Finite Group Databasebeta

← #11787593

Subgroups — #11787593

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5C2×#63567C211yesmaximal, characteristic, complemented
6#10589163C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70213—31nomaximal
9#69660—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×#3754—22no—
13C2×#3754—22no—
14C2×#3754C414yescomplemented
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3724—21no—
23C2×Dic32—21no—
24#63844—22no—
25#63844—22no—
26C3×#832—22no—
27#63567—22no—
28C22×#214—31no—
29C22×#214—31no—
30C22×#214—61no—
31C2×#887—31no—
32C2×C4×Dic6—31no—
33C2×C3×#102—31no—
34C3×#390—31no—
35#5221D311yescharacteristic
36C2×#832D311yescharacteristic
37C2×#816—31no—
38C2×#810—31no—
39#4550—31no—
40#4529—31no—
41#4529—31no—
42#4524—31no—
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2×C412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634C2×C412yes—
56C2×#634D412yes—
57C2×#634D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62#3754—28no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)C2×C412yes—
66C3×#217—42no—
67C3×#217—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3D412yes—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#3724—24no—
78Dic32—24no—
79#1880—91noSylow
80C22×C3×D4—21no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C22×Dic6—31no—
84C22×Dic6—31no—
85C22×Dic6—61no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C42—31no—
92C2×#217—21no—
93C2×#217—21no—
94C2×#214—34no—
95C2×#214—34no—
96C2×#214—64no—
97C2×#214—62no—
98C2×#214—62no—
99C2×#214—62no—
100C2×#214—62no—
101C2×#214—64no—
102C2×#214—64no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114#887—62no—
115#887—62no—
116C4×Dic6—62no—
117C4×Dic6—62no—
118C3×#102—62no—
119#832—22no—
120#816—62no—
121#810—62no—
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32C2×D411yescharacteristic
130C32×D4—22no—
131C32×D4—22no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143#634—22no—
144#634—22no—
145#634—22no—
146#634C22⋊C414yescomplemented
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3SD1612yescomplemented
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—41no—
161C22×SD16—91no—
162C2×C4×Q8—91no—
163C2×#103—91no—
164C2×#102—31no—
165#390—31no—
166#340—91no—
167#336—91no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—41no—
171C2×C3×D4—22no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—22no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4C4×D312yes—
188C2×C3×D4C4×D312yes—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C22×Dic3—121no—
201C22×Dic3#6711yescharacteristic
202C22×Dic3#6711yescharacteristic
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—32no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—32no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C2×Dic6—121no—
220C2×Dic6—121no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—122no—
229C3×C22⋊C4—122no—
230C3×C42—61no—
231C3×C42—61no—
232#217—42no—
233#217—42no—
234#214—68no—
235#214—68no—
236#214—616no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3#6712yes—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243C4×Dic3—21no—
244C4×Dic3—21no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32—42no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—81no—
263C22×C32—81no—
264C22×C32—81no—
265C22×C32—81no—
266C22×C32C4×D411yescharacteristic
267C22×C32#12011yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32C2×SD1611yescharacteristic
270C22×C32#13511yescharacteristic
271C22×C32AGL(1,ℤ/8)11yescharacteristic
272C22×C32#13711yescharacteristic
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12311yescharacteristic
277C3⋊Dic3—24no—
278C3×Dic3—22no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C3×Dic3—81no—
282C22×Q8—91no—
283C22×D4D3211yescharacteristic
284C2×SD16—94no—
285C2×SD16—182no—
286C2×SD16—182no—
287C22×C8—31no—
288C22×C8—91no—
289C4×Q8—182no—
290C4×Q8—182no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—181no—
294C2×C22⋊C4—61no—
295C2×C22⋊C4—61no—
296C2×C42—31no—
297C2×C42—181no—
298#103—182no—
299#102—62no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—81no—
319C23×C3—81no—
320C23×C3—81no—
321C23×C3—81no—
322C23×C3D3×D411yescharacteristic
323C23×C3C2×#6711yescharacteristic
324C3×D4—24no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—42no—
332C3×D4—41no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—41no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4C2×C4×D311yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—21no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3#21412yescomplemented
387Dic6—34no—
388Dic6—34no—
389Dic6—64no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—122no—
397Dic6—122no—
398Dic6—122no—
399C3×C8—121no—
400C3⋊C8—41no—
401C3⋊C8—64no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C2×C32—82no—
405C2×C32#38611yescharacteristic
406C2×C32C4×SD1611yescharacteristic
407C2×C32#44011yescharacteristic
408C2×C32#44811yescharacteristic
409C2×C32#44911yescharacteristic
410C2×C32#46011yescharacteristic
411C2×C32#46411yescharacteristic
412C24—21no—
413C2×Q8—92no—
414C2×Q8—92no—
415C2×Q8—92no—
416C2×Q8—181no—
417C2×Q8—181no—
418C2×Q8—181no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4#62412yes—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—181no—
430C22×C4C2×D3211yescharacteristic
431SD16—188no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—92no—
436C2×C8—181no—
437C2×C8—181no—
438C4⋊C4—32no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—184no—
443C22⋊C4—122no—
444C22⋊C4—122no—
445C42—61no—
446C42—61no—
447C42—184no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—44no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—82no—
463C22×C3—82no—
464C22×C3—82no—
465C22×C3—82no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3—81no—
471C22×C3—81no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3—81no—
475C22×C3—81no—
476C22×C3#67⋊C411yescharacteristic
477C22×C3#88411yescharacteristic
478C22×C3#91111yescharacteristic
479C22×C3#91211yescharacteristic
480C22×C3D3×SD1611yescharacteristic
481C22×C3#91511yescharacteristic
482C22×C3C4×#6711yescharacteristic
483C22×C3#93211yescharacteristic
484C22×C3C2×#21411yescharacteristic
485C22×C3#93711yescharacteristic
486C22×C3#93711yescharacteristic
487C22×C3#93811yescharacteristic
488C22×C3#95011yescharacteristic
489C22×C3#95111yescharacteristic
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—62no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4—241no—
498C3×C4D3×C22⋊C411yescharacteristic
499C3×C4D3×C22⋊C411yescharacteristic
500C3×C4#67⋊C411yescharacteristic
501C3×C4#88311yescharacteristic
502C3×C4#88311yescharacteristic
503C3×C4#88411yescharacteristic
504C3×C4C4×#6711yescharacteristic
505C3×C4#93811yescharacteristic
506Dic3—22no—
507Dic3—42no—
508Dic3—41no—
509Dic3—64no—
510Dic3—64no—
511Dic3—81no—
512Dic3—124no—
513C32#188011yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23D3×#6711yescharacteristic
522Q8—94no—
523Q8—182no—
524Q8—182no—
525Q8—182no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—32no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4#380411yescharacteristic
546C2×C4#380411yescharacteristic
547C2×C4C2×#62411yescharacteristic
548C2×C4D3×#6711yescharacteristic
549C2×C4#381111yescharacteristic
550C2×C4#381111yescharacteristic
551C8—121no—
552C8—182no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—84no—
561C2×C3—82no—
562C2×C3—82no—
563C2×C3#475711yescharacteristic
564C2×C3#475811yescharacteristic
565C2×C3#476211yescharacteristic
566C2×C3#476711yescharacteristic
567C2×C3#495611yescharacteristic
568C2×C3#495611yescharacteristic
569C2×C3C4×#21411yescharacteristic
570C2×C3#501811yescharacteristic
571C2×C3#503711yescharacteristic
572C2×C3#504011yescharacteristic
573C2×C3#505411yescharacteristic
574C2×C3#507511yescharacteristic
575C2×C3#515811yescharacteristic
576C2×C3#517011yescharacteristic
577C22—42no—
578C22—42no—
579C22—42no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22D3×#21411yescharacteristic
585C22#6392911yescharacteristic
586C22#6393211yescharacteristic
587C22#6393311yescharacteristic
588C22#6395211yescharacteristic
589C22#6395811yescharacteristic
590C22#6398311yescharacteristic
591C4—62no—
592C4—121no—
593C4—122no—
594C4—184no—
595C4—241no—
596C4#6395211yescharacteristic
597C4#6395811yescharacteristic
598C4#6397411yescharacteristic
599C4#6397511yescharacteristic
600C3—21no—
601C3#6966011yescharacteristic, complemented
602C3#7021311yescharacteristic, complemented
603C2—82no—
604C2#1059140111yescharacteristic
605C2#1059140511yescharacteristic
606C2#1059143911yescharacteristic
607C2#1059144111yescharacteristic
608C2#1059151711yescharacteristic
609C2#1059151911yescharacteristic
610C2#1059172211yescharacteristic
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#1880
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
2. C2×#63844C2semidirect
5. C2×#63567C2semidirect
6. #10589163C2semidirect
7. #10589155C2semidirect
14. C2×#3754C4semidirect
146. #634C22⋊C4semidirect
158. C2×C3×Dic3SD16semidirect
386. C2×Dic3#214semidirect
513. C32#1880semidirect
601. C3#69660semidirect
602. C3#70213semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C2×#638442
C3×#52212
C2×C3×#8322
C2×#635672
#105891632
#105891552
#702133
#696603