Finite Group Databasebeta

← #11787445

Subgroups — #11787445

Order 1152.

1017 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72047—31nomaximal
9#70171—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C22×C3×Dic6C2211yescharacteristic
13C2×#3757—21no—
14D4×C3⋊Dic3—22no—
15D4×C3⋊Dic3—22no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#214—22no—
19C2×C3×#214—22no—
20C2×C3×#214C414yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#832—22no—
25#63579—21no—
26#63579—21no—
27#63566—22no—
28C22×C3×SD16—31no—
29C2×D4×Dic3—31no—
30C2×D4×Dic3—31no—
31C2×D4×Dic3—61no—
32C22×#214D311yescharacteristic
33C2×C3×#102—31no—
34#5229—31no—
35C2×#835—31no—
36C2×#832D311yescharacteristic
37C2×#816—31no—
38#4973—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—31no—
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C2×C32×D4D412yes—
49C2×C32×D4D412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—24no—
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—42no—
54C22×C3⋊Dic3—42no—
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2×C412yescomplemented
65#3757—24no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)D412yes—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C3×#214—28no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yescomplemented
79#1877—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C2×D311yescharacteristic
84C23×Dic3—61no—
85C23×Dic3—61no—
86C23×Dic3—62no—
87C22×Dic6C2×D311yescharacteristic
88C2×C3×SD16—34no—
89C2×C3×SD16—62no—
90C2×C3×SD16—62no—
91C22×C3×C8—31no—
92C22×C3×C8—31no—
93C2×C3×C4⋊C4—31no—
94C2×#217—61no—
95C2×#217—61no—
96C2×#217—62no—
97D4×Dic3—62no—
98D4×Dic3—62no—
99D4×Dic3—64no—
100D4×Dic3—64no—
101D4×Dic3—62no—
102D4×Dic3—62no—
103C2×#214—22no—
104C2×#214—22no—
105C2×#214Dic314yescomplemented
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C3×#102—62no—
116#835—62no—
117#832—22no—
118C3⋊#95—61no—
119C3⋊#95—61no—
120C3⋊#95—61no—
121C3⋊#95—61no—
122#816—62no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32C2×D411yescharacteristic
131C32×D4—22no—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4C22⋊C414yes—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—48no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3SD1612yescomplemented
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—41no—
160C3×Dic6—41no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—41no—
163C22×SD16—31no—
164C2×C4×D4—91no—
165C2×#103—91no—
166C2×#102—31no—
167#391—91no—
168#340—91no—
169#336—91no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
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—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4C4×D312yes—
192C2×C3×D4D1212yes—
193C2×C3×D4C2×Dic312yes—
194C2×C3×D4#6712yes—
195C2×C3×D4#6712yes—
196C2×C3×D4#6712yes—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—62no—
211C22×Dic3—68no—
212C22×Dic3—64no—
213C22×Dic3—64no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—122no—
217C22×Dic3—122no—
218C22×Dic3—124no—
219C22×Dic3—124no—
220C22×Dic3—122no—
221C22×Dic3—122no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6C2×Dic312yescomplemented
228C3×SD16—68no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237#217—68no—
238#217—64no—
239#217—64no—
240#214—28no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8C2×Dic312yescomplemented
261C22×C32—24no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32—42no—
268C22×C32C4×D411yescharacteristic
269C22×C32#12011yescharacteristic
270C22×C32#12111yescharacteristic
271C22×C32C2×SD1611yescharacteristic
272C22×C32#13511yescharacteristic
273C22×C32AGL(1,ℤ/8)11yescharacteristic
274C22×C32#13711yescharacteristic
275C32×C4C2×C22⋊C411yescharacteristic
276C32×C4C4×D411yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12311yescharacteristic
279C3⋊Dic3—22no—
280C3⋊Dic3—42no—
281C3⋊Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—81no—
284C22×Q8—31no—
285C22×D4D3211yescharacteristic
286C23×C4—181no—
287C2×SD16—34no—
288C2×SD16—62no—
289C2×SD16—62no—
290C22×C8—31no—
291C22×C8—31no—
292C4×D4—182no—
293C4×D4—182no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—91no—
296C2×C22⋊C4—181no—
297C2×C42—91no—
298#103—182no—
299#102—62no—
300#95—181no—
301#95—181no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
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×C3D3×D411yescharacteristic
325C23×C3D3×D411yescharacteristic
326C3×Q8—62no—
327C3×Q8—62no—
328C3×Q8—121no—
329C3×Q8—121no—
330C3×D4—24no—
331C3×D4—24no—
332C3×D4—24no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—24no—
340C3×D4(C2×D3)⋊C414yes—
341C3×D4#21714yes—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—62no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4C22×Dic311yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×Dic3—22no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—62no—
382C2×Dic3—64no—
383C2×Dic3—61no—
384C2×Dic3—62no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—62no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—1216no—
394C2×Dic3—128no—
395C2×Dic3—128no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402Dic6—22no—
403Dic6—22no—
404Dic6—41no—
405Dic6—41no—
406C3×C8—62no—
407C3×C8—121no—
408C3⋊C8—22no—
409C3⋊C8—41no—
410C2×C32—44no—
411C2×C32#38611yescharacteristic
412C2×C32C4×SD1611yescharacteristic
413C2×C32#44011yescharacteristic
414C2×C32#45011yescharacteristic
415C2×C32#45211yescharacteristic
416C2×C32#46111yescharacteristic
417C2×C32#46311yescharacteristic
418C24—21no—
419C2×Q8—32no—
420C2×Q8—61no—
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4D3×Dic312yes—
429C2×D4#62512yes—
430C2×D4#62612yes—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—184no—
436C22×C4—181no—
437C22×C4—362no—
438C22×C4—362no—
439C22×C4C2×D3211yescharacteristic
440SD16—68no—
441C2×C8—32no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C4⋊C4—61no—
448C4⋊C4—61no—
449C4⋊C4—92no—
450C4⋊C4—181no—
451C22⋊C4—184no—
452C42—181no—
453C42—181no—
454C22×C3—28no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3#67⋊C411yescharacteristic
483C22×C3#88211yescharacteristic
484C22×C3#91111yescharacteristic
485C22×C3#91211yescharacteristic
486C22×C3D3×SD1611yescharacteristic
487C22×C3D3×SD1611yescharacteristic
488C22×C3#91411yescharacteristic
489C22×C3#91511yescharacteristic
490C22×C3#91511yescharacteristic
491C22×C3#91611yescharacteristic
492C22×C3D4×Dic311yescharacteristic
493C22×C3#93711yescharacteristic
494C22×C3#93911yescharacteristic
495C22×C3#93911yescharacteristic
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—122no—
501C3×C4—241no—
502C3×C4#67⋊C411yescharacteristic
503C3×C4#88611yescharacteristic
504C3×C4C2×(C2×D3)⋊C411yescharacteristic
505C3×C4D4×Dic311yescharacteristic
506C3×C4#93511yescharacteristic
507C3×C4#93911yescharacteristic
508C3×C4#93911yescharacteristic
509C3×C4C2×#21711yescharacteristic
510Dic3—42no—
511Dic3—64no—
512Dic3—62no—
513Dic3—62no—
514Dic3—81no—
515Dic3—124no—
516Dic3—122no—
517Dic3—122no—
518Dic3—121no—
519Dic3—122no—
520Dic3—121no—
521C32#187711yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—22no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23#381111yescharacteristic
530Q8—62no—
531Q8—62no—
532Q8—121no—
533Q8—121no—
534D4—22no—
535D4—22no—
536D4—22no—
537D4(C2×D3)⋊Dic314yes—
538C2×C4—62no—
539C2×C4—92no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—182no—
551C2×C4—368no—
552C2×C4—361no—
553C2×C4—361no—
554C2×C4C2×D3×Dic311yescharacteristic
555C2×C4#380511yescharacteristic
556C2×C4#380511yescharacteristic
557C2×C4C2×#62511yescharacteristic
558C2×C4C2×#62611yescharacteristic
559C2×C4#381111yescharacteristic
560C8—62no—
561C8—121no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—48no—
570C2×C3—44no—
571C2×C3—44no—
572C2×C3#475711yescharacteristic
573C2×C3#475811yescharacteristic
574C2×C3#477611yescharacteristic
575C2×C3#478311yescharacteristic
576C2×C3#495811yescharacteristic
577C2×C3#515311yescharacteristic
578C2×C3Dic3×SD1611yescharacteristic
579C2×C3#516211yescharacteristic
580C2×C3#516211yescharacteristic
581C2×C3#516411yescharacteristic
582C2×C3#516511yescharacteristic
583C2×C3#516911yescharacteristic
584C2×C3#517311yescharacteristic
585C2×C3#522011yescharacteristic
586C22—24no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22#6393011yescharacteristic
594C22#6393111yescharacteristic
595C22#6393611yescharacteristic
596C22#6393711yescharacteristic
597C22#67⋊Dic311yescharacteristic
598C22#6398011yescharacteristic
599C22#6398111yescharacteristic
600C4—122no—
601C4—182no—
602C4—241no—
603C4—361no—
604C4—362no—
605C4C2×(C2×D3)⋊Dic311yescharacteristic
606C4#6396211yescharacteristic
607C4#67⋊Dic311yescharacteristic
608C4#6398011yescharacteristic
609C3—21no—
610C3#7017111yescharacteristic, complemented
611C3#7204711yescharacteristic, complemented
612C2—44no—
613C2#1059144511yescharacteristic
614C2#1059144611yescharacteristic
615C2#1059146611yescharacteristic
616C2#1059146711yescharacteristic
617C2#1059147611yescharacteristic
618C2#1059149711yescharacteristic
619C2#1059171311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1877
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
4. #10591221C2semidirect
5. C2×#63566C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
20. C2×C3×#214C4semidirect
64. C2×C3×Dic6C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
105. C2×#214Dic3semidirect
150. C2×C3⋊Dic3SD16semidirect
227. C2×Dic6C2×Dic3semidirect
260. C2×C3⋊C8C2×Dic3semidirect
521. C32#1877semidirect
610. C3#70171semidirect
611. C3#72047semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×C3×#2142
C2×C3×#8322
#105912212
C2×#635662
#105891642
#105891562
#720473
#701713