Finite Group Databasebeta

← #11803497

Subgroups — #11803497

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4#10592627C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591313C211yesmaximal, characteristic
7#10591284C212yesmaximal
8#10591281C212yesmaximal
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591256C212yesmaximal, complemented
11#10591255C212yesmaximal, complemented
12#82235—31nomaximal
13#76611—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#872—24no—
27C2×#3724C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×Dic32C2212yes—
32C2×Dic32C2212yes—
33#63856C418yescomplemented
34Dic3×Dic6—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#946—31no—
42C2×Q8×Dic3—31no—
43C2×#924—31no—
44C2×#872D311yescharacteristic
45C2×C4×Dic6—31no—
46C3×#391—31no—
47#5212—31no—
48#4987—31no—
49#4978—32no—
50#4976—32no—
51Dic3×C4⋊C4—31no—
52#4945—32no—
53#4944—32no—
54C4×C4⋊Dic3—31no—
55#4929D311yescharacteristic, complemented
56#4928—31no—
57#4928—31no—
58#4928—61no—
59#4670—32no—
60#4669—32no—
61#4652—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3C2×C414yes—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yes—
80C32×C42—22no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)C2×C414yes—
83#3750—42no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3D414yes—
90#3724C2×C418yes—
91Dic3⋊Dic3—24no—
92(C2×D3)⋊Dic3—42no—
93(C2×D3)⋊Dic3C2×C418yes—
94Dic32—24no—
95Dic32—42no—
96#2323—91noSylow
97C22×C3×Q8—31no—
98C23×C3×C4—31no—
99C22×C4×D3C2×D311yescharacteristic
100C22×Dic6C2×D311yescharacteristic
101C3×#117—64no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C42—21no—
108C2×C3×C42—31no—
109C2×C3×C42C2×D311yescharacteristic
110C2×C3×C42C2×D311yescharacteristic
111C2×#217—32no—
112C2×#217—32no—
113#946—38no—
114Q8×Dic3—64no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4C2×D311yescharacteristic
118C2×(C2×D3)⋊C4C2×D311yescharacteristic
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—61no—
125C2×C4⋊Dic3—61no—
126C2×C4⋊Dic3C2×D311yescharacteristic
127#924—38no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—62no—
134C2×Dic3⋊C4C2×D311yescharacteristic
135C2×Dic3⋊C4C2×D311yescharacteristic
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3C2×D311yescharacteristic
141#872—24no—
142C4×Dic6—64no—
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—62no—
152C3⋊#95C2×D312yes—
153C3⋊#95C2×D312yes—
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—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4#4112yes—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C22×C414yes—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C22×C414yes—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C2×D412yes—
191C2×C3×Dic3C2×D412yes—
192C3×C4×D3—28no—
193C3×Dic6—28no—
194C2×C22⋊Q8—91no—
195C2×C4×Q8—91no—
196C2×#117—31no—
197#391—31no—
198#389—92no—
199#389—91no—
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—34no—
208C2×C3×Q8—62no—
209C2×C3×Q8—62no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—31no—
217C22×C3×C4—34no—
218C22×C3×C4—32no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3C4×D314yes—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6C4×D314yes—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—62no—
249C3×C42—22no—
250C3×C42—22no—
251C3×C42—34no—
252C3×C42—42no—
253#217—38no—
254#217—122no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—122no—
259C4⋊Dic3—22no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—64no—
266C4⋊Dic3—122no—
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—64no—
272Dic3⋊C4—122no—
273Dic3⋊C4—122no—
274Dic3⋊C4—124no—
275C4×Dic3—64no—
276C4×Dic3—64no—
277C4×Dic3—122no—
278C4×Dic3—122no—
279C4×Dic3#6714yes—
280C22×C32C23×C411yescharacteristic
281C22×C32C22×D411yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32H(5,𝔽2)11yescharacteristic
284C22×C322−1+411yescharacteristic
285C22×C322−1+411yescharacteristic
286C22×C322−1+411yescharacteristic
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C4×D414yes—
297C3⋊Dic3—24no—
298C3⋊Dic3—42no—
299C3×Dic3—24no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C22×Q8—31no—
305C23×C4—31no—
306C22⋊Q8—98no—
307C4×Q8—184no—
308#117—64no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—92no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—92no—
320C2×C22⋊C4—92no—
321C2×C42—31no—
322C2×C42—92no—
323C2×C42—92no—
324C2×C42D3211yescharacteristic
325#95—32no—
326#95—32no—
327#95—92no—
328#95—92no—
329#95—92no—
330C23×C3—21no—
331C23×C3—32no—
332C23×C3—61no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3C2×C4×D312yes—
347C3×Q8—68no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—32no—
366C2×C3×C4—34no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—68no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4#23512yes—
388C2×C3×C4D3×D412yes—
389C2×C3×C4#23712yes—
390C2×C3×C4C2×#6712yes—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—34no—
403C2×Dic3—34no—
404C2×Dic3—64no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3C2×C4×D312yes—
421C2×Dic3C2×C4×D314yes—
422C2×Dic3C2×#6712yes—
423C2×Dic3C2×#6712yes—
424C4×D3—28no—
425Dic6—28no—
426C2×C32C2×C4×D411yescharacteristic
427C2×C32#51911yescharacteristic
428C2×C32#52011yescharacteristic
429C2×C32#53611yescharacteristic
430C2×C32#53711yescharacteristic
431C2×C32#54111yescharacteristic
432C2×C32#54211yescharacteristic
433C3×D3—42no—
434C24—31no—
435C2×Q8—34no—
436C2×Q8—62no—
437C2×Q8—62no—
438C22×C4—32no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—34no—
443C22×C4—32no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—92no—
447C22×C4—92no—
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3211yescharacteristic
451C4⋊C4—62no—
452C4⋊C4—62no—
453C4⋊C4—62no—
454C4⋊C4—98no—
455C4⋊C4—94no—
456C4⋊C4—184no—
457C4⋊C4—182no—
458C4⋊C4—362no—
459C22⋊C4—62no—
460C22⋊C4—62no—
461C22⋊C4—98no—
462C22⋊C4—362no—
463C42—22no—
464C42—34no—
465C42—184no—
466C42—362no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C22×C4×D311yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×#23711yescharacteristic
486C22×C3#100711yescharacteristic
487C22×C3#100711yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3#100911yescharacteristic
490C22×C3#101011yescharacteristic
491C22×C3#101011yescharacteristic
492C22×C3#101011yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C3×C4—24no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—41no—
508C3×C4—41no—
509C3×C4—62no—
510C3×C4—64no—
511C3×C4—62no—
512C3×C4—62no—
513C3×C4—122no—
514C3×C4#67⋊C414yes—
515C3×C4C4×#6714yes—
516Dic3—24no—
517Dic3—22no—
518Dic3—22no—
519Dic3—22no—
520Dic3—42no—
521Dic3—64no—
522Dic3—64no—
523Dic3—124no—
524Dic3—122no—
525Dic3—122no—
526Dic3—242no—
527C32#232311yescharacteristic, complemented, Sylow
528C23—32no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23—61no—
533C23—61no—
534C23—61no—
535C23C22×D3211yescharacteristic
536Q8—68no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—68no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—94no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—182no—
565C2×C4#379512yes—
566C2×C4C4×D3212yes—
567C2×C4D3×#6712yes—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—122no—
576C2×C3C2×#67⋊C411yescharacteristic
577C2×C3#551611yescharacteristic
578C2×C3#551811yescharacteristic
579C2×C3#552311yescharacteristic
580C2×C3#553411yescharacteristic
581C2×C3#557211yescharacteristic
582C2×C3#557411yescharacteristic
583C2×C3#562811yescharacteristic
584C2×C3#562911yescharacteristic
585C2×C3#568211yescharacteristic
586C2×C3#573111yescharacteristic
587C2×C3C2×C4×#6711yescharacteristic
588C2×C3#582511yescharacteristic
589C2×C3#583311yescharacteristic
590D3—42no—
591C22—62no—
592C22—62no—
593C22—62no—
594C22—121no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22C2×#379511yescharacteristic
599C22#6429711yescharacteristic
600C22#6429711yescharacteristic
601C22#6429811yescharacteristic
602C22C2×C4×D3211yescharacteristic
603C22#6430811yescharacteristic
604C22C2×D3×#6711yescharacteristic
605C4—41no—
606C4—41no—
607C4—62no—
608C4—64no—
609C4—62no—
610C4—62no—
611C4—122no—
612C4—184no—
613C4—362no—
614C4#6387914yes—
615C3—21no—
616C3#7661111yescharacteristic, complemented
617C3#8223511yescharacteristic, complemented
618C2—122no—
619C2#1059386211yescharacteristic
620C2#1059388511yescharacteristic
621C2#1059389011yescharacteristic
622C2#1059396111yescharacteristic
623C2C2×#6387911yescharacteristic
624C2#1059488411yescharacteristic
625C2#1059489411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic6C2semidirect
4. #10592627C2semidirect
5. C3×#4929C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591256C2semidirect
11. #10591255C2semidirect
33. #63856C4semidirect
55. #4929D3semidirect
527. C32#2323semidirect
616. C3#76611semidirect
617. C3#82235semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×#638562
C2×Dic3×Dic62
#105926272
C3×#49292
#105913132
#105912842
#105912812
Dic3×C4⋊Dic32
#105912562
#105912552
#822353
#766113