Finite Group Databasebeta

← #11808792

Subgroups — #11808792

Order 1152.

1203 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3#10592685C211yesmaximal, characteristic, complemented
4C3×#4991C211yesmaximal, characteristic
5Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7#10591304C212yesmaximal, complemented
8#10591301C212yesmaximal, complemented
9#10591300C211yesmaximal, characteristic
10#10591239C211yesmaximal, characteristic, complemented
11#10591226C211yesmaximal, characteristic, complemented
12#82492—31nomaximal
13#76893—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#887—24no—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31Dic3×D12—24no—
32#63658C2211yescharacteristic
33#63658C2212yes—
34#63658C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×D4×Dic3—31no—
41C2×#887D311yescharacteristic, complemented
42C2×C4×D12—31no—
43C3×#394—31no—
44#5231—32no—
45#5222—31no—
46#4992—32no—
47#4991—31no—
48#4991D311yescharacteristic
49#4986—31no—
50#4986—31no—
51#4986—31no—
52#4986—61no—
53#4952—32no—
54#4947—32no—
55Dic3×C22⋊C4—32no—
56Dic3×C22⋊C4—32no—
57C4×(C2×D3)⋊C4—32no—
58C4×(C2×D3)⋊C4—32no—
59#4932—31no—
60#4659—31no—
61#4648—31no—
62C23×C3×D3C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×D12—24no—
74C2×C3×D12—22no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C32×C4⋊C4—22no—
82C4⋊(C3⋊Dic3)—22no—
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3D414yes—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×Q8—31no—
96C22×C3×D4—31no—
97C23×Dic3—32no—
98C22×D12C2×D311yescharacteristic
99C22×C4×D3—32no—
100C22×Dic6C2×D311yescharacteristic
101C3×C4×Q8—64no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C42—31no—
110C2×C3×C42—31no—
111C2×C3×C42—31no—
112C2×#217—32no—
113C2×#217—32no—
114C2×#217—32no—
115D4×Dic3—64no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4C2×D312yes—
120C2×(C2×D3)⋊C4C2×D312yes—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—61no—
124C2×Dic3⋊C4C2×D311yescharacteristic
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130C2×C4×Dic3C2×D311yescharacteristic
131#887—24no—
132C4×D12—64no—
133C3×#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
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⋊#95—62no—
149C3⋊#95C2×D311yescharacteristic
150C23×C32C2411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3#4114yes—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4#4112yes—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3#4112yes—
183C2×C3×Dic3#4114yes—
184C3×D12—28no—
185C3×Dic6—28no—
186D3×Dic3—48no—
187C2×C4×Q8—31no—
188C2×C4×D4—91no—
189#400—91no—
190#400—91no—
191#397—92no—
192#394—31no—
193#394—91no—
194#393—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—92no—
197#376—91no—
198C24×C3—32no—
199C23×D3C22×D312yes—
200C2×C3×Q8—62no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C2×C3×D4—64no—
204C2×C3×D4—62no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—31no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C2×D12—24no—
234C2×D12—22no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×Dic6—22no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—42no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—64no—
248C3×C42—34no—
249C3×C42—62no—
250C3×C42—62no—
251#217—64no—
252#217—64no—
253#217—64no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—24no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—122no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264C4×Dic3—22no—
265C4×Dic3—22no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3#6714yes—
269C22×C32C22×D411yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4112yes—
273C22×C32C2×#4112yes—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—41no—
284C3⋊Dic3—42no—
285C3⋊Dic3—42no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3#12414yes—
291C22×Q8—31no—
292C22×D4—31no—
293C23×C4—92no—
294C4×Q8—64no—
295C4×D4—184no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4D3211yescharacteristic
300C2×C22⋊C4—32no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—92no—
303C2×C22⋊C4—92no—
304C2×C22⋊C4—92no—
305C2×C42—31no—
306C2×C42—31no—
307C2×C42—31no—
308C2×C42—92no—
309#95—31no—
310#95—92no—
311#95—92no—
312#95—92no—
313#95—91no—
314#95—92no—
315#95—92no—
316C23×C3—21no—
317C23×C3—34no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3C23×D311yescharacteristic
325C23×C3C23×D311yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3#23714yes—
333C3×Q8—68no—
334C3×D4—68no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—34no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4#23512yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4#23712yes—
368C2×C3×C4C2×#6712yes—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
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—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—128no—
397C2×Dic3#23512yes—
398C2×Dic3#23914yes—
399C2×Dic3C2×#6712yes—
400C2×Dic3C2×#6712yes—
401D12—28no—
402C4×D3—128no—
403Dic6—28no—
404C2×C32#52511yescharacteristic
405C2×C32#52511yescharacteristic
406C2×C32C2×#12411yescharacteristic
407C2×C32#52912yes—
408C2×C32#52912yes—
409C3×D3—44no—
410C24—32no—
411C2×Q8—62no—
412C2×Q8—62no—
413C2×Q8—62no—
414C2×D4—64no—
415C2×D4—62no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—32no—
420C22×C4—31no—
421C22×C4—92no—
422C22×C4—92no—
423C22×C4—184no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4C2×D3211yescharacteristic
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—22no—
430C4⋊C4—62no—
431C4⋊C4—62no—
432C4⋊C4—182no—
433C22⋊C4—64no—
434C22⋊C4—64no—
435C22⋊C4—184no—
436C22⋊C4—184no—
437C22⋊C4—184no—
438C42—34no—
439C42—62no—
440C42—62no—
441C42—184no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3C2×#23511yescharacteristic
455C22×C3C2×#23511yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C2×#23711yescharacteristic
458C22×C3C2×#23712yes—
459C22×C3C2×#23912yes—
460C22×C3D3×#4111yescharacteristic
461C22×C3D3×#4112yes—
462C22×C3D3×#4112yes—
463C22×C3C22×#6711yescharacteristic
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—24no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—34no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—62no—
481C3×C4—62no—
482C3×C4—81no—
483C3×C4—122no—
484C3×C4—121no—
485Dic3—22no—
486Dic3—22no—
487Dic3—41no—
488Dic3—42no—
489Dic3—122no—
490Dic3—122no—
491Dic3—122no—
492Dic3—122no—
493Dic3—242no—
494Dic3—242no—
495Dic3#94714yes—
496C32#239811yescharacteristic, complemented, Sylow
497C23—34no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23C22×D3211yescharacteristic
505Q8—68no—
506D4—68no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—34no—
513C2×C4—32no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—61no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—368no—
532C2×C4#379512yes—
533C2×C4D3×#6712yes—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—124no—
540C2×C3#558012yes—
541C2×C3#558012yes—
542C2×C3#558611yescharacteristic
543C2×C3#560012yes—
544C2×C3#560611yescharacteristic
545C2×C3#564912yes—
546C2×C3D3×#12411yescharacteristic
547C2×C3#579111yescharacteristic
548C2×C3C2×#94711yescharacteristic
549C2×C3#582811yescharacteristic
550D3—44no—
551C22—64no—
552C22—64no—
553C22—64no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22C2×#379511yescharacteristic
559C22D3×#23511yescharacteristic
560C22D3×#23712yes—
561C22D3×#23912yes—
562C22C2×D3×#6711yescharacteristic
563C4—22no—
564C4—22no—
565C4—34no—
566C4—41no—
567C4—62no—
568C4—62no—
569C4—121no—
570C4—122no—
571C4—362no—
572C4—362no—
573C3—21no—
574C3#7689311yescharacteristic, complemented
575C3#8249211yescharacteristic, complemented
576C2—124no—
577C2#1059441612yes—
578C2#1059442612yes—
579C2#1059489211yescharacteristic
580C2#1059515411yescharacteristic
581C2D3×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
3. #10592685C2semidirect
5. Dic3×(C2×D3)⋊C4C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. #10591304C2semidirect
8. #10591301C2semidirect
10. #10591239C2semidirect
11. #10591226C2semidirect
41. C2×#887D3semidirect
496. C32#2398semidirect
574. C3#76893semidirect
575. C3#82492semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×Dic3×D122
#105926852
C3×#49912
Dic3×(C2×D3)⋊C42
#105913042
#105913012
#105913002
#105912392
#105912262
#824923
#768933