Finite Group Databasebeta

← #11803493

Subgroups — #11803493

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×#63855C211yesmaximal, characteristic
4#10592928C211yesmaximal, characteristic, complemented
5#10591357C211yesmaximal, characteristic, complemented
6#10591313C211yesmaximal, characteristic
7#10591307C212yesmaximal
8#10591305C212yesmaximal
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591265C212yesmaximal, complemented
11#10591201C212yesmaximal, complemented
12#82744—31nomaximal
13#82488—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C3×#946C418yescomplemented
19C3×Q8×Dic3—24no—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34#63855—24no—
35#63658C2212yes—
36#63658C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C22⋊Q8—31no—
41C2×C3×C4×Q8—31no—
42C2×#946D311yescharacteristic
43C2×Q8×Dic3D311yescharacteristic, complemented
44C2×#926—31no—
45C2×#872—31no—
46#5229—31no—
47#5229—31no—
48#5229—61no—
49#5212—31no—
50#4990—32no—
51#4987—31no—
52#4984—32no—
53#4984—31no—
54#4980—32no—
55#4976—32no—
56Dic3×C4⋊C4—31no—
57#4972—31no—
58#4951—32no—
59#4951—32no—
60#4940—32no—
61C4×C4⋊Dic3—31no—
62#4933—32no—
63C23×C3×D3C2311yescharacteristic
64C2×C32×Q8—22no—
65C2×C32×Q8—22no—
66C2×C32×Q8C2×C414yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C4⋊(C3⋊Dic3)—22no—
81C4×C3⋊Dic3—22no—
82C3×(C2×D3)⋊C4C2×C418yes—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—24no—
85C3×C4⋊Dic3C2×C414yes—
86C3×Dic3⋊C4C2×C418yes—
87C3×C4×Dic3—24no—
88C3×C4×Dic3D414yes—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—42no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—42no—
95Dic32—42no—
96#2323—91noSylow
97C22×C3×Q8—21no—
98C22×C3×Q8C2×D311yescharacteristic
99C22×C3×Q8C2×D311yescharacteristic
100C23×C3×C4—31no—
101C22×C4×D3C2×D311yescharacteristic
102C3×C22⋊Q8—38no—
103C3×C4×Q8—64no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—32no—
114#946Dic318yescomplemented
115Q8×Dic3—24no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4C2×D312yes—
120#926—64no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3C2×D312yes—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4C2×D312yes—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3C2×D312yes—
140C2×C4×Dic3C2×D311yescharacteristic
141#872—64no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—62no—
153C3⋊#95—62no—
154C23×C32C2411yescharacteristic
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3C22×C412yes—
162C32×Q8—28no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C414yes—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4#4112yes—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C414yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C3×C4×D3—28no—
194C2×C22⋊Q8—31no—
195C2×C4×Q8—31no—
196C2×#117—91no—
197#391—91no—
198#389—91no—
199#389—92no—
200#388—92no—
201#388—92no—
202#387—92no—
203#380—91no—
204C4×C4⋊C4—91no—
205C24×C3—31no—
206C23×D3C22×D311yescharacteristic
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—22no—
210C2×C3×Q8—22no—
211C2×C3×Q8—24no—
212C2×C3×Q8—42no—
213C2×C3×Q8—42no—
214C2×C3×Q8C4×D314yes—
215C2×C3×Q8C2×Dic314yes—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—32no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—31no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D311yescharacteristic
244C2×C4×D3—22no—
245C2×C4×D3—22no—
246C2×C4×D3C2×Dic314yes—
247C3×C4⋊C4—38no—
248C3×C4⋊C4—34no—
249C3×C4⋊C4—64no—
250C3×C4⋊C4—62no—
251C3×C22⋊C4—38no—
252C3×C42—34no—
253C3×C42—64no—
254#217—62no—
255#217—62no—
256#217—122no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—122no—
260(C2×D3)⋊C4C2×Dic318yes—
261C4⋊Dic3—22no—
262C4⋊Dic3—24no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—122no—
268C4⋊Dic3—122no—
269C4⋊Dic3C2×Dic314yes—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—122no—
273Dic3⋊C4C2×Dic318yes—
274C4×Dic3—24no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—122no—
278C4×Dic3—122no—
279C4×Dic3—122no—
280C4×Dic3#6714yes—
281C22×C32C23×C411yescharacteristic
282C22×C32C22×D411yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32H(5,𝔽2)11yescharacteristic
285C22×C322−1+411yescharacteristic
286C22×C322−1+411yescharacteristic
287C22×C322−1+411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C32×C4—24no—
296C32×C4C4×D414yes—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C3⋊Dic3—42no—
300C3×Dic3—22no—
301C3×Dic3—24no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C22×Q8D3211yescharacteristic
306C23×C4—31no—
307C22⋊Q8—38no—
308C4×Q8—64no—
309#117—184no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—32no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—92no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—92no—
322C2×C42—31no—
323C2×C42—32no—
324C2×C42—91no—
325C2×C42—92no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—92no—
330#95—92no—
331C23×C3—21no—
332C23×C3—32no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3C23×D311yescharacteristic
340C23×C3C23×D311yescharacteristic
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3C22×Dic312yes—
348C3×Q8—28no—
349C3×Q8—28no—
350C3×Q8—48no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—24no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—34no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—68no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4C2×C4×D314yes—
378C2×C3×C4C2×C4×D312yes—
379C2×C3×C4#23512yes—
380C2×C3×C4D3×D412yes—
381C2×C3×C4#23712yes—
382C2×C3×C4C22×Dic314yes—
383C2×C3×C4C22×Dic312yes—
384C2×C3×C4C2×#6712yes—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—62no—
405C2×Dic3—61no—
406C2×Dic3—62no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3C22×Dic312yes—
424C2×Dic3C22×Dic314yes—
425C2×Dic3C2×#6712yes—
426C2×Dic3C2×#6712yes—
427C4×D3—28no—
428C2×C32C2×C4×D411yescharacteristic
429C2×C32#51911yescharacteristic
430C2×C32#52011yescharacteristic
431C2×C32#53611yescharacteristic
432C2×C32#53711yescharacteristic
433C2×C32#54111yescharacteristic
434C2×C32#54211yescharacteristic
435C3×D3—42no—
436C24—31no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8D3×Dic314yes—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—34no—
445C22×C4—32no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—91no—
449C22×C4—92no—
450C22×C4—91no—
451C22×C4C2×D3212yes—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—38no—
454C4⋊C4—34no—
455C4⋊C4—64no—
456C4⋊C4—62no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C4⋊C4—362no—
461C22⋊C4—38no—
462C22⋊C4—182no—
463C22⋊C4—182no—
464C22⋊C4—362no—
465C42—34no—
466C42—64no—
467C42—182no—
468C42—362no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3C22×C4×D311yescharacteristic
484C22×C3C2×#23511yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×#23711yescharacteristic
487C22×C3#100711yescharacteristic
488C22×C3#100711yescharacteristic
489C22×C3#100711yescharacteristic
490C22×C3#100711yescharacteristic
491C22×C3#100911yescharacteristic
492C22×C3#100911yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3#101011yescharacteristic
495C22×C3C23×Dic311yescharacteristic
496C22×C3C22×#6711yescharacteristic
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—41no—
504C3×C4—24no—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—44no—
508C3×C4—62no—
509C3×C4—64no—
510C3×C4—62no—
511C3×C4—62no—
512C3×C4—122no—
513C3×C4C4×#6714yes—
514C3×C4D4×Dic314yes—
515Dic3—22no—
516Dic3—22no—
517Dic3—24no—
518Dic3—22no—
519Dic3—42no—
520Dic3—122no—
521Dic3—122no—
522Dic3—122no—
523Dic3—121no—
524Dic3—121no—
525Dic3—122no—
526Dic3—121no—
527Dic3—121no—
528Dic3—242no—
529C32#232311yescharacteristic, complemented, Sylow
530C23—32no—
531C23—61no—
532C23—61no—
533C23—61no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23C22×D3211yescharacteristic
538Q8—28no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—62no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—68no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—182no—
560C2×C4—181no—
561C2×C4—182no—
562C2×C4—181no—
563C2×C4—182no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4C2×D3×Dic314yes—
567C2×C4C2×D3×Dic312yes—
568C2×C4#380412yes—
569C2×C4D3×#6712yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—122no—
578C2×C3#557211yescharacteristic
579C2×C3#557411yescharacteristic
580C2×C3#558211yescharacteristic
581C2×C3#558311yescharacteristic
582C2×C3#562511yescharacteristic
583C2×C3#562811yescharacteristic
584C2×C3#562911yescharacteristic
585C2×C3#564311yescharacteristic
586C2×C3C2×C4×#6711yescharacteristic
587C2×C3C2×D4×Dic311yescharacteristic
588C2×C3#581211yescharacteristic
589C2×C3#581611yescharacteristic
590C2×C3#582711yescharacteristic
591C2×C3#583311yescharacteristic
592D3—42no—
593C22—62no—
594C22—62no—
595C22—62no—
596C22—121no—
597C22—121no—
598C22—121no—
599C22—121no—
600C22#6431511yescharacteristic
601C22#6431511yescharacteristic
602C22#6431611yescharacteristic
603C22#6432011yescharacteristic
604C22C22×D3×Dic311yescharacteristic
605C22C2×#380411yescharacteristic
606C22C2×D3×#6711yescharacteristic
607C4—24no—
608C4—64no—
609C4—62no—
610C4—62no—
611C4—62no—
612C4—122no—
613C4—362no—
614C4—361no—
615C4—361no—
616C4Dic3×#6714yes—
617C3—21no—
618C3#8248811yescharacteristic, complemented
619C3#8274411yescharacteristic, complemented
620C2—122no—
621C2#1059534611yescharacteristic
622C2#1059534711yescharacteristic
623C2#1059534811yescharacteristic
624C2#1059539411yescharacteristic
625C2#1059539711yescharacteristic
626C2#1059539811yescharacteristic
627C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
4. #10592928C2semidirect
5. #10591357C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591265C2semidirect
11. #10591201C2semidirect
18. C3×#946C4semidirect
43. C2×Q8×Dic3D3semidirect
114. #946Dic3semidirect
529. C32#2323semidirect
618. C3#82488semidirect
619. C3#82744semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C2×C3×Q8×Dic32
C2×#638552
#105929282
#105913572
#105913132
#105913072
#105913052
Dic3×C4⋊Dic32
#105912652
#105912012
#827443
#824883