Finite Group Databasebeta

← #11803393

Subgroups — #11803393

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63961C211yesmaximal, characteristic
4#10592645C211yesmaximal, characteristic, complemented
5C3×#4943C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591333C212yesmaximal, complemented
9#10591284C212yesmaximal, complemented
10#10591278C212yesmaximal, complemented
11#10591256C212yesmaximal, complemented
12#82326—31nomaximal
13#74056—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3750C2212yes—
22C2×C3×#217C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#67⋊C4—24no—
27C2×#3724C2212yes—
28C2×Dic3⋊Dic3—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31#63961C418yescomplemented
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×#935—31no—
42C2×#929—31no—
43C22×C4⋊Dic3—31no—
44C22×Dic3⋊C4—31no—
45C2×#67⋊C4D311yescharacteristic
46C3×#381—31no—
47#5220—31no—
48#5210—32no—
49C4×#217—31no—
50#4976—32no—
51#4958—31no—
52#4946—31no—
53#4946—31no—
54#4946—61no—
55#4945—32no—
56#4943D311yescharacteristic, complemented
57Dic3×C22⋊C4—31no—
58#4933—32no—
59#4670—32no—
60#4668—32no—
61#4655—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—22no—
68C22×C3⋊Dic3—42no—
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C2×C3×#67C2×C414yes—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3C2×C414yescomplemented
78C22×C3×Dic3D414yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—42no—
86C32×C22⋊C4—22no—
87#3757C2×C414yescomplemented
88#3750—42no—
89C3×#217—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93#3724C2×C418yescomplemented
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—42no—
97(C2×D3)⋊Dic3C2×C418yescomplemented
98Dic32—42no—
99#2322—91noSylow
100C22×C3×D4—31no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C22×#67C2×D311yescharacteristic
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3C2×D311yescharacteristic
111C3×C4×D4—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×C3×C42—31no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—61no—
124C2×#217C2×D311yescharacteristic
125#935—38no—
126#929—38no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4C2×D311yescharacteristic
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—64no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—62no—
140C2×Dic3⋊C4—64no—
141C2×Dic3⋊C4C2×D311yescharacteristic
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3C2×D311yescharacteristic
145#67⋊C4—24no—
146C3×#95—32no—
147C3×#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—62no—
155C3⋊#95C2×D312yes—
156C3⋊#95C2×D312yes—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32C22×C412yes—
160C23×C32C2×D412yes—
161C23×C32#4112yes—
162C23×C32C2411yescharacteristic
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3C22×C412yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—44no—
178C2×C3⋊Dic3C22×C414yes—
179C3×#67—28no—
180C2×C3×Dic3—28no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—44no—
191C2×C3×Dic3C22×C414yes—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C3×C4×D3—44no—
196C2×#123—91no—
197C2×C4×D4—31no—
198C22×C4⋊C4—91no—
199#389—92no—
200#388—92no—
201#387—92no—
202#386—91no—
203#385—92no—
204#385—91no—
205#381—31no—
206C4×C22⋊C4—91no—
207C24×C3—21no—
208C24×C3—31no—
209C24×C3C22×D311yescharacteristic
210C24×C3C22×D311yescharacteristic
211C23×D3C22×D311yescharacteristic
212C2×C3×D4—34no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—34no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4—31no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4—122no—
228C22×C3×C4—122no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—22no—
234C2×#67—22no—
235C2×#67C4×D314yes—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—42no—
243C22×Dic3—62no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—122no—
248C22×Dic3—122no—
249C22×Dic3—122no—
250C22×Dic3—124no—
251C22×Dic3C4×D314yescomplemented
252C22×Dic3#6714yes—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D311yescharacteristic
258C2×C4×D3—22no—
259C2×C4×D3—42no—
260C3×C4⋊C4—62no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—42no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266C3×C42—62no—
267#217—22no—
268#217—34no—
269#217—34no—
270#217—38no—
271#217—64no—
272#217—122no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—122no—
276C4⋊Dic3—64no—
277C4⋊Dic3—64no—
278Dic3⋊C4—22no—
279Dic3⋊C4—38no—
280Dic3⋊C4—38no—
281Dic3⋊C4—64no—
282Dic3⋊C4—64no—
283Dic3⋊C4—122no—
284Dic3⋊C4—122no—
285Dic3⋊C4—124no—
286C4×Dic3—22no—
287C4×Dic3—122no—
288C4×Dic3—122no—
289C22×C32—24no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—24no—
293C22×C32C4×D414yes—
294C22×C32C23×C411yescharacteristic
295C22×C32C22×D411yescharacteristic
296C22×C32C2×#4111yescharacteristic
297C22×C32H(5,𝔽2)12yes—
298C22×C322−1+412yes—
299C2×C3×D3—22no—
300C2×C3×D3—24no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C2×C3×D3—42no—
304C32×C4—41no—
305C32×C4—41no—
306C3⋊Dic3—24no—
307C3⋊Dic3—42no—
308C3×Dic3—24no—
309C3×Dic3—22no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C22×D4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—91no—
318#123—98no—
319C4×D4—64no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—184no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—92no—
329C2×C22⋊C4—91no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4D3211yescharacteristic
332C2×C42—31no—
333C2×C42—92no—
334#95—32no—
335#95—32no—
336#95—92no—
337#95—92no—
338#95—92no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—32no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—61no—
351C23×C3—61no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3C2×C4×D312yes—
355C23×C3C2×C4×D312yes—
356C23×C3#23512yes—
357C23×C3D3×D412yes—
358C23×C3#23712yes—
359C23×C3C2×#6712yes—
360C23×C3C23×D311yescharacteristic
361C23×C3C23×D311yescharacteristic
362C22×D3—21no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—21no—
366C22×D3C2×C4×D312yes—
367C3×D4—68no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—32no—
377C2×C3×C4—34no—
378C2×C3×C4—32no—
379C2×C3×C4—32no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—42no—
384C2×C3×C4—68no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—124no—
395C2×C3×C4—124no—
396#67—28no—
397C2×Dic3—28no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—44no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3—124no—
428C2×Dic3—128no—
429C2×Dic3C2×C4×D312yes—
430C2×Dic3C2×C4×D314yes—
431C2×Dic3C2×#6712yes—
432C2×Dic3C2×#6712yes—
433C4×D3—44no—
434C2×C32—24no—
435C2×C32C2×C4×D411yescharacteristic
436C2×C32#52012yes—
437C2×C32#53411yescharacteristic
438C2×C32#53611yescharacteristic
439C2×C32#53912yes—
440C3×D3—42no—
441C24—31no—
442C24C2×D3211yescharacteristic
443C2×D4—34no—
444C2×D4—62no—
445C2×D4—62no—
446C22×C4—32no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—34no—
451C22×C4—34no—
452C22×C4—32no—
453C22×C4—62no—
454C22×C4—62no—
455C22×C4—62no—
456C22×C4—92no—
457C22×C4—92no—
458C22×C4—122no—
459C22×C4—122no—
460C22×C4—182no—
461C22×C4—362no—
462C22×C4C2×D3211yescharacteristic
463C22×C4C2×D3211yescharacteristic
464C4⋊C4—62no—
465C4⋊C4—98no—
466C4⋊C4—184no—
467C4⋊C4—184no—
468C4⋊C4—362no—
469C22⋊C4—22no—
470C22⋊C4—62no—
471C22⋊C4—62no—
472C22⋊C4—98no—
473C22⋊C4—94no—
474C22⋊C4—362no—
475C42—62no—
476C42—362no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—22no—
483C22×C3—24no—
484C22×C3—22no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—24no—
491C22×C3—42no—
492C22×C3—44no—
493C22×C3—44no—
494C22×C3—42no—
495C22×C3—62no—
496C22×C3—64no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—122no—
500C22×C3#67⋊C414yes—
501C22×C3C4×#6714yes—
502C22×C3C22×C4×D311yescharacteristic
503C22×C3C22×C4×D311yescharacteristic
504C22×C3C2×#23511yescharacteristic
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C2×#23711yescharacteristic
507C22×C3#100412yes—
508C22×C3#100912yes—
509C22×C3#101012yes—
510C22×C3#101012yes—
511C22×C3C22×#6711yescharacteristic
512C2×D3—22no—
513C2×D3—24no—
514C2×D3—41no—
515C2×D3—42no—
516C2×D3—41no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—64no—
525C3×C4—81no—
526C3×C4—81no—
527C3×C4—122no—
528Dic3—24no—
529Dic3—22no—
530Dic3—22no—
531Dic3—22no—
532Dic3—42no—
533Dic3—64no—
534Dic3—64no—
535Dic3—124no—
536Dic3—124no—
537Dic3—122no—
538Dic3—122no—
539C32#232211yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—32no—
543C23—61no—
544C23—62no—
545C23—62no—
546C23—61no—
547C23#379512yes—
548C23C4×D3212yes—
549C23D3×#6712yes—
550C23C22×D3211yescharacteristic
551D4—68no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—34no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—61no—
565C2×C4—62no—
566C2×C4—68no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—94no—
571C2×C4—124no—
572C2×C4—124no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—364no—
579C2×C3—24no—
580C2×C3—24no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—44no—
587C2×C3—122no—
588C2×C3C2×#67⋊C411yescharacteristic
589C2×C3#552312yes—
590C2×C3#554612yes—
591C2×C3#556412yes—
592C2×C3#564811yescharacteristic
593C2×C3#565311yescharacteristic
594C2×C3#566512yes—
595C2×C3C2×C4×#6711yescharacteristic
596C2×C3#580411yescharacteristic
597C2×C3#582511yescharacteristic
598D3—42no—
599C22—24no—
600C22—24no—
601C22—22no—
602C22—22no—
603C22—64no—
604C22—62no—
605C22—122no—
606C22—121no—
607C22—121no—
608C22#6387914yes—
609C22C2×#379511yescharacteristic
610C22C2×C4×D3211yescharacteristic
611C22#6430912yes—
612C22#6431412yes—
613C22C2×D3×#6711yescharacteristic
614C4—41no—
615C4—41no—
616C4—64no—
617C4—62no—
618C4—62no—
619C4—62no—
620C4—122no—
621C4—184no—
622C4—362no—
623C3—21no—
624C3#7405611yescharacteristic, complemented
625C3#8232611yescharacteristic, complemented
626C2—24no—
627C2—122no—
628C2#1059404912yes—
629C2#1059417712yes—
630C2C2×#6387911yescharacteristic
631C2#1059523411yescharacteristic
632C2#1059527011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3⋊Dic3C2semidirect
4. #10592645C2semidirect
5. C3×#4943C2semidirect
7. Dic3×#217C2semidirect
8. #10591333C2semidirect
9. #10591284C2semidirect
10. #10591278C2semidirect
11. #10591256C2semidirect
31. #63961C4semidirect
56. #4943D3semidirect
77. C22×C3×Dic3C2×C4semidirect
87. #3757C2×C4semidirect
93. #3724C2×C4semidirect
97. (C2×D3)⋊Dic3C2×C4semidirect
251. C22×Dic3C4×D3semidirect
539. C32#2322semidirect
624. C3#74056semidirect
625. C3#82326semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C22×Dic3⋊Dic32
C2×#639612
#105926452
C3×#49432
#105917132
Dic3×#2172
#105913332
#105912842
#105912782
#105912562
#823263
#740563