Finite Group Databasebeta

← #11805784

Subgroups — #11805784

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
4#10591710C212yesmaximal
5Dic3×#217C212yesmaximal, complemented
6#10591316C212yesmaximal, complemented
7#10591294C211yesmaximal, characteristic, complemented
8#10591272C212yesmaximal, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591237C211yesmaximal, characteristic, complemented
11#10591223C211yesmaximal, characteristic, complemented
12#82336—31nomaximal
13#73336—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×#3757C2212yes—
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×C4×#67C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29#63658C2211yescharacteristic
30#63658C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67D311yescharacteristic
40C2×C3×#95—31no—
41#5220—32no—
42#5213—32no—
43#5212—31no—
44#5212—31no—
45#5212—61no—
46#5211—31no—
47C4×#217—32no—
48C4×#217—31no—
49C2×C3⋊#95D311yescharacteristic, complemented
50#4980—32no—
51#4951—32no—
52Dic3×C22⋊C4—32no—
53#4937—31no—
54#4932—31no—
55#4670—32no—
56#4666—31no—
57#4664—31no—
58#4655—32no—
59#4651—31no—
60#4648—31no—
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
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×Dic3—24no—
73C22×C3×Dic3—24no—
74C22×C3×Dic3—42no—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C2×C3×C4×D3—42no—
81C2×C3×C4×D3C2×C414yescomplemented
82#3757—24no—
83C4⋊(C3⋊Dic3)—42no—
84C3×#217C2×C414yes—
85C3×(C2×D3)⋊C4C2×C414yescomplemented
86C3×Dic3⋊C4C2×C414yescomplemented
87C3×C4×Dic3C2×C414yescomplemented
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3—42no—
90Dic32—24no—
91Dic32—42no—
92#2353—91noSylow
93C22×C3×D4—31no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4—32no—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C22×#67C2×D311yescharacteristic
100C23×Dic3C2×D312yes—
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×C42—31no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—62no—
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×C4⋊Dic3—62no—
120C2×Dic3⋊C4C2×D311yescharacteristic
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3C2×D311yescharacteristic
126C3×#95—31no—
127C3×#95—31no—
128C3×#95—32no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
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⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D312yes—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C22×C412yes—
149C23×C32#4112yes—
150C23×C32#4112yes—
151C23×C32C2411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C412yes—
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×Dic3—48no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3#4114yes—
183C3×C4×D3—44no—
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—91no—
192C4×C22⋊C4—92no—
193#376—91no—
194C2×#95—31no—
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—31no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—44no—
215C22×C3×C4—64no—
216C22×C3×C4—64no—
217C22×C3×C4—122no—
218C22×C3×C4—122no—
219C22×C3×C4C4×D314yes—
220C22×C3×C4C2×Dic314yes—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—22no—
226C2×#67—22no—
227C2×#67C2×Dic314yes—
228C22×Dic3—24no—
229C22×Dic3—24no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—42no—
235C22×Dic3—62no—
236C22×Dic3—62no—
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×C42—34no—
248#217—64no—
249#217—64no—
250#217—64no—
251#217—124no—
252#217—122no—
253#217C2×Dic314yes—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4C2×Dic314yescomplemented
257C4⋊Dic3—122no—
258C4⋊Dic3—122no—
259C4⋊Dic3—124no—
260Dic3⋊C4C2×Dic314yescomplemented
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—122no—
264C4×Dic3—122no—
265C4×Dic3C2×Dic314yescomplemented
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—24no—
269C22×C32—24no—
270C22×C32#11714yes—
271C22×C32C23×C411yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4112yes—
275C22×C32H(5,𝔽2)12yes—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C32×C4—22no—
282C32×C4—22no—
283C3⋊Dic3—42no—
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—24no—
289C3×Dic3—42no—
290C22×D4—31no—
291C23×C4—31no—
292C23×C4—32no—
293C23×C4D3211yescharacteristic
294C4×D4—38no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—92no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—31no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—92no—
302C2×C42—31no—
303C2×C42—92no—
304C2×C42—92no—
305#95—31no—
306#95—31no—
307#95—32no—
308#95—92no—
309#95—92no—
310#95—92no—
311#95—92no—
312#95—91no—
313#95—91no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—21no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—32no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—62no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C23×C3C2×C4×D312yes—
330C23×C3#23512yes—
331C23×C3#23512yes—
332C23×C3#23712yes—
333C23×C3#23912yes—
334C23×C3C22×Dic312yes—
335C23×C3C23×D311yescharacteristic
336C23×C3C23×D311yescharacteristic
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3C22×Dic312yes—
342C3×D4—68no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—44no—
356C2×C3×C4—44no—
357C2×C3×C4—48no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—124no—
368C2×C3×C4—128no—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×C4×D312yes—
371C2×C3×C4C22×Dic312yes—
372C2×C3×C4C22×Dic312yes—
373#67—28no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—48no—
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—62no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3#23514yes—
403C2×Dic3C22×Dic312yes—
404C2×Dic3C22×Dic312yes—
405C2×Dic3C22×Dic312yes—
406C4×D3—44no—
407C2×C32—24no—
408C2×C32C2×#11711yescharacteristic
409C2×C32C4×#4111yescharacteristic
410C2×C32#51811yescharacteristic
411C2×C32#55112yes—
412C2×C32#55312yes—
413C3×D3—42no—
414C24—31no—
415C24C2×D3211yescharacteristic
416C2×D4—34no—
417C2×D4—62no—
418C2×D4—62no—
419C22×C4—32no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—34no—
424C22×C4—32no—
425C22×C4—42no—
426C22×C4—64no—
427C22×C4—64no—
428C22×C4—92no—
429C22×C4—92no—
430C22×C4—122no—
431C22×C4—122no—
432C22×C4D3×Dic314yes—
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—34no—
436C4⋊C4—362no—
437C22⋊C4—34no—
438C22⋊C4—34no—
439C22⋊C4—184no—
440C22⋊C4—184no—
441C22⋊C4—362no—
442C42—34no—
443C42—184no—
444C42—362no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—22no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—24no—
459C22×C3—42no—
460C22×C3—44no—
461C22×C3—42no—
462C22×C3—44no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3#89214yes—
469C22×C3#92614yes—
470C22×C3C22×C4×D311yescharacteristic
471C22×C3C2×#23511yescharacteristic
472C22×C3C2×#23511yescharacteristic
473C22×C3C2×#23512yes—
474C22×C3C2×#23711yescharacteristic
475C22×C3#100412yes—
476C22×C3#100412yes—
477C22×C3C2×#23911yescharacteristic
478C22×C3D3×#4112yes—
479C22×C3C23×Dic311yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—42no—
484C2×D3—42no—
485C3×C4—24no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—42no—
491C3×C4—62no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4—64no—
495C3×C4—122no—
496Dic3—24no—
497Dic3—22no—
498Dic3—22no—
499Dic3—22no—
500Dic3—42no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504Dic3—122no—
505Dic3—242no—
506Dic3—242no—
507C32#235311yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—32no—
511C23—61no—
512C23—61no—
513C23—62no—
514C23—62no—
515C23#379512yes—
516C23#379912yes—
517C23C2×D3×Dic312yes—
518C23C22×D3211yescharacteristic
519D4—68no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—44no—
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—62no—
536C2×C4—124no—
537C2×C4—128no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4C2×D3×Dic312yes—
545C2×C4C2×D3×Dic312yes—
546C2×C3—24no—
547C2×C3—24no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—44no—
554C2×C3—122no—
555C2×C3C4×#23511yescharacteristic
556C2×C3#548611yescharacteristic
557C2×C3#549512yes—
558C2×C3C2×#89211yescharacteristic
559C2×C3#551412yes—
560C2×C3#554012yes—
561C2×C3#555612yes—
562C2×C3C2×#92611yescharacteristic
563C2×C3#579811yescharacteristic
564C2×C3Dic3×#4111yescharacteristic
565D3—42no—
566C22—24no—
567C22—22no—
568C22—22no—
569C22—24no—
570C22—62no—
571C22—62no—
572C22—62no—
573C22—122no—
574C22—122no—
575C22#6384114yes—
576C22C2×#379511yescharacteristic
577C22C2×#379911yescharacteristic
578C22D3×#23512yes—
579C22C22×D3×Dic311yescharacteristic
580C22#6433012yes—
581C4—22no—
582C4—22no—
583C4—64no—
584C4—62no—
585C4—62no—
586C4—62no—
587C4—122no—
588C4—362no—
589C4—362no—
590C3—21no—
591C3#7333611yescharacteristic, complemented
592C3#8233611yescharacteristic, complemented
593C2—24no—
594C2—122no—
595C2C2×#6384111yescharacteristic
596C2#1059493812yes—
597C2Dic3×#23511yescharacteristic
598C2#1059502812yes—
599C2#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. #10592911C2semidirect
3. C2×C3×C3⋊#95C2semidirect
5. Dic3×#217C2semidirect
6. #10591316C2semidirect
7. #10591294C2semidirect
8. #10591272C2semidirect
9. #10591239C2semidirect
10. #10591237C2semidirect
11. #10591223C2semidirect
21. C3×C4×#67C4semidirect
49. C2×C3⋊#95D3semidirect
81. C2×C3×C4×D3C2×C4semidirect
85. C3×(C2×D3)⋊C4C2×C4semidirect
86. C3×Dic3⋊C4C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
113. C4×#67Dic3semidirect
243. C2×C4×D3C2×Dic3semidirect
256. (C2×D3)⋊C4C2×Dic3semidirect
260. Dic3⋊C4C2×Dic3semidirect
265. C4×Dic3C2×Dic3semidirect
507. C32#2353semidirect
591. C3#73336semidirect
592. 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
#105929112
C2×C3×C3⋊#952
#105917102
Dic3×#2172
#105913162
#105912942
#105912722
#105912392
#105912372
#105912232
#823363
#733363