Finite Group Databasebeta

← #11805771

Subgroups — #11805771

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4#10591721C212yesmaximal
5#10591701C212yesmaximal, complemented
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591223C211yesmaximal, characteristic, complemented
11#10591201C212yesmaximal, complemented
12#82336—31nomaximal
13#73576—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×C4×#67C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29#63658C2211yescharacteristic
30#63658C2211yescharacteristic
31#63658C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67D311yescharacteristic
40C3×C4×C22⋊C4—31no—
41#5220—32no—
42#5212—31no—
43#5211—31no—
44#5211—31no—
45#5211—61no—
46C4×#217D311yescharacteristic, complemented
47C2×C3⋊#95—31no—
48#4980—32no—
49#4956—32no—
50#4951—32no—
51#4944—32no—
52Dic3×C22⋊C4—32no—
53C4×(C2×D3)⋊C4—32no—
54#4937—31no—
55#4933—32no—
56#4932—31no—
57#4667—31no—
58D3×#95—31no—
59#4651—31no—
60#4648—31no—
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yescomplemented
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C2×C3×#67C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yes—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—42no—
82#3757—42no—
83C3×#217—24no—
84C3×#217C2×C414yescomplemented
85C3×(C2×D3)⋊C4C2×C414yes—
86C3×Dic3⋊C4C2×C414yescomplemented
87C3×C4×Dic3—42no—
88C3×C4×Dic3C2×C414yescomplemented
89Dic3⋊Dic3—42no—
90(C2×D3)⋊Dic3—24no—
91Dic32—24no—
92#2353—91noSylow
93C22×C3×D4—31no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C22×#67C2×D311yescharacteristic
99C23×Dic3—32no—
100C22×C4×D3—32no—
101C22×C4×D3C2×D311yescharacteristic
102C3×C4×D4—38no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—32no—
112C2×#217—62no—
113C2×#217C2×D312yes—
114C2×#217C2×D311yescharacteristic
115C4×#67Dic318yescomplemented
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4C2×D311yescharacteristic
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4C2×D311yescharacteristic
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D312yes—
124C2×C4×Dic3C2×D311yescharacteristic
125C3×#95—31no—
126C3×#95—31no—
127C3⋊#95—31no—
128C3⋊#95—31no—
129C3⋊#95—31no—
130C3⋊#95—32no—
131C3⋊#95—31no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95—61no—
143C3⋊#95—62no—
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C23×C32—22no—
147C23×C32—22no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32C22×C412yes—
151C23×C32C2411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4112yes—
156C22×C3×D3#4112yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—44no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C3×#67—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3#4114yes—
182C3×C4×D3—44no—
183D3×Dic3—48no—
184C2×C4×D4—31no—
185#388—92no—
186#387—92no—
187#386—92no—
188#383—91no—
189#381—91no—
190#380—91no—
191C4×C22⋊C4—31no—
192C4×C22⋊C4—92no—
193#376—91no—
194C2×#95—91no—
195C24×C3—21no—
196C24×C3—31no—
197C24×C3C22×D311yescharacteristic
198C24×C3C22×D311yescharacteristic
199C23×D3C22×D311yescharacteristic
200C2×C3×D4—34no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C22×C3×C4—24no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—44no—
215C22×C3×C4—122no—
216C22×C3×C4C4×D314yescomplemented
217C22×C3×C4C2×Dic314yescomplemented
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—22no—
223C2×#67—22no—
224C2×#67C2×Dic314yes—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—64no—
232C22×Dic3—64no—
233C22×Dic3—122no—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D311yescharacteristic
239C2×C4×D3—42no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—122no—
243C2×C4×D3C2×Dic314yes—
244C3×C4⋊C4—34no—
245C3×C22⋊C4—34no—
246C3×C22⋊C4—34no—
247C3×C22⋊C4—64no—
248C3×C42—34no—
249C3×C42—122no—
250#217—24no—
251#217—64no—
252#217—122no—
253#217—122no—
254#217—124no—
255#217C2×Dic314yescomplemented
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4C2×Dic314yes—
258C4⋊Dic3—122no—
259Dic3⋊C4—122no—
260Dic3⋊C4C2×Dic314yescomplemented
261C4×Dic3—42no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3C2×Dic314yescomplemented
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C23×C411yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32H(5,𝔽2)12yes—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—24no—
278C2×C3×D3—24no—
279C2×C3×D3#11714yes—
280C32×C4—22no—
281C32×C4—22no—
282C3⋊Dic3—42no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—24no—
288C3×Dic3—42no—
289C22×D4—31no—
290C23×C4—31no—
291C23×C4—92no—
292C23×C4D3211yescharacteristic
293C4×D4—38no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C42—31no—
302C2×C42—32no—
303C2×C42—92no—
304#95—31no—
305#95—31no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—92no—
310#95—91no—
311#95—91no—
312#95—92no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—32no—
325C23×C3—32no—
326C23×C3—32no—
327C23×C3—42no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3C2×C4×D312yes—
333C23×C3C22×Dic312yes—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3—22no—
337C22×D3—22no—
338C22×D3#23512yes—
339C22×D3#23512yes—
340C22×D3C22×Dic312yes—
341C3×D4—68no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—34no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—44no—
355C2×C3×C4—44no—
356C2×C3×C4—48no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—124no—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C22×Dic312yes—
370C2×C3×C4C22×Dic312yes—
371#67—28no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—128no—
400C2×Dic3#23514yes—
401C2×Dic3C22×Dic312yes—
402C2×Dic3C22×Dic312yes—
403C2×Dic3C22×Dic312yes—
404C4×D3—44no—
405C4×D3—128no—
406C2×C32—42no—
407C2×C32C2×#11711yescharacteristic
408C2×C32C4×#4111yescharacteristic
409C2×C32#51811yescharacteristic
410C2×C32#55112yes—
411C2×C32#55312yes—
412C3×D3—24no—
413C24—31no—
414C24C2×D3211yescharacteristic
415C2×D4—34no—
416C2×D4—62no—
417C2×D4—62no—
418C22×C4—32no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—34no—
423C22×C4—32no—
424C22×C4—42no—
425C22×C4—92no—
426C22×C4—92no—
427C22×C4—122no—
428C22×C4—184no—
429C22×C4—184no—
430C22×C4—362no—
431C22×C4D3×Dic314yescomplemented
432C22×C4C2×D3211yescharacteristic
433C22×C4C2×D3211yescharacteristic
434C4⋊C4—34no—
435C4⋊C4—362no—
436C22⋊C4—34no—
437C22⋊C4—34no—
438C22⋊C4—64no—
439C22⋊C4—184no—
440C22⋊C4—362no—
441C42—34no—
442C42—122no—
443C42—184no—
444C22×C3—24no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—22no—
456C22×C3—34no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3C22×C4×D311yescharacteristic
470C22×C3C2×#23512yes—
471C22×C3C2×#23511yescharacteristic
472C22×C3C2×#23511yescharacteristic
473C22×C3#100412yes—
474C22×C3#100412yes—
475C22×C3D3×#4111yescharacteristic
476C22×C3D3×#4111yescharacteristic
477C22×C3D3×#4112yes—
478C22×C3C23×Dic311yescharacteristic
479C2×D3—24no—
480C2×D3—22no—
481C2×D3—24no—
482C2×D3—22no—
483C2×D3#92614yes—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—62no—
493C3×C4—64no—
494C3×C4—122no—
495Dic3—22no—
496Dic3—22no—
497Dic3—24no—
498Dic3—22no—
499Dic3—42no—
500Dic3—122no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504Dic3—242no—
505Dic3—242no—
506C32#235311yescharacteristic, complemented, Sylow
507C23—22no—
508C23—21no—
509C23—21no—
510C23—22no—
511C23—32no—
512C23—32no—
513C23—32no—
514C23—62no—
515C23—62no—
516C23C2×D3×Dic312yes—
517C23C22×D3211yescharacteristic
518D4—68no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—34no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—44no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—124no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—368no—
543C2×C4C2×D3×Dic312yes—
544C2×C4C2×D3×Dic312yes—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—44no—
551C2×C3—42no—
552C2×C3—42no—
553C2×C3—64no—
554C2×C3C4×#23511yescharacteristic
555C2×C3#548611yescharacteristic
556C2×C3D3×#11711yescharacteristic
557C2×C3#554012yes—
558C2×C3#555612yes—
559C2×C3#555612yes—
560C2×C3#555812yes—
561C2×C3C2×#92611yescharacteristic
562C2×C3#579811yescharacteristic
563C2×C3Dic3×#4111yescharacteristic
564D3—24no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—34no—
569C22—42no—
570C22—42no—
571C22—64no—
572C22—64no—
573C22—62no—
574C22—62no—
575C22D3×#23511yescharacteristic
576C22D3×#23512yes—
577C22D3×#23511yescharacteristic
578C22C22×D3×Dic311yescharacteristic
579C22#6433012yes—
580C4—22no—
581C4—22no—
582C4—64no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—122no—
587C4—362no—
588C4—362no—
589C3—21no—
590C3#7357611yescharacteristic, complemented
591C3#8233611yescharacteristic, complemented
592C2—42no—
593C2—64no—
594C2D3×#92611yescharacteristic
595C2#1059494312yes—
596C2Dic3×#23511yescharacteristic
597C2#1059508712yes—
598C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592910C2semidirect
3. C3×C4×#217C2semidirect
5. #10591701C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591295C2semidirect
9. #10591239C2semidirect
10. #10591223C2semidirect
11. #10591201C2semidirect
21. C3×C4×#67C4semidirect
46. C4×#217D3semidirect
64. C22×C32×C4C2×C4semidirect
84. C3×#217C2×C4semidirect
86. C3×Dic3⋊C4C2×C4semidirect
88. C3×C4×Dic3C2×C4semidirect
115. C4×#67Dic3semidirect
216. C22×C3×C4C4×D3semidirect
217. C22×C3×C4C2×Dic3semidirect
255. #217C2×Dic3semidirect
260. Dic3⋊C4C2×Dic3semidirect
264. C4×Dic3C2×Dic3semidirect
431. C22×C4D3×Dic3semidirect
506. C32#2353semidirect
590. C3#73576semidirect
591. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
#105929102
C3×C4×#2172
#105917212
#105917012
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105912952
#105912392
#105912232
#105912012
#823363
#735763