Finite Group Databasebeta

← #11786371

Subgroups — #11786371

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3710C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4524C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70477—31nomaximal
9#68666—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C411yescharacteristic
13C2×#3752C411yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3710—22no—
20C2×#3710—22no—
21C2×#3710—22no—
22#63658C411yescharacteristic
23#63658C411yescharacteristic
24C3×C4⋊(C3⋊C8)—22no—
25#63572—22no—
26#63557—22no—
27C22×D3×C8—31no—
28C22×D3×C8—31no—
29C2×C3×C4⋊C8—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8—31no—
32C2×Dic3⋊C8—31no—
33C2×Dic3⋊C8—31no—
34C4×(C2×D3)⋊C4—31no—
35C4×(C2×D3)⋊C4—31no—
36C4×(C2×D3)⋊C4—61no—
37C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
38C3×#336—31no—
39#4550—31no—
40#4550—31no—
41#4524D311yescharacteristic, complemented
42C23×C3⋊D3C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3Q812yes—
55C32×C42—21no—
56C32×C42—21no—
57#3752—22no—
58#3752C814yescomplemented
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73#3710—28no—
74#1850—91noSylow
75C22×C4×D3—31no—
76C22×C4×D3—31no—
77C22×C4×D3—61no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C42—21no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98C2×D3×C8—62no—
99C2×D3×C8—62no—
100C2×D3×C8—62no—
101C2×D3×C8—62no—
102C2×D3×C8—62no—
103C2×D3×C8—62no—
104C3×C4⋊C8—62no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111(C2×D3)⋊C8—62no—
112(C2×D3)⋊C8—62no—
113Dic3⋊C8—62no—
114Dic3⋊C8—62no—
115C4⋊(C3⋊C8)—22no—
116C23×C32C22×C411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3C4⋊C412yes—
122C22×C3⋊D3C2×C812yes—
123C22×C3⋊D3M1612yes—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4C2×C812yescomplemented
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×Q811yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3C4⋊C412yes—
144C2×C3⋊Dic3C2×C812yescomplemented
145C4×C3⋊D3—22no—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153C23×C8—91no—
154C2×C4⋊C8—31no—
155C2×C4⋊C8—91no—
156C2×C22⋊C8—91no—
157C4×C22⋊C4—91no—
158#336—31no—
159#336—91no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4C4×D311yescharacteristic
167C22×C3×C4C4×D311yescharacteristic
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4C4×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—121no—
196C2×C4×D3—121no—
197C2×C4×D3—121no—
198C2×C4×D3—121no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—41no—
216C3×C42—41no—
217(C2×D3)⋊C4—34no—
218(C2×D3)⋊C4—34no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—64no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228C4×Dic3—121no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8D1212yes—
240C2×C3⋊C8#6712yes—
241D3×C8—68no—
242D3×C8—68no—
243C22×C32C2×C4⋊C411yescharacteristic
244C22×C32C4×D411yescharacteristic
245C22×C32C4×D411yescharacteristic
246C22×C32C22×C811yescharacteristic
247C22×C32C2×M1611yescharacteristic
248C22×C32#13111yescharacteristic
249C22×C32#13111yescharacteristic
250C2×C3⋊D3—22no—
251C2×C3⋊D3—22no—
252C2×C3⋊D3—22no—
253C2×C3⋊D3—22no—
254C2×C3⋊D3—22no—
255C2×C3⋊D3—22no—
256C2×C3⋊D3C4⋊C814yescomplemented
257C32×C4—22no—
258C32×C4—41no—
259C32×C4#12011yescharacteristic
260C32×C4C22⋊Q811yescharacteristic
261C32×C4C22⋊Q811yescharacteristic
262C32×C4#12311yescharacteristic
263C3⋊Dic3—22no—
264C3⋊Dic3—22no—
265C3⋊Dic3—41no—
266C23×C4—91no—
267C22×C8—31no—
268C22×C8—31no—
269C22×C8—31no—
270C22×C8—31no—
271C22×C8—182no—
272C22×C8—182no—
273C22×C8—182no—
274C2×C22⋊C4—91no—
275C2×C22⋊C4—91no—
276C2×C42—91no—
277C2×C42D3211yescharacteristic
278C4⋊C8—62no—
279C4⋊C8—182no—
280C22⋊C8—182no—
281#95—91no—
282#95—91no—
283C23×C3—21no—
284C23×C3C2×C4×D311yescharacteristic
285C23×C3C2×C4×D311yescharacteristic
286C22×D3—32no—
287C22×D3—32no—
288C22×D3—32no—
289C22×D3—32no—
290C22×D3—32no—
291C22×D3—32no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4D3×C812yescomplemented
330C2×C3×C4D3×C812yescomplemented
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4D3×Q811yescharacteristic
340C2×C3×C4D3×Q811yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—122no—
382C3×C8—62no—
383C3×C8—62no—
384C3×C8—121no—
385C3×C8—121no—
386C3⋊C8—22no—
387C3⋊C8—22no—
388C3⋊C8—41no—
389C3⋊C8—41no—
390C2×C32#38511yescharacteristic
391C2×C32C2×C4⋊C811yescharacteristic
392C2×C32#42411yescharacteristic
393C2×C32C8×D411yescharacteristic
394C2×C32C8×D411yescharacteristic
395C2×C32#43511yescharacteristic
396C2×C32#43511yescharacteristic
397C3⋊D3—24no—
398C24—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—92no—
402C22×C4—92no—
403C22×C4—91no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408C22×C4#62411yescharacteristic
409C22×C4#62411yescharacteristic
410C22×C4C2×D3211yescharacteristic
411C2×C8—32no—
412C2×C8—32no—
413C2×C8—61no—
414C2×C8—61no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—188no—
424C22⋊C4—94no—
425C22⋊C4—182no—
426C42—21no—
427C42—21no—
428C42—181no—
429C42—181no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3C4×D1211yescharacteristic
438C22×C3#67⋊C411yescharacteristic
439C22×C3D3×C4⋊C411yescharacteristic
440C22×C3D3×C4⋊C411yescharacteristic
441C22×C3#89311yescharacteristic
442C22×C3C2×D3×C811yescharacteristic
443C22×C3C2×D3×C811yescharacteristic
444C22×C3#90111yescharacteristic
445C22×C3#90111yescharacteristic
446C22×C3D3×M1611yescharacteristic
447C22×C3D3×M1611yescharacteristic
448C22×C3#90711yescharacteristic
449C22×C3#90711yescharacteristic
450C22×C3C4×#6711yescharacteristic
451C2×D3—34no—
452C2×D3—34no—
453C2×D3—64no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—122no—
467C2×D3—122no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4#88211yescharacteristic
483C3×C4#88311yescharacteristic
484C3×C4#89411yescharacteristic
485C3×C4#89611yescharacteristic
486C3×C4#89611yescharacteristic
487C3×C4#89711yescharacteristic
488C3×C4#93711yescharacteristic
489C3×C4#94611yescharacteristic
490Dic3—62no—
491Dic3—62no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—122no—
496Dic3—122no—
497Dic3—121no—
498Dic3—121no—
499C32#185011yescharacteristic, complemented, Sylow
500C23—92no—
501C23—92no—
502C23—92no—
503C23—181no—
504C23—181no—
505C23—181no—
506C23—181no—
507C23C2×#62411yescharacteristic
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4#371012yescomplemented
527C2×C4#379711yescharacteristic
528C2×C4#379911yescharacteristic
529C2×C4D3×D1211yescharacteristic
530C2×C4#380211yescharacteristic
531C2×C4#380411yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C8—62no—
534C8—62no—
535C8—121no—
536C8—121no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3#466811yescharacteristic
545C2×C3C8×D1211yescharacteristic
546C2×C3#470611yescharacteristic
547C2×C3#67⋊C811yescharacteristic
548C2×C3#472811yescharacteristic
549C2×C3D3×C4⋊C811yescharacteristic
550C2×C3D3×C4⋊C811yescharacteristic
551C2×C3#483411yescharacteristic
552C2×C3#483611yescharacteristic
553C2×C3#483911yescharacteristic
554C2×C3#483911yescharacteristic
555C2×C3#498911yescharacteristic
556C2×C3C8×#6711yescharacteristic
557C2×C3#512711yescharacteristic
558D3—64no—
559D3—64no—
560D3—124no—
561C22—94no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22—182no—
566C22—182no—
567C22—182no—
568C22C2×#371011yescharacteristic
569C22#6381711yescharacteristic
570C22#6381711yescharacteristic
571C22#6381811yescharacteristic
572C22#6389411yescharacteristic
573C22#6390011yescharacteristic
574C22#6395211yescharacteristic
575C4—22no—
576C4—41no—
577C4—182no—
578C4—182no—
579C4—361no—
580C4#6385411yescharacteristic
581C4#6388811yescharacteristic
582C4#6389511yescharacteristic
583C4#6392211yescharacteristic
584C3—21no—
585C3#6866611yescharacteristic, complemented
586C3#7047711yescharacteristic, complemented
587C2—184no—
588C2#1059032711yescharacteristic
589C2#1059032811yescharacteristic
590C2#1059033111yescharacteristic
591C2#1059033211yescharacteristic
592C2#1059114811yescharacteristic
593C2#1059114911yescharacteristic
594C2#1059137811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1850
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C2×#63572C2semidirect
6. C3×#4524C2semidirect
7. #10589156C2semidirect
37. C2×C4⋊(C3⋊C8)D3semidirect
41. #4524D3semidirect
58. #3752C8semidirect
129. C2×C32×C4C2×C8semidirect
144. C2×C3⋊Dic3C2×C8semidirect
256. C2×C3⋊D3C4⋊C8semidirect
329. C2×C3×C4D3×C8semidirect
330. C2×C3×C4D3×C8semidirect
499. C32#1850semidirect
526. C2×C4#3710semidirect
585. C3#68666semidirect
586. C3#70477semidirect

Maximal subgroups

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

subgroupindex
C22×#37102
C4×#37522
C2×C3×C4⋊(C3⋊C8)2
C2×#635722
C2×#635572
C3×#45242
#105891562
#704773
#686663