Finite Group Databasebeta

← #11787357

Subgroups — #11787357

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71678—31nomaximal
9#70201—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#938—22no—
17C3×#938C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22C2×Dic32—21no—
23#63841—22no—
24#63841—22no—
25#63659—22no—
26C3×#832—22no—
27(C2×D3)⋊(C3⋊C8)—22no—
28C2×C3×#121—31no—
29C2×#938D311yescharacteristic
30C2×#926—31no—
31C2×#892—31no—
32C2×C3×#102—31no—
33C2×#832—31no—
34C2×#832—31no—
35C2×#832—61no—
36C2×#832D311yescharacteristic, complemented
37C2×#830—31no—
38C2×(C2×D3)⋊C8—31no—
39#4551—31no—
40#4529—31no—
41#4529—31no—
42#4529—31no—
43C24×C32—21no—
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4C2×C412yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C3×#67—24no—
54C2×C3×#67—42no—
55C2×C3×#67—42no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3D412yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yescomplemented
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2×C412yes—
74C3×C4⋊Dic3D412yescomplemented
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78(C2×D3)⋊Dic3—24no—
79Dic32—24no—
80#1875—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4—61no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C2×D311yescharacteristic
85C23×C3×C4—31no—
86C22×#67—21no—
87C22×C4×D3C2×D311yescharacteristic
88C22×C3×C8—31no—
89C3×#121—34no—
90C3×#121—62no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×#217—21no—
95C2×#217—61no—
96#938—22no—
97#938Dic314yescomplemented
98C2×(C2×D3)⋊C4—61no—
99#926—62no—
100#926—62no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—61no—
111C22×C3⋊C8C2×D311yescharacteristic
112#892—62no—
113#892—62no—
114C3×#102—62no—
115#832—22no—
116#832—62no—
117#832—62no—
118#832—64no—
119#830—62no—
120(C2×D3)⋊C8—62no—
121C23×C32—22no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3C22⋊C412yes—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C3×#67—48no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3C22⋊C412yes—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3⋊(C3⋊C8)—41no—
164C3×C3⋊C8—41no—
165C2×#121—31no—
166C2×#117—91no—
167C2×#102—31no—
168C2×#102—91no—
169C2×C22⋊C8—91no—
170#340—91no—
171#340—91no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—31no—
175C24×C3—41no—
176C23×D3#6711yescharacteristic
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—22no—
190C2×C3×D4—41no—
191C2×C3×D4—41no—
192C2×C3×D4—41no—
193C2×C3×D4—64no—
194C2×C3×D4—122no—
195C2×C3×D4—122no—
196C2×C3×D4C4×D312yes—
197C2×C3×D4C2×Dic312yes—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—24no—
211C2×#67—42no—
212C2×#67—42no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—121no—
218C22×Dic3#6711yescharacteristic
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×C4×D3C2×Dic312yes—
224C2×C4×D3#6712yes—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—64no—
233#217—24no—
234#217—64no—
235(C2×D3)⋊C4—64no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4⋊Dic3C2×Dic312yes—
245C4⋊Dic3#6712yescomplemented
246C4×Dic3—64no—
247C4×Dic3—64no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—121no—
259C2×C3⋊C8—121no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—81no—
264C22×C32—81no—
265C22×C32—81no—
266C22×C32—81no—
267C22×C32C2×C22⋊C411yescharacteristic
268C22×C32#12011yescharacteristic
269C22×C32#12311yescharacteristic
270C22×C32#13511yescharacteristic
271C22×C32#13511yescharacteristic
272C22×C32AGL(1,ℤ/8)11yescharacteristic
273C22×C32AGL(1,ℤ/8)11yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4C4×D411yescharacteristic
282C32×C4C4×D411yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C3⋊Dic3—42no—
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C22×D4—61no—
290C22×D4D3211yescharacteristic
291C23×C4—31no—
292C22×C8—31no—
293C22×C8—91no—
294#121—34no—
295#121—62no—
296#117—182no—
297#117—182no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—91no—
301C2×C22⋊C4—61no—
302C2×C22⋊C4—181no—
303C2×C42—181no—
304#102—62no—
305#102—182no—
306C22⋊C8—182no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—81no—
333C23×C3—81no—
334C23×C3—81no—
335C23×C3—81no—
336C23×C3D3×D411yescharacteristic
337C23×C3C2×#6711yescharacteristic
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3#21712yes—
345C3×D4—24no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—42no—
351C3×D4—42no—
352C3×D4—42no—
353C3×D4—41no—
354C3×D4—41no—
355C3×D4—41no—
356C3×D4—41no—
357C3×D4—128no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—32no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4#23711yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4C22×Dic311yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389#67—48no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—241no—
406C2×Dic3—241no—
407C2×Dic3#21712yes—
408C4×D3—22no—
409C4×D3—22no—
410C4×D3—22no—
411C4×D3—22no—
412C3×C8—121no—
413C3⋊C8—41no—
414C3⋊C8—122no—
415C3⋊C8—121no—
416C3⋊C8—121no—
417C2×C32—82no—
418C2×C32#38611yescharacteristic
419C2×C32#41611yescharacteristic
420C2×C32#41811yescharacteristic
421C2×C32#44911yescharacteristic
422C2×C32#44911yescharacteristic
423C2×C32#48211yescharacteristic
424C2×C32#48211yescharacteristic
425C3×D3—42no—
426C24—21no—
427C24—31no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—64no—
434C2×D4—122no—
435C2×D4—122no—
436C2×D4D3×Dic312yes—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4—181no—
447C22×C4C2×D3211yescharacteristic
448C2×C8—61no—
449C2×C8—61no—
450C2×C8—61no—
451C2×C8—181no—
452C2×C8—181no—
453C2×C8—181no—
454C4⋊C4—32no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—92no—
459C4⋊C4—181no—
460C22⋊C4—64no—
461C22⋊C4—184no—
462C42—184no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—44no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—82no—
481C22×C3—82no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3D3×C22⋊C411yescharacteristic
499C22×C3#88311yescharacteristic
500C22×C3#91111yescharacteristic
501C22×C3#91211yescharacteristic
502C22×C3#91411yescharacteristic
503C22×C3#91611yescharacteristic
504C22×C3#93211yescharacteristic
505C22×C3#93211yescharacteristic
506C22×C3#93511yescharacteristic
507C22×C3#93711yescharacteristic
508C22×C3#93711yescharacteristic
509C22×C3#95011yescharacteristic
510C22×C3#95011yescharacteristic
511C22×C3C2×#21711yescharacteristic
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—41no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—62no—
524C3×C4—122no—
525C3×C4—122no—
526C3×C4#67⋊C411yescharacteristic
527C3×C4#88411yescharacteristic
528C3×C4C4×#6711yescharacteristic
529C3×C4D4×Dic311yescharacteristic
530C3×C4D4×Dic311yescharacteristic
531C3×C4#93811yescharacteristic
532C3×C4#93911yescharacteristic
533C3×C4#93911yescharacteristic
534Dic3—22no—
535Dic3—42no—
536Dic3—42no—
537Dic3—122no—
538Dic3—122no—
539Dic3—242no—
540C32#187511yescharacteristic, complemented, Sylow
541C23—22no—
542C23—32no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—61no—
550C23—61no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—61no—
555C23D3×#6711yescharacteristic
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4—128no—
561C2×C4—32no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—182no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4C2×D3×Dic311yescharacteristic
578C2×C4#380411yescharacteristic
579C2×C4#380511yescharacteristic
580C2×C4D3×#6711yescharacteristic
581C2×C4D3×#6711yescharacteristic
582C2×C4#381111yescharacteristic
583C8—121no—
584C8—361no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—84no—
593C2×C3—82no—
594C2×C3—82no—
595C2×C3—122no—
596C2×C3#477011yescharacteristic
597C2×C3#477211yescharacteristic
598C2×C3#477911yescharacteristic
599C2×C3#478411yescharacteristic
600C2×C3#495611yescharacteristic
601C2×C3#503511yescharacteristic
602C2×C3#503511yescharacteristic
603C2×C3#503711yescharacteristic
604C2×C3#503711yescharacteristic
605C2×C3#515811yescharacteristic
606C2×C3#517211yescharacteristic
607C2×C3#521511yescharacteristic
608C2×C3#522011yescharacteristic
609C2×C3#523311yescharacteristic
610D3—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—62no—
615C22—62no—
616C22—62no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—121no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22#6393211yescharacteristic
626C22#6393311yescharacteristic
627C22#6393411yescharacteristic
628C22#6393511yescharacteristic
629C22D3×#21711yescharacteristic
630C22#6396911yescharacteristic
631C22#6398311yescharacteristic
632C4—62no—
633C4—122no—
634C4—122no—
635C4—362no—
636C4#6397011yescharacteristic
637C4#6397111yescharacteristic
638C4Dic3×#6711yescharacteristic
639C4#67⋊Dic311yescharacteristic
640C3—21no—
641C3#7020111yescharacteristic, complemented
642C3#7167811yescharacteristic, complemented
643C2—82no—
644C2—122no—
645C2#1059142011yescharacteristic
646C2#1059142111yescharacteristic
647C2#1059142211yescharacteristic
648C2#1059142311yescharacteristic
649C2#1059151911yescharacteristic
650C2#1059152111yescharacteristic
651C2#1059172111yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1875
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. C2×#63659C2semidirect
4. C2×C3×#832C2semidirect
5. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
17. C3×#938C4semidirect
36. C2×#832D3semidirect
66. C4⋊(C3⋊Dic3)D4semidirect
74. C3×C4⋊Dic3D4semidirect
97. #938Dic3semidirect
245. C4⋊Dic3#67semidirect
540. C32#1875semidirect
641. C3#70201semidirect
642. C3#71678semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×#638412
C2×#636592
C2×C3×#8322
C2×(C2×D3)⋊(C3⋊C8)2
#105891642
#105891632
#716783
#702013