Finite Group Databasebeta

← #11819082

Subgroups — #11819082

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic, complemented
2C2×#63871C211yesmaximal, characteristic
3C4×#3752C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic, complemented
5#10591343C212yesmaximal, complemented
6#10591325C211yesmaximal, characteristic
7#10591310C212yesmaximal
8#10591274C211yesmaximal, characteristic, complemented
9#10591266C212yesmaximal
10#10591261C212yesmaximal, complemented
11#10591221C211yesmaximal, characteristic, complemented
12#83258—31nomaximal
13#76633—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#869—24no—
26C2×Dic3⋊Dic3C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30#63871—24no—
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4⋊Q8—31no—
40C2×#946—31no—
41C2×#897—31no—
42C2×#869D311yescharacteristic, complemented
43C3×#391—31no—
44#5231—32no—
45#5229—31no—
46#5229—32no—
47#4990—32no—
48#4987—31no—
49#4987—31no—
50#4986—32no—
51Dic3×C4⋊C4—31no—
52Dic3×C4⋊C4—31no—
53#4973—31no—
54C4×(C2×D3)⋊C4—31no—
55C4×(C2×D3)⋊C4—31no—
56C4×(C2×D3)⋊C4—61no—
57#4929D311yescharacteristic, complemented
58#4673—32no—
59#4670—32no—
60#4660—32no—
61#4646—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—22no—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—42no—
82C32×C42—22no—
83#3752—22no—
84#3752Q814yescomplemented
85C4×C3⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—24no—
89C3×C4⋊Dic3D414yes—
90Dic3⋊Dic3—24no—
91#3722—24no—
92#3722—42no—
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—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C42—21no—
108C2×C3×C42C2×D311yescharacteristic
109C2×C3×C42C2×D311yescharacteristic
110#946—64no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—31no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—61no—
120C2×(C2×D3)⋊C4—61no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3C2×D312yes—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×Dic3⋊C4—32no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132#897—64no—
133#869—24no—
134C3×#95—32no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95—61no—
150C3⋊#95C2×D312yes—
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—21no—
159C22×C3⋊D3C2×Q812yes—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×Q812yes—
166C2×C32×C4#4112yes—
167C2×C32×C4#4112yes—
168C2×C32×C4#4112yes—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3C2×Q812yes—
178C4×C3⋊D3—44no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D414yes—
191C3×Dic6—48no—
192C3×Dic6—44no—
193C2×C4⋊Q8—31no—
194C2×C22⋊Q8—91no—
195#400—92no—
196#393—92no—
197#391—31no—
198#391—92no—
199#391—91no—
200#388—92no—
201#380—91no—
202C4×C4⋊C4—91no—
203C4×C22⋊C4—91no—
204C23×D3—31no—
205C23×D3—31no—
206C23×D3—61no—
207C2×C3×Q8—64no—
208C2×C3×Q8—64no—
209C2×C3×Q8—62no—
210C2×C3×Q8—62no—
211C2×C3×Q8—62no—
212C2×C3×Q8—122no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C2×C4×D3—64no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×Dic6—22no—
249C2×Dic6—22no—
250C2×Dic6—24no—
251C2×Dic6—22no—
252C2×Dic6—24no—
253C2×Dic6—42no—
254C3×C4⋊C4—34no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C42—22no—
259C3×C42—22no—
260C3×C42—42no—
261(C2×D3)⋊C4—34no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—122no—
270(C2×D3)⋊C4—122no—
271C4⋊Dic3—22no—
272C4⋊Dic3—22no—
273C4⋊Dic3—24no—
274C4⋊Dic3—64no—
275C4⋊Dic3#6714yes—
276Dic3⋊C4—64no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—122no—
280C4×Dic3—122no—
281C4×Dic3—122no—
282C22×C32C22×D411yescharacteristic
283C22×C32C22×Q811yescharacteristic
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C22×C322−1+411yescharacteristic
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C32×C4—22no—
297C32×C4—22no—
298C32×C4#12414yes—
299C3⋊Dic3—22no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3—42no—
305C3×Dic3—42no—
306C22×Q8—31no—
307C22×Q8—32no—
308C23×C4—91no—
309C4⋊Q8—64no—
310C22⋊Q8—184no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—32no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—92no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—92no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—92no—
320C2×C42—91no—
321C2×C42—92no—
322C2×C42D3211yescharacteristic
323#95—32no—
324#95—32no—
325#95—92no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—91no—
330#95—91no—
331C23×C3—21no—
332C23×C3C23×D311yescharacteristic
333C23×C3C23×D311yescharacteristic
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C3×Q8—128no—
356C3×Q8—124no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—34no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4#23512yes—
387C2×C3×C4D3×D412yes—
388C2×C3×C4#23712yes—
389C2×C3×C4#23712yes—
390C2×C3×C4D3×Q812yes—
391C2×C3×C4D3×Q812yes—
392C2×C3×C4#23912yes—
393C2×C3×C4#23912yes—
394C2×C3×C4#23912yes—
395C2×C3×C4C2×#6712yes—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3C2×#6714yes—
435C4×D3—128no—
436C4×D3—124no—
437C4×D3—124no—
438Dic6—48no—
439Dic6—44no—
440C2×C32C2×#12411yescharacteristic
441C2×C32#53311yescharacteristic
442C2×C32#54211yescharacteristic
443C2×C32#54611yescharacteristic
444C2×C32D4×Q811yescharacteristic
445C2×C32#55411yescharacteristic
446C2×C32#55611yescharacteristic
447C3⋊D3—42no—
448C24—91no—
449C2×Q8—64no—
450C2×Q8—64no—
451C2×Q8—62no—
452C2×Q8—62no—
453C2×Q8—62no—
454C2×Q8—122no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—182no—
463C22×C4—182no—
464C22×C4—182no—
465C22×C4C2×D3211yescharacteristic
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—34no—
469C4⋊C4—64no—
470C4⋊C4—62no—
471C4⋊C4—62no—
472C4⋊C4—184no—
473C22⋊C4—94no—
474C22⋊C4—184no—
475C22⋊C4—182no—
476C22⋊C4—362no—
477C42—22no—
478C42—182no—
479C42—362no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3C2×#23511yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C22×C3C2×#23711yescharacteristic
491C22×C3#100411yescharacteristic
492C22×C3C2×D3×Q811yescharacteristic
493C22×C3C2×D3×Q811yescharacteristic
494C22×C3C2×#23911yescharacteristic
495C22×C3C2×#23911yescharacteristic
496C22×C3C2×#23911yescharacteristic
497C22×C3#100711yescharacteristic
498C22×C3#100911yescharacteristic
499C22×C3#101011yescharacteristic
500C22×C3C22×#6711yescharacteristic
501C2×D3—64no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—121no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—24no—
527C3×C4—42no—
528C3×C4—42no—
529C3×C4—64no—
530C3×C4—122no—
531C3×C4—122no—
532C3×C4—122no—
533C3×C4#88514yes—
534C3×C4#94714yes—
535Dic3—24no—
536Dic3—42no—
537Dic3—42no—
538Dic3—42no—
539Dic3—62no—
540Dic3—62no—
541Dic3—122no—
542Dic3—122no—
543Dic3—122no—
544Dic3—121no—
545Dic3—121no—
546Dic3—121no—
547Dic3—121no—
548C32#249211yescharacteristic, complemented, Sylow
549C23—92no—
550C23—181no—
551C23—181no—
552C23—181no—
553C23—181no—
554C23—181no—
555C23—181no—
556C23C22×D3211yescharacteristic
557Q8—128no—
558Q8—124no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—34no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—92no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—364no—
585C2×C4#379612yes—
586C2×C4#379612yes—
587C2×C4#379712yes—
588C2×C4#379912yes—
589C2×C4D3×#6712yes—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3C2×#88511yescharacteristic
598C2×C3#557911yescharacteristic
599C2×C3#558411yescharacteristic
600C2×C3#563011yescharacteristic
601C2×C3#563211yescharacteristic
602C2×C3#568211yescharacteristic
603C2×C3#572811yescharacteristic
604C2×C3#572811yescharacteristic
605C2×C3#573011yescharacteristic
606C2×C3#573211yescharacteristic
607C2×C3#573311yescharacteristic
608C2×C3#580611yescharacteristic
609C2×C3C2×#94711yescharacteristic
610C2×C3Q8×#6711yescharacteristic
611D3—124no—
612D3—122no—
613D3—122no—
614C22—182no—
615C22—182no—
616C22—182no—
617C22—361no—
618C22—361no—
619C22—361no—
620C22—361no—
621C22C2×#379611yescharacteristic
622C22C2×#379611yescharacteristic
623C22#6429711yescharacteristic
624C22C2×#379711yescharacteristic
625C22C2×#379911yescharacteristic
626C22#6430711yescharacteristic
627C22C2×D3×#6711yescharacteristic
628C4—22no—
629C4—22no—
630C4—64no—
631C4—122no—
632C4—122no—
633C4—122no—
634C4—182no—
635C4—361no—
636C4—361no—
637C4#6390714yes—
638C3—21no—
639C3#7663311yescharacteristic, complemented
640C3#8325811yescharacteristic, complemented
641C2—362no—
642C2#1059386511yescharacteristic
643C2#1059386611yescharacteristic
644C2#1059395511yescharacteristic
645C2#1059395811yescharacteristic
646C2#1059480311yescharacteristic
647C2#1059488911yescharacteristic
648C2C2×#6390711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#869C2semidirect
4. C3×#4929C2semidirect
5. #10591343C2semidirect
8. #10591274C2semidirect
10. #10591261C2semidirect
11. #10591221C2semidirect
42. C2×#869D3semidirect
57. #4929D3semidirect
84. #3752Q8semidirect
548. C32#2492semidirect
639. C3#76633semidirect
640. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8692
C2×#638712
C4×#37522
C3×#49292
#105913432
#105913252
#105913102
#105912742
#105912662
#105912612
#105912212
#832583
#766333