Finite Group Databasebeta

← #11787251

Subgroups — #11787251

Order 1152.

1017 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×#63566C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70268—31nomaximal
9#68878—31nomaximal
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C4⋊C4×C3⋊D3—22no—
17C4⋊C4×C3⋊D3—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×#3722—21no—
23#63871—22no—
24#63871C414yescomplemented
25C3×#810—22no—
26#63566—22no—
27#63557—22no—
28C2×#946—31no—
29C2×#897—31no—
30C2×D3×C4⋊C4—31no—
31C2×D3×C4⋊C4—31no—
32C2×D3×C4⋊C4—61no—
33C2×C3×#103—31no—
34C2×#835—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×#816—31no—
38C2×#810D311yescharacteristic, complemented
39C3×#340—31no—
40#4551—31no—
41#4529—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—42no—
54C2×C4×C3⋊D3—42no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3D412yes—
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
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yes—
69#3750—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2×C412yescomplemented
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⋊C8—21no—
78Dic3⋊Dic3—24no—
79#3722—24no—
80#1872—91noSylow
81C22×C3×Q8—31no—
82C22×C4×D3—31no—
83C22×C4×D3—31no—
84C22×C4×D3—61no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C22×C4×D3—62no—
88C22×Dic6C2×D311yescharacteristic
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95#946—34no—
96#946—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×Dic3⋊C4—62no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110#897—34no—
111#897—62no—
112D3×C4⋊C4—62no—
113D3×C4⋊C4—62no—
114D3×C4⋊C4—64no—
115D3×C4⋊C4—64no—
116D3×C4⋊C4—62no—
117D3×C4⋊C4—62no—
118C3×#103—62no—
119#835—62no—
120(C2×D3)⋊C8—62no—
121(C2×D3)⋊C8—62no—
122#816—62no—
123#810—22no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3C22⋊C412yes—
130C22×C3⋊D3SD1612yes—
131C22×C3⋊D3Q1612yes—
132C2×C32×C4—22no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
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—22no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—48no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—41no—
161C3×Dic6—41no—
162C3×C3⋊C8—41no—
163C3×C3⋊C8—41no—
164C2×C22⋊Q8—91no—
165C22×C4⋊C4—91no—
166C2×#103—31no—
167C2×#103—91no—
168C2×C22⋊C8—91no—
169#340—31no—
170#340—91no—
171C23×D3—31no—
172C23×D3—31no—
173C23×D3—61no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—68no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—122no—
218C2×C4×D3—122no—
219C2×C4×D3—124no—
220C2×C4×D3—124no—
221C2×C4×D3—122no—
222C2×C4×D3—122no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6C4×D312yescomplemented
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4D1212yes—
242C3×C4⋊C4#6712yes—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—21no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—64no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3C4×D312yescomplemented
254Dic3⋊C4—64no—
255Dic3⋊C4—68no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12011yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32C2×SD1611yescharacteristic
268C22×C32C2×Q1611yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32#13711yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3#10314yescomplemented
278C32×C4—42no—
279C32×C4C4×D411yescharacteristic
280C32×C4C4×D411yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12111yescharacteristic
283C3⋊Dic3—22no—
284C3⋊Dic3—42no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C22×Q8—31no—
288C23×C4—91no—
289C23×C4—181no—
290C22×C8—31no—
291C22×C8—31no—
292C22⋊Q8—94no—
293C22⋊Q8—182no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—182no—
297C2×C4⋊C4—181no—
298C2×C4⋊C4—181no—
299C2×C4⋊C4—182no—
300C2×C4⋊C4D3211yescharacteristic
301C2×C22⋊C4—181no—
302#103—62no—
303#103—182no—
304C22⋊C8—182no—
305C23×C3—21no—
306C23×C3D3×D411yescharacteristic
307C23×C3D3×D411yescharacteristic
308C22×D3—32no—
309C22×D3—32no—
310C22×D3—32no—
311C22×D3—32no—
312C22×D3—32no—
313C22×D3—32no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—61no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—121no—
332C3×Q8—121no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4C2×C4×D311yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23911yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—32no—
369C2×Dic3—32no—
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—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C4×D3—64no—
391C4×D3—64no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—1216no—
403C4×D3—128no—
404C4×D3—128no—
405Dic6—22no—
406Dic6—22no—
407Dic6—41no—
408Dic6—41no—
409C3×C8—121no—
410C3×C8—121no—
411C3⋊C8—41no—
412C3⋊C8—41no—
413C2×C32#38611yescharacteristic
414C2×C32C2×#10311yescharacteristic
415C2×C32#41711yescharacteristic
416C2×C32#45011yescharacteristic
417C2×C32#45111yescharacteristic
418C2×C32#48311yescharacteristic
419C2×C32#48411yescharacteristic
420C3⋊D3—24no—
421C24—91no—
422C2×Q8—32no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×Q8—61no—
427C2×Q8—61no—
428C22×C4—21no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—91no—
432C22×C4—92no—
433C22×C4—92no—
434C22×C4—184no—
435C22×C4—181no—
436C22×C4—181no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4—362no—
441C22×C4—362no—
442C22×C4C2×D3211yescharacteristic
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C2×C8—61no—
448C2×C8—61no—
449C4⋊C4—21no—
450C4⋊C4—32no—
451C4⋊C4—61no—
452C4⋊C4—92no—
453C4⋊C4—184no—
454C4⋊C4—184no—
455C4⋊C4—181no—
456C4⋊C4#62612yes—
457C22⋊C4—184no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3D3×C22⋊C411yescharacteristic
466C22×C3D3×C22⋊C411yescharacteristic
467C22×C3#88211yescharacteristic
468C22×C3#88311yescharacteristic
469C22×C3#89411yescharacteristic
470C22×C3#91111yescharacteristic
471C22×C3D3×SD1611yescharacteristic
472C22×C3D3×SD1611yescharacteristic
473C22×C3#91411yescharacteristic
474C22×C3#91511yescharacteristic
475C22×C3D3×Q1611yescharacteristic
476C22×C3D3×Q1611yescharacteristic
477C22×C3#91811yescharacteristic
478C22×C3#93711yescharacteristic
479C2×D3—34no—
480C2×D3—34no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—44no—
505C3×C4—42no—
506C3×C4—42no—
507C3×C4—122no—
508C3×C4—122no—
509C3×C4C4×D1211yescharacteristic
510C3×C4#67⋊C411yescharacteristic
511C3×C4#88411yescharacteristic
512C3×C4#88411yescharacteristic
513C3×C4#89311yescharacteristic
514C3×C4#89511yescharacteristic
515C3×C4C4×#6711yescharacteristic
516C3×C4#93811yescharacteristic
517Dic3—42no—
518Dic3—42no—
519Dic3—64no—
520Dic3—62no—
521Dic3—62no—
522Dic3—124no—
523Dic3—122no—
524Dic3—122no—
525C32#187211yescharacteristic, complemented, Sylow
526C23—92no—
527C23—92no—
528C23—92no—
529C23—181no—
530C23—181no—
531C23—181no—
532C23—181no—
533C23#381111yescharacteristic
534Q8—62no—
535Q8—62no—
536Q8—121no—
537Q8—121no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—92no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—121no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—182no—
555C2×C4—368no—
556C2×C4—361no—
557C2×C4—361no—
558C2×C4#379611yescharacteristic
559C2×C4#379811yescharacteristic
560C2×C4C4×D3211yescharacteristic
561C2×C4#380211yescharacteristic
562C2×C4C2×#62611yescharacteristic
563C2×C4#381111yescharacteristic
564C8—121no—
565C8—121no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3#466511yescharacteristic
574C2×C3#477111yescharacteristic
575C2×C3#477611yescharacteristic
576C2×C3D3×#10311yescharacteristic
577C2×C3D3×#10311yescharacteristic
578C2×C3#480311yescharacteristic
579C2×C3#480511yescharacteristic
580C2×C3#480911yescharacteristic
581C2×C3#481111yescharacteristic
582C2×C3#486211yescharacteristic
583C2×C3#488411yescharacteristic
584C2×C3#495611yescharacteristic
585C2×C3#516911yescharacteristic
586C2×C3#518611yescharacteristic
587D3—68no—
588D3—64no—
589D3—64no—
590C22—94no—
591C22—182no—
592C22—182no—
593C22—182no—
594C22—182no—
595C22—182no—
596C22—182no—
597C22#6385311yescharacteristic
598C22#6392111yescharacteristic
599C22#6393011yescharacteristic
600C22#6393711yescharacteristic
601C22#6394411yescharacteristic
602C22#6395111yescharacteristic
603C22#6398111yescharacteristic
604C4—42no—
605C4—122no—
606C4—122no—
607C4—182no—
608C4—362no—
609C4#6388111yescharacteristic
610C4C4×#62611yescharacteristic
611C4#6391211yescharacteristic
612C4#6391611yescharacteristic
613C3—21no—
614C3#6887811yescharacteristic, complemented
615C3#7026811yescharacteristic, complemented
616C2—184no—
617C2#1059052811yescharacteristic
618C2#1059052911yescharacteristic
619C2#1059060111yescharacteristic
620C2#1059061211yescharacteristic
621C2#1059138711yescharacteristic
622C2#1059146711yescharacteristic
623C2#1059160311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1872
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
3. C2×C3×#810C2semidirect
4. C2×#63566C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
24. #63871C4semidirect
38. C2×#810D3semidirect
42. #4529D3semidirect
64. C2×C3×Dic6C2×C4semidirect
71. C3×C4⋊Dic3C2×C4semidirect
228. C2×Dic6C4×D3semidirect
253. C4⋊Dic3C4×D3semidirect
277. C2×C3⋊D3#103semidirect
525. C32#1872semidirect
614. C3#68878semidirect
615. C3#70268semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#638712
C2×C3×#8102
C2×#635662
C2×#635572
C3×#45292
#105891642
#702683
#688783