3×C8—62no—
357C3×C8—121no—
358C3⋊C8—22no—
359C3⋊C8—41no—
360C2×C32#38511yescharacteristic
361C2×C32C4×D811yescharacteristic
362C2×C32#44011yescharacteristic
363C2×C32#44711yescharacteristic
364C2×C32#45211yescharacteristic
365C2×C32#47411yescharacteristic
366C2×C32#47811yescharacteristic
367C3×D3—44no—
368C24—61no—
369C2×D4—32no—
370C2×D4—32no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C22×C4—64no—
376C22×C4—61no—
377C22×C4—122no—
378C22×C4—122no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4#62611yescharacteristic
382C22×C4#62611yescharacteristic
383C22×C4C2×D3211yescharacteristic
384C2×C8—32no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—32no—
391C4⋊C4—61no—
392C4⋊C4—92no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—362no—
397C22⋊C4—64no—
398C42—21no—
399C42—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—64no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3C4×D1211yescharacteristic
415C22×C3#88211yescharacteristic
416C22×C3#89711yescharacteristic
417C22×C3C2×D2411yescharacteristic
418C22×C3#90411yescharacteristic
419C22×C3#90811yescharacteristic
420C22×C3#90911yescharacteristic
421C22×C3#92411yescharacteristic
422C22×C3C4×#6711yescharacteristic
423C22×C3C2×#21311yescharacteristic
424C22×C3#93211yescharacteristic
425C22×C3#95011yescharacteristic
426C22×C3#95111yescharacteristic
427C22×C3#95311yescharacteristic
428C2×D3—24no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—122no—
446C3×C4#67⋊C411yescharacteristic
447C3×C4#88311yescharacteristic
448C3×C4D3×C4⋊C411yescharacteristic
449C3×C4#89611yescharacteristic
450C3×C4C2×Dic3⋊C411yescharacteristic
451C3×C4#92411yescharacteristic
452C3×C4C4×#6711yescharacteristic
453C3×C4#92911yescharacteristic
454Dic3—42no—
455Dic3—124no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459Dic3—241no—
460Dic3—241no—
461C32#186211yescharacteristic, complemented, Sylow
462C23—62no—
463C23—62no—
464C23—62no—
465C23—121no—
466C23—121no—
467C23—121no—
468C23—121no—
469C23C2×#62611yescharacteristic
470D4—34no—
471D4—62no—
472D4—62no—
473D4—62no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—62no—
480C2×C4—128no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—182no—
484C2×C4—361no—
485C2×C4—361no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4#371412yes—
490C2×C4D3×Dic611yescharacteristic
491C2×C4#379511yescharacteristic
492C2×C4#379811yescharacteristic
493C2×C4C4×D3211yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C2×C4D3×#6711yescharacteristic
496C8—62no—
497C8—121no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—124no—
506C2×C3#466811yescharacteristic
507C2×C3C4×D2411yescharacteristic
508C2×C3#471011yescharacteristic
509C2×C3#473211yescharacteristic
510C2×C3#473311yescharacteristic
511C2×C3#484611yescharacteristic
512C2×C3#484711yescharacteristic
513C2×C3#500711yescharacteristic
514C2×C3#500911yescharacteristic
515C2×C3C4×#21311yescharacteristic
516C2×C3#501811yescharacteristic
517C2×C3#521011yescharacteristic
518C2×C3#521711yescharacteristic
519C2×C3#523911yescharacteristic
520D3—44no—
521C22—64no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—122no—
526C22—122no—
527C22—122no—
528C22C2×#371411yescharacteristic
529C22#6382911yescharacteristic
530C22#6383011yescharacteristic
531C22#6383111yescharacteristic
532C22#6385711yescharacteristic
533C22C4×#62611yescharacteristic
534C22#6397711yescharacteristic
535C4—22no—
536C4—41no—
537C4—122no—
538C4—362no—
539C4—721no—
540C4#6385111yescharacteristic
541C4D3×Dic3⋊C411yescharacteristic
542C4#6387911yescharacteristic
543C4#6390511yescharacteristic
544C3—21no—
545C3#6867011yescharacteristic, complemented
546C3#7160611yescharacteristic, complemented
547C2—124no—
548C2#1059027111yescharacteristic
549C2#1059027211yescharacteristic
550C2C4×#371411yescharacteristic
551C2#1059036011yescharacteristic
552C2#1059116211yescharacteristic
553C2#1059117311yescharacteristic
554C2#1059127811yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1862
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592627C2semidirect
3. C2×#63575C2semidirect
6. C3×#4524C2semidirect
7. #10589164C2semidirect
25. #63563C4semidirect
40. #4524D3semidirect
62. C4⋊(C3⋊Dic3)C2×C4semidirect
72. C2×C3×C3⋊C8C2×C4semidirect
143. C3×D12C4⋊C4semidirect
229. C2×C3⋊C8C4×D3semidirect
354. D12Dic3⋊C4semidirect
461. C32#1862semidirect
545. C3#68670semidirect
546. C3#71606semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
#105926272
C2×#635752
C2×#635632
C3×#45242
#105891642
#716063
#686703