Finite Group Databasebeta

← #11787542

Subgroups — #11787542

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72037—31nomaximal
9#70172—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C22×C3×D12C2211yescharacteristic
13C2×#3757—21no—
14D4×C3⋊Dic3—22no—
15D4×C3⋊Dic3—22no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#213—22no—
19C2×C3×#213—22no—
20C2×C3×#213C414yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×(C2×D3)⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26C3×#832—22no—
27#63563—22no—
28C22×C3×D8—31no—
29C2×D4×Dic3—31no—
30C2×D4×Dic3—31no—
31C2×D4×Dic3—61no—
32C22×#213D311yescharacteristic
33C2×C3×#102—31no—
34#5221—31no—
35C2×#832—31no—
36C2×#832D311yescharacteristic, complemented
37C2×#821—31no—
38#4988—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—31no—
43C24×C32—21no—
44C23×C3×D3—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C2×C32×D4D412yes—
50C2×C32×D4D412yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—24no—
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—42no—
55C22×C3⋊Dic3—42no—
56C22×C3⋊Dic3D411yescharacteristic
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3×Dic3—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2×C412yescomplemented
65#3757—24no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)D412yes—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C3×#213—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(C2×D3)⋊Dic3—42no—
80(C2×D3)⋊Dic3—42no—
81#1879—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4—31no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C23×Dic3—61no—
87C23×Dic3—61no—
88C23×Dic3—62no—
89C22×D12C2×D311yescharacteristic
90C2×C3×D8—34no—
91C2×C3×D8—62no—
92C2×C3×D8—62no—
93C22×C3×C8—31no—
94C22×C3×C8—31no—
95C2×C3×C4⋊C4—31no—
96C2×#217—61no—
97C2×#217—61no—
98C2×#217—62no—
99C2×#217—61no—
100C2×#217—61no—
101D4×Dic3—62no—
102D4×Dic3—62no—
103D4×Dic3—64no—
104D4×Dic3—64no—
105D4×Dic3—62no—
106D4×Dic3—62no—
107C2×#213—22no—
108C2×#213—22no—
109C2×#213Dic314yescomplemented
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121C3×#102—62no—
122#832—22no—
123#832—62no—
124#821—62no—
125C23×C32—22no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32—41no—
131C23×C32—41no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3—41no—
139C22×C3×D3—41no—
140C32×D4—22no—
141C32×D4—22no—
142C32×D4—22no—
143C32×D4C22⋊C414yescomplemented
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—48no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159C2×C3⋊Dic3D812yescomplemented
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—41no—
166C3×D12—41no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—41no—
169C22×D8—31no—
170C2×C4×D4—91no—
171C2×#102—31no—
172C2×#102—91no—
173#390—91no—
174#340—91no—
175#336—91no—
176C24×C3—22no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—61no—
180C23×D3—21no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—32no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4C4×D312yes—
200C2×C3×D4D1212yes—
201C2×C3×D4C2×Dic312yes—
202C2×C3×D4#6712yes—
203C2×C3×D4#6712yes—
204C2×C3×D4#6712yes—
205C22×C3×C4—21no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3—21no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—62no—
217C22×Dic3—68no—
218C22×Dic3—64no—
219C22×Dic3—64no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—122no—
223C22×Dic3—122no—
224C22×Dic3—124no—
225C22×Dic3—124no—
226C22×Dic3—122no—
227C22×Dic3—122no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12C2×Dic312yescomplemented
234C3×D8—68no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243#217—68no—
244#217—64no—
245#217—64no—
246#217—122no—
247#217—122no—
248#213—28no—
249(C2×D3)⋊C4—122no—
250(C2×D3)⋊C4—122no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8C2×Dic312yescomplemented
271C22×C32—24no—
272C22×C32—42no—
273C22×C32—42no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32C4×D411yescharacteristic
279C22×C32#12011yescharacteristic
280C22×C32#12111yescharacteristic
281C22×C32C2×D811yescharacteristic
282C22×C32#13511yescharacteristic
283C22×C32AGL(1,ℤ/8)11yescharacteristic
284C22×C32AGL(1,ℤ/8)11yescharacteristic
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—81no—
289C2×C3×D3—81no—
290C2×C3×D3—81no—
291C2×C3×D3—81no—
292C32×C4C2×C22⋊C411yescharacteristic
293C32×C4C4×D411yescharacteristic
294C32×C4#12111yescharacteristic
295C32×C4#12311yescharacteristic
296C3⋊Dic3—22no—
297C3⋊Dic3—42no—
298C3⋊Dic3—41no—
299C3×Dic3—81no—
300C22×D4—31no—
301C22×D4D3211yescharacteristic
302C23×C4—181no—
303C2×D8—34no—
304C2×D8—62no—
305C2×D8—62no—
306C22×C8—31no—
307C22×C8—31no—
308C4×D4—182no—
309C4×D4—182no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—91no—
312C2×C22⋊C4—181no—
313C2×C22⋊C4—181no—
314C2×C22⋊C4—181no—
315C2×C42—91no—
316#102—62no—
317#102—182no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—21no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—62no—
341C23×C3—121no—
342C23×C3—121no—
343C23×C3—121no—
344C23×C3—121no—
345C23×C3—121no—
346C23×C3—121no—
347C23×C3D3×D411yescharacteristic
348C23×C3D3×D411yescharacteristic
349C22×D3—22no—
350C22×D3—41no—
351C22×D3—41no—
352C22×D3—41no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—41no—
356C3×D4—24no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—24no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—121no—
369C3×D4—121no—
370C3×D4(C2×D3)⋊C414yescomplemented
371C3×D4#21714yescomplemented
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4—121no—
381C2×C3×C4C2×C4×D311yescharacteristic
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4#23711yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4C22×Dic311yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×Dic3—32no—
394C2×Dic3—32no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—64no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—1216no—
418C2×Dic3—128no—
419C2×Dic3—128no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426D12—22no—
427D12—22no—
428D12—41no—
429D12—41no—
430C3×C8—62no—
431C3×C8—121no—
432C3⋊C8—22no—
433C3⋊C8—41no—
434C2×C32—44no—
435C2×C32#38611yescharacteristic
436C2×C32C4×D811yescharacteristic
437C2×C32#44211yescharacteristic
438C2×C32#44711yescharacteristic
439C2×C32#44911yescharacteristic
440C2×C32#45911yescharacteristic
441C2×C32#46311yescharacteristic
442C3×D3—82no—
443C24—21no—
444C24—61no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—32no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4D3×Dic312yes—
455C2×D4#62512yes—
456C2×D4#62612yes—
457C22×C4—61no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—184no—
461C22×C4—181no—
462C22×C4—362no—
463C22×C4—362no—
464C22×C4C2×D3211yescharacteristic
465D8—68no—
466C2×C8—32no—
467C2×C8—61no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—92no—
475C4⋊C4—181no—
476C22⋊C4—184no—
477C22⋊C4—362no—
478C22⋊C4—362no—
479C42—181no—
480C42—181no—
481C22×C3—28no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—44no—
494C22×C3—44no—
495C22×C3—44no—
496C22×C3—44no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—122no—
510C22×C3—122no—
511C22×C3—122no—
512C22×C3—241no—
513C22×C3—241no—
514C22×C3—241no—
515C22×C3—241no—
516C22×C3#67⋊C411yescharacteristic
517C22×C3#88211yescharacteristic
518C22×C3D3×D811yescharacteristic
519C22×C3D3×D811yescharacteristic
520C22×C3#91111yescharacteristic
521C22×C3#91111yescharacteristic
522C22×C3#91111yescharacteristic
523C22×C3#91211yescharacteristic
524C22×C3#91411yescharacteristic
525C22×C3#91611yescharacteristic
526C22×C3D4×Dic311yescharacteristic
527C22×C3#93711yescharacteristic
528C22×C3#93911yescharacteristic
529C22×C3#93911yescharacteristic
530C2×D3—42no—
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—81no—
534C2×D3—81no—
535C2×D3—81no—
536C2×D3—81no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—241no—
542C3×C4#67⋊C411yescharacteristic
543C3×C4#88611yescharacteristic
544C3×C4C2×(C2×D3)⋊C411yescharacteristic
545C3×C4D4×Dic311yescharacteristic
546C3×C4#93511yescharacteristic
547C3×C4#93911yescharacteristic
548C3×C4#93911yescharacteristic
549C3×C4C2×#21711yescharacteristic
550Dic3—64no—
551Dic3—62no—
552Dic3—62no—
553Dic3—81no—
554Dic3—124no—
555Dic3—122no—
556Dic3—122no—
557Dic3—121no—
558Dic3—122no—
559Dic3—121no—
560C32#187911yescharacteristic, complemented, Sylow
561C23—22no—
562C23—22no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—62no—
569C23—121no—
570C23—121no—
571C23—121no—
572C23—121no—
573C23—121no—
574C23—121no—
575C23#381111yescharacteristic
576D4—22no—
577D4—22no—
578D4—22no—
579D4—62no—
580D4—62no—
581D4—121no—
582D4—121no—
583D4(C2×D3)⋊Dic314yescomplemented
584C2×C4—92no—
585C2×C4—121no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—182no—
594C2×C4—368no—
595C2×C4—361no—
596C2×C4—361no—
597C2×C4C2×D3×Dic311yescharacteristic
598C2×C4#380511yescharacteristic
599C2×C4#380511yescharacteristic
600C2×C4C2×#62511yescharacteristic
601C2×C4C2×#62611yescharacteristic
602C2×C4#381111yescharacteristic
603C8—62no—
604C8—121no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—48no—
613C2×C3—44no—
614C2×C3—44no—
615C2×C3—242no—
616C2×C3#475611yescharacteristic
617C2×C3#477311yescharacteristic
618C2×C3#478111yescharacteristic
619C2×C3#478511yescharacteristic
620C2×C3#495811yescharacteristic
621C2×C3Dic3×D811yescharacteristic
622C2×C3#515011yescharacteristic
623C2×C3#515011yescharacteristic
624C2×C3#515211yescharacteristic
625C2×C3#515311yescharacteristic
626C2×C3#515611yescharacteristic
627C2×C3#515811yescharacteristic
628C2×C3#516511yescharacteristic
629C2×C3#522011yescharacteristic
630D3—82no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—122no—
639C22—122no—
640C22—122no—
641C22—241no—
642C22—241no—
643C22—241no—
644C22—241no—
645C22#6392611yescharacteristic
646C22#6392711yescharacteristic
647C22#6393611yescharacteristic
648C22#6393711yescharacteristic
649C22#67⋊Dic311yescharacteristic
650C22#6398011yescharacteristic
651C22#6398111yescharacteristic
652C4—182no—
653C4—241no—
654C4—362no—
655C4—361no—
656C4C2×(C2×D3)⋊Dic311yescharacteristic
657C4#6396211yescharacteristic
658C4#67⋊Dic311yescharacteristic
659C4#6398011yescharacteristic
660C3—21no—
661C3#7017211yescharacteristic, complemented
662C3#7203711yescharacteristic, complemented
663C2—44no—
664C2—242no—
665C2#1059143511yescharacteristic
666C2#1059143611yescharacteristic
667C2#1059145611yescharacteristic
668C2#1059145711yescharacteristic
669C2#1059147611yescharacteristic
670C2#1059148611yescharacteristic
671C2#1059171311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1879
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
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×C3×#832C2semidirect
4. #10591323C2semidirect
5. C2×#63563C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
20. C2×C3×#213C4semidirect
36. C2×#832D3semidirect
64. C2×C3×D12C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
109. C2×#213Dic3semidirect
143. C32×D4C22⋊C4semidirect
159. C2×C3⋊Dic3D8semidirect
233. C2×D12C2×Dic3semidirect
270. C2×C3⋊C8C2×Dic3semidirect
370. C3×D4(C2×D3)⋊C4semidirect
371. C3×D4#217semidirect
560. C32#1879semidirect
583. D4(C2×D3)⋊Dic3semidirect
661. C3#70172semidirect
662. C3#72037semidirect

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×#2132
C2×C3×#8322
#105913232
C2×#635632
#105891642
#105891562
#720373
#701723