Finite Group Databasebeta

← #11793169

Subgroups — #11793169

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71679—31nomaximal
9#69934—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×D12C2211yescharacteristic
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C3×#930—22no—
17C3×#930—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63658—21no—
23C3×#830—22no—
24#63575—22no—
25#63563—22no—
26#63563—22no—
27C2×C3×#121—31no—
28C2×#930D311yescharacteristic
29C2×C3×C22⋊C8—31no—
30C2×#832—31no—
31C2×#832—31no—
32#5212—31no—
33#5212—31no—
34#5212—61no—
35C2×#830D311yescharacteristic, complemented
36C2×#821—31no—
37C2×#821—31no—
38C2×#818—31no—
39C2×#807—31no—
40#4551—31no—
41#4529—31no—
42C24×C32D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C2×C3×#67—24no—
55C2×C3×#67—42no—
56C2×C3×#67—42no—
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12D412yes—
64#3757—42no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yescomplemented
78#2033—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C2×D311yescharacteristic
84C22×#67—21no—
85C22×D12C2×D311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C3×#121—62no—
89C3×#121—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×#217—62no—
93C2×#217—61no—
94C2×#217—61no—
95#930—22no—
96#930—22no—
97C2×(C2×D3)⋊C4—21no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107C3×C22⋊C8—62no—
108#832—62no—
109#832—62no—
110C3⋊#95—62no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#830—22no—
114#821—62no—
115#821—62no—
116#818—62no—
117#807—62no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32D812yes—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C3×#67—48no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×#121—31no—
163C2×#107—91no—
164C2×#102—91no—
165C2×#102—91no—
166C2×C22⋊C8—31no—
167#380—91no—
168#340—91no—
169C24×C3—21no—
170C24×C3—61no—
171C24×C3D1211yescharacteristic
172C24×C3#6711yescharacteristic
173C23×D3—21no—
174C2×C3×D4—32no—
175C2×C3×D4—64no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—41no—
203C22×C3×C4—61no—
204C22×C3×C4D1211yescharacteristic
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—24no—
209C2×#67—42no—
210C2×#67—42no—
211C22×Dic3—21no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12#6712yes—
224C2×C3×C8—32no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—64no—
233#217—124no—
234#217—122no—
235#217—122no—
236(C2×D3)⋊C4—24no—
237C4⋊Dic3—21no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4⋊Dic3—121no—
248C4⋊Dic3—121no—
249C4⋊Dic3—121no—
250C4⋊Dic3#6712yes—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8#6712yescomplemented
257C22×C32—22no—
258C22×C32—22no—
259C22×C32—22no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32#12011yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32C2×D811yescharacteristic
268C22×C32#13511yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32#13711yescharacteristic
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C32×C4—41no—
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12311yescharacteristic
282C32×C4#12411yescharacteristic
283C3⋊Dic3—81no—
284C3⋊Dic3—81no—
285C3×Dic3—42no—
286C22×D4—31no—
287C22×D4—61no—
288C23×C4D3211yescharacteristic
289C22×C8—31no—
290C22×C8—31no—
291#121—62no—
292#121—62no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C22⋊C4—61no—
297C2×C22⋊C4—181no—
298#107—182no—
299#102—182no—
300#102—182no—
301C22⋊C8—62no—
302#95—181no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—22no—
318C23×C3—21no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—62no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3—121no—
329C23×C3—121no—
330C23×C3D2412yes—
331C23×C3#21312yes—
332C23×C3C2×D1211yescharacteristic
333C23×C3C2×#6711yescharacteristic
334C22×D3—22no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C22×D3—41no—
340C22×D3—41no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—128no—
344C3×D4—121no—
345C3×D4—121no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
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—21no—
358C2×C3×C4—21no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—62no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4#23511yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4#23711yescharacteristic
381C2×C3×C4#23711yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4#23711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388#67—48no—
389C2×Dic3—22no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410D12—22no—
411D12—22no—
412D12—41no—
413D12—41no—
414C3×C8—62no—
415C3×C8—121no—
416C3⋊C8—22no—
417C3⋊C8—41no—
418C2×C32—42no—
419C2×C32#39411yescharacteristic
420C2×C32#44711yescharacteristic
421C2×C32#45211yescharacteristic
422C2×C32#46611yescharacteristic
423C2×C32#46811yescharacteristic
424C2×C32#48011yescharacteristic
425C2×C32#48211yescharacteristic
426C3×D3—82no—
427C24—61no—
428C24#62611yescharacteristic
429C2×D4—32no—
430C2×D4—64no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—122no—
437C2×D4—122no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—61no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4#62611yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C2×C8—32no—
450C2×C8—61no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8—61no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—64no—
462C22⋊C4—362no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3—241no—
497C22×C3—241no—
498C22×C3#88211yescharacteristic
499C22×C3#88611yescharacteristic
500C22×C3C2×D2411yescharacteristic
501C22×C3#90411yescharacteristic
502C22×C3#90811yescharacteristic
503C22×C3#90911yescharacteristic
504C22×C3#93011yescharacteristic
505C22×C3C2×#21311yescharacteristic
506C22×C3#93211yescharacteristic
507C22×C3#93511yescharacteristic
508C22×C3#93911yescharacteristic
509C22×C3#95011yescharacteristic
510C22×C3#95111yescharacteristic
511C22×C3#95311yescharacteristic
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—81no—
516C2×D3—81no—
517C2×D3—81no—
518C2×D3—81no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—122no—
527C3×C4#88311yescharacteristic
528C3×C4#88511yescharacteristic
529C3×C4#93511yescharacteristic
530C3×C4#93611yescharacteristic
531C3×C4#93811yescharacteristic
532C3×C4#93811yescharacteristic
533C3×C4#93911yescharacteristic
534C3×C4#93911yescharacteristic
535Dic3—42no—
536Dic3—242no—
537Dic3—242no—
538Dic3—241no—
539Dic3—241no—
540Dic3—241no—
541Dic3—241no—
542C32#203311yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—62no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23—121no—
556C23#371412yes—
557C23C2×#62611yescharacteristic
558D4—62no—
559D4—62no—
560D4—128no—
561D4—121no—
562D4—121no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—62no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—361no—
574C2×C4—361no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4—361no—
578C2×C4—361no—
579C2×C4#380411yescharacteristic
580C2×C4#380511yescharacteristic
581C2×C4#380511yescharacteristic
582C2×C4D3×#6711yescharacteristic
583C2×C4D3×#6711yescharacteristic
584C2×C4D3×#6711yescharacteristic
585C8—62no—
586C8—121no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—44no—
595C2×C3—42no—
596C2×C3—42no—
597C2×C3—242no—
598C2×C3#473211yescharacteristic
599C2×C3#473311yescharacteristic
600C2×C3#473611yescharacteristic
601C2×C3#473711yescharacteristic
602C2×C3#496111yescharacteristic
603C2×C3#503311yescharacteristic
604C2×C3#503511yescharacteristic
605C2×C3#503811yescharacteristic
606C2×C3#504211yescharacteristic
607C2×C3#511511yescharacteristic
608C2×C3#513411yescharacteristic
609C2×C3#521711yescharacteristic
610C2×C3#522211yescharacteristic
611C2×C3#523911yescharacteristic
612D3—82no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—122no—
621C22—122no—
622C22—122no—
623C22—241no—
624C22—241no—
625C22—241no—
626C22—241no—
627C22C2×#371411yescharacteristic
628C22#6382911yescharacteristic
629C22#6383011yescharacteristic
630C22#6383111yescharacteristic
631C22#6396211yescharacteristic
632C22#6397711yescharacteristic
633C22#6397811yescharacteristic
634C4—41no—
635C4—122no—
636C4—721no—
637C4—721no—
638C4#6395911yescharacteristic
639C4#6396911yescharacteristic
640C4#6397011yescharacteristic
641C4#6397011yescharacteristic
642C3—21no—
643C3#6993411yescharacteristic, complemented
644C3#7167911yescharacteristic, complemented
645C2—42no—
646C2—242no—
647C2#1059109311yescharacteristic
648C2#1059109411yescharacteristic
649C2#1059116211yescharacteristic
650C2#1059116411yescharacteristic
651C2#1059117311yescharacteristic
652C2#1059117611yescharacteristic
653C2#1059170911yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592911C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63575C2semidirect
5. C2×#63563C2semidirect
6. C2×#63563C2semidirect
7. #10589164C2semidirect
35. C2×#830D3semidirect
77. C2×C3×C3⋊C8D4semidirect
256. C2×C3⋊C8#67semidirect
542. C32#2033semidirect
643. C3#69934semidirect
644. C3#71679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
#105929112
C2×C3×#8302
C2×#635752
C2×#635632
#105891642
#716793
#699343