Finite Group Databasebeta

← #11786838

Subgroups — #11786838

Order 1152.

781 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
2C2×C3×#807C211yesmaximal, characteristic, complemented
3#10591212C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic
5C2×#63562C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71606—31nomaximal
9#70638—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×#893—22no—
21C2×#3724—21no—
22C3×#807—22no—
23#63579—21no—
24#63563C414yescomplemented
25#63562—22no—
26C2×C3×C4×D4—31no—
27C2×#893D311yescharacteristic
28C2×C3×#107—31no—
29C2×#832—31no—
30C2×#832—31no—
31C2×#821—31no—
32#4972—31no—
33C2×#809—31no—
34C2×#807D311yescharacteristic, complemented
35#4928—31no—
36#4550—31no—
37#4529—31no—
38#4529—31no—
39#4529—61no—
40#4524—31no—
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×D12D412yes—
53C2×C3×D12Q812yes—
54C2×C3×C4×D3—24no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D412yes—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C412yescomplemented
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×(C2×D3)⋊C4—24no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72#3724—42no—
73#1862—91noSylow
74C22×C3×D4—31no—
75C23×C3×C4—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—21no—
78C22×C3×C8—31no—
79C3×C4×D4—62no—
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×Dic3⋊C4—61no—
93C2×Dic3⋊C4—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#893—22no—
101C3×#107—62no—
102#832—34no—
103#832—62no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#821—34no—
107#809—62no—
108#807—22no—
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×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
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—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3D812yes—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12C4⋊C414yescomplemented
142C3×C4×D3—48no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C2×C4×D4—31no—
146C2×#107—31no—
147C2×#102—91no—
148C2×#102—91no—
149#389—91no—
150#340—91no—
151#336—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×D12Dic612yes—
182C2×D12C4×D312yes—
183C2×D12#6712yes—
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—41no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4#6712yes—
197C3×C4⋊C4#6712yes—
198C3×C22⋊C4—64no—
199C3×C42—61no—
200C3×C42—61no—
201(C2×D3)⋊C4—24no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—62no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—121no—
210Dic3⋊C4—122no—
211Dic3⋊C4—122no—
212C4×Dic3—21no—
213C4×Dic3—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
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×C32C4×D411yescharacteristic
227C22×C32#12011yescharacteristic
228C22×C32C22⋊Q811yescharacteristic
229C22×C32C2×D811yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32AGL(1,ℤ/8)11yescharacteristic
232C22×C32#13711yescharacteristic
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×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—42no—
246C3×Dic3—22no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C22×D4—31no—
250C23×C4—61no—
251C22×C8—31no—
252C22×C8—91no—
253C4×D4—62no—
254C4×D4—62no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—61no—
260C2×C42—31no—
261#107—62no—
262#102—94no—
263#102—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—42no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—81no—
306C2×C3×C4—81no—
307C2×C3×C4—128no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×Dic611yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4#23511yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×Q811yescharacteristic
319C2×C3×C4#23911yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—241no—
339C2×Dic3—241no—
340C2×Dic3#21312yes—
341D12—22no—
342D12—22no—
343D12—22no—
344D12Dic3⋊C414yescomplemented
345C4×D3—48no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—122no—
349C3⋊C8—121no—
350C3⋊C8—121no—
351C2×C32#38511yescharacteristic
352C2×C32C4×D811yescharacteristic
353C2×C32#44011yescharacteristic
354C2×C32#44711yescharacteristic
355C2×C32#45211yescharacteristic
356C2×C32#47411yescharacteristic
357C2×C32#47811yescharacteristic
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—181no—
379C2×C8—181no—
380C2×C8—181no—
381C4⋊C4—21no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4—92no—
385C4⋊C4—181no—
386C4⋊C4—362no—
387C4⋊C4#62512yes—
388C22⋊C4—64no—
389C42—61no—
390C42—61no—
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×C3#89311yescharacteristic
406C22×C3#89611yescharacteristic
407C22×C3D3×D811yescharacteristic
408C22×C3#91111yescharacteristic
409C22×C3#91811yescharacteristic
410C22×C3#91911yescharacteristic
411C22×C3#92411yescharacteristic
412C22×C3C4×#6711yescharacteristic
413C22×C3C2×#21311yescharacteristic
414C22×C3#93211yescharacteristic
415C22×C3#93711yescharacteristic
416C22×C3#95011yescharacteristic
417C22×C3#95111yescharacteristic
418C22×C3#95311yescharacteristic
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—42no—
431C3×C4—42no—
432C3×C4—62no—
433C3×C4—82no—
434C3×C4—121no—
435C3×C4—241no—
436C3×C4D3×C4⋊C411yescharacteristic
437C3×C4#89411yescharacteristic
438C3×C4C2×Dic3⋊C411yescharacteristic
439C3×C4#92411yescharacteristic
440C3×C4C4×#6711yescharacteristic
441C3×C4C4×#6711yescharacteristic
442C3×C4#92911yescharacteristic
443C3×C4#94611yescharacteristic
444Dic3—22no—
445Dic3—41no—
446Dic3—81no—
447Dic3—122no—
448Dic3—122no—
449Dic3—242no—
450C32#186211yescharacteristic, 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—41no—
466C2×C4—41no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—128no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—182no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4D3×Dic611yescharacteristic
480C2×C4#379811yescharacteristic
481C2×C4#379911yescharacteristic
482C2×C4C4×D3211yescharacteristic
483C2×C4C2×#62511yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C8—62no—
486C8—361no—
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#487211yescharacteristic
496C2×C3#488911yescharacteristic
497C2×C3#489011yescharacteristic
498C2×C3#489111yescharacteristic
499C2×C3#498911yescharacteristic
500C2×C3#500711yescharacteristic
501C2×C3#500911yescharacteristic
502C2×C3C4×#21311yescharacteristic
503C2×C3#501811yescharacteristic
504C2×C3#515611yescharacteristic
505C2×C3#518711yescharacteristic
506C2×C3#521011yescharacteristic
507C2×C3#521711yescharacteristic
508C2×C3#523911yescharacteristic
509D3—44no—
510C22—64no—
511C22—122no—
512C22—122no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22#6385111yescharacteristic
518C22#6390411yescharacteristic
519C22D3×#21311yescharacteristic
520C22#6393211yescharacteristic
521C22#6394311yescharacteristic
522C22#6394911yescharacteristic
523C22#6397611yescharacteristic
524C4—42no—
525C4—62no—
526C4—121no—
527C4—241no—
528C4—362no—
529C4#6385011yescharacteristic
530C4#6385611yescharacteristic
531C4D3×Dic3⋊C411yescharacteristic
532C4C4×#62511yescharacteristic
533C3—21no—
534C3#7063811yescharacteristic, complemented
535C3#7160611yescharacteristic, complemented
536C2—124no—
537C2#1059045611yescharacteristic
538C2#1059054211yescharacteristic
539C2#1059055511yescharacteristic
540C2#1059059011yescharacteristic
541C2#1059127711yescharacteristic
542C2#1059144711yescharacteristic
543C2#1059159711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1862
LCSG ▷ C2×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. C2×C3×#807C2semidirect
3. #10591212C2semidirect
6. #10589395C2semidirect
7. #10589155C2semidirect
24. #63563C4semidirect
34. C2×#807D3semidirect
60. C4⋊(C3⋊Dic3)C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
141. C3×D12C4⋊C4semidirect
225. C2×C3⋊C8C4×D3semidirect
344. D12Dic3⋊C4semidirect
450. C32#1862semidirect
534. C3#70638semidirect
535. C3#71606semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8072
#105912122
C2×#635632
C2×#635622
#105893952
#105891552
#716063
#706383