Finite Group Databasebeta

← #11787539

Subgroups — #11787539

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×#64102C211yesmaximal, characteristic, complemented
2C22×#3714C211yesmaximal, characteristic
3C2×C3×#809C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70208—31nomaximal
9#68897—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C22×C3×D12C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102—22no—
17#64102—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3714—22no—
24C2×#3714—22no—
25C2×#3714C414yescomplemented
26C3×#809—22no—
27#63564—22no—
28C22×#213—31no—
29C22×D24—31no—
30C2×#893—31no—
31C2×#893—31no—
32C2×#893—61no—
33C2×C3×#102—31no—
34#5221—31no—
35C2×#821—31no—
36#4988—31no—
37C2×#809—31no—
38C2×#809D311yescharacteristic, complemented
39C3×#340—31no—
40#4550—31no—
41#4550—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C2×C4⋊(C3⋊D3)D412yes—
54C2×C4⋊(C3⋊D3)D412yes—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3—42no—
57C2×C4×C3⋊D3—42no—
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
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67#3752—24no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
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×C412yescomplemented
78(C2×D3)⋊Dic3—42no—
79(C2×D3)⋊Dic3—42no—
80#3714—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C22×C4×D3—62no—
90C22×C3×C8—31no—
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×#217—61no—
97C2×#217—61no—
98C2×#213—34no—
99C2×#213—62no—
100C2×#213—62no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4×Dic3—31no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×D24—34no—
113C2×D24—62no—
114C2×D24—62no—
115#893—62no—
116#893—62no—
117#893—64no—
118#893—64no—
119#893—62no—
120#893—62no—
121C3×#102—62no—
122#821—62no—
123#809—22no—
124#809—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
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—
140C2×C32×C4—22no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3D812yescomplemented
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)C22⋊C414yescomplemented
159C4×C3⋊D3—48no—
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—91no—
170C2×C4×D4—91no—
171C2×#102—31no—
172C2×#102—91no—
173#390—91no—
174#340—31no—
175#336—91no—
176C24×C3—61no—
177C23×D3—21no—
178C23×D3—62no—
179C23×D3—61no—
180C23×D3—61no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12C4×D312yescomplemented
225C2×C4×D3—68no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3—124no—
231C2×C4×D3—124no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C2×C3×C8—32no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4D1212yes—
247C3×C4⋊C4#6712yes—
248#217—122no—
249#217—122no—
250#213—68no—
251(C2×D3)⋊C4—68no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8C4×D312yescomplemented
270D24—68no—
271C22×C32C4×D411yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32C2×D811yescharacteristic
275C22×C32#13511yescharacteristic
276C22×C32AGL(1,ℤ/8)11yescharacteristic
277C22×C32AGL(1,ℤ/8)11yescharacteristic
278C2×C3⋊D3—24no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
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×C4—42no—
293C32×C4C2×C22⋊C411yescharacteristic
294C32×C4C4×D411yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12311yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3—41no—
299C3×Dic3—81no—
300C22×D4—31no—
301C22×D4—91no—
302C23×C4—181no—
303C2×D8—94no—
304C2×D8—182no—
305C2×D8—182no—
306C22×C8—31no—
307C22×C8—31no—
308C4×D4—182no—
309C4×D4—182no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4D3211yescharacteristic
312C2×C22⋊C4—181no—
313C2×C22⋊C4—181no—
314C2×C22⋊C4—181no—
315C2×C42—91no—
316#102—62no—
317#102—182no—
318C23×C3—21no—
319C23×C3—62no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3D3×D411yescharacteristic
327C23×C3D3×D411yescharacteristic
328C22×D3—22no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C3×D4—62no—
357C3×D4—62no—
358C3×D4—121no—
359C3×D4—121no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4C2×C4×D311yescharacteristic
379C2×C3×C4C2×C4×D311yescharacteristic
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4#23511yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4#23911yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—41no—
393C2×Dic3—41no—
394C2×Dic3—41no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—62no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—121no—
410C2×Dic3—121no—
411D12—22no—
412D12—22no—
413D12—34no—
414D12—34no—
415D12—41no—
416D12—41no—
417D12—64no—
418D12—64no—
419D12—64no—
420D12—64no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—62no—
425D12—62no—
426D12—62no—
427C4×D3—1216no—
428C4×D3—128no—
429C4×D3—128no—
430C3×C8—62no—
431C3×C8—121no—
432C3⋊C8—22no—
433C3⋊C8—41no—
434C2×C32#38611yescharacteristic
435C2×C32C4×D811yescharacteristic
436C2×C32#44211yescharacteristic
437C2×C32#44711yescharacteristic
438C2×C32#44911yescharacteristic
439C2×C32#45911yescharacteristic
440C2×C32#46311yescharacteristic
441C3⋊D3—44no—
442C3×D3—82no—
443C24—61no—
444C24—181no—
445C2×D4—32no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—92no—
452C2×D4—92no—
453C2×D4—92no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—181no—
457C22×C4—21no—
458C22×C4—61no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—184no—
462C22×C4—362no—
463C22×C4—362no—
464C22×C4C2×D3211yescharacteristic
465D8—188no—
466C2×C8—32no—
467C2×C8—61no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C4⋊C4—21no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C4⋊C4#62612yes—
476C22⋊C4—184no—
477C22⋊C4—362no—
478C22⋊C4—362no—
479C42—181no—
480C42—181no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—241no—
492C22×C3—241no—
493C22×C3—241no—
494C22×C3—241no—
495C22×C3#67⋊C411yescharacteristic
496C22×C3#88211yescharacteristic
497C22×C3#88411yescharacteristic
498C22×C3#88411yescharacteristic
499C22×C3#89311yescharacteristic
500C22×C3D3×D811yescharacteristic
501C22×C3D3×D811yescharacteristic
502C22×C3#91111yescharacteristic
503C22×C3#91411yescharacteristic
504C22×C3#91411yescharacteristic
505C22×C3#91411yescharacteristic
506C22×C3#91611yescharacteristic
507C22×C3#91911yescharacteristic
508C22×C3#93711yescharacteristic
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—68no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—81no—
516C2×D3—81no—
517C2×D3—81no—
518C2×D3—81no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—124no—
522C2×D3—124no—
523C2×D3—124no—
524C2×D3—124no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—44no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—241no—
545C3×C4C4×D1211yescharacteristic
546C3×C4D3×C22⋊C411yescharacteristic
547C3×C4D3×C22⋊C411yescharacteristic
548C3×C4#88311yescharacteristic
549C3×C4#89411yescharacteristic
550C3×C4#89511yescharacteristic
551C3×C4C4×#6711yescharacteristic
552C3×C4#93811yescharacteristic
553Dic3—64no—
554Dic3—62no—
555Dic3—62no—
556Dic3—81no—
557Dic3—122no—
558Dic3—121no—
559Dic3—121no—
560C32#187911yescharacteristic, complemented, Sylow
561C23—62no—
562C23—121no—
563C23—121no—
564C23—121no—
565C23—121no—
566C23—121no—
567C23—121no—
568C23—182no—
569C23—182no—
570C23—182no—
571C23—361no—
572C23—361no—
573C23—361no—
574C23—361no—
575C23#381111yescharacteristic
576D4—62no—
577D4—62no—
578D4—94no—
579D4—121no—
580D4—121no—
581D4—182no—
582D4—182no—
583D4—182no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—92no—
588C2×C4—121no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—368no—
597C2×C4#379611yescharacteristic
598C2×C4#379811yescharacteristic
599C2×C4C4×D3211yescharacteristic
600C2×C4#380211yescharacteristic
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—242no—
613C2×C3#466511yescharacteristic
614C2×C3#475611yescharacteristic
615C2×C3#477311yescharacteristic
616C2×C3#478511yescharacteristic
617C2×C3#478611yescharacteristic
618C2×C3#478611yescharacteristic
619C2×C3#478711yescharacteristic
620C2×C3#481011yescharacteristic
621C2×C3#481911yescharacteristic
622C2×C3#486911yescharacteristic
623C2×C3#487211yescharacteristic
624C2×C3#495611yescharacteristic
625C2×C3#515611yescharacteristic
626C2×C3#517211yescharacteristic
627D3—82no—
628D3—128no—
629D3—124no—
630D3—124no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—184no—
635C22—241no—
636C22—241no—
637C22—241no—
638C22—241no—
639C22—362no—
640C22—362no—
641C22—362no—
642C22—362no—
643C22—362no—
644C22—362no—
645C22#6388111yescharacteristic
646C22#6391211yescharacteristic
647C22#6392611yescharacteristic
648C22#6393711yescharacteristic
649C22#6394111yescharacteristic
650C22#6395011yescharacteristic
651C22#6398111yescharacteristic
652C4—42no—
653C4—182no—
654C4—241no—
655C4—361no—
656C4#6385311yescharacteristic
657C4C4×#62611yescharacteristic
658C4#6391611yescharacteristic
659C4#6392111yescharacteristic
660C3—21no—
661C3#6889711yescharacteristic, complemented
662C3#7020811yescharacteristic, complemented
663C2—242no—
664C2—364no—
665C2#1059045911yescharacteristic
666C2#1059046211yescharacteristic
667C2#1059054011yescharacteristic
668C2#1059055111yescharacteristic
669C2#1059138711yescharacteristic
670C2#1059145611yescharacteristic
671C2#1059159311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
3. C2×C3×#809C2semidirect
4. #10591323C2semidirect
5. C2×#63564C2semidirect
6. C3×#4529C2semidirect
7. #10589156C2semidirect
25. C2×#3714C4semidirect
38. C2×#809D3semidirect
42. #4529D3semidirect
64. C2×C3×D12C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
154. C2×C3⋊Dic3D8semidirect
158. C4⋊(C3⋊D3)C22⋊C4semidirect
224. C2×D12C4×D3semidirect
269. C2×C3⋊C8C4×D3semidirect
560. C32#1879semidirect
661. C3#68897semidirect
662. C3#70208semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C22×#37142
C2×C3×#8092
#105913232
C2×#635642
C3×#45292
#105891562
#702083
#688973