Finite Group Databasebeta

← #11808785

Subgroups — #11808785

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#63880C211yesmaximal, characteristic
3#10592930C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic, complemented
5#10591392C212yesmaximal
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7#10591343C212yesmaximal, complemented
8#10591326C211yesmaximal, characteristic, complemented
9#10591314C211yesmaximal, characteristic, complemented
10#10591239C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal, complemented
12#82492—31nomaximal
13#76779—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×#626C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×D3×Dic3C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3752C2211yescharacteristic
20C3×Q8×Dic3—24no—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×#3722C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31#63880—24no—
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×Q8×Dic3D311yescharacteristic, complemented
41C2×#67⋊C4—31no—
42C2×C4×D12—31no—
43C3×#393—31no—
44#5231—31no—
45#5231—31no—
46#5231—61no—
47#5231D311yescharacteristic, complemented
48#4992—31no—
49#4992—31no—
50#4991—32no—
51#4986—32no—
52#4961—32no—
53#4953—31no—
54Dic3×C22⋊C4—32no—
55C4×(C2×D3)⋊C4—32no—
56C4×(C2×D3)⋊C4—32no—
57#4932—31no—
58#4674—31no—
59#4666—32no—
60#4660—32no—
61#4648—31no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C2×C32×Q8—22no—
65C2×C32×Q8—24no—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#626—22no—
78C2×#624—22no—
79C2×#624—24no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—24no—
82#3752—22no—
83#3752—24no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—24no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—24no—
88C3×C4×Dic3—24no—
89C3×C4×Dic3D414yes—
90Dic3⋊Dic3—22no—
91#3722—24no—
92(C2×D3)⋊Dic3—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×Q8—21no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C2×D311yescharacteristic
98C22×#67—31no—
99C23×Dic3—31no—
100C22×D12—31no—
101C22×C4×D3—31no—
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C3×C4×Q8—64no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111C2×#217—32no—
112Q8×Dic3—24no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—61no—
121C2×(C2×D3)⋊C4—62no—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×(C2×D3)⋊C4C2×D311yescharacteristic
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3C2×D312yes—
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×Dic3⋊C4—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3C2×D312yes—
131C2×C4×Dic3C2×D311yescharacteristic
132#67⋊C4—64no—
133C4×D12—64no—
134C3×#95—31no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—61no—
147C3⋊#95—62no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3#4112yes—
156C22×C3×D3—21no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—21no—
160C22×C3×D3#4112yes—
161C32×Q8—28no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4#4114yes—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C2×C3×Dic3#4114yes—
185#626—28no—
186#624—44no—
187D3×Dic3—44no—
188C2×C4×Q8—31no—
189C2×C4×D4—91no—
190#400—92no—
191#397—91no—
192#397—91no—
193#394—92no—
194#393—31no—
195#393—91no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—92no—
198#376—91no—
199C24×C3—31no—
200C23×D3—31no—
201C23×D3—31no—
202C23×D3—61no—
203C23×D3C22×D311yescharacteristic
204C2×C3×Q8—24no—
205C2×C3×Q8—22no—
206C2×C3×Q8—24no—
207C2×C3×Q8—22no—
208C2×C3×Q8—44no—
209C2×C3×Q8—42no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—32no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—62no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—62no—
229C22×Dic3—61no—
230C22×Dic3—64no—
231C22×Dic3—62no—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D311yescharacteristic
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—62no—
240C2×C4×D3—62no—
241C2×C4×D3—64no—
242C2×C4×D3—62no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—62no—
246C3×C4⋊C4—64no—
247C3×C4⋊C4—62no—
248C3×C22⋊C4—64no—
249C3×C22⋊C4—62no—
250C3×C42—34no—
251C3×C42—64no—
252#217—64no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—124no—
263(C2×D3)⋊C4—122no—
264C4⋊Dic3—22no—
265C4⋊Dic3—24no—
266C4⋊Dic3—62no—
267Dic3⋊C4—62no—
268C4×Dic3—24no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3#6714yes—
272C22×C32C22×D411yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4112yes—
276C22×C32C2×#4111yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—24no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—42no—
282C2×C3×D3—22no—
283C2×C3×D3—24no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C32×C4—22no—
288C32×C4—24no—
289C3⋊Dic3—41no—
290C3⋊Dic3—42no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3#12414yes—
296C22×Q8D3211yescharacteristic
297C22×D4—91no—
298C23×C4—91no—
299C23×C4—91no—
300C4×Q8—64no—
301C4×D4—184no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—31no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—92no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—92no—
311C2×C42—31no—
312C2×C42—32no—
313C2×C42—92no—
314#95—31no—
315#95—32no—
316#95—92no—
317#95—92no—
318#95—92no—
319#95—91no—
320#95—92no—
321C23×C3—21no—
322C23×C3—32no—
323C23×C3—62no—
324C23×C3—62no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C22×D3—21no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3—21no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—61no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—61no—
341C22×D3—62no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—122no—
345C22×D3—121no—
346C22×D3—122no—
347C22×D3—121no—
348C22×D3#23912yes—
349C3×Q8—28no—
350C3×Q8—28no—
351C3×Q8—48no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—24no—
359C2×C3×C4—22no—
360C2×C3×C4—32no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4#23514yes—
377C2×C3×C4D3×D412yes—
378C2×C3×C4#23714yes—
379C2×C3×C4C2×#6712yes—
380#67—68no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—62no—
392C2×Dic3—61no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—122no—
402C2×Dic3—121no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—124no—
407C2×Dic3#23914yes—
408C2×Dic3C2×#6712yes—
409C2×Dic3C2×#6712yes—
410D12—68no—
411C4×D3—124no—
412C4×D3—124no—
413C4×D3—124no—
414C2×C32#52511yescharacteristic
415C2×C32#52511yescharacteristic
416C2×C32C2×#12411yescharacteristic
417C2×C32#52912yes—
418C2×C32#52912yes—
419C3⋊D3—42no—
420C3×D3—42no—
421C24—31no—
422C24—91no—
423C2×Q8—24no—
424C2×Q8—22no—
425C2×D4—182no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—92no—
434C22×C4—91no—
435C22×C4—182no—
436C22×C4—184no—
437C22×C4—182no—
438C22×C4—184no—
439C22×C4C2×D3212yes—
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—64no—
442C4⋊C4—62no—
443C4⋊C4—182no—
444C22⋊C4—64no—
445C22⋊C4—62no—
446C22⋊C4—184no—
447C22⋊C4—184no—
448C22⋊C4—184no—
449C22⋊C4—182no—
450C42—34no—
451C42—64no—
452C42—184no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—62no—
459C22×C3—64no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—122no—
463C22×C3C2×#23512yes—
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C2×#23712yes—
466C22×C3C2×#23912yes—
467C22×C3C2×#23911yescharacteristic
468C22×C3D3×#4112yes—
469C22×C3D3×#4111yescharacteristic
470C22×C3D3×#4111yescharacteristic
471C22×C3D3×#4111yescharacteristic
472C22×C3C22×#6711yescharacteristic
473C2×D3—24no—
474C2×D3—22no—
475C2×D3—41no—
476C2×D3—42no—
477C2×D3—41no—
478C2×D3—64no—
479C2×D3—62no—
480C2×D3—64no—
481C2×D3—62no—
482C2×D3—124no—
483C2×D3—122no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—122no—
488C2×D3—121no—
489C2×D3—122no—
490C2×D3—242no—
491C2×D3—241no—
492C2×D3—241no—
493C3×C4—24no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—24no—
497C3×C4—34no—
498C3×C4—44no—
499C3×C4—42no—
500C3×C4—62no—
501C3×C4—121no—
502C3×C4—122no—
503C3×C4—122no—
504Dic3—22no—
505Dic3—41no—
506Dic3—42no—
507Dic3—42no—
508Dic3—121no—
509Dic3—121no—
510Dic3—122no—
511Dic3—122no—
512Dic3—242no—
513Dic3—241no—
514Dic3#94714yes—
515C32#239811yescharacteristic, complemented, Sylow
516C23—32no—
517C23—62no—
518C23—61no—
519C23—62no—
520C23—61no—
521C23—92no—
522C23—182no—
523C23—181no—
524C23—182no—
525C23—181no—
526C23C22×D3211yescharacteristic
527Q8—28no—
528D4—188no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—34no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—61no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—181no—
550C2×C4—364no—
551C2×C4—364no—
552C2×C4#380414yes—
553C2×C4D3×#6712yes—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—122no—
560C2×C3#558012yes—
561C2×C3#558012yes—
562C2×C3#558611yescharacteristic
563C2×C3#562412yes—
564C2×C3#562711yescharacteristic
565C2×C3D3×#12411yescharacteristic
566C2×C3#568012yes—
567C2×C3#579111yescharacteristic
568C2×C3C2×#94711yescharacteristic
569C2×C3#582811yescharacteristic
570D3—42no—
571D3—122no—
572D3—122no—
573D3—242no—
574C22—64no—
575C22—62no—
576C22—122no—
577C22—121no—
578C22—121no—
579C22—184no—
580C22—182no—
581C22—362no—
582C22—361no—
583C22—361no—
584C22D3×#23911yescharacteristic
585C22D3×#23912yes—
586C22#6431911yescharacteristic
587C22C2×#380412yes—
588C22C2×D3×#6711yescharacteristic
589C4—24no—
590C4—22no—
591C4—34no—
592C4—62no—
593C4—122no—
594C4—122no—
595C4—121no—
596C4—362no—
597C4—361no—
598C3—21no—
599C3#7677911yescharacteristic, complemented
600C3#8249211yescharacteristic, complemented
601C2—122no—
602C2—362no—
603C2#1059537612yes—
604C2#1059538212yes—
605C2#1059542411yescharacteristic
606C2D3×#94711yescharacteristic
607C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC22×#626C22
hypercenterC22×Q8D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. #10592930C2semidirect
4. C3×#5231C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. #10591343C2semidirect
8. #10591326C2semidirect
9. #10591314C2semidirect
10. #10591239C2semidirect
11. #10591233C2semidirect
40. C2×Q8×Dic3D3semidirect
47. #5231D3semidirect
515. C32#2398semidirect
599. C3#76779semidirect
600. C3#82492semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×#638802
#105929302
C3×#52312
#105913922
Dic3×(C2×D3)⋊C42
#105913432
#105913262
#105913142
#105912392
#105912332
#824923
#767793