Finite Group Databasebeta

← #11794020

Subgroups — #11794020

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#72040—31nomaximal
9#70212—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×#3757—21no—
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#213—22no—
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24C3×#832—22no—
25#63572—22no—
26#63563—22no—
27C22×C3×D8—31no—
28C22×#213D311yescharacteristic
29C2×C3×#102—31no—
30#5221—31no—
31#5221—31no—
32#5221—31no—
33#5221—61no—
34C2×#832—31no—
35C2×#832D311yescharacteristic, complemented
36C2×#821—31no—
37C2×Dic3⋊C8—31no—
38C2×Dic3⋊C8—31no—
39#4988—31no—
40#4551—31no—
41#4529—31no—
42C24×C32—21no—
43C23×C3×D3—21no—
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—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61#3757—42no—
62#3757—42no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C3×#213—28no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3—42no—
78#2054—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4—31no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C22×D12C2×D311yescharacteristic
84C2×C3×D8—62no—
85C2×C3×D8—62no—
86C2×C3×D8—62no—
87C22×C3×C8—31no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—31no—
90C2×#217—61no—
91C2×#217—61no—
92C2×#217—61no—
93C2×#217—61no—
94C2×#217—61no—
95C2×#217—61no—
96C2×#217—62no—
97C2×#217—62no—
98C2×#213—22no—
99C2×#213—22no—
100C2×#213—22no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4×Dic3—31no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C3×#102—62no—
113#832—22no—
114#832—62no—
115#821—62no—
116Dic3⋊C8—62no—
117Dic3⋊C8—62no—
118C23×C32—22no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
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—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—41no—
136C32×D4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3D812yescomplemented
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161C22×D8—31no—
162C2×C4⋊C8—91no—
163C2×#102—31no—
164C2×#102—91no—
165#390—91no—
166#390—91no—
167#340—91no—
168C24×C3—22no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—61no—
172C23×D3—21no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
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—22no—
185C2×C3×D4—32no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4#6712yes—
196C2×C3×D4#6712yes—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—62no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12#6712yes—
217C3×D8—68no—
218C2×C3×C8—32no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226#217—122no—
227#217—122no—
228#217—122no—
229#217—122no—
230#217—124no—
231#217—124no—
232#217—122no—
233#217—122no—
234#213—28no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4⋊Dic3—121no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8#6712yes—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—81no—
261C22×C32—81no—
262C22×C32—81no—
263C22×C32—81no—
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32C2×D811yescharacteristic
268C22×C32#13511yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32AGL(1,ℤ/8)11yescharacteristic
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#12011yescharacteristic
279C32×C4#12311yescharacteristic
280C32×C4#12311yescharacteristic
281C32×C4#12411yescharacteristic
282C3⋊Dic3—22no—
283C3⋊Dic3—41no—
284C3⋊Dic3—81no—
285C3×Dic3—81no—
286C22×D4—31no—
287C22×D4D3211yescharacteristic
288C2×D8—62no—
289C2×D8—62no—
290C2×D8—62no—
291C22×C8—31no—
292C22×C8—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—91no—
295C2×C22⋊C4—181no—
296C2×C22⋊C4—181no—
297C2×C22⋊C4—181no—
298C2×C22⋊C4—181no—
299C2×C42—91no—
300C4⋊C8—182no—
301#102—62no—
302#102—182no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—62no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3—121no—
329C23×C3—121no—
330C23×C3—121no—
331C23×C3—121no—
332C23×C3D3×D411yescharacteristic
333C23×C3D3×D411yescharacteristic
334C22×D3—22no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C22×D3—41no—
340C22×D3—41no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—42no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—41no—
350C3×D4—41no—
351C3×D4—41no—
352C3×D4—41no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—121no—
356C3×D4—121no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4#23711yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—62no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408D12—22no—
409D12—22no—
410D12—41no—
411D12—41no—
412C3×C8—62no—
413C3×C8—121no—
414C3⋊C8—22no—
415C3⋊C8—41no—
416C2×C32—82no—
417C2×C32#39411yescharacteristic
418C2×C32#45911yescharacteristic
419C2×C32#45911yescharacteristic
420C2×C32#46311yescharacteristic
421C2×C32#46311yescharacteristic
422C2×C32#46611yescharacteristic
423C2×C32#46911yescharacteristic
424C3×D3—82no—
425C24—21no—
426C24—61no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—32no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4#62512yes—
439C22×C4—61no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444D8—68no—
445C2×C8—32no—
446C2×C8—61no—
447C2×C8—61no—
448C2×C8—61no—
449C2×C8—61no—
450C2×C8—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C22⋊C4—362no—
456C22⋊C4—362no—
457C22⋊C4—362no—
458C22⋊C4—362no—
459C42—181no—
460C42—181no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—44no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—82no—
478C22×C3—82no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—241no—
493C22×C3—241no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3#88411yescharacteristic
497C22×C3#88411yescharacteristic
498C22×C3D3×D811yescharacteristic
499C22×C3D3×D811yescharacteristic
500C22×C3#91111yescharacteristic
501C22×C3#91111yescharacteristic
502C22×C3#91111yescharacteristic
503C22×C3#91211yescharacteristic
504C22×C3#91411yescharacteristic
505C22×C3#91611yescharacteristic
506C22×C3#93811yescharacteristic
507C22×C3#93911yescharacteristic
508C22×C3#93911yescharacteristic
509C22×C3#93911yescharacteristic
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—81no—
514C2×D3—81no—
515C2×D3—81no—
516C2×D3—81no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—241no—
522C3×C4#88311yescharacteristic
523C3×C4#88511yescharacteristic
524C3×C4#92911yescharacteristic
525C3×C4#93511yescharacteristic
526C3×C4#93511yescharacteristic
527C3×C4#93611yescharacteristic
528C3×C4#93711yescharacteristic
529C3×C4#95311yescharacteristic
530Dic3—62no—
531Dic3—62no—
532Dic3—81no—
533Dic3—122no—
534Dic3—122no—
535Dic3—121no—
536Dic3—121no—
537Dic3—242no—
538Dic3—241no—
539Dic3—241no—
540C32#205411yescharacteristic, complemented, Sylow
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—62no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23#381111yescharacteristic
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4—62no—
561D4—62no—
562D4—121no—
563D4—121no—
564C2×C4—92no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—181no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—361no—
574C2×C4—361no—
575C2×C4—361no—
576C2×C4#380411yescharacteristic
577C2×C4#380411yescharacteristic
578C2×C4#380511yescharacteristic
579C2×C4C2×#62511yescharacteristic
580C2×C4D3×#6711yescharacteristic
581C2×C4D3×#6711yescharacteristic
582C8—62no—
583C8—121no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—84no—
592C2×C3—82no—
593C2×C3—82no—
594C2×C3—242no—
595C2×C3#477511yescharacteristic
596C2×C3#478211yescharacteristic
597C2×C3#478611yescharacteristic
598C2×C3#478711yescharacteristic
599C2×C3#495911yescharacteristic
600C2×C3#515011yescharacteristic
601C2×C3#515011yescharacteristic
602C2×C3#515011yescharacteristic
603C2×C3#515311yescharacteristic
604C2×C3#515311yescharacteristic
605C2×C3#515711yescharacteristic
606C2×C3#515911yescharacteristic
607C2×C3#516511yescharacteristic
608C2×C3#522211yescharacteristic
609D3—82no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22—241no—
621C22—241no—
622C22—241no—
623C22—241no—
624C22#6392611yescharacteristic
625C22#6392711yescharacteristic
626C22#6393611yescharacteristic
627C22#6393711yescharacteristic
628C22#6395811yescharacteristic
629C22#6397111yescharacteristic
630C22#6398011yescharacteristic
631C4—182no—
632C4—241no—
633C4—361no—
634C4—721no—
635C4#6395911yescharacteristic
636C4#6396111yescharacteristic
637C4#6396911yescharacteristic
638C4#6397611yescharacteristic
639C3—21no—
640C3#7021211yescharacteristic, complemented
641C3#7204011yescharacteristic, complemented
642C2—82no—
643C2—242no—
644C2#1059143311yescharacteristic
645C2#1059143411yescharacteristic
646C2#1059145411yescharacteristic
647C2#1059145511yescharacteristic
648C2#1059147611yescharacteristic
649C2#1059148611yescharacteristic
650C2#1059170811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
hypercenterC22×D4D32
hypocenterC32#2054
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. #10592920C2semidirect
3. C2×C3×#832C2semidirect
4. #10591323C2semidirect
5. C2×#63572C2semidirect
6. C2×#63563C2semidirect
7. #10589164C2semidirect
35. C2×#832D3semidirect
151. C2×C3⋊Dic3D8semidirect
540. C32#2054semidirect
640. C3#70212semidirect
641. C3#72040semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
#105929202
C2×C3×#8322
#105913232
C2×#635722
C2×#635632
#105891642
#720403
#702123