Finite Group Databasebeta

← #11783941

Subgroups — #11783941

Order 1152.

849 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×C3×#893C211yesmaximal, characteristic
2Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63563C211yesmaximal, characteristic
4C2×#63562C211yesmaximal, characteristic
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C4×#832—31nomaximal
9#68780—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#893—22no—
20C3×#893C414yescomplemented
21C2×Dic32—21no—
22#63579—21no—
23#63563C414yescomplemented
24#63562C414yescomplemented
25Dic3×C3⋊C8—22no—
26C2×C3×C4×D4—31no—
27C2×#893D311yescharacteristic
28C2×#832—31no—
29C2×#832—31no—
30C2×#821—31no—
31C2×C8×Dic3—31no—
32Dic3×C4⋊C4—31no—
33C2×#809—31no—
34C4×C4⋊Dic3—31no—
35C2×C4×C3⋊C8—31no—
36C3×#340—31no—
37#4529—31no—
38#4529—31no—
39#4529—61no—
40#4529D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D411yescharacteristic
47C22×C3×Dic3D411yescharacteristic
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12C2×C412yes—
53C2×C3×D12C2×C412yes—
54C2×C3×C4×D3—24no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2×C412yes—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C412yescomplemented
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)C2×C412yescomplemented
64C3×(C2×D3)⋊C4—24no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yescomplemented
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72Dic32—42no—
73C4×#102—91noSylow
74C22×C3×D4—31no—
75C23×C3×C4—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—21no—
78C22×C3×C8—31no—
79C3×C4×D4—34no—
80C3×C4×D4—62no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C22⋊C4—61no—
86C2×C3×C42—31no—
87C2×(C2×D3)⋊C4—21no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3C2×D311yescharacteristic
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99#893—22no—
100#893Dic314yescomplemented
101#832—34no—
102#832—34no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#821—34no—
106C8×Dic3—62no—
107#809—34no—
108C4×C3⋊C8—62no—
109C23×C32C2×D411yescharacteristic
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—41no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C2×C32×C4—22no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
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×Dic3C22⋊C412yes—
135C2×C3×Dic3C22⋊C412yes—
136C2×C3×Dic3D812yes—
137C2×C3×Dic3SD1612yes—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12C4214yescomplemented
142C3×C4×D3—48no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145C2×C4×D4—31no—
146C2×#102—91no—
147C2×#102—91no—
148C2×C4×C8—91no—
149C4×C4⋊C4—91no—
150#340—31no—
151#340—91no—
152C24×C3—61no—
153C23×D3—21no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—32no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—41no—
166C22×C3×C4—64no—
167C22×C3×C4—61no—
168C22×C3×C4—122no—
169C22×C3×C4—122no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3#6711yescharacteristic
177C22×Dic3#6711yescharacteristic
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12C4×D312yes—
182C2×D12C4×D312yes—
183C2×D12C2×Dic312yes—
184C2×C4×D3—24no—
185C2×C4×D3—42no—
186C2×C4×D3—42no—
187C2×C3×C8—32no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4C4×D312yes—
197C3×C4⋊C4C2×Dic312yes—
198C3×C22⋊C4—64no—
199C3×C42—32no—
200C3×C42—32no—
201(C2×D3)⋊C4—24no—
202C4⋊Dic3—21no—
203C4⋊Dic3—32no—
204C4⋊Dic3—32no—
205C4⋊Dic3—62no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4⋊Dic3C4×D312yescomplemented
210C4×Dic3—122no—
211C4×Dic3—122no—
212C4×Dic3C2×Dic312yes—
213C4×Dic3#6712yes—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8C4×D312yescomplemented
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C22×C32C4×D411yescharacteristic
229C22×C32C2×D811yescharacteristic
230C22×C32C2×SD1611yescharacteristic
231C22×C32#13511yescharacteristic
232C22×C32#13511yescharacteristic
233C2×C3×D3—24no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C32×C4—42no—
241C32×C4C2×C4211yescharacteristic
242C32×C4#11711yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C3⋊Dic3—42no—
246C3×Dic3—22no—
247C3×Dic3—42no—
248C3×Dic3#10214yescomplemented
249C22×D4—31no—
250C23×C4—61no—
251C22×C8—31no—
252C22×C8—91no—
253C4×D4—34no—
254C4×D4—62no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4D3211yescharacteristic
258C2×C22⋊C4—61no—
259C2×C42—31no—
260C2×C42—181no—
261#102—94no—
262#102—94no—
263C4×C8—182no—
264#95—181no—
265C23×C3—21no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—121no—
270C23×C3—121no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3D3×D411yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—41no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3—41no—
282C3×D4—34no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—42no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—81no—
307C2×C3×C4—81no—
308C2×C3×C4—128no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4#23911yescharacteristic
321C2×C3×C4C22×Dic311yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—22no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—241no—
336C2×Dic3—241no—
337C2×Dic3#21312yes—
338C2×Dic3#21412yes—
339C2×Dic3#21712yes—
340C2×Dic3#21712yes—
341D12—22no—
342D12—22no—
343D12—22no—
344D12C4×Dic314yescomplemented
345C4×D3—48no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—62no—
349C3⋊C8—62no—
350C3⋊C8—122no—
351C2×C32C4×C22⋊C411yescharacteristic
352C2×C32C2×#10211yescharacteristic
353C2×C32#41611yescharacteristic
354C2×C32C4×D811yescharacteristic
355C2×C32C4×D811yescharacteristic
356C2×C32C4×SD1611yescharacteristic
357C2×C32C4×SD1611yescharacteristic
358C3×D3—44no—
359C24—61no—
360C2×D4—32no—
361C2×D4—32no—
362C2×D4—32no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C22×C4—21no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—64no—
370C22×C4—61no—
371C22×C4—122no—
372C22×C4—122no—
373C22×C4—181no—
374C22×C4C2×D3211yescharacteristic
375C2×C8—32no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—92no—
379C2×C8—181no—
380C2×C8—181no—
381C4⋊C4—21no—
382C4⋊C4—32no—
383C4⋊C4—61no—
384C4⋊C4—92no—
385C4⋊C4—181no—
386C4⋊C4D3×Dic312yes—
387C22⋊C4—64no—
388C42—32no—
389C42—32no—
390C42—362no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—64no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3D3×C22⋊C411yescharacteristic
406C22×C3#67⋊C411yescharacteristic
407C22×C3#89311yescharacteristic
408C22×C3D3×D811yescharacteristic
409C22×C3D3×SD1611yescharacteristic
410C22×C3#91611yescharacteristic
411C22×C3#91911yescharacteristic
412C22×C3C4×#6711yescharacteristic
413C22×C3C4×#6711yescharacteristic
414C22×C3C2×#21311yescharacteristic
415C22×C3C2×#21411yescharacteristic
416C22×C3#95011yescharacteristic
417C22×C3#95011yescharacteristic
418C22×C3C2×#21711yescharacteristic
419C2×D3—24no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—34no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—122no—
436C3×C4C42×D311yescharacteristic
437C3×C4#67⋊C411yescharacteristic
438C3×C4#89211yescharacteristic
439C3×C4#89311yescharacteristic
440C3×C4C2×C4×Dic311yescharacteristic
441C3×C4#92611yescharacteristic
442C3×C4C4×#6711yescharacteristic
443C3×C4C4×#6711yescharacteristic
444Dic3—22no—
445Dic3—42no—
446Dic3—122no—
447Dic3—122no—
448Dic3—242no—
449Dic3#83214yescomplemented
450C32C4×#10211yescharacteristic, complemented, Sylow
451C23—62no—
452C23—62no—
453C23—62no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23D3×#6711yescharacteristic
459D4—34no—
460D4—62no—
461D4—62no—
462D4—62no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—62no—
473C2×C4—128no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—182no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4#379511yescharacteristic
480C2×C4#379911yescharacteristic
481C2×C4C4×D3211yescharacteristic
482C2×C4C4×D3211yescharacteristic
483C2×C4C2×D3×Dic311yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C8—62no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3#466611yescharacteristic
496C2×C3#475611yescharacteristic
497C2×C3D3×#10211yescharacteristic
498C2×C3#478811yescharacteristic
499C2×C3#480411yescharacteristic
500C2×C3#485211yescharacteristic
501C2×C3#487211yescharacteristic
502C2×C3C4×#21311yescharacteristic
503C2×C3C4×#21311yescharacteristic
504C2×C3C4×#21411yescharacteristic
505C2×C3C4×#21411yescharacteristic
506C2×C3C4×#21711yescharacteristic
507C2×C3C2×#83211yescharacteristic
508C2×C3#523311yescharacteristic
509D3—44no—
510C22—64no—
511C22—122no—
512C22—122no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22#6387911yescharacteristic
518C22#6390411yescharacteristic
519C22D3×#21311yescharacteristic
520C22D3×#21411yescharacteristic
521C22#6394711yescharacteristic
522C22#6394911yescharacteristic
523C22D3×#21711yescharacteristic
524C4—34no—
525C4—42no—
526C4—62no—
527C4—122no—
528C4—362no—
529C4#6384111yescharacteristic
530C4C4×D3×Dic311yescharacteristic
531C4#6387911yescharacteristic
532C4#6390411yescharacteristic
533C3—21no—
534C3#6878011yescharacteristic, complemented
535C3C4×#83211yescharacteristic, complemented
536C2—124no—
537C2#1059045211yescharacteristic
538C2#1059045611yescharacteristic
539C2#1059047511yescharacteristic
540C2#1059047911yescharacteristic
541C2#1059123711yescharacteristic
542C2D3×#83211yescharacteristic
543C2#1059155611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. Dic3×C4⋊Dic3C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. #10589395C2semidirect
7. C3×#4529C2semidirect
20. C3×#893C4semidirect
23. #63563C4semidirect
24. #63562C4semidirect
40. #4529D3semidirect
60. C4⋊(C3⋊Dic3)C2×C4semidirect
63. C2×C3⋊(C3⋊C8)C2×C4semidirect
66. C3×C4⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
100. #893Dic3semidirect
141. C3×D12C42semidirect
209. C4⋊Dic3C4×D3semidirect
225. C2×C3⋊C8C4×D3semidirect
248. C3×Dic3#102semidirect
344. D12C4×Dic3semidirect
449. Dic3#832semidirect
450. C32C4×#102semidirect
534. C3#68780semidirect
535. C3C4×#832semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
Dic3×C4⋊Dic32
C2×#635632
C2×#635622
C2×Dic3×C3⋊C82
#105893952
C3×#45292
C4×#8323
#687803