Finite Group Databasebeta

← #11801839

Subgroups — #11801839

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C2×#63855C211yesmaximal, characteristic
4C4×#3750C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10591373C212yesmaximal
7#10591372C212yesmaximal
8C4×#3724C211yesmaximal, characteristic, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#10591246C212yesmaximal, complemented
11#10591234C212yesmaximal, complemented
12#82226—31nomaximal
13#73755—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#872—24no—
27C2×#3724C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×Dic32C2212yes—
34C4×D3×Dic3—24no—
35#63855C418yescomplemented
36#63658C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#926—31no—
42C22×C4×Dic3—31no—
43C2×#872—31no—
44C2×#872D311yescharacteristic
45C2×C42×D3—31no—
46C3×C4×C4⋊C4—31no—
47#4989—32no—
48#4976—32no—
49#4972—32no—
50#4972—32no—
51#4946—32no—
52#4946—32no—
53C4×C4⋊Dic3—31no—
54C4×Dic3⋊C4—31no—
55C4×Dic3⋊C4—31no—
56C4×Dic3⋊C4—31no—
57C4×Dic3⋊C4—31no—
58C4×Dic3⋊C4—31no—
59C4×Dic3⋊C4—61no—
60C4×Dic3⋊C4D311yescharacteristic, complemented
61#4668—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3D414yes—
76C2×C3×C4×D3Q814yes—
77C2×D3×Dic3—24no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C32×C42—22no—
81#3750—24no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2×C414yescomplemented
84C3×(C2×D3)⋊C4—24no—
85C3×Dic3⋊C4—24no—
86C3×Dic3⋊C4—24no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3C2×C414yescomplemented
90#3724—24no—
91Dic3⋊Dic3—24no—
92Dic3⋊Dic3C2×C414yescomplemented
93Dic3⋊Dic3C2×C414yescomplemented
94(C2×D3)⋊Dic3C2×C414yes—
95(C2×D3)⋊Dic3C2×C414yes—
96Dic32—24no—
97#2296—91noSylow
98C23×C3×C4—31no—
99C23×Dic3—32no—
100C22×C4×D3—32no—
101C22×C4×D3C2×D311yescharacteristic
102C3×#117—64no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112C2×#217—31no—
113C2×#217—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4C2×D312yes—
117#926—38no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—32no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—62no—
129C2×Dic3⋊C4C2×D312yes—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3—64no—
140C2×C4×Dic3C2×D311yescharacteristic
141C2×C4×Dic3C2×D311yescharacteristic
142C2×C4×Dic3C2×D311yescharacteristic
143#872—24no—
144#872—38no—
145C42×D3—64no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3C22×C412yes—
159C22×C3×D3C2×D412yes—
160C22×C3×D3C2×Q812yes—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4C22×C412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×Q812yes—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3#4114yes—
174C2×C3×Dic3—22no—
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×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×Q812yes—
186C2×C3×Dic3#4114yes—
187C3×C4×D3C4⋊C4116yescomplemented
188D3×Dic3—216no—
189C2×#117—31no—
190C2×#117—91no—
191C22×C42—91no—
192#389—92no—
193#389—92no—
194#385—92no—
195#385—92no—
196C4×C4⋊C4—31no—
197C4×C4⋊C4—91no—
198C4×C4⋊C4—91no—
199C4×C4⋊C4—91no—
200C24×C3—31no—
201C23×D3C22×D311yescharacteristic
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—34no—
206C22×C3×C4—34no—
207C22×C3×C4—34no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3Dic614yes—
237C2×C4×D3C4×D314yes—
238C2×C4×D3#6714yes—
239C3×C4⋊C4—64no—
240C3×C4⋊C4—64no—
241C3×C22⋊C4—64no—
242C3×C42—22no—
243C3×C42—22no—
244C3×C42—34no—
245C3×C42—42no—
246C3×C42—62no—
247C3×C42—62no—
248#217—34no—
249#217—34no—
250(C2×D3)⋊C4—24no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255C4⋊Dic3—64no—
256Dic3⋊C4—24no—
257Dic3⋊C4—24no—
258Dic3⋊C4—34no—
259Dic3⋊C4—34no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—68no—
265Dic3⋊C4—64no—
266C4×Dic3—22no—
267C4×Dic3—22no—
268C4×Dic3—34no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3—64no—
275C4×Dic3—122no—
276C4×Dic3C4×D314yescomplemented
277C22×C32C23×C411yescharacteristic
278C22×C32C22×D411yescharacteristic
279C22×C32C22×Q811yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32C2×#4112yes—
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—24no—
285C2×C3×D3—24no—
286C2×C3×D3C2×C4⋊C414yes—
287C32×C4—42no—
288C32×C4C2×C4⋊C414yes—
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—24no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—24no—
295C3×Dic3—42no—
296C3×Dic3C2×C4⋊C414yes—
297C23×C4—31no—
298C23×C4—92no—
299#117—64no—
300#117—98no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—92no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—92no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C42—31no—
312C2×C42—31no—
313C2×C42—31no—
314C2×C42—91no—
315C2×C42—92no—
316C2×C42—91no—
317C2×C42—184no—
318C2×C42D3211yescharacteristic
319#95—32no—
320#95—92no—
321#95—92no—
322#95—92no—
323C23×C3—21no—
324C23×C3—32no—
325C23×C3—32no—
326C23×C3—32no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3C23×D311yescharacteristic
330C23×C3C23×D311yescharacteristic
331C22×D3—22no—
332C22×D3—22no—
333C22×D3C2×Dic612yes—
334C22×D3C2×C4×D312yes—
335C22×D3C2×#6712yes—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—316no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—34no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4C2×Dic612yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×Q812yes—
367C2×C3×C4C2×#6712yes—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—64no—
384C2×Dic3—616no—
385C2×Dic3—64no—
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—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3C2×Dic612yes—
398C2×Dic3C2×C4×D312yes—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3C2×C4×D312yes—
401C2×Dic3#23514yes—
402C2×Dic3C2×#6712yes—
403C4×D3—616no—
404C4×D3Dic3⋊C4116yescomplemented
405C2×C32C22×C4⋊C411yescharacteristic
406C2×C32C4×#4111yescharacteristic
407C2×C32C4×#4111yescharacteristic
408C2×C32#52512yes—
409C2×C32#53312yes—
410C3×D3—24no—
411C24—31no—
412C22×C4—31no—
413C22×C4—34no—
414C22×C4—34no—
415C22×C4—34no—
416C22×C4—31no—
417C22×C4—32no—
418C22×C4—31no—
419C22×C4—32no—
420C22×C4—92no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—184no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4C2×D3212yes—
427C22×C4C2×D3211yescharacteristic
428C4⋊C4—64no—
429C4⋊C4—64no—
430C4⋊C4—94no—
431C4⋊C4—94no—
432C4⋊C4—184no—
433C4⋊C4—184no—
434C4⋊C4—184no—
435C22⋊C4—64no—
436C22⋊C4—94no—
437C22⋊C4—94no—
438C42—22no—
439C42—34no—
440C42—62no—
441C42—62no—
442C42—94no—
443C42—184no—
444C42—182no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—34no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—64no—
454C22×C3—64no—
455C22×C3C22×Dic611yescharacteristic
456C22×C3C22×C4×D311yescharacteristic
457C22×C3C22×C4×D311yescharacteristic
458C22×C3C2×#23512yes—
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C2×D3×Q811yescharacteristic
461C22×C3D3×#4112yes—
462C22×C3D3×#4112yes—
463C22×C3D3×#4112yes—
464C22×C3C22×#6711yescharacteristic
465C2×D3—24no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—24no—
469C2×D3C2×Dic3⋊C414yes—
470C3×C4—24no—
471C3×C4—34no—
472C3×C4—44no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4—64no—
478C3×C4—122no—
479C3×C4D3×C4⋊C414yes—
480C3×C4C2×Dic3⋊C414yes—
481Dic3—22no—
482Dic3—22no—
483Dic3—24no—
484Dic3—42no—
485Dic3—64no—
486Dic3—62no—
487Dic3—62no—
488Dic3—62no—
489Dic3—62no—
490Dic3—64no—
491Dic3—64no—
492Dic3—122no—
493Dic3—124no—
494Dic3C2×Dic3⋊C414yes—
495C32#229611yescharacteristic, complemented, Sylow
496C23—32no—
497C23—32no—
498C23—32no—
499C23—62no—
500C23—62no—
501C23C22×D3211yescharacteristic
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—316no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—34no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—94no—
522C2×C4—1816no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4D3×Dic612yes—
528C2×C4C4×D3212yes—
529C2×C4D3×#6712yes—
530C2×C3—21no—
531C2×C3—22no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—64no—
536C2×C3C4×#23511yescharacteristic
537C2×C3C2×D3×C4⋊C411yescharacteristic
538C2×C3#551712yes—
539C2×C3#552211yescharacteristic
540C2×C3#552211yescharacteristic
541C2×C3#552211yescharacteristic
542C2×C3#554712yes—
543C2×C3#557812yes—
544C2×C3C22×Dic3⋊C411yescharacteristic
545C2×C3#582812yes—
546D3—24no—
547C22—34no—
548C22—64no—
549C22—62no—
550C22—62no—
551C22—64no—
552C22C2×D3×Dic611yescharacteristic
553C22C2×C4×D3211yescharacteristic
554C22D3×#23512yes—
555C22#6430612yes—
556C22C2×D3×#6711yescharacteristic
557C4—34no—
558C4—42no—
559C4—62no—
560C4—62no—
561C4—64no—
562C4—122no—
563C4—182no—
564C4—182no—
565C4—184no—
566C4D3×Dic3⋊C414yes—
567C3—21no—
568C3#7375511yescharacteristic, complemented
569C3#8222611yescharacteristic, complemented
570C2—64no—
571C2#1059392612yes—
572C2#1059396511yescharacteristic
573C2#1059396611yescharacteristic
574C2C2×D3×Dic3⋊C411yescharacteristic
575C2#1059506012yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C4×#3750C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
8. C4×#3724C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
10. #10591246C2semidirect
11. #10591234C2semidirect
35. #63855C4semidirect
60. C4×Dic3⋊C4D3semidirect
83. C4×C3⋊Dic3C2×C4semidirect
89. C3×C4×Dic3C2×C4semidirect
92. Dic3⋊Dic3C2×C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
187. C3×C4×D3C4⋊C4semidirect
276. C4×Dic3C4×D3semidirect
404. C4×D3Dic3⋊C4semidirect
495. C32#2296semidirect
568. C3#73755semidirect
569. C3#82226semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C4×D3×Dic32
C2×#638552
C4×#37502
C3×C4×Dic3⋊C42
#105913732
#105913722
C4×#37242
C4×Dic3⋊Dic32
#105912462
#105912342
#822263
#737553