Finite Group Databasebeta

← #11819079

Subgroups — #11819079

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63871C211yesmaximal, characteristic
3#10592686C211yesmaximal, characteristic
4C3×#4973C211yesmaximal, characteristic, complemented
5#10591341C212yesmaximal, complemented
6#10591310C212yesmaximal
7C4×#3722C211yesmaximal, characteristic
8Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#10591261C212yesmaximal, complemented
10#10591258C212yesmaximal
11#10591220C211yesmaximal, characteristic, complemented
12#83258—31nomaximal
13#76632—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#888—24no—
25C2×Dic3⋊Dic3C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2211yescharacteristic
28C2×#3722C2211yescharacteristic
29C2×Dic32C2212yes—
30#63871—24no—
31#63658C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2211yescharacteristic
39C2×C3×C4⋊Q8—31no—
40C2×#946—31no—
41C2×#897—31no—
42C2×#888D311yescharacteristic, complemented
43C3×#391—31no—
44#5231—32no—
45#5229—31no—
46#5229—32no—
47#4990—32no—
48#4987—31no—
49#4987—31no—
50#4987—61no—
51#4986—32no—
52Dic3×C4⋊C4—31no—
53#4973D311yescharacteristic, complemented
54C4×(C2×D3)⋊C4—31no—
55C4×(C2×D3)⋊C4—31no—
56C4×C4⋊Dic3—31no—
57#4929—31no—
58#4673—32no—
59#4669—32no—
60#4658—32no—
61#4646—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—24no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—42no—
82C32×C4⋊C4—22no—
83#3752—42no—
84C4⋊(C3⋊Dic3)—22no—
85C3×C4⋊Dic3D414yes—
86C3×Dic3⋊C4—24no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—22no—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3722—22no—
92#3722Q814yescomplemented
93Dic32—42no—
94#2492—91noSylow
95C22×C3×Q8—31no—
96C22×C3×Q8—32no—
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C22×C4×D3—61no—
100C22×Dic6C2×D311yescharacteristic
101C22×Dic6C2×D312yes—
102C3×C4⋊Q8—64no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110#946—64no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—31no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—62no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4C2×D312yes—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3C2×D311yescharacteristic
130C2×C4×Dic3C2×D311yescharacteristic
131#897—64no—
132#888—24no—
133C3×#95—32no—
134C3×#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—32no—
147C3⋊#95—62no—
148C3⋊#95C2×D312yes—
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—21no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3C2×Q812yes—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C4×C3⋊D3—44no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D414yes—
186C2×C3×Dic3C2×Q812yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3#4112yes—
189C3×Dic6—48no—
190C3×Dic6—44no—
191C2×C4⋊Q8—31no—
192C2×C22⋊Q8—91no—
193#400—92no—
194#393—92no—
195#391—31no—
196#391—92no—
197#391—91no—
198#388—92no—
199#380—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—91no—
202C23×D3—31no—
203C23×D3—31no—
204C23×D3—61no—
205C2×C3×Q8—64no—
206C2×C3×Q8—64no—
207C2×C3×Q8—62no—
208C2×C3×Q8—62no—
209C2×C3×Q8—62no—
210C2×C3×Q8—122no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—61no—
228C22×Dic3—62no—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C2×C4×D3—64no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×Dic6—22no—
245C2×Dic6—22no—
246C2×Dic6—22no—
247C2×Dic6—24no—
248C2×Dic6—24no—
249C2×Dic6—42no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—34no—
253C3×C4⋊C4—42no—
254C3×C4⋊C4—64no—
255C3×C42—62no—
256C3×C42—62no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—122no—
264(C2×D3)⋊C4—122no—
265(C2×D3)⋊C4—124no—
266C4⋊Dic3—64no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—122no—
270C4⋊Dic3#6714yes—
271Dic3⋊C4—24no—
272Dic3⋊C4—64no—
273C4×Dic3—22no—
274C4×Dic3—22no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C22×C32C22×D411yescharacteristic
278C22×C32C22×Q811yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C322−1+411yescharacteristic
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#12414yes—
293C3⋊Dic3—41no—
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C3×Dic3—41no—
301C22×Q8—31no—
302C22×Q8—32no—
303C23×C4—91no—
304C4⋊Q8—64no—
305C22⋊Q8—184no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4D3211yescharacteristic
311C2×C22⋊C4—91no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—92no—
315C2×C42—31no—
316C2×C42—31no—
317C2×C42—92no—
318#95—32no—
319#95—32no—
320#95—91no—
321#95—91no—
322#95—92no—
323#95—92no—
324#95—92no—
325#95—92no—
326C23×C3—21no—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C3×Q8—128no—
351C3×Q8—124no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4#23512yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4#23712yes—
385C2×C3×C4#23912yes—
386C2×C3×C4#23912yes—
387C2×C3×C4C2×#6712yes—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3#23712yes—
421C2×Dic3D3×Q812yes—
422C2×Dic3D3×Q812yes—
423C2×Dic3C2×#6714yes—
424C4×D3—128no—
425C4×D3—124no—
426C4×D3—124no—
427Dic6—48no—
428Dic6—44no—
429C2×C32C2×#12411yescharacteristic
430C2×C32#53311yescharacteristic
431C2×C32#54211yescharacteristic
432C2×C32#54611yescharacteristic
433C2×C32D4×Q811yescharacteristic
434C2×C32#55411yescharacteristic
435C2×C32#55611yescharacteristic
436C3⋊D3—42no—
437C24—91no—
438C2×Q8—64no—
439C2×Q8—64no—
440C2×Q8—62no—
441C2×Q8—62no—
442C2×Q8—62no—
443C2×Q8—122no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—92no—
451C22×C4—91no—
452C22×C4—182no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4C2×D3212yes—
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—22no—
458C4⋊C4—34no—
459C4⋊C4—64no—
460C4⋊C4—184no—
461C4⋊C4—182no—
462C22⋊C4—94no—
463C22⋊C4—184no—
464C22⋊C4—182no—
465C22⋊C4—362no—
466C42—62no—
467C42—62no—
468C42—362no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3C2×#23511yescharacteristic
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C2×#23711yescharacteristic
479C22×C3C2×#23711yescharacteristic
480C22×C3#100411yescharacteristic
481C22×C3C2×D3×Q811yescharacteristic
482C22×C3C2×D3×Q811yescharacteristic
483C22×C3C2×#23911yescharacteristic
484C22×C3C2×#23911yescharacteristic
485C22×C3#100711yescharacteristic
486C22×C3#100711yescharacteristic
487C22×C3D3×#4111yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3C22×#6711yescharacteristic
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C3×C4—24no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—62no—
515C3×C4—64no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4—82no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4#88514yes—
522C3×C4#94714yes—
523Dic3—22no—
524Dic3—22no—
525Dic3—24no—
526Dic3—22no—
527Dic3—41no—
528Dic3—42no—
529Dic3—122no—
530Dic3—122no—
531Dic3—121no—
532Dic3—121no—
533Dic3—122no—
534Dic3—242no—
535C32#249211yescharacteristic, complemented, Sylow
536C23—92no—
537C23—181no—
538C23—181no—
539C23—181no—
540C23—181no—
541C23—181no—
542C23—181no—
543C23C22×D3211yescharacteristic
544Q8—128no—
545Q8—124no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—181no—
568C2×C4—182no—
569C2×C4—181no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—181no—
573C2×C4—364no—
574C2×C4#379612yes—
575C2×C4#379912yes—
576C2×C4D3×#6712yes—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3C2×#88511yescharacteristic
585C2×C3#557811yescharacteristic
586C2×C3#558211yescharacteristic
587C2×C3#563511yescharacteristic
588C2×C3#564111yescharacteristic
589C2×C3#567611yescharacteristic
590C2×C3#572711yescharacteristic
591C2×C3#572811yescharacteristic
592C2×C3#573011yescharacteristic
593C2×C3#573211yescharacteristic
594C2×C3#573311yescharacteristic
595C2×C3#580611yescharacteristic
596C2×C3C2×#94711yescharacteristic
597C2×C3Q8×#6711yescharacteristic
598D3—124no—
599D3—122no—
600D3—122no—
601C22—182no—
602C22—182no—
603C22—182no—
604C22—361no—
605C22—361no—
606C22—361no—
607C22—361no—
608C22C2×#379611yescharacteristic
609C22C2×#379911yescharacteristic
610C22D3×#23711yescharacteristic
611C22#6431411yescharacteristic
612C22#6431611yescharacteristic
613C22D32×Q811yescharacteristic
614C22C2×D3×#6711yescharacteristic
615C4—42no—
616C4—62no—
617C4—62no—
618C4—62no—
619C4—64no—
620C4—122no—
621C4—121no—
622C4—362no—
623C4—361no—
624C4#6390714yes—
625C3—21no—
626C3#7663211yescharacteristic, complemented
627C3#8325811yescharacteristic, complemented
628C2—362no—
629C2#1059435211yescharacteristic
630C2#1059439311yescharacteristic
631C2#1059439711yescharacteristic
632C2#1059455711yescharacteristic
633C2C2×#6390711yescharacteristic
634C2#1059522911yescharacteristic
635C2#1059540311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
4. C3×#4973C2semidirect
5. #10591341C2semidirect
8. Dic3×C4⋊Dic3C2semidirect
9. #10591261C2semidirect
11. #10591220C2semidirect
42. C2×#888D3semidirect
53. #4973D3semidirect
92. #3722Q8semidirect
535. C32#2492semidirect
626. C3#76632semidirect
627. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638712
#105926862
C3×#49732
#105913412
#105913102
C4×#37222
Dic3×C4⋊Dic32
#105912612
#105912582
#105912202
#832583
#766323