Finite Group Databasebeta

← #11788139

Subgroups — #11788139

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63908C211yesmaximal, characteristic
2C22×#3711C211yesmaximal, characteristic, complemented
3C3×#4987C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70203—31nomaximal
9#69517—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×#625—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20#63908—22no—
21#63908C414yescomplemented
22C2×#3711—22no—
23C2×#3711—22no—
24C2×#3711—22no—
25C3×C3⋊#95—21no—
26C3×#809—22no—
27#63562—22no—
28C2×#938—31no—
29C2×#930—31no—
30C22×#208—31no—
31C22×ΓL(1,𝔽25)—31no—
32C2×C3×#102—31no—
33C3×#380—31no—
34C2×#832—31no—
35#4987D311yescharacteristic, complemented
36C2×#809—31no—
37C2×#809D311yescharacteristic, complemented
38#4551—31no—
39#4529—31no—
40#4529—31no—
41#4529—31no—
42#4529—61no—
43C23×C3×D3—21no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
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×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3D412yes—
62C2×#625—24no—
63C2×#625—42no—
64C2×#625—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2×C412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yescomplemented
72C3×(C2×D3)⋊C4—42no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yescomplemented
78(C2×D3)⋊Dic3—24no—
79#3711—28no—
80#1895—91noSylow
81C22×C3×D4—31no—
82C23×C3×C4—31no—
83C22×#67—61no—
84C22×#67—61no—
85C22×D12C2×D311yescharacteristic
86C22×C4×D3C2×D311yescharacteristic
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C22⋊C4—61no—
93C2×#217—61no—
94#938—34no—
95#938—62no—
96#930—34no—
97#930—62no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×#208—62no—
105C2×#208—62no—
106C2×#208—62no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—62no—
112C2×ΓL(1,𝔽25)—62no—
113C2×ΓL(1,𝔽25)—62no—
114C3×#102—62no—
115C3×#95—61no—
116#832—62no—
117C3⋊#95—21no—
118#809—22no—
119#809—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—22no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3C22⋊C412yes—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3C22⋊C412yes—
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161#625—48no—
162C3⋊(C3⋊C8)—22no—
163C3×C3⋊C8—22no—
164C22×M16—91no—
165C2×#121—91no—
166C2×#102—31no—
167C2×#102—91no—
168#380—31no—
169#340—91no—
170#340—91no—
171C24×C3—31no—
172C24×C3—61no—
173C23×D3—21no—
174C23×D3#6711yescharacteristic
175C2×C3×D4—32no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—41no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—122no—
198C2×#67—122no—
199C2×#67—122no—
200C2×#67—122no—
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6711yescharacteristic
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C4×D312yes—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3C4×D312yes—
217C2×C4×D3D1212yes—
218C2×C3×C8—32no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—122no—
230#217—64no—
231(C2×D3)⋊C4—42no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241#208—68no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8—121no—
253C2×C3⋊C8#6712yescomplemented
254ΓL(1,𝔽25)—68no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C22×C32AGL(1,ℤ/8)11yescharacteristic
261C22×C32#13711yescharacteristic
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C2×C3×D3—41no—
268C2×C3×D3—41no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C32×C4—81no—
277C32×C4C4×D411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12011yescharacteristic
280C32×C4#12311yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—22no—
283C3×Dic3—81no—
284C22×D4—31no—
285C22×D4—181no—
286C23×C4—31no—
287C2×M16—182no—
288C2×M16—182no—
289C2×M16—182no—
290C22×C8—31no—
291C22×C8—91no—
292#121—94no—
293#121—182no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4D3211yescharacteristic
297C2×C22⋊C4—61no—
298C2×C22⋊C4—181no—
299#102—62no—
300#102—182no—
301#95—61no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—62no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—22no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3(C2×D3)⋊C412yes—
333C3×D4—62no—
334C3×D4—62no—
335C3×D4—121no—
336C3×D4—121no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—81no—
358C2×C3×C4—81no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23511yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4#23711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374#67—128no—
375#67—128no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—241no—
389C2×Dic3—241no—
390C2×Dic3(C2×D3)⋊C412yes—
391D12—22no—
392D12—22no—
393D12—41no—
394D12—41no—
395C4×D3—22no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—22no—
399C3×C8—62no—
400C3⋊C8—22no—
401C3⋊C8—62no—
402C3⋊C8—62no—
403C3⋊C8—122no—
404C2×C32#38611yescharacteristic
405C2×C32#41711yescharacteristic
406C2×C32#41811yescharacteristic
407C2×C32#46811yescharacteristic
408C2×C32#46811yescharacteristic
409C2×C32#46911yescharacteristic
410C2×C32#46911yescharacteristic
411C3×D3—42no—
412C3×D3—82no—
413C24—31no—
414C24—61no—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—184no—
422C2×D4—362no—
423C2×D4—362no—
424C22×C4—21no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—181no—
434C22×C4C2×D3211yescharacteristic
435M16—188no—
436C2×C8—32no—
437C2×C8—61no—
438C2×C8—61no—
439C2×C8—92no—
440C2×C8—181no—
441C2×C8—181no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C4⋊C4—92no—
447C4⋊C4—181no—
448C22⋊C4—122no—
449C22⋊C4—184no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—62no—
458C22×C3—62no—
459C22×C3—62no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3—121no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—241no—
468C22×C3—241no—
469C22×C3—241no—
470C22×C3—241no—
471C22×C3D3×C22⋊C411yescharacteristic
472C22×C3#88411yescharacteristic
473C22×C3#91111yescharacteristic
474C22×C3#91111yescharacteristic
475C22×C3#91411yescharacteristic
476C22×C3#91511yescharacteristic
477C22×C3C2×(C2×D3)⋊C411yescharacteristic
478C22×C3#93211yescharacteristic
479C22×C3#93811yescharacteristic
480C22×C3#93911yescharacteristic
481C22×C3#93911yescharacteristic
482C22×C3#94211yescharacteristic
483C22×C3#94911yescharacteristic
484C22×C3#94911yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—81no—
496C2×D3—81no—
497C2×D3—81no—
498C2×D3—81no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—62no—
504C3×C4—82no—
505C3×C4—81no—
506C3×C4—81no—
507C3×C4—241no—
508C3×C4#67⋊C411yescharacteristic
509C3×C4#67⋊C411yescharacteristic
510C3×C4#67⋊C411yescharacteristic
511C3×C4#88211yescharacteristic
512C3×C4#88311yescharacteristic
513C3×C4#88611yescharacteristic
514C3×C4C4×#6711yescharacteristic
515C3×C4#93711yescharacteristic
516Dic3—22no—
517Dic3—81no—
518Dic3—122no—
519Dic3—122no—
520Dic3—242no—
521C32#189511yescharacteristic, complemented, Sylow
522C23—32no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—62no—
530C23—121no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23D3×#6711yescharacteristic
537D4—62no—
538D4—62no—
539D4—121no—
540D4—121no—
541D4—368no—
542C2×C4—32no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—121no—
553C2×C4—121no—
554C2×C4—121no—
555C2×C4—182no—
556C2×C4—361no—
557C2×C4—361no—
558C2×C4#379511yescharacteristic
559C2×C4C4×D3211yescharacteristic
560C2×C4D3×D1211yescharacteristic
561C2×C4#380211yescharacteristic
562C2×C4#380511yescharacteristic
563C2×C4D3×#6711yescharacteristic
564C8—62no—
565C8—182no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—122no—
574C2×C3—242no—
575C2×C3#477011yescharacteristic
576C2×C3#477111yescharacteristic
577C2×C3#478011yescharacteristic
578C2×C3#478211yescharacteristic
579C2×C3#495611yescharacteristic
580C2×C3#495811yescharacteristic
581C2×C3#496611yescharacteristic
582C2×C3#500111yescharacteristic
583C2×C3#503911yescharacteristic
584C2×C3#503911yescharacteristic
585C2×C3#504911yescharacteristic
586C2×C3#504911yescharacteristic
587C2×C3#515911yescharacteristic
588C2×C3#517411yescharacteristic
589D3—42no—
590D3—82no—
591C22—62no—
592C22—62no—
593C22—62no—
594C22—121no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—241no—
602C22—241no—
603C22—241no—
604C22—241no—
605C22#6388511yescharacteristic
606C22D3×(C2×D3)⋊C411yescharacteristic
607C22#6392511yescharacteristic
608C22#6393211yescharacteristic
609C22#6393911yescharacteristic
610C22#6394611yescharacteristic
611C22#6397011yescharacteristic
612C4—62no—
613C4—81no—
614C4—241no—
615C4—362no—
616C4#6387911yescharacteristic
617C4#6389111yescharacteristic
618C4#6390211yescharacteristic
619C4#6392211yescharacteristic
620C3—21no—
621C3#6951711yescharacteristic, complemented
622C3#7020311yescharacteristic, complemented
623C2—122no—
624C2—242no—
625C2#1059050311yescharacteristic
626C2#1059050411yescharacteristic
627C2#1059059211yescharacteristic
628C2#1059060711yescharacteristic
629C2#1059136311yescharacteristic
630C2#1059145111yescharacteristic
631C2#1059158711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1895
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
2. C22×#3711C2semidirect
3. C3×#4987C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63562C2semidirect
6. #10589395C2semidirect
7. #10589164C2semidirect
21. #63908C4semidirect
35. #4987D3semidirect
37. C2×#809D3semidirect
71. C2×C3⋊(C3⋊C8)D4semidirect
77. C2×C3×C3⋊C8D4semidirect
253. C2×C3⋊C8#67semidirect
521. C32#1895semidirect
621. C3#69517semidirect
622. C3#70203semidirect

Maximal subgroups

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

subgroupindex
C2×#639082
C22×#37112
C3×#49872
C2×C3×#8092
C2×#635622
#105893952
#105891642
#702033
#695173