Finite Group Databasebeta

← #11803056

Subgroups — #11803056

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 599 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×#63658C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4#10591719C212yesmaximal, complemented
5#10591713C212yesmaximal
6#10591305C212yesmaximal, complemented
7#10591295C211yesmaximal, characteristic, complemented
8#10591294C211yesmaximal, characteristic, complemented
9#10591223C211yesmaximal, characteristic, complemented
10#10591206C211yesmaximal, characteristic, complemented
11#10591201C212yesmaximal, complemented
12#82324—31nomaximal
13#73568—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C3×C4×#67C418yescomplemented
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
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—
44C4×#217D311yescharacteristic, complemented
45C2×C3⋊#95—31no—
46C2×C3⋊#95—31no—
47C2×C3⋊#95—61no—
48#4980—32no—
49#4958—32no—
50#4951—32no—
51#4950—32no—
52#4946—32no—
53#4940—32no—
54#4937—31no—
55#4936—31no—
56#4933—32no—
57#4667—31no—
58#4664—31no—
59#4651—31no—
60#4650—31no—
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3—42no—
69C22×C3⋊Dic3—42no—
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C3×#67—24no—
73C2×C3×#67C2×C414yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×C3×C4×D3—42no—
80C2×C3×C4×D3C2×C414yescomplemented
81C3×#217—24no—
82C3×#217C2×C414yes—
83C3×(C2×D3)⋊C4C2×C414yescomplemented
84C3×Dic3⋊C4C2×C414yescomplemented
85C3×C4×Dic3—42no—
86C3×C4×Dic3C2×C414yescomplemented
87Dic3⋊Dic3—42no—
88Dic3⋊Dic3—42no—
89(C2×D3)⋊Dic3—42no—
90(C2×D3)⋊Dic3—42no—
91#2318—91noSylow
92C22×C3×D4—31no—
93C23×C3×C4—21no—
94C23×C3×C4—31no—
95C23×C3×C4C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C22×#67C2×D311yescharacteristic
98C23×Dic3—32no—
99C23×Dic3—32no—
100C23×Dic3—62no—
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×#217C2×D312yes—
112C2×#217C2×D311yescharacteristic
113C4×#67Dic318yescomplemented
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4C2×D311yescharacteristic
122C2×C4×Dic3C2×D312yes—
123C2×C4×Dic3C2×D311yescharacteristic
124C3×#95—31no—
125C3×#95—31no—
126C3⋊#95—31no—
127C3⋊#95—31no—
128C3⋊#95—32no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—32no—
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—61no—
141C3⋊#95—61no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C23×C32—21no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32C22×C412yes—
149C23×C32#4114yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3C22×C412yes—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—44no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C412yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—48no—
168C3×#67—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
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×Dic3—22no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C3×C4×D3—44no—
183C2×C4×D4—31no—
184#388—92no—
185#387—92no—
186#386—92no—
187#385—92no—
188#383—91no—
189#382—91no—
190#381—91no—
191#380—91no—
192C4×C22⋊C4—31no—
193C2×#95—91no—
194C24×C3—21no—
195C24×C3—31no—
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—64no—
201C22×C3×C4—24no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—44no—
213C22×C3×C4—122no—
214C22×C3×C4C4×D314yes—
215C22×C3×C4C2×Dic314yes—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—24no—
221C2×#67C2×Dic314yes—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—68no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231C22×Dic3—122no—
232C22×Dic3—122no—
233C22×Dic3—122no—
234C22×Dic3—122no—
235C22×Dic3—124no—
236C22×Dic3—124no—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D311yescharacteristic
242C2×C4×D3—42no—
243C2×C4×D3C2×Dic314yescomplemented
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—122no—
252#217—122no—
253#217C2×Dic314yes—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4C2×Dic314yescomplemented
257C4⋊Dic3—122no—
258C4⋊Dic3—122no—
259Dic3⋊C4—122no—
260Dic3⋊C4—122no—
261Dic3⋊C4C2×Dic314yescomplemented
262C4×Dic3—42no—
263C4×Dic3C2×Dic314yescomplemented
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—24no—
268C22×C32#11714yes—
269C22×C32C23×C411yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32H(5,𝔽2)12yes—
272C22×C32H(5,𝔽2)11yescharacteristic
273C22×C322−1+411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—22no—
280C32×C4—22no—
281C3⋊Dic3—42no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C22×D4—31no—
289C23×C4—31no—
290C23×C4—92no—
291C23×C4D3211yescharacteristic
292C4×D4—38no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—92no—
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—
303#95—31no—
304#95—31no—
305#95—92no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—91no—
310#95—91no—
311#95—92no—
312C23×C3—22no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—32no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3C2×C4×D312yes—
330C23×C3#23514yes—
331C23×C3#23514yes—
332C23×C3C22×Dic312yes—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3C22×Dic312yes—
340C3×D4—68no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—44no—
353C2×C3×C4—44no—
354C2×C3×C4—48no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—124no—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C22×Dic312yes—
369C2×C3×C4C22×Dic312yes—
370#67—28no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—64no—
382C2×Dic3—64no—
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—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—1216no—
400C2×Dic3—128no—
401C2×Dic3—128no—
402C2×Dic3C22×Dic312yes—
403C2×Dic3C22×Dic312yes—
404C2×Dic3C22×Dic312yes—
405C4×D3—44no—
406C2×C32—24no—
407C2×C32C2×#11711yescharacteristic
408C2×C32#51811yescharacteristic
409C2×C32#52011yescharacteristic
410C2×C32#53812yes—
411C2×C32#53912yes—
412C3×D3—42no—
413C24—31no—
414C24C2×D3211yescharacteristic
415C2×D4—34no—
416C2×D4—64no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—34no—
421C22×C4—32no—
422C22×C4—32no—
423C22×C4—42no—
424C22×C4—92no—
425C22×C4—92no—
426C22×C4—122no—
427C22×C4—184no—
428C22×C4—362no—
429C22×C4—362no—
430C22×C4D3×Dic314yes—
431C22×C4C2×D3211yescharacteristic
432C22×C4C2×D3211yescharacteristic
433C4⋊C4—34no—
434C4⋊C4—362no—
435C4⋊C4—362no—
436C22⋊C4—34no—
437C22⋊C4—34no—
438C22⋊C4—64no—
439C22⋊C4—362no—
440C22⋊C4—362no—
441C42—34no—
442C42—122no—
443C22×C3—28no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—28no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—24no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3#87214yes—
467C22×C3#92614yes—
468C22×C3C22×C4×D311yescharacteristic
469C22×C3C2×#23512yes—
470C22×C3C2×#23512yes—
471C22×C3#100412yes—
472C22×C3#100412yes—
473C22×C3#100911yescharacteristic
474C22×C3#100911yescharacteristic
475C22×C3#101011yescharacteristic
476C22×C3#101011yescharacteristic
477C22×C3C23×Dic311yescharacteristic
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—42no—
482C2×D3—42no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—62no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—122no—
493C3×C4—122no—
494Dic3—22no—
495Dic3—22no—
496Dic3—22no—
497Dic3—42no—
498Dic3—42no—
499Dic3—124no—
500Dic3—124no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504Dic3—122no—
505C32#231811yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—22no—
509C23—32no—
510C23—61no—
511C23—62no—
512C23—61no—
513C23—62no—
514C23#379814yes—
515C23C2×D3×Dic312yes—
516C23C22×D3211yescharacteristic
517D4—68no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—44no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—124no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—368no—
542C2×C4C2×D3×Dic312yes—
543C2×C4C2×D3×Dic312yes—
544C2×C3—28no—
545C2×C3—24no—
546C2×C3—24no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—122no—
553C2×C3C2×#87211yescharacteristic
554C2×C3#548611yescharacteristic
555C2×C3#552311yescharacteristic
556C2×C3#556012yes—
557C2×C3#556012yes—
558C2×C3#556412yes—
559C2×C3#556412yes—
560C2×C3C2×#92611yescharacteristic
561C2×C3#579811yescharacteristic
562C2×C3#582711yescharacteristic
563D3—42no—
564C22—22no—
565C22—22no—
566C22—24no—
567C22—24no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—122no—
572C22—122no—
573C22#6385514yes—
574C22#6429811yescharacteristic
575C22C2×#379812yes—
576C22#6430811yescharacteristic
577C22C22×D3×Dic311yescharacteristic
578C22#6433012yes—
579C4—22no—
580C4—22no—
581C4—62no—
582C4—62no—
583C4—62no—
584C4—122no—
585C4—122no—
586C4—362no—
587C4—362no—
588C3—21no—
589C3#7356811yescharacteristic, complemented
590C3#8232411yescharacteristic, complemented
591C2—24no—
592C2—122no—
593C2C2×#6385511yescharacteristic
594C2#1059499211yescharacteristic
595C2#1059503712yes—
596C2#1059503912yes—
597C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63658C2semidirect
3. C3×C4×#217C2semidirect
4. #10591719C2semidirect
6. #10591305C2semidirect
7. #10591295C2semidirect
8. #10591294C2semidirect
9. #10591223C2semidirect
10. #10591206C2semidirect
11. #10591201C2semidirect
20. C3×C4×#67C4semidirect
44. C4×#217D3semidirect
80. C2×C3×C4×D3C2×C4semidirect
83. C3×(C2×D3)⋊C4C2×C4semidirect
84. C3×Dic3⋊C4C2×C4semidirect
86. C3×C4×Dic3C2×C4semidirect
113. C4×#67Dic3semidirect
243. C2×C4×D3C2×Dic3semidirect
256. (C2×D3)⋊C4C2×Dic3semidirect
261. Dic3⋊C4C2×Dic3semidirect
263. C4×Dic3C2×Dic3semidirect
505. C32#2318semidirect
589. C3#73568semidirect
590. C3#82324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×#636582
C3×C4×#2172
#105917192
#105917132
#105913052
#105912952
#105912942
#105912232
#105912062
#105912012
#823243
#735683