Finite Group Databasebeta

← #11794028

Subgroups — #11794028

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3713C211yesmaximal, characteristic
2C3×#4988C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70212—31nomaximal
9#69650—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×#3713—22no—
22C2×#3713—22no—
23C2×#3713—22no—
24C3×#809—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63563—22no—
27C22×#213—31no—
28C22×#213—31no—
29C2×C3×#102—31no—
30C3×#390—31no—
31#5221—31no—
32C2×#832—31no—
33C2×#821—31no—
34C2×Dic3⋊C8—31no—
35#4988D311yescharacteristic, complemented
36C2×#809D311yescharacteristic, complemented
37#4939—31no—
38C2×C4⋊(C3⋊C8)—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42C23×C3×D3—21no—
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12D412yes—
60C2×C3×D12D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77#3713—28no—
78#2054—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C22×D12C2×D311yescharacteristic
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—31no—
90C2×#217—61no—
91C2×#217—61no—
92C2×#213—62no—
93C2×#213—62no—
94C2×#213—62no—
95C2×#213—62no—
96C2×#213—62no—
97C2×#213—62no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C3×#102—62no—
111#832—62no—
112#821—62no—
113Dic3⋊C8—62no—
114#809—22no—
115C4⋊(C3⋊C8)—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
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×D3—41no—
131C2×C32×C4—41no—
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—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3D812yescomplemented
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×D12—41no—
156C3×D12—41no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—41no—
159C22×D8—91no—
160C2×C4⋊C8—91no—
161C2×#102—31no—
162C2×#102—91no—
163#390—31no—
164#390—91no—
165#340—91no—
166C24×C3—61no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—21no—
170C2×C3×D4—32no—
171C2×C3×D4—32no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—41no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3#6711yescharacteristic
194C22×Dic3#6711yescharacteristic
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12D1212yes—
206C2×D12#6712yes—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8—61no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—41no—
216C3×C22⋊C4—122no—
217C3×C22⋊C4—122no—
218C3×C42—61no—
219C3×C42—61no—
220#217—122no—
221#217—122no—
222#213—68no—
223#213—68no—
224(C2×D3)⋊C4—42no—
225(C2×D3)⋊C4—42no—
226(C2×D3)⋊C4—122no—
227(C2×D3)⋊C4—122no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—121no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—121no—
247C2×C3⋊C8—121no—
248C22×C32#12111yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32C2×D811yescharacteristic
252C22×C32#13511yescharacteristic
253C22×C32AGL(1,ℤ/8)11yescharacteristic
254C22×C32AGL(1,ℤ/8)11yescharacteristic
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—81no—
262C2×C3×D3—81no—
263C2×C3×D3—81no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C2×C3×D3—81no—
267C2×C3×D3—81no—
268C2×C3×D3—81no—
269C32×C4—81no—
270C32×C4#12011yescharacteristic
271C32×C4#12311yescharacteristic
272C32×C4#12311yescharacteristic
273C32×C4#12411yescharacteristic
274C3⋊Dic3—81no—
275C3×Dic3—22no—
276C3×Dic3—41no—
277C22×D4—31no—
278C22×D4—31no—
279C2×D8—182no—
280C2×D8—182no—
281C2×D8—182no—
282C22×C8—31no—
283C22×C8—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4D3211yescharacteristic
286C2×C22⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—181no—
289C2×C22⋊C4—181no—
290C2×C42—31no—
291C4⋊C8—182no—
292#102—62no—
293#102—182no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C22×D3—41no—
317C22×D3—41no—
318C22×D3—41no—
319C22×D3—41no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C3×D4—62no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—62no—
329C3×D4—121no—
330C3×D4—121no—
331C3×D4—121no—
332C3×D4—121no—
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—32no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—81no—
353C2×C3×C4—81no—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4#23511yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—241no—
379C2×Dic3—241no—
380C2×Dic3#21312yescomplemented
381D12—22no—
382D12—22no—
383D12—22no—
384D12—22no—
385D12—41no—
386D12—41no—
387D12—41no—
388D12—41no—
389C3×C8—121no—
390C3⋊C8—41no—
391C3⋊C8—62no—
392C3⋊C8—62no—
393C3⋊C8—122no—
394C2×C32#39411yescharacteristic
395C2×C32#45911yescharacteristic
396C2×C32#45911yescharacteristic
397C2×C32#46311yescharacteristic
398C2×C32#46311yescharacteristic
399C2×C32#46611yescharacteristic
400C2×C32#46911yescharacteristic
401C3×D3—82no—
402C3×D3—82no—
403C24—61no—
404C24—61no—
405C2×D4—32no—
406C2×D4—32no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—61no—
417C22×C4—21no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—181no—
421C22×C4C2×D3211yescharacteristic
422D8—188no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—61no—
426C2×C8—92no—
427C2×C8—181no—
428C2×C8—181no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C22⋊C4—122no—
434C22⋊C4—122no—
435C22⋊C4—362no—
436C22⋊C4—362no—
437C42—61no—
438C42—61no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—241no—
453C22×C3—241no—
454C22×C3—241no—
455C22×C3—241no—
456C22×C3—241no—
457C22×C3—241no—
458C22×C3—241no—
459C22×C3—241no—
460C22×C3#88411yescharacteristic
461C22×C3#88411yescharacteristic
462C22×C3D3×D811yescharacteristic
463C22×C3#91111yescharacteristic
464C22×C3#91411yescharacteristic
465C22×C3#91611yescharacteristic
466C22×C3#93011yescharacteristic
467C22×C3C2×#21311yescharacteristic
468C22×C3#93211yescharacteristic
469C22×C3#93811yescharacteristic
470C22×C3#93911yescharacteristic
471C22×C3#93911yescharacteristic
472C22×C3#94911yescharacteristic
473C22×C3#95011yescharacteristic
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—81no—
481C2×D3—81no—
482C2×D3—81no—
483C2×D3—81no—
484C2×D3—81no—
485C2×D3—81no—
486C2×D3—81no—
487C2×D3—81no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—62no—
493C3×C4—82no—
494C3×C4—81no—
495C3×C4—81no—
496C3×C4—121no—
497C3×C4#88211yescharacteristic
498C3×C4#88311yescharacteristic
499C3×C4#88311yescharacteristic
500C3×C4#88511yescharacteristic
501C3×C4#88511yescharacteristic
502C3×C4#88611yescharacteristic
503C3×C4#92911yescharacteristic
504C3×C4#93711yescharacteristic
505Dic3—22no—
506Dic3—41no—
507Dic3—242no—
508Dic3—241no—
509Dic3—241no—
510C32#205411yescharacteristic, complemented, Sylow
511C23—62no—
512C23—62no—
513C23—121no—
514C23—121no—
515C23—121no—
516C23—121no—
517C23—121no—
518C23—121no—
519C23—121no—
520C23—121no—
521C23—121no—
522C23—121no—
523C23—121no—
524C23—121no—
525C23D3×#6711yescharacteristic
526D4—62no—
527D4—62no—
528D4—62no—
529D4—62no—
530D4—121no—
531D4—121no—
532D4—121no—
533D4—121no—
534C2×C4—32no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—361no—
544C2×C4—361no—
545C2×C4—361no—
546C2×C4#379511yescharacteristic
547C2×C4#379811yescharacteristic
548C2×C4D3×D1211yescharacteristic
549C2×C4#380211yescharacteristic
550C2×C4#380511yescharacteristic
551C2×C4D3×#6711yescharacteristic
552C8—121no—
553C8—182no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—242no—
562C2×C3—242no—
563C2×C3#477511yescharacteristic
564C2×C3#478211yescharacteristic
565C2×C3#478611yescharacteristic
566C2×C3#478711yescharacteristic
567C2×C3#495911yescharacteristic
568C2×C3#496111yescharacteristic
569C2×C3#501511yescharacteristic
570C2×C3#501611yescharacteristic
571C2×C3#503811yescharacteristic
572C2×C3#503911yescharacteristic
573C2×C3#505711yescharacteristic
574C2×C3#507211yescharacteristic
575C2×C3#515011yescharacteristic
576C2×C3#516511yescharacteristic
577D3—82no—
578D3—82no—
579C22—122no—
580C22—122no—
581C22—122no—
582C22—122no—
583C22—122no—
584C22—122no—
585C22—241no—
586C22—241no—
587C22—241no—
588C22—241no—
589C22—241no—
590C22—241no—
591C22—241no—
592C22—241no—
593C22#6388511yescharacteristic
594C22#6390611yescharacteristic
595C22D3×#21311yescharacteristic
596C22#6393211yescharacteristic
597C22#6393911yescharacteristic
598C22#6394711yescharacteristic
599C22#6397011yescharacteristic
600C4—62no—
601C4—81no—
602C4—121no—
603C4—721no—
604C4#6389111yescharacteristic
605C4#6390511yescharacteristic
606C4#6391511yescharacteristic
607C4#6392211yescharacteristic
608C3—21no—
609C3#6965011yescharacteristic, complemented
610C3#7021211yescharacteristic, complemented
611C2—242no—
612C2—242no—
613C2#1059049911yescharacteristic
614C2#1059050411yescharacteristic
615C2#1059053011yescharacteristic
616C2#1059054711yescharacteristic
617C2#1059139011yescharacteristic
618C2#1059142811yescharacteristic
619C2#1059156711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2054
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. C3×#4988C2semidirect
3. C2×C3×#809C2semidirect
4. #10591318C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63563C2semidirect
7. #10589395C2semidirect
35. #4988D3semidirect
36. C2×#809D3semidirect
148. C2×C3×Dic3D8semidirect
380. C2×Dic3#213semidirect
510. C32#2054semidirect
609. C3#69650semidirect
610. C3#70212semidirect

Maximal subgroups

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

subgroupindex
C22×#37132
C3×#49882
C2×C3×#8092
#105913182
C2×Dic3⋊(C3⋊C8)2
C2×#635632
#105893952
#702123
#696503