Finite Group Databasebeta

← #11786372

Subgroups — #11786372

Order 1152.

755 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
1C22×D3×C3⋊C8C211yesmaximal, characteristic
2C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589390C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70477—31nomaximal
9#69449—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C411yescharacteristic
15C2×C3×(C2×D3)⋊C4C411yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×D3×C3⋊C8—22no—
20C2×D3×C3⋊C8—22no—
21C2×D3×C3⋊C8—22no—
22C3×C3⋊#95C411yescharacteristic
23C3×C3⋊#95C411yescharacteristic
24C3×C4⋊(C3⋊C8)—22no—
25Dic3⋊(C3⋊C8)—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C23×C3⋊C8—31no—
28C22×D3×C8—31no—
29C2×C3×C4⋊C8—31no—
30C3×C4×C22⋊C4—31no—
31C2×#830—31no—
32C2×(C2×D3)⋊C8—31no—
33C2×Dic3⋊C8—31no—
34C4×(C2×D3)⋊C4D311yescharacteristic
35C2×C4⋊(C3⋊C8)—31no—
36C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
37#4550—31no—
38#4524—31no—
39#4524—31no—
40#4524—31no—
41#4524—61no—
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3Q812yes—
55C32×C42—21no—
56C32×C42—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)D412yes—
63C3×(C2×D3)⋊C4—22no—
64C3×(C2×D3)⋊C4C814yescomplemented
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
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⋊C8D412yes—
73D3×C3⋊C8—28no—
74#1850—91noSylow
75C23×C3×C4—31no—
76C22×C4×D3C2×D311yescharacteristic
77C22×C3×C8—31no—
78C22×C3×C8—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—31no—
81C2×C3×C42—21no—
82C2×C3×C42—31no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85C2×(C2×D3)⋊C4Dic311yescharacteristic
86C2×(C2×D3)⋊C4Dic311yescharacteristic
87C2×C4×Dic3C2×D311yescharacteristic
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8—61no—
94C22×C3⋊C8—62no—
95C22×C3⋊C8—62no—
96C22×C3⋊C8—62no—
97C22×C3⋊C8C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99C2×D3×C8—62no—
100C2×D3×C8—62no—
101C2×D3×C8—62no—
102C3×C4⋊C8—62no—
103C3×#95—31no—
104C3×#95—31no—
105C3⋊#95Dic311yescharacteristic
106C3⋊#95Dic311yescharacteristic
107#830—62no—
108(C2×D3)⋊C8—62no—
109Dic3⋊C8—62no—
110C4⋊(C3⋊C8)—22no—
111C4⋊(C3⋊C8)—62no—
112C23×C32C22×C411yescharacteristic
113C22×C3×D3—21no—
114C22×C3×D3—21no—
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3C4⋊C412yes—
118C22×C3×D3C2×C812yes—
119C22×C3×D3M1612yes—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4C2×C812yescomplemented
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q811yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3C4⋊C412yes—
140C2×C3×Dic3C2×C812yescomplemented
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3⋊(C3⋊C8)—22no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C23×C8—91no—
150C2×C4⋊C8—31no—
151C2×C4⋊C8—91no—
152C2×C22⋊C8—91no—
153C4×C22⋊C4—31no—
154#336—91no—
155#336—91no—
156C24×C3—31no—
157C23×D3C2×Dic311yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—32no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4C4×D311yescharacteristic
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C2×Dic311yescharacteristic
173C22×C3×C4C2×Dic311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3C2×Dic311yescharacteristic
177C22×Dic3C2×Dic311yescharacteristic
178C22×Dic3C2×Dic311yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3Dic612yes—
184C2×C4×D3D1212yes—
185C2×C3×C8—32no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C3×C22⋊C4—34no—
192C3×C22⋊C4—62no—
193C3×C42—21no—
194C3×C42—21no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—41no—
198C3×C42—41no—
199C3×C42—61no—
200C3×C42—61no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4C3⋊C814yescomplemented
203C4×Dic3—21no—
204C4×Dic3—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8—68no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8#6712yes—
230D3×C8—68no—
231C22×C32C2×C4⋊C411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C22×C811yescharacteristic
235C22×C32C2×M1611yescharacteristic
236C22×C32#13111yescharacteristic
237C22×C32#13111yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—22no—
244C2×C3×D3C4⋊C814yescomplemented
245C32×C4—22no—
246C32×C4—41no—
247C32×C4#12011yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4C22⋊Q811yescharacteristic
250C32×C4#12311yescharacteristic
251C3×Dic3—22no—
252C3×Dic3—22no—
253C3×Dic3—41no—
254C23×C4—31no—
255C22×C8—31no—
256C22×C8—31no—
257C22×C8—91no—
258C22×C8—91no—
259C22×C8—182no—
260C22×C8—182no—
261C22×C8—182no—
262C2×C22⋊C4—31no—
263C2×C22⋊C4—31no—
264C2×C42—31no—
265C2×C42D3211yescharacteristic
266C4⋊C8—62no—
267C4⋊C8—182no—
268C22⋊C8—182no—
269#95—31no—
270#95—31no—
271C23×C3—21no—
272C23×C3—32no—
273C23×C3—32no—
274C23×C3—32no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C22×Dic311yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3C2×C3⋊C812yes—
286C22×D3#20812yes—
287C22×D3C4⋊Dic312yes—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4D3×C812yescomplemented
324C2×C3×C4C2×C3⋊C812yescomplemented
325C2×C3×C4C2×Dic611yescharacteristic
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4D3×Q811yescharacteristic
335C2×C3×C4#23911yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3C2×C3⋊C812yescomplemented
345C2×Dic3C4⋊Dic312yes—
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—22no—
350C3×C8—62no—
351C3×C8—121no—
352C3⋊C8—22no—
353C3⋊C8—41no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C3⋊C8—122no—
358C3⋊C8—121no—
359C3⋊C8—121no—
360C2×C32#38511yescharacteristic
361C2×C32C2×C4⋊C811yescharacteristic
362C2×C32#42411yescharacteristic
363C2×C32C8×D411yescharacteristic
364C2×C32C8×D411yescharacteristic
365C2×C32#43511yescharacteristic
366C2×C32#43511yescharacteristic
367C3×D3—24no—
368C24—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—31no—
374C22×C4—61no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4D3×Dic311yescharacteristic
379C22×C4D3×Dic311yescharacteristic
380C22×C4C2×D3211yescharacteristic
381C2×C8—32no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—92no—
388C2×C8—188no—
389C2×C8—181no—
390C2×C8—181no—
391C2×C8—181no—
392C2×C8—181no—
393C2×C8—181no—
394C22⋊C4—34no—
395C22⋊C4—62no—
396C42—21no—
397C42—21no—
398C42—61no—
399C42—61no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—34no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3D3×C4⋊C411yescharacteristic
415C22×C3#89311yescharacteristic
416C22×C3C2×D3×C811yescharacteristic
417C22×C3#90111yescharacteristic
418C22×C3D3×M1611yescharacteristic
419C22×C3#90711yescharacteristic
420C22×C3C22×C3⋊C811yescharacteristic
421C22×C3C2×#20811yescharacteristic
422C22×C3C2×C4⋊Dic311yescharacteristic
423C22×C3C4×#6711yescharacteristic
424C22×C3D4×Dic311yescharacteristic
425C22×C3D4×Dic311yescharacteristic
426C22×C3#94811yescharacteristic
427C22×C3#94811yescharacteristic
428C2×D3—22no—
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—22no—
434C2×D3C4⋊(C3⋊C8)14yescomplemented
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—62no—
446C3×C4—62no—
447C3×C4—121no—
448C3×C4#87811yescharacteristic
449C3×C4#87811yescharacteristic
450C3×C4#88211yescharacteristic
451C3×C4#88611yescharacteristic
452C3×C4#89411yescharacteristic
453C3×C4#89611yescharacteristic
454C3×C4#93711yescharacteristic
455C3×C4#94611yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—41no—
459C32#185011yescharacteristic, complemented, Sylow
460C23—32no—
461C23—32no—
462C23—32no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23C2×D3×Dic311yescharacteristic
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4D3×C3⋊C812yescomplemented
487C2×C4D3×Dic611yescharacteristic
488C2×C4#379611yescharacteristic
489C2×C4D3×D1211yescharacteristic
490C2×C4#380211yescharacteristic
491C2×C4#380411yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C8—62no—
494C8—121no—
495C8—182no—
496C8—361no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—64no—
505C2×C3D3×C4⋊C811yescharacteristic
506C2×C3#483411yescharacteristic
507C2×C3#483611yescharacteristic
508C2×C3#483911yescharacteristic
509C2×C3C2×C4⋊(C3⋊C8)11yescharacteristic
510C2×C3#495011yescharacteristic
511C2×C3#498911yescharacteristic
512C2×C3#499911yescharacteristic
513C2×C3D4×C3⋊C811yescharacteristic
514C2×C3D4×C3⋊C811yescharacteristic
515C2×C3#501111yescharacteristic
516C2×C3#501111yescharacteristic
517C2×C3C8×#6711yescharacteristic
518C2×C3#512711yescharacteristic
519D3—24no—
520C22—34no—
521C22—62no—
522C22—62no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22C2×D3×C3⋊C811yescharacteristic
528C22D3×#20811yescharacteristic
529C22#6381411yescharacteristic
530C22#6381511yescharacteristic
531C22D3×C4⋊Dic311yescharacteristic
532C22#6389811yescharacteristic
533C22Dic3×#6711yescharacteristic
534C4—22no—
535C4—41no—
536C4—62no—
537C4—62no—
538C4—121no—
539C4#6388711yescharacteristic
540C4#6389011yescharacteristic
541C4#6389911yescharacteristic
542C4#6392211yescharacteristic
543C3—21no—
544C3#6944911yescharacteristic, complemented
545C3#7047711yescharacteristic, complemented
546C2—64no—
547C2D3×C4⋊(C3⋊C8)11yescharacteristic
548C2#1059032411yescharacteristic
549C2#1059032911yescharacteristic
550C2#1059033011yescharacteristic
551C2C3⋊C8×#6711yescharacteristic
552C2#1059114711yescharacteristic
553C2#1059137711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1850
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C2×Dic3⋊(C3⋊C8)C2semidirect
6. #10589390C2semidirect
7. #10589155C2semidirect
36. C2×C4⋊(C3⋊C8)D3semidirect
64. C3×(C2×D3)⋊C4C8semidirect
125. C2×C32×C4C2×C8semidirect
140. C2×C3×Dic3C2×C8semidirect
202. (C2×D3)⋊C4C3⋊C8semidirect
244. C2×C3×D3C4⋊C8semidirect
323. C2×C3×C4D3×C8semidirect
324. C2×C3×C4C2×C3⋊C8semidirect
344. C2×Dic3C2×C3⋊C8semidirect
434. C2×D3C4⋊(C3⋊C8)semidirect
459. C32#1850semidirect
486. C2×C4D3×C3⋊C8semidirect
544. C3#69449semidirect
545. C3#70477semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊C82
C3×C4×(C2×D3)⋊C42
C2×C3×C4⋊(C3⋊C8)2
C2×Dic3⋊(C3⋊C8)2
C2×(C2×D3)⋊(C3⋊C8)2
#105893902
#105891552
#704773
#694493