Finite Group Databasebeta

← #11803482

Subgroups — #11803482

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×#63857C211yesmaximal, characteristic
3C2×#63855C211yesmaximal, characteristic
4C3×#4987C211yesmaximal, characteristic
5C3×#4972C211yesmaximal, characteristic, complemented
6#10591335C212yesmaximal, complemented
7#10591283C212yesmaximal
8#10591281C212yesmaximal
9#10591274C211yesmaximal, characteristic, complemented
10#10591234C212yesmaximal, complemented
11#10591213C211yesmaximal, characteristic, complemented
12#76197—31nomaximal
13#73871—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64096—24no—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33#63857C418yescomplemented
34#63855—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#926—31no—
41C2×#924—31no—
42C2×#897—31no—
43C2×#887—31no—
44C2×#887—31no—
45C2×#887—61no—
46C2×#872—31no—
47C3×#389—31no—
48C3×#380—31no—
49#4990—32no—
50#4987D311yescharacteristic
51Dic3×C4⋊C4—31no—
52Dic3×C4⋊C4—31no—
53#4973—31no—
54#4972—32no—
55#4972D311yescharacteristic, complemented
56#4945—32no—
57#4944—32no—
58#4929—31no—
59#4669—32no—
60#4655—32no—
61#4654—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×#634—22no—
70C2×#634—22no—
71C2×#634C2×C414yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C32×C4⋊C4—22no—
81#3750—24no—
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3D414yes—
84C3×(C2×D3)⋊C4—42no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4—42no—
88C3×C4×Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3C2×C418yes—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3C2×C418yes—
95Dic32—42no—
96#2323—91noSylow
97C23×C3×C4—31no—
98C22×C4×D3C2×D311yescharacteristic
99C22×Dic6—31no—
100C22×Dic6—31no—
101C22×Dic6—61no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C22⋊C4—32no—
109C2×C3×C42—31no—
110C2×#217—32no—
111C2×#217—31no—
112C2×#217—31no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4C2×D312yes—
117#926—64no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123#924—38no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—62no—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3—62no—
139C2×C4×Dic3C2×D311yescharacteristic
140#897—38no—
141#887—64no—
142#887—64no—
143#887—68no—
144#872—64no—
145C3×#95—32no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95C2×D312yes—
154C3⋊#95C2×D312yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3C22×C412yes—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4#4112yes—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C22×C414yes—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—28no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C22×C414yes—
193C2×C3×Dic3C22×C412yes—
194C3×C4×D3—28no—
195C2×C22⋊Q8—91no—
196C2×C4×Q8—91no—
197C2×#117—91no—
198#391—91no—
199#389—31no—
200#389—92no—
201#388—92no—
202#388—92no—
203#387—92no—
204#380—31no—
205C4×C4⋊C4—91no—
206C24×C3—31no—
207C23×D3C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—34no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3—61no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D311yescharacteristic
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×C4×D3C4×D314yes—
239C2×Dic6—34no—
240C2×Dic6—34no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C2×Dic6—64no—
244C2×Dic6—62no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—34no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—122no—
254C3×C22⋊C4—122no—
255C3×C42—62no—
256#217—38no—
257#217—62no—
258#217—62no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—42no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3—22no—
264C4⋊Dic3—38no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3C4×D314yes—
268Dic3⋊C4—38no—
269Dic3⋊C4—42no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—68no—
275C4×Dic3—22no—
276C4×Dic3—34no—
277C4×Dic3—34no—
278C4×Dic3—64no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—68no—
282C4×Dic3—122no—
283C4×Dic3—122no—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C22×C322−1+411yescharacteristic
289C22×C322−1+411yescharacteristic
290C22×C322−1+411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C32×C4—42no—
299C32×C4C4×D414yes—
300C3⋊Dic3—24no—
301C3⋊Dic3—22no—
302C3⋊Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C3×Dic3—42no—
308C22×Q8—91no—
309C23×C4—31no—
310C22⋊Q8—98no—
311C4×Q8—184no—
312#117—184no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4D3211yescharacteristic
321C2×C22⋊C4—32no—
322C2×C22⋊C4—92no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—91no—
325C2×C42—31no—
326C2×C42—91no—
327C2×C42—92no—
328C2×C42—92no—
329#95—32no—
330#95—32no—
331#95—92no—
332#95—92no—
333#95—92no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3C23×D311yescharacteristic
343C23×C3C23×D311yescharacteristic
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3C2×C4×D312yes—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—32no—
362C2×C3×C4—34no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—68no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4C2×C4×D312yes—
380C2×C3×C4C2×C4×D312yes—
381C2×C3×C4D3×D412yes—
382C2×C3×C4D3×D412yes—
383C2×C3×C4#23712yes—
384C2×C3×C4#23912yes—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—64no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—62no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3C2×C4×D314yes—
426C2×Dic3C2×C4×D312yes—
427C4×D3—28no—
428Dic6—616no—
429Dic6—68no—
430Dic6—68no—
431C2×C32C2×C4×D411yescharacteristic
432C2×C32#51911yescharacteristic
433C2×C32#52011yescharacteristic
434C2×C32#53611yescharacteristic
435C2×C32#53711yescharacteristic
436C2×C32#54111yescharacteristic
437C2×C32#54211yescharacteristic
438C3×D3—42no—
439C24—31no—
440C2×Q8—94no—
441C2×Q8—182no—
442C2×Q8—182no—
443C22×C4—31no—
444C22×C4—32no—
445C22×C4—34no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—91no—
452C22×C4—92no—
453C22×C4—91no—
454C22×C4C2×D3212yes—
455C22×C4C2×D3211yescharacteristic
456C4⋊C4—22no—
457C4⋊C4—34no—
458C4⋊C4—62no—
459C4⋊C4—98no—
460C4⋊C4—122no—
461C4⋊C4—184no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C22⋊C4—98no—
465C22⋊C4—122no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C42—62no—
469C42—94no—
470C42—184no—
471C42—362no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3C22×C4×D311yescharacteristic
487C22×C3C22×C4×D311yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C22×C3C2×#23711yescharacteristic
491C22×C3#100411yescharacteristic
492C22×C3#100411yescharacteristic
493C22×C3C2×#23911yescharacteristic
494C22×C3#100711yescharacteristic
495C22×C3#100711yescharacteristic
496C22×C3#101011yescharacteristic
497C22×C3#101011yescharacteristic
498C22×C3#101011yescharacteristic
499C22×C3#101011yescharacteristic
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—41no—
506C2×D3—41no—
507C3×C4—24no—
508C3×C4—44no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—62no—
512C3×C4—64no—
513C3×C4—122no—
514C3×C4—121no—
515C3×C4—121no—
516C3×C4#67⋊C414yes—
517C3×C4#89314yes—
518Dic3—22no—
519Dic3—24no—
520Dic3—42no—
521Dic3—41no—
522Dic3—41no—
523Dic3—68no—
524Dic3—64no—
525Dic3—64no—
526Dic3—64no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—62no—
531Dic3—122no—
532C32#232311yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23C22×D3211yescharacteristic
541Q8—188no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—34no—
546C2×C4—32no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—68no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—62no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—94no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—182no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—182no—
570C2×C4#379612yes—
571C2×C4C4×D3212yes—
572C2×C4#381112yes—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—122no—
581C2×C3C2×#67⋊C411yescharacteristic
582C2×C3C2×#89311yescharacteristic
583C2×C3#550411yescharacteristic
584C2×C3#551611yescharacteristic
585C2×C3#554611yescharacteristic
586C2×C3#557211yescharacteristic
587C2×C3#560311yescharacteristic
588C2×C3#560811yescharacteristic
589C2×C3#560811yescharacteristic
590C2×C3#562511yescharacteristic
591C2×C3#562811yescharacteristic
592C2×C3#562811yescharacteristic
593C2×C3#569811yescharacteristic
594C2×C3#573311yescharacteristic
595D3—42no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—121no—
600C22—121no—
601C22—121no—
602C22—121no—
603C22C2×#379611yescharacteristic
604C22C2×C4×D3211yescharacteristic
605C22#6430911yescharacteristic
606C22#6431311yescharacteristic
607C22#6431511yescharacteristic
608C22#6431511yescharacteristic
609C22C2×#381111yescharacteristic
610C4—42no—
611C4—64no—
612C4—62no—
613C4—121no—
614C4—121no—
615C4—122no—
616C4—184no—
617C4—182no—
618C4—182no—
619C4#6388114yes—
620C3—21no—
621C3#7387111yescharacteristic, complemented
622C3#7619711yescharacteristic, complemented
623C2—122no—
624C2#1059434611yescharacteristic
625C2#1059435711yescharacteristic
626C2#1059435911yescharacteristic
627C2#1059449411yescharacteristic
628C2C2×#6388111yescharacteristic
629C2#1059524011yescharacteristic
630C2#1059540511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
5. C3×#4972C2semidirect
6. #10591335C2semidirect
9. #10591274C2semidirect
10. #10591234C2semidirect
11. #10591213C2semidirect
33. #63857C4semidirect
55. #4972D3semidirect
532. C32#2323semidirect
621. C3#73871semidirect
622. C3#76197semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638572
C2×#638552
C3×#49872
C3×#49722
#105913352
#105912832
#105912812
#105912742
#105912342
#105912132
#761973
#738713