Finite Group Databasebeta

← #11787599

Subgroups — #11787599

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C22×#3716C211yesmaximal, characteristic
3C3×#4939C211yesmaximal, characteristic
4C2×#63567C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C3×#4524C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69660—31nomaximal
9#68686—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3—21no—
16C4×#634—22no—
17C4×#634—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716C414yescomplemented
26#63567—22no—
27#63563—22no—
28C22×#214—31no—
29C22×#204—31no—
30C2×C4×Dic6—31no—
31C2×C4×Dic6—31no—
32C2×C4×Dic6—61no—
33C3×#390—31no—
34C2×#832—31no—
35C2×#821—31no—
36C2×#816—31no—
37C2×#810—31no—
38#4939D311yescharacteristic
39C3×#336—31no—
40#4551—31no—
41#4529—31no—
42#4524D311yescharacteristic, complemented
43C23×C3×D3—21no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yes—
53C2×#634D412yes—
54C2×#634D412yes—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C32×C42—21no—
63C32×C42—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yes—
66#3750—24no—
67C4×C3⋊Dic3—24no—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8C2×C412yes—
78#3716—28no—
79#1880—91noSylow
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C22×Dic6—31no—
83C22×Dic6—31no—
84C22×Dic6—61no—
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—21no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C2×D311yescharacteristic
93C2×#214—34no—
94C2×#214—62no—
95C2×#214—62no—
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—21no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—62no—
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—62no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—34no—
111C2×#204—62no—
112C2×#204—62no—
113C4×Dic6—62no—
114C4×Dic6—62no—
115C4×Dic6—62no—
116C4×Dic6—62no—
117C4×Dic6—64no—
118C4×Dic6—64no—
119#832—62no—
120#821—62no—
121#816—62no—
122#810—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4SD1612yescomplemented
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149#634—22no—
150#634—22no—
151#634—22no—
152#634C22⋊C414yescomplemented
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C22×SD16—91no—
163C2×C4×Q8—91no—
164C2×#103—91no—
165C2×#102—91no—
166#390—31no—
167#340—91no—
168#336—31no—
169C24×C3—61no—
170C23×D3—21no—
171C2×C3×D4—32no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4D1211yescharacteristic
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—62no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C4×D312yes—
200C2×Dic6—32no—
201C2×Dic6—32no—
202C2×Dic6—32no—
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—32no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×C3×C8—32no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—122no—
227C3×C22⋊C4—122no—
228C3×C42—22no—
229C3×C42—22no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234#214—68no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—42no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245Dic3⋊C4—68no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C4×Dic3—68no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8C4×D312yes—
257#204—68no—
258C22×C32C4×D411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32C2×SD1611yescharacteristic
262C22×C32#13511yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32#13711yescharacteristic
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C32×C4—22no—
273C32×C4—41no—
274C32×C4C2×C22⋊C411yescharacteristic
275C32×C4C4×D411yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12311yescharacteristic
278C3⋊Dic3—24no—
279C3⋊Dic3—42no—
280C3×Dic3—81no—
281C22×Q8—91no—
282C22×D4—31no—
283C2×SD16—94no—
284C2×SD16—182no—
285C2×SD16—182no—
286C22×C8—31no—
287C22×C8—31no—
288C4×Q8—182no—
289C4×Q8—182no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—61no—
294C2×C22⋊C4—61no—
295C2×C42—181no—
296C2×C42D3211yescharacteristic
297#103—182no—
298#102—182no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3C2×D1211yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—22no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—121no—
319C3×D4—121no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4#20412yescomplemented
346C2×C3×C4#21412yescomplemented
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4#23911yescharacteristic
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380D12—22no—
381D12—22no—
382D12—41no—
383D12—41no—
384Dic6—34no—
385Dic6—34no—
386Dic6—64no—
387Dic6—64no—
388Dic6—64no—
389Dic6—64no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C2×C32#38611yescharacteristic
401C2×C32C4×SD1611yescharacteristic
402C2×C32#44011yescharacteristic
403C2×C32#44811yescharacteristic
404C2×C32#44911yescharacteristic
405C2×C32#46011yescharacteristic
406C2×C32#46411yescharacteristic
407C3×D3—82no—
408C24—61no—
409C2×Q8—92no—
410C2×Q8—92no—
411C2×Q8—92no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C22×C4—61no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4#62611yescharacteristic
425C22×C4#62611yescharacteristic
426C22×C4C2×D3211yescharacteristic
427SD16—188no—
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—92no—
437C4⋊C4—184no—
438C4⋊C4—181no—
439C22⋊C4—122no—
440C22⋊C4—122no—
441C42—21no—
442C42—21no—
443C42—184no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—241no—
455C22×C3—241no—
456C22×C3—241no—
457C22×C3—241no—
458C22×C3C4×D1211yescharacteristic
459C22×C3#88211yescharacteristic
460C22×C3#89511yescharacteristic
461C22×C3C2×#20411yescharacteristic
462C22×C3#90411yescharacteristic
463C22×C3#90811yescharacteristic
464C22×C3#90911yescharacteristic
465C22×C3C4×#6711yescharacteristic
466C22×C3#93211yescharacteristic
467C22×C3C2×#21411yescharacteristic
468C22×C3#93711yescharacteristic
469C22×C3#93811yescharacteristic
470C22×C3#95011yescharacteristic
471C22×C3#95111yescharacteristic
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—81no—
476C2×D3—81no—
477C2×D3—81no—
478C2×D3—81no—
479C3×C4—24no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—42no—
487C3×C4—41no—
488C3×C4—41no—
489C3×C4—241no—
490C3×C4D3×C22⋊C411yescharacteristic
491C3×C4D3×C22⋊C411yescharacteristic
492C3×C4#67⋊C411yescharacteristic
493C3×C4#88311yescharacteristic
494C3×C4#88411yescharacteristic
495C3×C4#88411yescharacteristic
496C3×C4#89311yescharacteristic
497C3×C4#89411yescharacteristic
498Dic3—68no—
499Dic3—64no—
500Dic3—64no—
501Dic3—81no—
502Dic3—124no—
503Dic3—122no—
504Dic3—122no—
505C32#188011yescharacteristic, complemented, Sylow
506C23—62no—
507C23—121no—
508C23—121no—
509C23—121no—
510C23—121no—
511C23—121no—
512C23—121no—
513C23C2×#62611yescharacteristic
514Q8—94no—
515Q8—182no—
516Q8—182no—
517Q8—182no—
518D4—62no—
519D4—62no—
520D4—121no—
521D4—121no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—361no—
535C2×C4—361no—
536C2×C4#371612yescomplemented
537C2×C4#379611yescharacteristic
538C2×C4#379811yescharacteristic
539C2×C4C4×D3211yescharacteristic
540C2×C4#380211yescharacteristic
541C2×C4#381111yescharacteristic
542C2×C4#381111yescharacteristic
543C8—62no—
544C8—121no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—242no—
553C2×C3#466511yescharacteristic
554C2×C3C4×#20411yescharacteristic
555C2×C3#471011yescharacteristic
556C2×C3#473411yescharacteristic
557C2×C3#473811yescharacteristic
558C2×C3#484511yescharacteristic
559C2×C3#484811yescharacteristic
560C2×C3#495611yescharacteristic
561C2×C3C4×#21411yescharacteristic
562C2×C3#501811yescharacteristic
563C2×C3#503711yescharacteristic
564C2×C3#504011yescharacteristic
565C2×C3#505411yescharacteristic
566C2×C3#507511yescharacteristic
567D3—82no—
568C22—122no—
569C22—122no—
570C22—122no—
571C22—241no—
572C22—241no—
573C22—241no—
574C22—241no—
575C22C2×#371611yescharacteristic
576C22#6382911yescharacteristic
577C22#6383011yescharacteristic
578C22#6383111yescharacteristic
579C22C4×#62611yescharacteristic
580C22#6391611yescharacteristic
581C22#6398111yescharacteristic
582C4—22no—
583C4—41no—
584C4—184no—
585C4—241no—
586C4—362no—
587C4#6385311yescharacteristic
588C4#6388111yescharacteristic
589C4#6391211yescharacteristic
590C4#6392111yescharacteristic
591C3—21no—
592C3#6868611yescharacteristic, complemented
593C3#6966011yescharacteristic, complemented
594C2—242no—
595C2C4×#371611yescharacteristic
596C2#1059036011yescharacteristic
597C2#1059037711yescharacteristic
598C2#1059037811yescharacteristic
599C2#1059118111yescharacteristic
600C2#1059118211yescharacteristic
601C2#1059138711yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
4. C2×#63567C2semidirect
6. C3×#4524C2semidirect
7. #10589164C2semidirect
25. C2×#3716C4semidirect
42. #4524D3semidirect
136. C2×C32×C4SD16semidirect
152. #634C22⋊C4semidirect
345. C2×C3×C4#204semidirect
346. C2×C3×C4#214semidirect
505. C32#1880semidirect
536. C2×C4#3716semidirect
592. C3#68686semidirect
593. C3#69660semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C22×#37162
C3×#49392
C2×#635672
C2×#635632
C3×#45242
#105891642
#696603
#686863