Finite Group Databasebeta

← #11787603

Subgroups — #11787603

Order 1152.

807 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
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic
4C2×#63565C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#68909—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204C414yescomplemented
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63843—22no—
25#63843—22no—
26#63565—22no—
27#63562—22no—
28C22×C3×SD16—31no—
29C2×Q8×Dic3—31no—
30C22×#204D311yescharacteristic
31C2×#887—31no—
32C2×#835—31no—
33#5221—31no—
34C2×#832—31no—
35#4988—31no—
36C2×#810—31no—
37C2×#809—31no—
38C3×#340—31no—
39#4551D311yescharacteristic, complemented
40#4550—31no—
41#4550—31no—
42#4550—61no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8C2×C412yes—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C3×#204—28no—
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3—42no—
78Dic32—24no—
79#1880—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C22×D12C2×D311yescharacteristic
83C22×Dic6C2×D311yescharacteristic
84C2×C3×SD16—34no—
85C2×C3×SD16—62no—
86C2×C3×SD16—62no—
87C22×C3×C8—21no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93C2×#217—61no—
94Q8×Dic3—62no—
95Q8×Dic3—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C2×#204—22no—
111C2×#204—22no—
112C2×#204Dic314yescomplemented
113#887—62no—
114#887—62no—
115#835—62no—
116#832—62no—
117#810—62no—
118#809—62no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3SD1612yescomplemented
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6C22⋊C414yescomplemented
156C32×C8—22no—
157C3⋊(C3⋊C8)—41no—
158C22×SD16—31no—
159C2×C4×Q8—91no—
160C2×#103—91no—
161C2×#102—91no—
162#390—91no—
163#340—31no—
164#336—91no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—32no—
168C2×C3×Q8—32no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C2×Dic312yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6C2×Dic312yes—
204C2×Dic6#6712yes—
205C2×Dic6#6712yes—
206C3×SD16—68no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—22no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8C4×D312yes—
215C2×C3×C8C2×Dic312yes—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220#217—122no—
221#217—122no—
222(C2×D3)⋊C4—122no—
223(C2×D3)⋊C4—122no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—64no—
228C4⋊Dic3D1212yes—
229Dic3⋊C4—64no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C4×Dic3—61no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—121no—
237C4×Dic3—121no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—121no—
246C2×C3⋊C8—121no—
247#204—28no—
248C22×C32C4×D411yescharacteristic
249C22×C32#12011yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32C2×SD1611yescharacteristic
252C22×C32#13511yescharacteristic
253C22×C32AGL(1,ℤ/8)11yescharacteristic
254C22×C32#13711yescharacteristic
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C2×C3×D3—81no—
262C32×C4C2×C22⋊C411yescharacteristic
263C32×C4C4×D411yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12311yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3—41no—
268C3×Dic3—24no—
269C3×Dic3—42no—
270C3×Dic3—81no—
271C22×Q8—31no—
272C22×D4—31no—
273C2×SD16—34no—
274C2×SD16—62no—
275C2×SD16—62no—
276C22×C8—91no—
277C22×C8D3211yescharacteristic
278C4×Q8—182no—
279C4×Q8—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C42—91no—
286C2×C42—181no—
287#103—182no—
288#102—182no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3D3×D411yescharacteristic
298C23×C3D3×D411yescharacteristic
299C22×D3—22no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C22×D3—41no—
306C3×Q8—34no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×Q8—62no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—121no—
313C3×D4—121no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4#23911yescharacteristic
338C2×C3×C4C22×Dic311yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368D12—22no—
369D12—22no—
370D12—41no—
371D12—41no—
372Dic6—22no—
373Dic6—22no—
374Dic6—22no—
375Dic6#21714yescomplemented
376C3×C8—22no—
377C3×C8—22no—
378C3×C8—42no—
379C3⋊C8—122no—
380C3⋊C8—121no—
381C3⋊C8—121no—
382C2×C32#38611yescharacteristic
383C2×C32C4×SD1611yescharacteristic
384C2×C32#44011yescharacteristic
385C2×C32#44811yescharacteristic
386C2×C32#44911yescharacteristic
387C2×C32#46011yescharacteristic
388C2×C32#46411yescharacteristic
389C3×D3—82no—
390C24—61no—
391C2×Q8—32no—
392C2×Q8—32no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×D4—32no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4C2×D3211yescharacteristic
409SD16—68no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—181no—
413C2×C8—181no—
414C2×C8—181no—
415C2×C8D3×Dic312yes—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—184no—
421C22⋊C4—362no—
422C22⋊C4—362no—
423C42—184no—
424C42—181no—
425C42—181no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3#88211yescharacteristic
441C22×C3#88411yescharacteristic
442C22×C3#89311yescharacteristic
443C22×C3#91111yescharacteristic
444C22×C3D3×SD1611yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91411yescharacteristic
447C22×C3#91511yescharacteristic
448C22×C3#91611yescharacteristic
449C22×C3#91611yescharacteristic
450C22×C3#91811yescharacteristic
451C22×C3D4×Dic311yescharacteristic
452C22×C3#93711yescharacteristic
453C22×C3#93911yescharacteristic
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—81no—
458C2×D3—81no—
459C2×D3—81no—
460C2×D3—81no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—64no—
466C3×C4—122no—
467C3×C4—241no—
468C3×C4C4×D1211yescharacteristic
469C3×C4D3×C22⋊C411yescharacteristic
470C3×C4#89411yescharacteristic
471C3×C4#89511yescharacteristic
472C3×C4D4×Dic311yescharacteristic
473C3×C4#93511yescharacteristic
474C3×C4#93911yescharacteristic
475C3×C4C2×#21711yescharacteristic
476Dic3—24no—
477Dic3—42no—
478Dic3—62no—
479Dic3—62no—
480Dic3—81no—
481Dic3—122no—
482Dic3—122no—
483Dic3—121no—
484Dic3—121no—
485C32#188011yescharacteristic, complemented, Sylow
486C23—62no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23—121no—
493C23#380211yescharacteristic
494Q8—34no—
495Q8—62no—
496Q8—62no—
497Q8—62no—
498D4—62no—
499D4—62no—
500D4—121no—
501D4—121no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—92no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4#379511yescharacteristic
518C2×C4#379611yescharacteristic
519C2×C4D3×D1211yescharacteristic
520C2×C4C2×D3×Dic311yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4D3×#6711yescharacteristic
523C8—22no—
524C8—361no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—242no—
533C2×C3#466511yescharacteristic
534C2×C3#476211yescharacteristic
535C2×C3#478111yescharacteristic
536C2×C3#479811yescharacteristic
537C2×C3#480611yescharacteristic
538C2×C3#485211yescharacteristic
539C2×C3#488911yescharacteristic
540C2×C3Dic3×SD1611yescharacteristic
541C2×C3#516311yescharacteristic
542C2×C3#516411yescharacteristic
543C2×C3#516611yescharacteristic
544C2×C3#517011yescharacteristic
545C2×C3#517211yescharacteristic
546C2×C3#522011yescharacteristic
547D3—82no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—241no—
552C22—241no—
553C22—241no—
554C22—241no—
555C22#6379611yescharacteristic
556C22#6379811yescharacteristic
557C22#6380911yescharacteristic
558C22#6381111yescharacteristic
559C22#6388511yescharacteristic
560C22#6389811yescharacteristic
561C22#6392211yescharacteristic
562C4—64no—
563C4—122no—
564C4—182no—
565C4—241no—
566C4—361no—
567C4#6388411yescharacteristic
568C4#6388611yescharacteristic
569C4Dic3×D1211yescharacteristic
570C4D3×#21711yescharacteristic
571C3—21no—
572C3#6890911yescharacteristic, complemented
573C3#7204811yescharacteristic, complemented
574C2—242no—
575C2#1059077511yescharacteristic
576C2#1059077911yescharacteristic
577C2#1059079611yescharacteristic
578C2#1059082411yescharacteristic
579C2#1059087611yescharacteristic
580C2#1059096411yescharacteristic
581C2#1059137611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
4. C2×#63565C2semidirect
6. #10589416C2semidirect
7. C3×#4551C2semidirect
19. C2×C3×#204C4semidirect
39. #4551D3semidirect
112. C2×#204Dic3semidirect
138. C2×C3⋊Dic3SD16semidirect
155. C3×Dic6C22⋊C4semidirect
375. Dic6#217semidirect
485. C32#1880semidirect
572. C3#68909semidirect
573. C3#72048semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638432
#105913232
C2×#635652
C2×#635622
#105894162
C3×#45512
#720483
#689093