Finite Group Databasebeta

← #11794018

Subgroups — #11794018

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70212—31nomaximal
9#69650—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×#3753—22no—
13C2×#3753—22no—
14C2×#3753—22no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3722—21no—
23C2×#3722—21no—
24C3×#832—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63564—22no—
27C22×#213—31no—
28C22×#213—31no—
29C22×#213—61no—
30C2×C3×#102—31no—
31C3×#390—31no—
32#5221D311yescharacteristic, complemented
33C2×#832D311yescharacteristic, complemented
34C2×#821—31no—
35C2×Dic3⋊C8—31no—
36#4988—31no—
37C2×#809—31no—
38#4939—31no—
39C2×C4⋊(C3⋊C8)—31no—
40#4529—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
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)D412yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61#3753—28no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×#217—42no—
66C3×#217—42no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
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⋊C8—21no—
76#3722—42no—
77#3722—42no—
78#2054—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4C2×D311yescharacteristic
81C22×C3×D4C2×D311yescharacteristic
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—31no—
91C2×#217—21no—
92C2×#217—21no—
93C2×#213—62no—
94C2×#213—62no—
95C2×#213—62no—
96C2×#213—62no—
97C2×#213—64no—
98C2×#213—64no—
99C2×#213—64no—
100C2×#213—62no—
101C2×#213—62no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8C2×D311yescharacteristic
113C3×#102—62no—
114#832—22no—
115#821—62no—
116Dic3⋊C8—62no—
117#809—62no—
118C4⋊(C3⋊C8)—62no—
119C23×C32—22no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C32×D4—22no—
135C32×D4—22no—
136C32×D4—41no—
137C32×D4—41no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—41no—
147C4⋊(C3⋊D3)—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3D812yescomplemented
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8—41no—
162C22×D8—91no—
163C2×C4⋊C8—91no—
164C2×#102—31no—
165C2×#102—91no—
166#390—31no—
167#390—91no—
168#340—91no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—41no—
172C23×D3—61no—
173C23×D3—61no—
174C23×D3—121no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
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—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4D1212yes—
192C2×C3×D4#6712yes—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3#6711yescharacteristic
203C22×Dic3#6711yescharacteristic
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—121no—
220C2×D12—121no—
221C2×D12—121no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—122no—
230C3×C22⋊C4—122no—
231C3×C42—61no—
232C3×C42—61no—
233#217—42no—
234#217—42no—
235#213—616no—
236#213—68no—
237#213—68no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240(C2×D3)⋊C4—122no—
241(C2×D3)⋊C4—122no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4×Dic3—21no—
247C4×Dic3—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—81no—
264C22×C32—81no—
265C22×C32—81no—
266C22×C32—81no—
267C22×C32#12111yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32#12111yescharacteristic
270C22×C32C2×D811yescharacteristic
271C22×C32#13511yescharacteristic
272C22×C32AGL(1,ℤ/8)11yescharacteristic
273C22×C32AGL(1,ℤ/8)11yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—81no—
278C2×C3⋊D3—81no—
279C2×C3⋊D3—81no—
280C2×C3⋊D3—81no—
281C32×C4#12011yescharacteristic
282C32×C4#12311yescharacteristic
283C32×C4#12311yescharacteristic
284C32×C4#12411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—81no—
288C3×Dic3—81no—
289C22×D4—91no—
290C22×D4D3211yescharacteristic
291C2×D8—182no—
292C2×D8—182no—
293C2×D8—182no—
294C22×C8—31no—
295C22×C8—91no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—31no—
298C2×C22⋊C4—61no—
299C2×C22⋊C4—61no—
300C2×C22⋊C4—181no—
301C2×C22⋊C4—181no—
302C2×C42—31no—
303C4⋊C8—182no—
304#102—62no—
305#102—182no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—41no—
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—81no—
325C23×C3—81no—
326C23×C3—81no—
327C23×C3—81no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×#6711yescharacteristic
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—121no—
341C22×D3—121no—
342C22×D3—121no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—241no—
348C22×D3—241no—
349C22×D3—241no—
350C22×D3—241no—
351C3×D4—24no—
352C3×D4—22no—
353C3×D4—22no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—42no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—41no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—32no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4—121no—
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4#23711yescharacteristic
391C2×C3×C4#23711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—41no—
403C2×Dic3—41no—
404C2×Dic3#21312yescomplemented
405D12—64no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—122no—
411D12—122no—
412D12—122no—
413D12—121no—
414D12—121no—
415D12—121no—
416D12—121no—
417C3×C8—121no—
418C3⋊C8—41no—
419C3⋊C8—64no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C2×C32—82no—
423C2×C32#39411yescharacteristic
424C2×C32#45911yescharacteristic
425C2×C32#45911yescharacteristic
426C2×C32#46311yescharacteristic
427C2×C32#46311yescharacteristic
428C2×C32#46611yescharacteristic
429C2×C32#46911yescharacteristic
430C3⋊D3—82no—
431C24—21no—
432C24—181no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—92no—
439C2×D4—181no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C2×D4—181no—
444C2×D4#62612yes—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4C2×D3211yescharacteristic
450D8—188no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8—92no—
455C2×C8—181no—
456C2×C8—181no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C22⋊C4—122no—
462C22⋊C4—122no—
463C22⋊C4—362no—
464C22⋊C4—362no—
465C42—61no—
466C42—61no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—82no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3#88411yescharacteristic
496C22×C3#88411yescharacteristic
497C22×C3D3×D811yescharacteristic
498C22×C3#91111yescharacteristic
499C22×C3#91411yescharacteristic
500C22×C3#91611yescharacteristic
501C22×C3#93011yescharacteristic
502C22×C3C2×#21311yescharacteristic
503C22×C3#93211yescharacteristic
504C22×C3#93811yescharacteristic
505C22×C3#93911yescharacteristic
506C22×C3#93911yescharacteristic
507C22×C3#94911yescharacteristic
508C22×C3#95011yescharacteristic
509C2×D3—124no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—242no—
517C2×D3—242no—
518C2×D3—242no—
519C2×D3—242no—
520C2×D3—242no—
521C2×D3—242no—
522C2×D3—241no—
523C2×D3—241no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3—241no—
527C2×D3—241no—
528C2×D3—241no—
529C2×D3—241no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—62no—
535C3×C4—121no—
536C3×C4—241no—
537C3×C4—241no—
538C3×C4#88211yescharacteristic
539C3×C4#88311yescharacteristic
540C3×C4#88311yescharacteristic
541C3×C4#88511yescharacteristic
542C3×C4#88511yescharacteristic
543C3×C4#88611yescharacteristic
544C3×C4#92911yescharacteristic
545C3×C4#93711yescharacteristic
546Dic3—22no—
547Dic3—41no—
548Dic3—81no—
549Dic3—81no—
550C32#205411yescharacteristic, complemented, Sylow
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—182no—
559C23—361no—
560C23—361no—
561C23—361no—
562C23—361no—
563C23—361no—
564C23—361no—
565C23D3×#6711yescharacteristic
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—182no—
571D4—182no—
572D4—361no—
573D4—361no—
574C2×C4—32no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—121no—
583C2×C4—121no—
584C2×C4—121no—
585C2×C4—121no—
586C2×C4#380411yescharacteristic
587C2×C4#380411yescharacteristic
588C2×C4#380411yescharacteristic
589C2×C4C2×#62611yescharacteristic
590C2×C4#381111yescharacteristic
591C2×C4#381111yescharacteristic
592C8—121no—
593C8—182no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—84no—
602C2×C3—82no—
603C2×C3—82no—
604C2×C3#477511yescharacteristic
605C2×C3#478211yescharacteristic
606C2×C3#478611yescharacteristic
607C2×C3#478711yescharacteristic
608C2×C3#495911yescharacteristic
609C2×C3#496111yescharacteristic
610C2×C3#501511yescharacteristic
611C2×C3#501611yescharacteristic
612C2×C3#503811yescharacteristic
613C2×C3#503911yescharacteristic
614C2×C3#505711yescharacteristic
615C2×C3#507211yescharacteristic
616C2×C3#515011yescharacteristic
617C2×C3#516511yescharacteristic
618D3—244no—
619D3—242no—
620D3—242no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—362no—
629C22—362no—
630C22—362no—
631C22—721no—
632C22—721no—
633C22—721no—
634C22—721no—
635C22D3×#21311yescharacteristic
636C22#6392511yescharacteristic
637C22#6393411yescharacteristic
638C22#6393511yescharacteristic
639C22#6395811yescharacteristic
640C22#6397111yescharacteristic
641C22#6397811yescharacteristic
642C4—62no—
643C4—121no—
644C4—241no—
645C4—241no—
646C4#6395311yescharacteristic
647C4#6396611yescharacteristic
648C4#6397511yescharacteristic
649C4#6398111yescharacteristic
650C3—21no—
651C3#6965011yescharacteristic, complemented
652C3#7021211yescharacteristic, complemented
653C2—82no—
654C2—722no—
655C2#1059142911yescharacteristic
656C2#1059143211yescharacteristic
657C2#1059144911yescharacteristic
658C2#1059145311yescharacteristic
659C2#1059147111yescharacteristic
660C2#1059148111yescharacteristic
661C2#1059171211yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
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. C3×#5221C2semidirect
3. C2×C3×#832C2semidirect
4. #10591320C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63564C2semidirect
7. #10589163C2semidirect
32. #5221D3semidirect
33. C2×#832D3semidirect
159. C2×C3×Dic3D8semidirect
404. C2×Dic3#213semidirect
550. C32#2054semidirect
651. C3#69650semidirect
652. C3#70212semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C3×#52212
C2×C3×#8322
#105913202
C2×Dic3⋊(C3⋊C8)2
C2×#635642
#105891632
#702123
#696503