Finite Group Databasebeta

← #11787248

Subgroups — #11787248

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×#63647C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70268—31nomaximal
9#68878—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×#624—21no—
13C22×C32×C8C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×#3724—21no—
19C2×Dic3⋊Dic3—21no—
20C2×#3722—21no—
21#63900—22no—
22#63900—22no—
23#63871—22no—
24#63871C414yescomplemented
25#63647—22no—
26C3×#816—22no—
27#63565—22no—
28C2×#946—31no—
29C2×#897—31no—
30C2×D3×C4⋊C4—31no—
31C2×D3×C4⋊C4—31no—
32C2×C3×#103—31no—
33C2×#835—31no—
34C2×(C2×D3)⋊C8—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8—61no—
37C2×#816D311yescharacteristic, complemented
38C2×#810—31no—
39C3×#340—31no—
40#4551D311yescharacteristic, complemented
41#4529—31no—
42#4529—31no—
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3C2×C412yes—
51C2×C4×C3⋊D3D412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×#624—24no—
63C2×#624—42no—
64C2×#624—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2×C412yescomplemented
75C3×C4⋊Dic3D412yes—
76C3×C4⋊Dic3D412yes—
77#3724—24no—
78Dic3⋊Dic3—24no—
79#3722—24no—
80#1872—91noSylow
81C22×C3×Q8—31no—
82C22×C4×D3—31no—
83C22×C4×D3—31no—
84C22×C4×D3—61no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C22×Dic6C2×D311yescharacteristic
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94#946—34no—
95#946—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108#897—34no—
109#897—62no—
110D3×C4⋊C4—62no—
111D3×C4⋊C4—62no—
112D3×C4⋊C4—62no—
113D3×C4⋊C4—62no—
114C3×#103—62no—
115#835—62no—
116(C2×D3)⋊C8—62no—
117(C2×D3)⋊C8—62no—
118(C2×D3)⋊C8—64no—
119#816—22no—
120#810—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3C22⋊C412yes—
127C22×C3⋊D3SD1612yes—
128C22×C3⋊D3Q1612yes—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3C22⋊C412yes—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158#624—48no—
159C32×C8—41no—
160C3⋊(C3⋊C8)—41no—
161C2×C22⋊Q8—91no—
162C22×C4⋊C4—91no—
163C2×#103—31no—
164C2×#103—91no—
165C2×C22⋊C8—91no—
166#340—31no—
167#340—91no—
168C23×D3—31no—
169C23×D3—31no—
170C23×D3—61no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—61no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—64no—
206C2×C4×D3—64no—
207C2×C4×D3—121no—
208C2×C4×D3—121no—
209C2×C4×D3—121no—
210C2×C4×D3—121no—
211C2×C4×D3—122no—
212C2×C4×D3—122no—
213C2×C4×D3—122no—
214C2×C4×D3—122no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6C4×D312yescomplemented
221C2×C3×C8—22no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—41no—
229C2×C3×C8—41no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—64no—
242C4⋊Dic3C4×D312yescomplemented
243C4⋊Dic3D1212yes—
244C4⋊Dic3#6712yes—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—121no—
256C2×C3⋊C8—121no—
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32#12011yescharacteristic
259C22×C32#12311yescharacteristic
260C22×C32C2×SD1611yescharacteristic
261C22×C32C2×Q1611yescharacteristic
262C22×C32AGL(1,ℤ/8)11yescharacteristic
263C22×C32#13711yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3#10314yescomplemented
271C32×C4C4×D411yescharacteristic
272C32×C4C4×D411yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12111yescharacteristic
275C3⋊Dic3—22no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C3×Dic3—42no—
280C22×Q8—31no—
281C23×C4—91no—
282C23×C4—181no—
283C22×C8—91no—
284C22×C8D3211yescharacteristic
285C22⋊Q8—94no—
286C22⋊Q8—182no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—182no—
291C2×C4⋊C4—182no—
292C2×C4⋊C4—181no—
293C2×C4⋊C4—181no—
294C2×C22⋊C4—181no—
295#103—62no—
296#103—182no—
297C22⋊C8—182no—
298C23×C3—21no—
299C23×C3D3×D411yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—32no—
302C22×D3—32no—
303C22×D3—32no—
304C22×D3—32no—
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—121no—
319C22×D3—121no—
320C22×D3—121no—
321C22×D3—121no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—121no—
325C3×Q8—121no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4#23911yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—62no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—122no—
388C4×D3—122no—
389C4×D3—128no—
390C4×D3—128no—
391Dic6—22no—
392Dic6—22no—
393Dic6—41no—
394Dic6—41no—
395C3×C8—42no—
396C3×C8—41no—
397C3×C8—41no—
398C3⋊C8—122no—
399C3⋊C8—121no—
400C3⋊C8—121no—
401C2×C32#38611yescharacteristic
402C2×C32C2×#10311yescharacteristic
403C2×C32#41711yescharacteristic
404C2×C32#45011yescharacteristic
405C2×C32#45111yescharacteristic
406C2×C32#48311yescharacteristic
407C2×C32#48411yescharacteristic
408C3⋊D3—24no—
409C24—91no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—91no—
421C22×C4—92no—
422C22×C4—92no—
423C22×C4—184no—
424C22×C4—181no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4—362no—
429C22×C4—362no—
430C22×C4C2×D3211yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—181no—
435C2×C8—181no—
436C2×C8—181no—
437C4⋊C4—32no—
438C4⋊C4—32no—
439C4⋊C4—32no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—184no—
444C4⋊C4—184no—
445C22⋊C4—184no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3D3×C22⋊C411yescharacteristic
454C22×C3D3×C22⋊C411yescharacteristic
455C22×C3#88211yescharacteristic
456C22×C3#88311yescharacteristic
457C22×C3#89411yescharacteristic
458C22×C3#91111yescharacteristic
459C22×C3D3×SD1611yescharacteristic
460C22×C3D3×SD1611yescharacteristic
461C22×C3#91411yescharacteristic
462C22×C3#91511yescharacteristic
463C22×C3D3×Q1611yescharacteristic
464C22×C3D3×Q1611yescharacteristic
465C22×C3#91811yescharacteristic
466C22×C3#93711yescharacteristic
467C2×D3—34no—
468C2×D3—34no—
469C2×D3—64no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—122no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—122no—
493C3×C4—122no—
494C3×C4—122no—
495C3×C4—122no—
496C3×C4C4×D1211yescharacteristic
497C3×C4#67⋊C411yescharacteristic
498C3×C4#88411yescharacteristic
499C3×C4#88411yescharacteristic
500C3×C4#89311yescharacteristic
501C3×C4#89511yescharacteristic
502C3×C4C4×#6711yescharacteristic
503C3×C4#93811yescharacteristic
504Dic3—42no—
505Dic3—42no—
506Dic3—42no—
507Dic3—42no—
508Dic3—62no—
509Dic3—62no—
510Dic3—122no—
511C32#187211yescharacteristic, complemented, Sylow
512C23—92no—
513C23—92no—
514C23—92no—
515C23—181no—
516C23—181no—
517C23—181no—
518C23—181no—
519C23#380211yescharacteristic
520Q8—62no—
521Q8—62no—
522Q8—121no—
523Q8—121no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—92no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—121no—
536C2×C4—121no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—368no—
544C2×C4#379911yescharacteristic
545C2×C4C4×D3211yescharacteristic
546C2×C4D3×D1211yescharacteristic
547C2×C4#380411yescharacteristic
548C2×C4D3×#6711yescharacteristic
549C2×C4#381111yescharacteristic
550C8—41no—
551C8—361no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3#466511yescharacteristic
560C2×C3#477111yescharacteristic
561C2×C3#477611yescharacteristic
562C2×C3D3×#10311yescharacteristic
563C2×C3D3×#10311yescharacteristic
564C2×C3#480311yescharacteristic
565C2×C3#480511yescharacteristic
566C2×C3#480911yescharacteristic
567C2×C3#481111yescharacteristic
568C2×C3#486211yescharacteristic
569C2×C3#488411yescharacteristic
570C2×C3#495611yescharacteristic
571C2×C3#516911yescharacteristic
572C2×C3#518611yescharacteristic
573D3—64no—
574D3—64no—
575D3—124no—
576C22—94no—
577C22—182no—
578C22—182no—
579C22—182no—
580C22—182no—
581C22—182no—
582C22—182no—
583C22#6379611yescharacteristic
584C22#6379811yescharacteristic
585C22#6380211yescharacteristic
586C22#6381111yescharacteristic
587C22#6385411yescharacteristic
588C22#6392111yescharacteristic
589C22#6392211yescharacteristic
590C4—122no—
591C4—122no—
592C4—122no—
593C4—122no—
594C4—182no—
595C4#6388011yescharacteristic
596C4#6390411yescharacteristic
597C4#6391011yescharacteristic
598C4#6395811yescharacteristic
599C3—21no—
600C3#6887811yescharacteristic, complemented
601C3#7026811yescharacteristic, complemented
602C2—184no—
603C2#1059067211yescharacteristic
604C2#1059068611yescharacteristic
605C2#1059068911yescharacteristic
606C2#1059094311yescharacteristic
607C2#1059095011yescharacteristic
608C2#1059095711yescharacteristic
609C2#1059127511yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1872
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×#63565C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
24. #63871C4semidirect
37. C2×#816D3semidirect
40. #4551D3semidirect
61. C2×C3×Dic6C2×C4semidirect
74. C3×C4⋊Dic3C2×C4semidirect
220. C2×Dic6C4×D3semidirect
242. C4⋊Dic3C4×D3semidirect
270. C2×C3⋊D3#103semidirect
511. C32#1872semidirect
600. C3#68878semidirect
601. C3#70268semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638712
C2×#636472
C2×C3×#8162
C2×#635652
C3×#45512
#105891632
#702683
#688783