Finite Group Databasebeta

← #11792020

Subgroups — #11792020

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#71700—31nomaximal
9#68888—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#897—22no—
20C3×#897—22no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23#63857—22no—
24#63857—22no—
25C2×#3719—22no—
26C2×#3719—22no—
27C2×#3719—22no—
28#63637—22no—
29#63565—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×C22⋊Q8—31no—
32C22×#216—31no—
33C2×#924—31no—
34C22×Dic12—31no—
35C2×#897—31no—
36C2×#897D311yescharacteristic
37C2×#835—31no—
38C2×#830—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×#810—31no—
41C2×#810—31no—
42C2×#810—31no—
43C2×#810—61no—
44C3×#340—31no—
45#4529D311yescharacteristic, complemented
46C23×C3×D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634D412yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4D412yes—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—24no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3D412yes—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yes—
83Dic3⋊Dic3—24no—
84(C2×D3)⋊Dic3—24no—
85#3719—28no—
86#2001—91noSylow
87C22×C3×Q8—31no—
88C23×C3×C4—31no—
89C22×C4×D3C2×D311yescharacteristic
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×C3×C8—31no—
95C3×C22⋊Q8—62no—
96C3×C22⋊Q8—62no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4—61no—
103C2×#217—61no—
104C2×#216—62no—
105C2×#216—62no—
106C2×#216—62no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112#924—62no—
113#924—62no—
114C2×Dic3⋊C4—61no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C2×Dic12—62no—
120C2×Dic12—62no—
121C2×Dic12—62no—
122#897—22no—
123#897—22no—
124#897—62no—
125#897—62no—
126#835—62no—
127#830—62no—
128(C2×D3)⋊C8—62no—
129#810—64no—
130#810—62no—
131#810—62no—
132#810—62no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3Q1612yescomplemented
141C2×C32×C4—22no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153#634—22no—
154#634—22no—
155#634—41no—
156#634—41no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—41no—
165C2×C3×Dic3—41no—
166C3×C4×D3—41no—
167C3×C4×D3—41no—
168C3×C4×D3—41no—
169C3×C4×D3—41no—
170C3×Dic6—22no—
171C3×Dic6—22no—
172C3×Dic6—41no—
173C3×Dic6—41no—
174C3⋊(C3⋊C8)—41no—
175C3×C3⋊C8—22no—
176C22×Q16—91no—
177C2×C22⋊Q8—31no—
178C2×C22⋊Q8—91no—
179C2×#103—91no—
180C2×#103—91no—
181C2×C22⋊C8—91no—
182#340—31no—
183C24×C3—31no—
184C23×D3#6711yescharacteristic
185C2×C3×Q8—32no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—121no—
211C22×Dic3#6711yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—32no—
224C2×Dic6—32no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—121no—
239C2×Dic6—121no—
240C2×Dic6—121no—
241C2×Dic6#6712yes—
242C2×C3×C8—32no—
243C2×C3×C8—61no—
244C2×C3×C8—61no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—64no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4D1212yes—
253C3×C4⋊C4#6712yes—
254C3×C22⋊C4—64no—
255#217—64no—
256#216—68no—
257(C2×D3)⋊C4—24no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—24no—
260C4⋊Dic3—21no—
261C4⋊Dic3—64no—
262C4⋊Dic3D1212yes—
263Dic3⋊C4—64no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—121no—
274C2×C3⋊C8—121no—
275C2×C3⋊C8D1212yes—
276Dic12—68no—
277C22×C32#12011yescharacteristic
278C22×C32#12011yescharacteristic
279C22×C32#12111yescharacteristic
280C22×C32C2×Q1611yescharacteristic
281C22×C32#13511yescharacteristic
282C22×C32#13711yescharacteristic
283C22×C32#13711yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C32×C4—42no—
292C32×C4#12011yescharacteristic
293C32×C4#12111yescharacteristic
294C32×C4#12111yescharacteristic
295C32×C4#12711yescharacteristic
296C3⋊Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—31no—
301C22×Q8—91no—
302C23×C4—31no—
303C2×Q16—182no—
304C2×Q16—182no—
305C2×Q16—182no—
306C22×C8—31no—
307C22×C8—91no—
308C22⋊Q8—62no—
309C22⋊Q8—62no—
310C22⋊Q8—182no—
311C22⋊Q8—182no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—61no—
314C2×C4⋊C4—181no—
315C2×C4⋊C4D3211yescharacteristic
316C2×C22⋊C4—61no—
317C2×C22⋊C4—181no—
318#103—182no—
319#103—182no—
320C22⋊C8—182no—
321C23×C3—21no—
322C23×C3—32no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3#21612yescomplemented
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—121no—
341C3×Q8—121no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—42no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—81no—
361C2×C3×C4—81no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4#23711yescharacteristic
379C2×C3×C4#23911yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C4×D3—41no—
401C4×D3—41no—
402C4×D3—41no—
403C4×D3—41no—
404Dic6—22no—
405Dic6—22no—
406Dic6—41no—
407Dic6—41no—
408Dic6—64no—
409Dic6—62no—
410Dic6—62no—
411Dic6—62no—
412Dic6—62no—
413Dic6—122no—
414Dic6—122no—
415Dic6—122no—
416Dic6—121no—
417Dic6—121no—
418Dic6—121no—
419Dic6—121no—
420C3×C8—62no—
421C3⋊C8—22no—
422C3⋊C8—122no—
423C3⋊C8—121no—
424C3⋊C8—121no—
425C2×C32#39211yescharacteristic
426C2×C32#45111yescharacteristic
427C2×C32#45111yescharacteristic
428C2×C32#45211yescharacteristic
429C2×C32#45211yescharacteristic
430C2×C32#46711yescharacteristic
431C2×C32#47011yescharacteristic
432C3×D3—42no—
433C24—31no—
434C2×Q8—32no—
435C2×Q8—61no—
436C2×Q8—61no—
437C2×Q8—61no—
438C2×Q8—61no—
439C2×Q8—61no—
440C2×Q8—92no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×Q8—181no—
444C2×Q8—181no—
445C2×Q8—181no—
446C22×C4—21no—
447C22×C4—31no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—181no—
457C22×C4C2×D3211yescharacteristic
458Q16—188no—
459C2×C8—32no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—181no—
463C2×C8—181no—
464C2×C8—181no—
465C4⋊C4—21no—
466C4⋊C4—32no—
467C4⋊C4—64no—
468C4⋊C4—61no—
469C4⋊C4—184no—
470C4⋊C4#62612yes—
471C22⋊C4—64no—
472C22⋊C4—184no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3#88211yescharacteristic
488C22×C3#88211yescharacteristic
489C22×C3#89511yescharacteristic
490C22×C3#91211yescharacteristic
491C22×C3#91511yescharacteristic
492C22×C3#91511yescharacteristic
493C22×C3D3×Q1611yescharacteristic
494C22×C3#93711yescharacteristic
495C22×C3#93911yescharacteristic
496C22×C3#94211yescharacteristic
497C22×C3C2×#21611yescharacteristic
498C22×C3#95011yescharacteristic
499C22×C3#95111yescharacteristic
500C22×C3#95311yescharacteristic
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—41no—
505C2×D3—41no—
506C2×D3—41no—
507C2×D3—41no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—82no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4—122no—
518C3×C4#87411yescharacteristic
519C3×C4#88211yescharacteristic
520C3×C4#89511yescharacteristic
521C3×C4#89511yescharacteristic
522C3×C4#93711yescharacteristic
523C3×C4#93811yescharacteristic
524C3×C4#93911yescharacteristic
525C3×C4#94011yescharacteristic
526Dic3—42no—
527Dic3—41no—
528Dic3—42no—
529Dic3—124no—
530Dic3—122no—
531Dic3—122no—
532C32#200111yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23D3×#6711yescharacteristic
541Q8—62no—
542Q8—62no—
543Q8—121no—
544Q8—121no—
545Q8—182no—
546Q8—182no—
547Q8—361no—
548Q8—361no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—182no—
566C2×C4—361no—
567C2×C4—361no—
568C2×C4#379611yescharacteristic
569C2×C4D3×D1211yescharacteristic
570C2×C4D3×D1211yescharacteristic
571C2×C4#380211yescharacteristic
572C2×C4C2×#62611yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C8—62no—
575C8—361no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—122no—
584C2×C3#467111yescharacteristic
585C2×C3#478311yescharacteristic
586C2×C3#478311yescharacteristic
587C2×C3#480911yescharacteristic
588C2×C3#480911yescharacteristic
589C2×C3#486711yescharacteristic
590C2×C3#488711yescharacteristic
591C2×C3#504711yescharacteristic
592C2×C3#505011yescharacteristic
593C2×C3#505111yescharacteristic
594C2×C3#505211yescharacteristic
595C2×C3#522311yescharacteristic
596C2×C3#522811yescharacteristic
597C2×C3#523911yescharacteristic
598D3—42no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22—121no—
603C22—121no—
604C22—121no—
605C22—121no—
606C22#6388611yescharacteristic
607C22#6392211yescharacteristic
608C22#6392911yescharacteristic
609C22#6393311yescharacteristic
610C22D3×#21611yescharacteristic
611C22#6394611yescharacteristic
612C22#6397711yescharacteristic
613C4—42no—
614C4—122no—
615C4—121no—
616C4—122no—
617C4—362no—
618C4#6388611yescharacteristic
619C4#6391111yescharacteristic
620C4#6391611yescharacteristic
621C4#6392211yescharacteristic
622C3—21no—
623C3#6888811yescharacteristic, complemented
624C3#7170011yescharacteristic, complemented
625C2—122no—
626C2#1059057911yescharacteristic
627C2#1059058711yescharacteristic
628C2#1059060411yescharacteristic
629C2#1059061411yescharacteristic
630C2#1059139111yescharacteristic
631C2#1059146311yescharacteristic
632C2#1059159511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2001
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
3. C22×#3719C2semidirect
4. C2×#63637C2semidirect
5. C2×#63565C2semidirect
7. C3×#4529C2semidirect
45. #4529D3semidirect
140. C22×C3×D3Q16semidirect
337. C22×D3#216semidirect
532. C32#2001semidirect
623. C3#68888semidirect
624. C3#71700semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×#638572
C22×#37192
C2×#636372
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C3×#45292
#717003
#688883