Finite Group Databasebeta

← #11792014

Subgroups — #11792014

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×#946C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#72071—31nomaximal
9#71700—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#946—22no—
16C3×#946—22no—
17C2×C3×#216—22no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63856—22no—
27#63856—22no—
28#63662—22no—
29#63565—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C22×C3×Q16—31no—
32C2×C3×C22⋊Q8—31no—
33C2×#946—31no—
34C2×#946D311yescharacteristic
35C22×#216D311yescharacteristic, complemented
36C2×#924—31no—
37C2×#835—31no—
38C2×#835—31no—
39C2×#835—31no—
40C2×#835—61no—
41C2×#830—31no—
42C2×(C2×D3)⋊C8—31no—
43C2×#810—31no—
44#4551—31no—
45#4529—31no—
46C23×C3×D3D411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8D412yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
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—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)D412yes—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C3×#216—28no—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3D412yes—
80C3×Dic3⋊C4—24no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yes—
84#3724—24no—
85(C2×D3)⋊Dic3—24no—
86#2001—91noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8—31no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C23×C3×C4—31no—
92C22×C4×D3C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C2×C3×Q16—62no—
95C2×C3×Q16—62no—
96C2×C3×Q16—62no—
97C22×C3×C8—31no—
98C3×C22⋊Q8—62no—
99C3×C22⋊Q8—62no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—61no—
102C2×C3×C22⋊C4—61no—
103C2×#217—61no—
104#946—22no—
105#946—22no—
106#946—62no—
107#946—62no—
108C2×#216—22no—
109C2×#216—22no—
110C2×#216—22no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—61no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117#924—62no—
118#924—62no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—61no—
121C2×Dic3⋊C4—61no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126#835—62no—
127#835—62no—
128#835—64no—
129#835—62no—
130#830—62no—
131(C2×D3)⋊C8—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
141C32×Q8—22no—
142C32×Q8—22no—
143C32×Q8—41no—
144C32×Q8—41no—
145C2×C32×C4—22no—
146C2×C32×C4—41no—
147C2×C32×C4—41no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—41no—
156C2×C3⋊Dic3—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—31no—
177C2×C22⋊Q8—31no—
178C2×C22⋊Q8—91no—
179C2×#103—91no—
180C2×#103—91no—
181C2×C22⋊C8—91no—
182#340—91no—
183C24×C3—31no—
184C23×D3#6711yescharacteristic
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—22no—
198C2×C3×Q8—32no—
199C2×C3×Q8—41no—
200C2×C3×Q8—41no—
201C2×C3×Q8—41no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×Q8—61no—
206C2×C3×Q8—61no—
207C2×C3×Q8#6712yes—
208C2×C3×Q8#6712yes—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—31no—
213C22×C3×C4—41no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—121no—
229C22×Dic3#6711yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6#6712yes—
242C3×Q16—68no—
243C2×C3×C8—32no—
244C2×C3×C8—61no—
245C2×C3×C8—61no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—64no—
248C3×C4⋊C4—61no—
249C3×C22⋊C4—64no—
250#217—64no—
251#216—28no—
252(C2×D3)⋊C4—24no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—21no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—121no—
261C4⋊Dic3#6712yes—
262Dic3⋊C4—24no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—121no—
275C2×C3⋊C8—121no—
276C2×C3⋊C8#6712yes—
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×Q8D3211yescharacteristic
302C23×C4—31no—
303C2×Q16—62no—
304C2×Q16—62no—
305C2×Q16—62no—
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—91no—
315C2×C4⋊C4—181no—
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—24no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—42no—
344C3×Q8—42no—
345C3×Q8—42no—
346C3×Q8—41no—
347C3×Q8—41no—
348C3×Q8—41no—
349C3×Q8—41no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—121no—
353C3×Q8—121no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—121no—
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×C4—121no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—41no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410C2×Dic3—241no—
411C2×Dic3—241no—
412C4×D3—41no—
413C4×D3—41no—
414C4×D3—41no—
415C4×D3—41no—
416Dic6—22no—
417Dic6—22no—
418Dic6—41no—
419Dic6—41no—
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—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—32no—
440C2×Q8—61no—
441C2×Q8—61no—
442C2×Q8—61no—
443C2×Q8—61no—
444C2×Q8—61no—
445C2×Q8#62512yes—
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—68no—
459C2×C8—32no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—181no—
463C2×C8—181no—
464C2×C8—181no—
465C4⋊C4—32no—
466C4⋊C4—64no—
467C4⋊C4—61no—
468C4⋊C4—92no—
469C4⋊C4—184no—
470C4⋊C4—181no—
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×C3D3×Q1611yescharacteristic
488C22×C3#91811yescharacteristic
489C22×C3#91811yescharacteristic
490C22×C3#91911yescharacteristic
491C22×C3#93711yescharacteristic
492C22×C3#93711yescharacteristic
493C22×C3#93711yescharacteristic
494C22×C3#93811yescharacteristic
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—44no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—122no—
516C3×C4—121no—
517C3×C4—122no—
518C3×C4#93711yescharacteristic
519C3×C4#93811yescharacteristic
520C3×C4#93911yescharacteristic
521C3×C4#93911yescharacteristic
522C3×C4#93911yescharacteristic
523C3×C4#94011yescharacteristic
524C3×C4#94011yescharacteristic
525C3×C4#95311yescharacteristic
526Dic3—42no—
527Dic3—41no—
528Dic3—42no—
529Dic3—122no—
530Dic3—122no—
531Dic3—242no—
532C32#200111yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—62no—
546Q8—62no—
547Q8—121no—
548Q8—121no—
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#380511yescharacteristic
569C2×C4C2×#62511yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4#381111yescharacteristic
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#504711yescharacteristic
585C2×C3#505011yescharacteristic
586C2×C3#505111yescharacteristic
587C2×C3#505211yescharacteristic
588C2×C3#518611yescharacteristic
589C2×C3#518611yescharacteristic
590C2×C3#518711yescharacteristic
591C2×C3#518711yescharacteristic
592C2×C3#518811yescharacteristic
593C2×C3#518911yescharacteristic
594C2×C3#522311yescharacteristic
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—
606C22D3×#21611yescharacteristic
607C22#6394311yescharacteristic
608C22#6394811yescharacteristic
609C22#6394911yescharacteristic
610C22#6397011yescharacteristic
611C22#6397611yescharacteristic
612C22#6398311yescharacteristic
613C4—42no—
614C4—122no—
615C4—121no—
616C4—122no—
617C4—362no—
618C4#6397011yescharacteristic
619C4#6397611yescharacteristic
620C4#6397911yescharacteristic
621C4#6398011yescharacteristic
622C3—21no—
623C3#7170011yescharacteristic, complemented
624C3#7207111yescharacteristic, complemented
625C2—122no—
626C2#1059159411yescharacteristic
627C2#1059159711yescharacteristic
628C2#1059163511yescharacteristic
629C2#1059163811yescharacteristic
630C2#1059165311yescharacteristic
631C2#1059165711yescharacteristic
632C2#1059172311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
4. C2×#63662C2semidirect
5. C2×#63565C2semidirect
7. #10589164C2semidirect
35. C22×#216D3semidirect
140. C22×C3×D3Q16semidirect
337. C22×D3#216semidirect
532. C32#2001semidirect
623. C3#71700semidirect
624. C3#72071semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C22×C3×#2162
C2×#638562
C2×#636622
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
#105891642
#720713
#717003