Finite Group Databasebeta

← #11793166

Subgroups — #11793166

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71679—31nomaximal
9#70175—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#938—22no—
17C3×#938—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22#63659—22no—
23C3×#832—22no—
24#63579—21no—
25#63575—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×#121—31no—
28C2×#938D311yescharacteristic
29C2×C3×#102—31no—
30C2×#832—31no—
31C2×#832—31no—
32C2×#832—61no—
33C2×#832D311yescharacteristic, complemented
34#5212—31no—
35C2×#830—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×#818—31no—
38#4987—31no—
39C2×#807—31no—
40#4529—31no—
41#4529—31no—
42C24×C32—21no—
43C23×C3×D3D411yescharacteristic
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×C3×#67—24no—
53C2×C3×#67—42no—
54C2×C3×#67—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
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—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#217—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
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—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C23×C3×C4—31no—
84C22×#67—21no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×#121—62no—
88C3×#121—62no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×#217—21no—
93C2×#217—61no—
94#938—22no—
95#938—22no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C22×C3⋊C8—31no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—61no—
105C22×C3⋊C8C2×D311yescharacteristic
106C3×#102—62no—
107#832—22no—
108#832—64no—
109#832—62no—
110#832—62no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#830—62no—
114(C2×D3)⋊C8—62no—
115#818—62no—
116#807—62no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3D812yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C3×#67—48no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—22no—
161C2×#121—31no—
162C2×#107—91no—
163C2×#102—31no—
164C2×#102—91no—
165C2×C22⋊C8—91no—
166#380—91no—
167#340—91no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—31no—
171C24×C3—41no—
172C23×D3#6711yescharacteristic
173C2×C3×D4—22no—
174C2×C3×D4—22no—
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—21no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—64no—
190C2×C3×D4—122no—
191C2×C3×D4—122no—
192C2×C3×D4D1212yes—
193C2×C3×D4#6712yes—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C2×#67—24no—
207C2×#67—42no—
208C2×#67—42no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—121no—
214C22×Dic3#6711yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C3×C8—32no—
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—64no—
229#217—24no—
230#217—122no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241C4⋊Dic3#6712yes—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
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
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32—81no—
260C22×C32—81no—
261C22×C32#12011yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32#12311yescharacteristic
264C22×C32C2×D811yescharacteristic
265C22×C32#13511yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C22×C32#13711yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4#12111yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12311yescharacteristic
278C32×C4#12411yescharacteristic
279C3⋊Dic3—81no—
280C3×Dic3—41no—
281C3×Dic3—42no—
282C3×Dic3—81no—
283C22×D4—61no—
284C22×D4D3211yescharacteristic
285C23×C4—31no—
286C22×C8—31no—
287C22×C8—91no—
288#121—62no—
289#121—62no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—91no—
293C2×C22⋊C4—61no—
294C2×C22⋊C4—181no—
295#107—182no—
296#102—62no—
297#102—182no—
298C22⋊C8—182no—
299#95—181no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
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—41no—
319C23×C3—61no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—81no—
326C23×C3—81no—
327C23×C3—81no—
328C23×C3—81no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3#21312yes—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—128no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4#23511yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4#23711yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382#67—48no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—21no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—122no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—241no—
400C2×Dic3—241no—
401C4×D3—41no—
402C4×D3—41no—
403C4×D3—41no—
404C4×D3—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C3⋊C8—122no—
408C3⋊C8—121no—
409C3⋊C8—121no—
410C2×C32—82no—
411C2×C32#39411yescharacteristic
412C2×C32#44711yescharacteristic
413C2×C32#45211yescharacteristic
414C2×C32#46611yescharacteristic
415C2×C32#46811yescharacteristic
416C2×C32#48011yescharacteristic
417C2×C32#48211yescharacteristic
418C3×D3—42no—
419C24—21no—
420C24—31no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—64no—
427C2×D4—122no—
428C2×D4—122no—
429C2×D4#62612yes—
430C22×C4—31no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441C2×C8—32no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—181no—
445C2×C8—181no—
446C2×C8—181no—
447C4⋊C4—32no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C4⋊C4—181no—
452C4⋊C4—181no—
453C22⋊C4—64no—
454C22⋊C4—362no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—44no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—82no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#88211yescharacteristic
491C22×C3#88311yescharacteristic
492C22×C3D3×D811yescharacteristic
493C22×C3#91211yescharacteristic
494C22×C3#91411yescharacteristic
495C22×C3#91511yescharacteristic
496C22×C3C2×#21311yescharacteristic
497C22×C3#93211yescharacteristic
498C22×C3#93511yescharacteristic
499C22×C3#93811yescharacteristic
500C22×C3#93911yescharacteristic
501C22×C3#95011yescharacteristic
502C22×C3#95111yescharacteristic
503C22×C3#95311yescharacteristic
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—41no—
508C2×D3—41no—
509C2×D3—41no—
510C2×D3—41no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4—241no—
518C3×C4#88511yescharacteristic
519C3×C4#88611yescharacteristic
520C3×C4#93011yescharacteristic
521C3×C4#93511yescharacteristic
522C3×C4#93611yescharacteristic
523C3×C4#93811yescharacteristic
524C3×C4#93911yescharacteristic
525C3×C4#93911yescharacteristic
526Dic3—42no—
527Dic3—41no—
528Dic3—81no—
529Dic3—242no—
530Dic3—241no—
531Dic3—241no—
532C32#203311yescharacteristic, complemented, Sylow
533C23—22no—
534C23—32no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—61no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23—61no—
546C23—61no—
547C23D3×#6711yescharacteristic
548D4—22no—
549D4—22no—
550D4—41no—
551D4—41no—
552D4—128no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—361no—
567C2×C4—361no—
568C2×C4—361no—
569C2×C4#380411yescharacteristic
570C2×C4#380511yescharacteristic
571C2×C4#380511yescharacteristic
572C2×C4C2×#62611yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4D3×#6711yescharacteristic
575C8—62no—
576C8—361no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—84no—
585C2×C3—82no—
586C2×C3—82no—
587C2×C3—122no—
588C2×C3#477311yescharacteristic
589C2×C3#477411yescharacteristic
590C2×C3#478311yescharacteristic
591C2×C3#478411yescharacteristic
592C2×C3#496111yescharacteristic
593C2×C3#503311yescharacteristic
594C2×C3#503511yescharacteristic
595C2×C3#503811yescharacteristic
596C2×C3#504211yescharacteristic
597C2×C3#515711yescharacteristic
598C2×C3#517411yescharacteristic
599C2×C3#521711yescharacteristic
600C2×C3#522211yescharacteristic
601C2×C3#523911yescharacteristic
602D3—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22D3×#21311yescharacteristic
618C22#6392911yescharacteristic
619C22#6393311yescharacteristic
620C22#6393411yescharacteristic
621C22#6396911yescharacteristic
622C22#6397011yescharacteristic
623C22#6397711yescharacteristic
624C4—122no—
625C4—121no—
626C4—241no—
627C4—721no—
628C4#6395911yescharacteristic
629C4#6396211yescharacteristic
630C4#6397011yescharacteristic
631C4#6397811yescharacteristic
632C3—21no—
633C3#7017511yescharacteristic, complemented
634C3#7167911yescharacteristic, complemented
635C2—82no—
636C2—122no—
637C2#1059141311yescharacteristic
638C2#1059142311yescharacteristic
639C2#1059144811yescharacteristic
640C2#1059146311yescharacteristic
641C2#1059149811yescharacteristic
642C2#1059150211yescharacteristic
643C2#1059170911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32#2033
LCSG ▷ C22×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×#63659C2semidirect
3. C2×C3×#832C2semidirect
4. #10591313C2semidirect
5. C2×#63575C2semidirect
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
7. #10589163C2semidirect
33. C2×#832D3semidirect
76. C2×C3×C3⋊C8D4semidirect
253. C2×C3⋊C8#67semidirect
532. C32#2033semidirect
633. C3#70175semidirect
634. C3#71679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×#636592
C2×C3×#8322
#105913132
C2×#635752
C2×(C2×D3)⋊(C3⋊C8)2
#105891632
#716793
#701753