Finite Group Databasebeta

← #11794019

Subgroups — #11794019

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#72040—31nomaximal
9#69650—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C2×C3×#213—22no—
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63659—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63562—22no—
27C22×C3×D8—31no—
28C22×#213D311yescharacteristic
29C3×#390—31no—
30#5221—31no—
31#5221D311yescharacteristic, complemented
32C2×#832—31no—
33C2×#832—31no—
34C2×#832—31no—
35C2×#832—61no—
36C2×Dic3⋊C8—31no—
37C2×#809—31no—
38#4939—31no—
39C2×C4⋊(C3⋊C8)—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×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—42no—
67C3×#217—42no—
68C3×#213—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—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—
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C42—31no—
92C2×#217—21no—
93C2×#217—21no—
94C2×#217—61no—
95C2×#217—61no—
96C2×#213—22no—
97C2×#213—22no—
98C2×#213—22no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#832—62no—
111#832—64no—
112#832—62no—
113#832—62no—
114Dic3⋊C8—62no—
115#809—62no—
116C4⋊(C3⋊C8)—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—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
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—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
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×Dic3D812yescomplemented
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—41no—
157C3×D12—41no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—22no—
160C22×D8—31no—
161C2×C4⋊C8—91no—
162C2×#102—91no—
163C2×#102—91no—
164#390—31no—
165#390—91no—
166#340—91no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×D4—22no—
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—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4D1212yes—
195C2×C3×D4#6712yes—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—121no—
206C22×Dic3#6711yescharacteristic
207C22×Dic3#6711yescharacteristic
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12#6712yes—
214C3×D8—68no—
215C2×C3×C8—32no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C22⋊C4—122no—
221C3×C22⋊C4—122no—
222C3×C42—61no—
223C3×C42—61no—
224#217—42no—
225#217—42no—
226#217—122no—
227#217—122no—
228#213—28no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—121no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8#6712yes—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—81no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32—81no—
260C22×C32#12111yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32C2×D811yescharacteristic
264C22×C32#13511yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C32×C4#12011yescharacteristic
275C32×C4#12311yescharacteristic
276C32×C4#12311yescharacteristic
277C32×C4#12411yescharacteristic
278C3⋊Dic3—81no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—81no—
282C22×D4—31no—
283C22×D4D3211yescharacteristic
284C2×D8—62no—
285C2×D8—62no—
286C2×D8—62no—
287C22×C8—31no—
288C22×C8—91no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—91no—
291C2×C22⋊C4—61no—
292C2×C22⋊C4—61no—
293C2×C22⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C42—31no—
296C4⋊C8—182no—
297#102—182no—
298#102—182no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—21no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—41no—
306C23×C3—41no—
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—62no—
318C23×C3—81no—
319C23×C3—81no—
320C23×C3—81no—
321C23×C3—81no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×#6711yescharacteristic
330C22×D3—22no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C3×D4—24no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—121no—
352C3×D4—121no—
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—32no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4#23511yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23711yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—241no—
396C2×Dic3—241no—
397C2×Dic3#21312yescomplemented
398D12—22no—
399D12—22no—
400D12—41no—
401D12—41no—
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—122no—
405C3⋊C8—121no—
406C3⋊C8—121no—
407C2×C32—82no—
408C2×C32#39411yescharacteristic
409C2×C32#45911yescharacteristic
410C2×C32#45911yescharacteristic
411C2×C32#46311yescharacteristic
412C2×C32#46311yescharacteristic
413C2×C32#46611yescharacteristic
414C2×C32#46911yescharacteristic
415C3×D3—82no—
416C24—21no—
417C24—61no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4#62612yes—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—181no—
434C22×C4C2×D3211yescharacteristic
435D8—68no—
436C2×C8—32no—
437C2×C8—61no—
438C2×C8—61no—
439C2×C8—181no—
440C2×C8—181no—
441C2×C8—181no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C22⋊C4—122no—
447C22⋊C4—122no—
448C22⋊C4—362no—
449C22⋊C4—362no—
450C42—61no—
451C42—61no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—44no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—82no—
471C22×C3—82no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3—81no—
475C22×C3—81no—
476C22×C3—81no—
477C22×C3—81no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3—122no—
483C22×C3—241no—
484C22×C3—241no—
485C22×C3—241no—
486C22×C3—241no—
487C22×C3D3×D811yescharacteristic
488C22×C3#91111yescharacteristic
489C22×C3#91111yescharacteristic
490C22×C3#91211yescharacteristic
491C22×C3#93011yescharacteristic
492C22×C3C2×#21311yescharacteristic
493C22×C3#93211yescharacteristic
494C22×C3#93811yescharacteristic
495C22×C3#93811yescharacteristic
496C22×C3#93911yescharacteristic
497C22×C3#93911yescharacteristic
498C22×C3#93911yescharacteristic
499C22×C3#94911yescharacteristic
500C22×C3#95011yescharacteristic
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—81no—
505C2×D3—81no—
506C2×D3—81no—
507C2×D3—81no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—62no—
513C3×C4—121no—
514C3×C4—241no—
515C3×C4#88211yescharacteristic
516C3×C4#88311yescharacteristic
517C3×C4#88511yescharacteristic
518C3×C4#88611yescharacteristic
519C3×C4#93511yescharacteristic
520C3×C4#93511yescharacteristic
521C3×C4#93611yescharacteristic
522C3×C4#95311yescharacteristic
523Dic3—22no—
524Dic3—41no—
525Dic3—81no—
526Dic3—242no—
527Dic3—241no—
528Dic3—241no—
529C32#205411yescharacteristic, complemented, Sylow
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—62no—
538C23—121no—
539C23—121no—
540C23—121no—
541C23—121no—
542C23—121no—
543C23—121no—
544C23D3×#6711yescharacteristic
545D4—22no—
546D4—22no—
547D4—41no—
548D4—41no—
549D4—62no—
550D4—62no—
551D4—121no—
552D4—121no—
553C2×C4—32no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—361no—
563C2×C4—361no—
564C2×C4—361no—
565C2×C4#380411yescharacteristic
566C2×C4#380511yescharacteristic
567C2×C4#380511yescharacteristic
568C2×C4C2×#62611yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C8—62no—
572C8—361no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—84no—
581C2×C3—82no—
582C2×C3—82no—
583C2×C3—242no—
584C2×C3#496111yescharacteristic
585C2×C3#501511yescharacteristic
586C2×C3#501611yescharacteristic
587C2×C3#503811yescharacteristic
588C2×C3#503911yescharacteristic
589C2×C3#505711yescharacteristic
590C2×C3#507211yescharacteristic
591C2×C3#515011yescharacteristic
592C2×C3#515011yescharacteristic
593C2×C3#515311yescharacteristic
594C2×C3#515311yescharacteristic
595C2×C3#515711yescharacteristic
596C2×C3#515911yescharacteristic
597C2×C3#522211yescharacteristic
598D3—82no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—241no—
610C22—241no—
611C22—241no—
612C22—241no—
613C22D3×#21311yescharacteristic
614C22#6392511yescharacteristic
615C22#6393211yescharacteristic
616C22#6393311yescharacteristic
617C22#6397011yescharacteristic
618C22#6397011yescharacteristic
619C22#6397811yescharacteristic
620C4—62no—
621C4—121no—
622C4—241no—
623C4—721no—
624C4#6395911yescharacteristic
625C4#6396211yescharacteristic
626C4#6396911yescharacteristic
627C4#6397711yescharacteristic
628C3—21no—
629C3#6965011yescharacteristic, complemented
630C3#7204011yescharacteristic, complemented
631C2—82no—
632C2—242no—
633C2#1059142811yescharacteristic
634C2#1059143111yescharacteristic
635C2#1059145111yescharacteristic
636C2#1059146811yescharacteristic
637C2#1059148111yescharacteristic
638C2#1059149811yescharacteristic
639C2#1059170911yescharacteristic
subgroupG/H
centerC23D3×#67
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. C2×#63659C2semidirect
3. C3×#5221C2semidirect
4. #10591318C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63562C2semidirect
7. #10589164C2semidirect
31. #5221D3semidirect
153. C2×C3×Dic3D8semidirect
397. C2×Dic3#213semidirect
529. C32#2054semidirect
629. C3#69650semidirect
630. 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
C2×#636592
C3×#52212
#105913182
C2×Dic3⋊(C3⋊C8)2
C2×#635622
#105891642
#720403
#696503