Finite Group Databasebeta

← #11806070

Subgroups — #11806070

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4#10591702C212yesmaximal, complemented
5#10591701C212yesmaximal, complemented
6Dic3×#217C212yesmaximal, complemented
7#10591696C212yesmaximal, complemented
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591274C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591224C211yesmaximal, characteristic, complemented
12#82338—31nomaximal
13#76303—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C2×#3757C2212yes—
17C2×#3757C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C3×D4×Dic3C418yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34#63579C2211yescharacteristic
35#63579C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×D4×Dic3D311yescharacteristic
40C3×#390—31no—
41#5221—31no—
42#5221—31no—
43#5221—61no—
44#5221D311yescharacteristic
45#5211—32no—
46C4×#217—32no—
47#4977—31no—
48Dic3×C4⋊C4—31no—
49Dic3×C4⋊C4—31no—
50Dic3×C4⋊C4—31no—
51#4951—32no—
52#4951—32no—
53#4945—32no—
54#4944—32no—
55#4943—32no—
56Dic3×C22⋊C4—32no—
57#4936—31no—
58C4×C4⋊Dic3—31no—
59C4×C4⋊Dic3—31no—
60C4×Dic3⋊C4—31no—
61C24×C32C2312yes—
62C2×C32×D4—22no—
63C2×C32×D4—22no—
64C2×C32×D4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3—42no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2×C418yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78#3757—24no—
79#3757—42no—
80C4⋊(C3⋊Dic3)—22no—
81C4×C3⋊Dic3—22no—
82C3×#217—24no—
83C3×#217—42no—
84C3×#217C2×C418yes—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2×C414yes—
87C3×C4×Dic3—22no—
88C3×C4×Dic3C2×C414yes—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic32—42no—
92Dic32—42no—
93#2357—91noSylow
94C22×C3×D4—21no—
95C22×C3×D4C2×D311yescharacteristic
96C22×C3×D4C2×D311yescharacteristic
97C23×C3×C4—32no—
98C23×Dic3C2×D312yes—
99C3×C4×D4—38no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C42—31no—
106C2×C3×C42—31no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—62no—
112C2×#217—62no—
113C2×#217C2×D312yes—
114C2×#217C2×D312yes—
115C2×#217C2×D312yes—
116D4×Dic3Dic318yescomplemented
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×C4×Dic3C2×D311yescharacteristic
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—32no—
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—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C22×C414yes—
154C23×C32C2411yescharacteristic
155C32×D4—28no—
156C2×C32×C4C22×C412yes—
157C2×C32×C4#4112yes—
158C2×C32×C4#4112yes—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3#4112yes—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—48no—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C414yes—
186C2×C3×Dic3#4112yes—
187C2×C4×D4—31no—
188#390—31no—
189#390—91no—
190#388—92no—
191#388—92no—
192#382—91no—
193#381—92no—
194C4×C4⋊C4—91no—
195C4×C4⋊C4—91no—
196C4×C4⋊C4—91no—
197C4×C22⋊C4—92no—
198C24×C3—22no—
199C24×C3C22×D312yes—
200C24×C3C22×D312yes—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—24no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4C4×D314yes—
209C2×C3×D4C2×Dic314yes—
210C22×C3×C4—21no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—38no—
216C22×C3×C4—32no—
217C22×C3×C4—31no—
218C22×C3×C4—122no—
219C22×C3×C4—122no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—32no—
226C22×Dic3—31no—
227C22×Dic3—32no—
228C22×Dic3—42no—
229C22×Dic3—42no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—62no—
233C22×Dic3C2×Dic318yes—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D311yescharacteristic
240C3×C4⋊C4—34no—
241C3×C4⋊C4—62no—
242C3×C22⋊C4—38no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4—122no—
245C3×C42—34no—
246C3×C42—62no—
247#217—24no—
248#217—42no—
249#217—64no—
250#217—64no—
251#217—124no—
252#217—122no—
253#217—122no—
254#217—124no—
255#217C2×Dic318yes—
256C4⋊Dic3—22no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—122no—
262C4⋊Dic3C2×Dic314yes—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265C4×Dic3—22no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—122no—
269C4×Dic3—122no—
270C4×Dic3—122no—
271C4×Dic3—122no—
272C4×Dic3—122no—
273C4×Dic3C2×Dic314yes—
274C22×C32—24no—
275C22×C32—24no—
276C22×C32—24no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C23×C411yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32H(5,𝔽2)11yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C32×C4#11714yes—
289C3⋊Dic3—22no—
290C3⋊Dic3—41no—
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—24no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C22×D4D3211yescharacteristic
299C23×C4—32no—
300C4×D4—38no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—91no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4—92no—
310C2×C22⋊C4—92no—
311C2×C42—31no—
312C2×C42—31no—
313C2×C42—91no—
314C2×C42—92no—
315C2×C42—92no—
316#95—91no—
317#95—92no—
318#95—91no—
319#95—92no—
320#95—92no—
321#95—92no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—21no—
335C23×C3—24no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3C2×C4×D314yes—
343C23×C3C22×Dic314yes—
344C23×C3C23×D311yescharacteristic
345C23×C3C23×D311yescharacteristic
346C3×D4—28no—
347C3×D4—28no—
348C3×D4—48no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—34no—
355C2×C3×C4—32no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—62no—
370C2×C3×C4—128no—
371C2×C3×C4C2×C4×D312yes—
372C2×C3×C4#23512yes—
373C2×C3×C4#23512yes—
374C2×C3×C4#23712yes—
375C2×C3×C4#23712yes—
376C2×C3×C4C22×Dic312yes—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—48no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3#23712yes—
420C2×Dic3C22×Dic312yes—
421C2×Dic3C22×Dic312yes—
422C2×Dic3C22×Dic314yes—
423C2×C32—44no—
424C2×C32C2×#11711yescharacteristic
425C2×C32C4×#4111yescharacteristic
426C2×C32#51811yescharacteristic
427C2×C32#55311yescharacteristic
428C2×C32#55311yescharacteristic
429C2×C32#55911yescharacteristic
430C2×C32#55911yescharacteristic
431C24C2×D3212yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4D3×Dic314yes—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—31no—
439C22×C4—38no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—92no—
445C22×C4—122no—
446C22×C4—122no—
447C22×C4C2×D3211yescharacteristic
448C4⋊C4—34no—
449C4⋊C4—62no—
450C4⋊C4—182no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C22⋊C4—38no—
454C22⋊C4—64no—
455C22⋊C4—122no—
456C22⋊C4—184no—
457C22⋊C4—362no—
458C42—34no—
459C42—62no—
460C42—182no—
461C42—362no—
462C42—362no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—44no—
477C22×C3—44no—
478C22×C3—44no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—82no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—82no—
491C22×C3C22×C4×D311yescharacteristic
492C22×C3C2×#23511yescharacteristic
493C22×C3C2×#23511yescharacteristic
494C22×C3C2×#23711yescharacteristic
495C22×C3C2×#23711yescharacteristic
496C22×C3C2×#23711yescharacteristic
497C22×C3#100411yescharacteristic
498C22×C3#100411yescharacteristic
499C22×C3#100411yescharacteristic
500C22×C3D3×#4111yescharacteristic
501C22×C3D3×#4111yescharacteristic
502C22×C3D3×#4111yescharacteristic
503C22×C3#100911yescharacteristic
504C22×C3C23×Dic311yescharacteristic
505C3×C4—24no—
506C3×C4—62no—
507C3×C4—62no—
508C3×C4—64no—
509C3×C4—62no—
510C3×C4—121no—
511C3×C4—122no—
512C3×C4#87714yes—
513C3×C4#92614yes—
514Dic3—22no—
515Dic3—24no—
516Dic3—22no—
517Dic3—22no—
518Dic3—42no—
519Dic3—41no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523Dic3—122no—
524Dic3—122no—
525Dic3—121no—
526Dic3—122no—
527Dic3—121no—
528Dic3—242no—
529C32#235711yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23C2×D3×Dic314yes—
537C23C22×D3211yescharacteristic
538D4—28no—
539C2×C4—32no—
540C2×C4—32no—
541C2×C4—32no—
542C2×C4—34no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—62no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—92no—
558C2×C4—128no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—182no—
567C2×C4C2×D3×Dic312yes—
568C2×C4#380412yes—
569C2×C4#380412yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—44no—
578C2×C3—44no—
579C2×C3—84no—
580C2×C3C2×#87711yescharacteristic
581C2×C3C4×#23711yescharacteristic
582C2×C3#554511yescharacteristic
583C2×C3#555811yescharacteristic
584C2×C3#555811yescharacteristic
585C2×C3#555911yescharacteristic
586C2×C3#555911yescharacteristic
587C2×C3#561411yescharacteristic
588C2×C3#561811yescharacteristic
589C2×C3#568111yescharacteristic
590C2×C3#571311yescharacteristic
591C2×C3C2×#92611yescharacteristic
592C2×C3#579811yescharacteristic
593C2×C3Dic3×#4111yescharacteristic
594C22—24no—
595C22—24no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22D3×#23711yescharacteristic
602C22#6431211yescharacteristic
603C22#6431311yescharacteristic
604C22#6431411yescharacteristic
605C22C22×D3×Dic311yescharacteristic
606C22C2×#380411yescharacteristic
607C22C2×#380411yescharacteristic
608C4—62no—
609C4—62no—
610C4—62no—
611C4—64no—
612C4—121no—
613C4—122no—
614C4—182no—
615C4—361no—
616C4—362no—
617C4#6395514yes—
618C3—21no—
619C3#7630311yescharacteristic, complemented
620C3#8233811yescharacteristic, complemented
621C2—44no—
622C2#1059512211yescharacteristic
623C2#1059518211yescharacteristic
624C2Dic3×#23711yescharacteristic
625C2#1059519811yescharacteristic
626C2#1059521011yescharacteristic
627C2#1059521511yescharacteristic
628C2C2×#6395511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591702C2semidirect
5. #10591701C2semidirect
6. Dic3×#217C2semidirect
7. #10591696C2semidirect
8. C4×Dic3⋊Dic3C2semidirect
9. #10591274C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591224C2semidirect
23. C3×D4×Dic3C4semidirect
116. D4×Dic3Dic3semidirect
529. C32#2357semidirect
619. C3#76303semidirect
620. C3#82338semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105929202
C3×#52212
#105917022
#105917012
Dic3×#2172
#105916962
C4×Dic3⋊Dic32
#105912742
Dic3×C4⋊Dic32
#105912242
#823383
#763033