Finite Group Databasebeta

← #11785182

Subgroups — #11785182

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591349C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71604—31nomaximal
9#70153—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3×Dic3—21no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—21no—
15C3×D4×Dic3—22no—
16C3×D4×Dic3C414yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×Dic3⋊Dic3—21no—
23#63659—22no—
24C3×#832—22no—
25Dic3⋊(C3⋊C8)—22no—
26C2×C3×C4×D4—31no—
27C2×D4×Dic3D311yescharacteristic
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#832—31no—
31C2×#832—61no—
32C2×#832D311yescharacteristic
33C2×Dic3⋊C8—31no—
34#4975—31no—
35#4935—31no—
36C2×C4⋊(C3⋊C8)—31no—
37#4551—31no—
38#4529—31no—
39#4529—31no—
40#4529—31no—
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C2×C32×D4D412yes—
47C2×C32×D4Q812yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—42no—
54C22×C3×Dic3—42no—
55C22×C3×Dic3D411yescharacteristic
56C22×C3×Dic3D411yescharacteristic
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—24no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yes—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—42no—
73Dic3⋊Dic3—42no—
74#1802—91noSylow
75C22×C3×D4—21no—
76C22×C3×D4C2×D311yescharacteristic
77C22×C3×D4C2×D311yescharacteristic
78C23×C3×C4—61no—
79C23×Dic3—21no—
80C22×C3×C8—31no—
81C3×C4×D4—34no—
82C3×C4×D4—62no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—61no—
86C2×C3×C42—31no—
87C2×#217—21no—
88D4×Dic3—22no—
89D4×Dic3Dic314yescomplemented
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104C3×#102—62no—
105#832—22no—
106#832—64no—
107#832—62no—
108#832—62no—
109Dic3⋊C8—62no—
110C4⋊(C3⋊C8)—62no—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32—22no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32C2×D411yescharacteristic
119C32×D4—22no—
120C32×D4—22no—
121C32×D4—22no—
122C32×D4C4⋊C414yescomplemented
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—48no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3C22⋊C412yes—
142C2×C3×Dic3C22⋊C412yes—
143C2×C3×Dic3D812yes—
144C2×C3×Dic3SD1612yes—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147C2×C4×D4—31no—
148C2×C4⋊C8—91no—
149C2×#102—31no—
150C2×#102—91no—
151#384—91no—
152#340—91no—
153#340—91no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—41no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4—41no—
169C2×C3×D4Dic612yes—
170C2×C3×D4Dic612yes—
171C2×C3×D4C4×D312yes—
172C2×C3×D4D1212yes—
173C2×C3×D4C2×Dic312yes—
174C2×C3×D4#6712yes—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—64no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—122no—
182C22×C3×C4—122no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—24no—
187C22×Dic3—21no—
188C22×Dic3—42no—
189C22×Dic3—42no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3#6711yescharacteristic
194C22×Dic3#6711yescharacteristic
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C22⋊C4—64no—
203C3×C42—32no—
204C3×C42—32no—
205#217—24no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215C4⋊Dic3—122no—
216C4⋊Dic3—122no—
217C4⋊Dic3C2×Dic312yes—
218Dic3⋊C4—122no—
219Dic3⋊C4—122no—
220C4×Dic3C2×Dic312yes—
221C4×Dic3#6712yes—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—121no—
233C2×C3⋊C8—121no—
234C22×C32—24no—
235C22×C32—42no—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32—42no—
239C22×C32—42no—
240C22×C32—42no—
241C22×C32C2×C22⋊C411yescharacteristic
242C22×C32#12111yescharacteristic
243C22×C32C22⋊Q811yescharacteristic
244C22×C32C2×D811yescharacteristic
245C22×C32C2×SD1611yescharacteristic
246C22×C32AGL(1,ℤ/8)11yescharacteristic
247C22×C32#13711yescharacteristic
248C32×C4C2×C4⋊C411yescharacteristic
249C32×C4#11711yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4C22⋊Q811yescharacteristic
252C3⋊Dic3—81no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C3×Dic3—81no—
256C3×Dic3#10214yescomplemented
257C22×D4D3211yescharacteristic
258C23×C4—61no—
259C22×C8—31no—
260C22×C8—91no—
261C4×D4—34no—
262C4×D4—62no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—181no—
267C2×C4⋊C4—181no—
268C2×C22⋊C4—61no—
269C2×C42—31no—
270C4⋊C8—182no—
271#102—62no—
272#102—182no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—41no—
290C23×C3—41no—
291C23×C3—81no—
292C23×C3—81no—
293C23×C3—81no—
294C23×C3—81no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—24no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4Dic3⋊C414yescomplemented
308C3×D4C4⋊Dic314yescomplemented
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—128no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4C2×Dic611yescharacteristic
329C2×C3×C4C2×Dic611yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4C22×Dic311yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—48no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—122no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—241no—
357C2×Dic3—241no—
358C2×Dic3#21312yes—
359C2×Dic3#21412yes—
360C2×Dic3#21712yes—
361C2×Dic3#21712yes—
362C3×C8—121no—
363C3⋊C8—41no—
364C3⋊C8—122no—
365C3⋊C8—121no—
366C3⋊C8—121no—
367C2×C32—44no—
368C2×C32#38011yescharacteristic
369C2×C32C2×#10211yescharacteristic
370C2×C32#41711yescharacteristic
371C2×C32#45911yescharacteristic
372C2×C32#46111yescharacteristic
373C2×C32#47411yescharacteristic
374C2×C32#47611yescharacteristic
375C24—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4D3×Dic312yes—
380C2×D4#62612yes—
381C2×D4#62712yes—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—64no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—122no—
388C22×C4—122no—
389C22×C4—181no—
390C22×C4C2×D3211yescharacteristic
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8—181no—
395C2×C8—181no—
396C2×C8—181no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—362no—
404C4⋊C4—362no—
405C22⋊C4—64no—
406C42—32no—
407C42—32no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—44no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3—82no—
436C22×C3#87811yescharacteristic
437C22×C3D3×C22⋊C411yescharacteristic
438C22×C3D3×D811yescharacteristic
439C22×C3#91111yescharacteristic
440C22×C3D3×SD1611yescharacteristic
441C22×C3#91511yescharacteristic
442C22×C3#92411yescharacteristic
443C22×C3#93011yescharacteristic
444C22×C3C2×#21311yescharacteristic
445C22×C3C2×#21411yescharacteristic
446C22×C3#93911yescharacteristic
447C22×C3#94911yescharacteristic
448C22×C3#95111yescharacteristic
449C22×C3C2×#21711yescharacteristic
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—34no—
455C3×C4—62no—
456C3×C4—122no—
457C3×C4—241no—
458C3×C4#87711yescharacteristic
459C3×C4#87811yescharacteristic
460C3×C4C2×Dic3⋊C411yescharacteristic
461C3×C4#92411yescharacteristic
462C3×C4C2×C4⋊Dic311yescharacteristic
463C3×C4#92611yescharacteristic
464C3×C4#93011yescharacteristic
465C3×C4#93911yescharacteristic
466Dic3—22no—
467Dic3—42no—
468Dic3—81no—
469Dic3—242no—
470Dic3—241no—
471Dic3—241no—
472Dic3#83214yescomplemented
473C32#180211yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23D3×#6711yescharacteristic
482D4—22no—
483D4—22no—
484D4—22no—
485D4Dic3⋊Dic314yescomplemented
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—128no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4C2×D3×Dic311yescharacteristic
503C2×C4#380411yescharacteristic
504C2×C4#380411yescharacteristic
505C2×C4C2×#62611yescharacteristic
506C2×C4C2×#62711yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C8—121no—
509C8—361no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—44no—
518C2×C3—44no—
519C2×C3—84no—
520C2×C3#475911yescharacteristic
521C2×C3#476111yescharacteristic
522C2×C3D3×#10211yescharacteristic
523C2×C3#477111yescharacteristic
524C2×C3#494211yescharacteristic
525C2×C3#500711yescharacteristic
526C2×C3#500811yescharacteristic
527C2×C3#501511yescharacteristic
528C2×C3#501911yescharacteristic
529C2×C3#515011yescharacteristic
530C2×C3#516211yescharacteristic
531C2×C3#521211yescharacteristic
532C2×C3C2×#83211yescharacteristic
533C2×C3#523211yescharacteristic
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22D3×#21311yescharacteristic
542C22#6392511yescharacteristic
543C22D3×#21411yescharacteristic
544C22#6392911yescharacteristic
545C22#6396411yescharacteristic
546C22D3×#21711yescharacteristic
547C22#6397811yescharacteristic
548C4—34no—
549C4—62no—
550C4—122no—
551C4—241no—
552C4—721no—
553C4#6395511yescharacteristic
554C4#6396411yescharacteristic
555C4C2×Dic3⋊Dic311yescharacteristic
556C4#6397811yescharacteristic
557C3—21no—
558C3#7015311yescharacteristic, complemented
559C3#7160411yescharacteristic, complemented
560C2—44no—
561C2#1059140811yescharacteristic
562C2#1059141011yescharacteristic
563C2D3×#83211yescharacteristic
564C2#1059141411yescharacteristic
565C2#1059148111yescharacteristic
566C2#1059148911yescharacteristic
567C2#1059171611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1802
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591349C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
16. C3×D4×Dic3C4semidirect
89. D4×Dic3Dic3semidirect
122. C32×D4C4⋊C4semidirect
256. C3×Dic3#102semidirect
307. C3×D4Dic3⋊C4semidirect
308. C3×D4C4⋊Dic3semidirect
472. Dic3#832semidirect
473. C32#1802semidirect
485. D4Dic3⋊Dic3semidirect
558. C3#70153semidirect
559. C3#71604semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#636592
C2×C3×#8322
#105913492
C2×Dic3⋊(C3⋊C8)2
#105891642
#105891632
#716043
#701533