Finite Group Databasebeta

← #11787450

Subgroups — #11787450

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C22×#3715C211yesmaximal, characteristic
3C3×#4973C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×#63566C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70171—31nomaximal
9#69687—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19Dic3×D12—22no—
20Dic3×D12—22no—
21C2×#3715—22no—
22C2×#3715—22no—
23C2×#3715C414yescomplemented
24C3×C3⋊#95—21no—
25C3×C3⋊#95—21no—
26C3×#809—22no—
27#63566—22no—
28C22×#215—31no—
29C2×D4×Dic3—31no—
30C22×#214—31no—
31C2×C4×D12—31no—
32C2×C3×#102—31no—
33C3×#391—31no—
34C2×#835—31no—
35C2×#816—31no—
36#4973D311yescharacteristic, complemented
37C2×#809D311yescharacteristic
38#4550—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4524—31no—
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12C2×C412yes—
54C2×C3×D12D412yes—
55C2×C3×D12D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)C2×C412yescomplemented
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77(C2×D3)⋊Dic3—24no—
78#3715—28no—
79#1877—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C23×Dic3—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—61no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C42—31no—
91C2×#217—61no—
92C2×#215—34no—
93C2×#215—62no—
94C2×#215—62no—
95D4×Dic3—62no—
96D4×Dic3—62no—
97C2×#214—34no—
98C2×#214—62no—
99C2×#214—62no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C4×D12—62no—
110C4×D12—62no—
111C3×#102—62no—
112C3×#95—61no—
113C3×#95—61no—
114#835—62no—
115C3⋊#95—21no—
116C3⋊#95—21no—
117#816—62no—
118#809—22no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12C22⋊C414yes—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156D3×Dic3—48no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—41no—
159C22×SD16—91no—
160C2×C4×D4—91no—
161C2×#103—91no—
162C2×#102—31no—
163#391—31no—
164#340—91no—
165#336—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—32no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×D4—32no—
175C2×C3×D4—32no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—41no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—64no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3—122no—
195C22×Dic3—122no—
196C22×Dic3#6711yescharacteristic
197C22×Dic3#6711yescharacteristic
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12C4×D312yes—
202C2×D12D1212yes—
203C2×D12#6712yes—
204C2×C4×D3—64no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6C4×D312yescomplemented
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—41no—
222C3×C42—61no—
223C3×C42—61no—
224#217—64no—
225#215—68no—
226#214—68no—
227(C2×D3)⋊C4—64no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—62no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—121no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—121no—
247C2×C3⋊C8—121no—
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—24no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C32×C4—81no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12311yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—41no—
271C22×Q8—31no—
272C22×D4—31no—
273C23×C4—181no—
274C2×SD16—94no—
275C2×SD16—182no—
276C2×SD16—182no—
277C22×C8—31no—
278C22×C8—91no—
279C4×D4—182no—
280C4×D4—182no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4D3211yescharacteristic
283C2×C22⋊C4—181no—
284C2×C42—31no—
285#103—182no—
286#102—62no—
287#95—61no—
288#95—61no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3D3×D411yescharacteristic
298C23×C3C2×#6711yescharacteristic
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—22no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C22×D3—41no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×Q8—121no—
310C3×D4—34no—
311C3×D4—62no—
312C3×D4—62no—
313C3×D4—62no—
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—32no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—62no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—81no—
335C2×C3×C4—81no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—128no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—241no—
367C2×Dic3—241no—
368C2×Dic3#21512yescomplemented
369D12—22no—
370D12—22no—
371D12—22no—
372D12(C2×D3)⋊C414yes—
373C4×D3—128no—
374Dic6—22no—
375Dic6—22no—
376Dic6—41no—
377Dic6—41no—
378C3×C8—121no—
379C3⋊C8—41no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C3⋊C8—122no—
383C2×C32#38611yescharacteristic
384C2×C32C4×SD1611yescharacteristic
385C2×C32#44011yescharacteristic
386C2×C32#45011yescharacteristic
387C2×C32#45211yescharacteristic
388C2×C32#46111yescharacteristic
389C2×C32#46311yescharacteristic
390C3×D3—44no—
391C24—61no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×D4—32no—
399C2×D4—32no—
400C2×D4—32no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C22×C4—21no—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—61no—
408C22×C4—184no—
409C22×C4—181no—
410C22×C4—362no—
411C22×C4—362no—
412C22×C4C2×D3211yescharacteristic
413SD16—188no—
414C2×C8—61no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—92no—
418C2×C8—181no—
419C2×C8—181no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—92no—
423C4⋊C4—181no—
424C22⋊C4—184no—
425C42—61no—
426C42—61no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—64no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3#67⋊C411yescharacteristic
442C22×C3#88211yescharacteristic
443C22×C3#91111yescharacteristic
444C22×C3#91211yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91511yescharacteristic
447C22×C3C4×#6711yescharacteristic
448C22×C3#93711yescharacteristic
449C22×C3#93811yescharacteristic
450C22×C3#93911yescharacteristic
451C22×C3C2×#21511yescharacteristic
452C22×C3#94211yescharacteristic
453C22×C3#94911yescharacteristic
454C22×C3#95011yescharacteristic
455C2×D3—24no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—42no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—62no—
467C3×C4—82no—
468C3×C4—81no—
469C3×C4—81no—
470C3×C4—122no—
471C3×C4—121no—
472C3×C4D3×C22⋊C411yescharacteristic
473C3×C4#67⋊C411yescharacteristic
474C3×C4#67⋊C411yescharacteristic
475C3×C4#88311yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4#88611yescharacteristic
478C3×C4C2×(C2×D3)⋊C411yescharacteristic
479C3×C4#93911yescharacteristic
480Dic3—22no—
481Dic3—42no—
482Dic3—41no—
483Dic3—122no—
484Dic3—122no—
485Dic3—242no—
486C32#187711yescharacteristic, complemented, Sylow
487C23—62no—
488C23—62no—
489C23—62no—
490C23—121no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23D3×#6711yescharacteristic
495Q8—62no—
496Q8—62no—
497Q8—121no—
498Q8—121no—
499D4—34no—
500D4—62no—
501D4—62no—
502D4—62no—
503C2×C4—32no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—182no—
516C2×C4—368no—
517C2×C4—361no—
518C2×C4—361no—
519C2×C4#379511yescharacteristic
520C2×C4C4×D3211yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4#380211yescharacteristic
523C2×C4#380511yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C8—121no—
526C8—182no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—124no—
535C2×C3#475711yescharacteristic
536C2×C3#475811yescharacteristic
537C2×C3#477611yescharacteristic
538C2×C3#478311yescharacteristic
539C2×C3#495611yescharacteristic
540C2×C3#495811yescharacteristic
541C2×C3C4×#21511yescharacteristic
542C2×C3#502611yescharacteristic
543C2×C3#504611yescharacteristic
544C2×C3#504711yescharacteristic
545C2×C3#505711yescharacteristic
546C2×C3#508311yescharacteristic
547C2×C3#515311yescharacteristic
548C2×C3#516211yescharacteristic
549D3—44no—
550C22—64no—
551C22—122no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22#6387911yescharacteristic
558C22#6392211yescharacteristic
559C22#6392511yescharacteristic
560C22#6393311yescharacteristic
561C22D3×#21511yescharacteristic
562C22#6394611yescharacteristic
563C22#6397011yescharacteristic
564C4—62no—
565C4—81no—
566C4—122no—
567C4—121no—
568C4—362no—
569C4#6388511yescharacteristic
570C4#6389111yescharacteristic
571C4#6390211yescharacteristic
572C4D3×(C2×D3)⋊C411yescharacteristic
573C3—21no—
574C3#6968711yescharacteristic, complemented
575C3#7017111yescharacteristic, complemented
576C2—124no—
577C2#1059045311yescharacteristic
578C2#1059045411yescharacteristic
579C2#1059059611yescharacteristic
580C2#1059061411yescharacteristic
581C2#1059136311yescharacteristic
582C2#1059143111yescharacteristic
583C2#1059156411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4973C2semidirect
5. C2×#63566C2semidirect
6. #10589395C2semidirect
7. #10589155C2semidirect
23. C2×#3715C4semidirect
36. #4973D3semidirect
61. C2×C3×Dic6C2×C4semidirect
71. C2×C3⋊(C3⋊C8)C2×C4semidirect
147. C2×C3×Dic3SD16semidirect
212. C2×Dic6C4×D3semidirect
368. C2×Dic3#215semidirect
486. C32#1877semidirect
574. C3#69687semidirect
575. C3#70171semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C22×#37152
C3×#49732
C2×C3×#8092
C2×#635662
#105893952
#105891552
#701713
#696873