Finite Group Databasebeta

← #11793176

Subgroups — #11793176

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×C3×#807C211yesmaximal, characteristic, complemented
3#10591313C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#71679—31nomaximal
9#70634—31nomaximal
10C22×C3×D12—21no—
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
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
19C3×#895—22no—
20C3×#895—22no—
21C2×(C2×D3)⋊Dic3—21no—
22C3×#807—22no—
23#63579—21no—
24#63563—22no—
25#63562—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×#121—31no—
28C2×#895D311yescharacteristic
29C2×C3×#107—31no—
30C2×#832—31no—
31C2×#832—31no—
32#5212—31no—
33C2×#830—31no—
34C2×#821—31no—
35C2×(C2×D3)⋊C8—31no—
36#4987—31no—
37C2×#809—31no—
38C2×#807D311yescharacteristic, complemented
39#4529—31no—
40#4529—31no—
41#4529—61no—
42C23×C3×D3—21no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—24no—
54C2×C3×D12—21no—
55C2×C3×D12—42no—
56C2×C3×D12—42no—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4D412yes—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77(C2×D3)⋊Dic3—42no—
78#2033—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—31no—
82C22×D12—21no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3C2×D311yescharacteristic
85C22×C3×C8—31no—
86C3×#121—62no—
87C3×#121—62no—
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—
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104#895—22no—
105#895—22no—
106C3×#107—62no—
107#832—62no—
108#832—62no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#830—62no—
112#821—62no—
113(C2×D3)⋊C8—62no—
114#809—62no—
115#807—22no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3D812yes—
131C2×C32×C4—22no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—48no—
152C3×D12—41no—
153C3×D12—41no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—22no—
160C2×#121—31no—
161C2×#107—31no—
162C2×#102—91no—
163C2×#102—91no—
164C2×C22⋊C8—91no—
165#380—91no—
166#340—91no—
167C24×C3—31no—
168C24×C3—61no—
169C23×D3—21no—
170C23×D3#6711yescharacteristic
171C2×C3×D4—32no—
172C2×C3×D4—64no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—122no—
179C2×C3×D4—122no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—41no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3#6711yescharacteristic
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—24no—
204C2×D12—21no—
205C2×D12—42no—
206C2×D12—42no—
207C2×D12#6712yes—
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C3×C8—32no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4#6712yes—
224C3×C4⋊C4#6712yes—
225C3×C22⋊C4—64no—
226#217—122no—
227(C2×D3)⋊C4—24no—
228(C2×D3)⋊C4—122no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3—62no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—121no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—121no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8D1212yescomplemented
249C22×C32#12011yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C22×C32C2×D811yescharacteristic
253C22×C32#13511yescharacteristic
254C22×C32AGL(1,ℤ/8)11yescharacteristic
255C22×C32#13711yescharacteristic
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—81no—
267C2×C3×D3—81no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C32×C4—42no—
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12311yescharacteristic
274C32×C4#12411yescharacteristic
275C3⋊Dic3—81no—
276C3×Dic3—41no—
277C3×Dic3—81no—
278C22×D4—31no—
279C22×D4—61no—
280C23×C4—31no—
281C22×C8—31no—
282C22×C8—91no—
283#121—62no—
284#121—62no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4D3211yescharacteristic
288C2×C22⋊C4—61no—
289C2×C22⋊C4—181no—
290#107—62no—
291#102—182no—
292#102—182no—
293C22⋊C8—182no—
294#95—181no—
295C23×C3—21no—
296C23×C3—32no—
297C23×C3—61no—
298C23×C3—61no—
299C23×C3—61no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—62no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×#6711yescharacteristic
312C22×D3—21no—
313C22×D3—21no—
314C22×D3—21no—
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—41no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3#21312yes—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—128no—
329C3×D4—121no—
330C3×D4—121no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—81no—
348C2×C3×C4—81no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23911yescharacteristic
364C2×C3×C4#23911yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—122no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—241no—
382C2×Dic3—241no—
383D12—22no—
384D12—22no—
385D12—48no—
386D12—41no—
387D12—41no—
388C4×D3—41no—
389C4×D3—41no—
390C4×D3—41no—
391C4×D3—41no—
392C3×C8—62no—
393C3⋊C8—22no—
394C3⋊C8—122no—
395C3⋊C8—121no—
396C3⋊C8—121no—
397C2×C32#39411yescharacteristic
398C2×C32#44711yescharacteristic
399C2×C32#45211yescharacteristic
400C2×C32#46611yescharacteristic
401C2×C32#46811yescharacteristic
402C2×C32#48011yescharacteristic
403C2×C32#48211yescharacteristic
404C3×D3—42no—
405C3×D3—82no—
406C24—31no—
407C24—61no—
408C2×D4—32no—
409C2×D4—64no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—122no—
416C2×D4—122no—
417C22×C4—21no—
418C22×C4—31no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—181no—
432C2×C8—181no—
433C2×C8—181no—
434C4⋊C4—21no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4#62512yes—
440C22⋊C4—64no—
441C22⋊C4—362no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3—241no—
460C22×C3—241no—
461C22×C3—241no—
462C22×C3—241no—
463C22×C3#89411yescharacteristic
464C22×C3#89511yescharacteristic
465C22×C3D3×D811yescharacteristic
466C22×C3#91111yescharacteristic
467C22×C3#91811yescharacteristic
468C22×C3#91911yescharacteristic
469C22×C3C2×#21311yescharacteristic
470C22×C3#93211yescharacteristic
471C22×C3#93511yescharacteristic
472C22×C3#93711yescharacteristic
473C22×C3#93911yescharacteristic
474C22×C3#95011yescharacteristic
475C22×C3#95111yescharacteristic
476C22×C3#95311yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—41no—
481C2×D3—41no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—81no—
488C2×D3—81no—
489C2×D3—81no—
490C2×D3—81no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—82no—
498C3×C4—121no—
499C3×C4—241no—
500C3×C4#89411yescharacteristic
501C3×C4#89511yescharacteristic
502C3×C4#93011yescharacteristic
503C3×C4#93511yescharacteristic
504C3×C4#93611yescharacteristic
505C3×C4#93811yescharacteristic
506C3×C4#93911yescharacteristic
507C3×C4#94711yescharacteristic
508Dic3—41no—
509Dic3—81no—
510Dic3—242no—
511Dic3—241no—
512Dic3—241no—
513C32#203311yescharacteristic, complemented, Sylow
514C23—32no—
515C23—61no—
516C23—61no—
517C23—61no—
518C23—61no—
519C23—61no—
520C23—61no—
521C23—62no—
522C23—121no—
523C23—121no—
524C23—121no—
525C23—121no—
526C23—121no—
527C23—121no—
528C23D3×#6711yescharacteristic
529D4—62no—
530D4—62no—
531D4—128no—
532D4—121no—
533D4—121no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—361no—
548C2×C4—361no—
549C2×C4—361no—
550C2×C4#379511yescharacteristic
551C2×C4#379611yescharacteristic
552C2×C4#379611yescharacteristic
553C2×C4D3×D1211yescharacteristic
554C2×C4C2×#62511yescharacteristic
555C2×C4D3×#6711yescharacteristic
556C8—62no—
557C8—361no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—122no—
566C2×C3—242no—
567C2×C3#488211yescharacteristic
568C2×C3#488311yescharacteristic
569C2×C3#488511yescharacteristic
570C2×C3#488611yescharacteristic
571C2×C3#499111yescharacteristic
572C2×C3#503311yescharacteristic
573C2×C3#503511yescharacteristic
574C2×C3#503811yescharacteristic
575C2×C3#504211yescharacteristic
576C2×C3#515611yescharacteristic
577C2×C3#518711yescharacteristic
578C2×C3#521711yescharacteristic
579C2×C3#522211yescharacteristic
580C2×C3#523911yescharacteristic
581D3—42no—
582D3—82no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—121no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—122no—
591C22—122no—
592C22—122no—
593C22—241no—
594C22—241no—
595C22—241no—
596C22—241no—
597C22#6388411yescharacteristic
598C22#6388611yescharacteristic
599C22D3×#21311yescharacteristic
600C22#6393211yescharacteristic
601C22#6394311yescharacteristic
602C22#6394911yescharacteristic
603C22#6397611yescharacteristic
604C4—42no—
605C4—121no—
606C4—241no—
607C4—721no—
608C4#6386311yescharacteristic
609C4#6388411yescharacteristic
610C4#6388611yescharacteristic
611C4#6390811yescharacteristic
612C3—21no—
613C3#7063411yescharacteristic, complemented
614C3#7167911yescharacteristic, complemented
615C2—122no—
616C2—242no—
617C2#1059043811yescharacteristic
618C2#1059044611yescharacteristic
619C2#1059057611yescharacteristic
620C2#1059058811yescharacteristic
621C2#1059130011yescharacteristic
622C2#1059144711yescharacteristic
623C2#1059159711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2033
LCSG ▷ C22×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. C2×C3×#807C2semidirect
3. #10591313C2semidirect
4. C2×#63563C2semidirect
5. C2×#63562C2semidirect
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
7. #10589395C2semidirect
38. C2×#807D3semidirect
76. C2×C3×C3⋊C8D4semidirect
248. C2×C3⋊C8D12semidirect
513. C32#2033semidirect
613. C3#70634semidirect
614. C3#71679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8072
#105913132
C2×#635632
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
#105893952
#716793
#706343