Finite Group Databasebeta

← C3×#72051 #11794037

Subgroups — C3×#72051 #11794037

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×SD16C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic
5C2×C3×#832C211yesmaximal, characteristic
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#72051C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C2×C32×SD16—22no—
13C2×C32×SD16—22no—
14C2×C32×SD16—22no—
15C22×C32×C8C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#835—22no—
23C3×#832—22no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95—21no—
26C3×Dic3⋊C8—22no—
27C22×C3×SD16—21no—
28C22×C3×SD16D311yescharacteristic
29C22×C3×SD16C2×C311yescharacteristic
30C2×C3×C4⋊C8—31no—
31C2×C3×#103—31no—
32C2×C3×#102—31no—
33C3×#391—31no—
34C3×#390—31no—
35#5229C2×C311yescharacteristic, complemented
36C2×#835C2×C311yescharacteristic, complemented
37#5221C2×C311yescharacteristic
38C2×#832C2×C311yescharacteristic
39C2×Dic3⋊C8C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4551C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4D412yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C32×SD16—28no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D412yes—
65C3×#217—42no—
66C3×#217—42no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#2055—31noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C22×C311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C22×C311yescharacteristic
83C2×C3×SD16—24no—
84C2×C3×SD16—24no—
85C2×C3×SD16—24no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C22×C311yescharacteristic
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—61no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C42—31no—
101C2×#217—21no—
102C2×#217—21no—
103C2×C4⋊Dic3C22×C311yescharacteristic
104C2×C4⋊Dic3C22×C311yescharacteristic
105C2×C4×Dic3C22×C311yescharacteristic
106C22×C3⋊C8C22×C311yescharacteristic
107C3×C4⋊C8—62no—
108C3×#103—62no—
109C3×#102—62no—
110C3×#95—61no—
111C3×#95—61no—
112#835—22no—
113#832—22no—
114C3⋊#95—21no—
115C3⋊#95—21no—
116Dic3⋊C8—22no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C32×Q8—22no—
126C32×Q8—22no—
127C32×Q8—41no—
128C32×Q8—41no—
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—22no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3SD1612yescomplemented
154C32×C8—22no—
155C3×C3⋊C8—41no—
156C22×SD16C3×D311yescharacteristic
157C2×C4⋊C8—31no—
158C2×#103—31no—
159C2×#102—31no—
160#391—31no—
161#390—31no—
162#340—31no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—41no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—41no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8#6712yes—
183C2×C3×Q8C3×D412yes—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—41no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4#6712yes—
201C2×C3×D4C3×D412yes—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—41no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C23×C311yescharacteristic
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3C3×D411yescharacteristic
215C22×Dic3C3×D411yescharacteristic
216C3×SD16—216no—
217C3×SD16—28no—
218C3×SD16—28no—
219C2×C3×C8—22no—
220C2×C3×C8—22no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8#6712yes—
230C2×C3×C8C3×D412yes—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—122no—
236C3×C22⋊C4—122no—
237C3×C42—61no—
238C3×C42—61no—
239#217—42no—
240#217—42no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—81no—
254C22×C32—81no—
255C22×C32—81no—
256C22×C32—81no—
257C22×C32#12111yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12111yescharacteristic
260C22×C32C2×SD1611yescharacteristic
261C22×C32#13511yescharacteristic
262C22×C32AGL(1,ℤ/8)11yescharacteristic
263C22×C32#13711yescharacteristic
264C32×C4—42no—
265C32×C4#12011yescharacteristic
266C32×C4#12311yescharacteristic
267C32×C4#12311yescharacteristic
268C32×C4#12411yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—81no—
272C3×Dic3—81no—
273C22×Q8C2×C3×D311yescharacteristic
274C22×D4C2×C3×D311yescharacteristic
275C2×SD16—22no—
276C2×SD16—22no—
277C2×SD16—22no—
278C22×C8—31no—
279C22×C8C2×C3×D311yescharacteristic
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C42—31no—
285C4⋊C8—62no—
286#103—62no—
287#102—62no—
288#95—61no—
289#95—61no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—81no—
309C23×C3—81no—
310C23×C3—81no—
311C23×C3—81no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×C3×D411yescharacteristic
314C3×Q8—24no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—42no—
322C3×Q8—41no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×Q8—41no—
326C3×D4—24no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—41no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—41no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4#23711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C3×#4111yescharacteristic
375C2×C3×C4C3×#4111yescharacteristic
376C2×C3×C4C3×#4111yescharacteristic
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3C3×SD1612yescomplemented
389C3×C8—24no—
390C3×C8—22no—
391C3×C8—22no—
392C3×C8—121no—
393C3⋊C8—41no—
394C2×C32—82no—
395C2×C32#39411yescharacteristic
396C2×C32#46011yescharacteristic
397C2×C32#46111yescharacteristic
398C2×C32#46311yescharacteristic
399C2×C32#46411yescharacteristic
400C2×C32#46511yescharacteristic
401C2×C32#46811yescharacteristic
402C24—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C3×#6712yes—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C3×#6712yes—
415C22×C4—21no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4C22×C3×D311yescharacteristic
421SD16—28no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—61no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8C3×#6712yes—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C22⋊C4—122no—
433C22⋊C4—122no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—82no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3D3×SD1611yescharacteristic
465C22×C3#91411yescharacteristic
466C22×C3#91511yescharacteristic
467C22×C3#91611yescharacteristic
468C22×C3#93811yescharacteristic
469C22×C3#93911yescharacteristic
470C22×C3#93911yescharacteristic
471C22×C3C3×#12111yescharacteristic
472C22×C3C3×#12111yescharacteristic
473C22×C3C3×#12111yescharacteristic
474C22×C3C2×C3×SD1611yescharacteristic
475C22×C3C3×#13511yescharacteristic
476C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
477C22×C3C3×#13711yescharacteristic
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—44no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—62no—
486C3×C4—121no—
487C3×C4—241no—
488C3×C4—241no—
489C3×C4#93511yescharacteristic
490C3×C4#93511yescharacteristic
491C3×C4#93611yescharacteristic
492C3×C4#95311yescharacteristic
493C3×C4C3×#12011yescharacteristic
494C3×C4C3×#12311yescharacteristic
495C3×C4C3×#12311yescharacteristic
496C3×C4C3×#12411yescharacteristic
497Dic3—22no—
498Dic3—41no—
499Dic3—81no—
500Dic3—81no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C3×D3×D411yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—22no—
519C2×C4—32no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4C3×#23711yescharacteristic
534C2×C4C3×#23711yescharacteristic
535C2×C4C3×#23711yescharacteristic
536C2×C4C2×C3×#6711yescharacteristic
537C2×C4C2×C3×#6711yescharacteristic
538C2×C4C2×C3×#6711yescharacteristic
539C8—22no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—84no—
549C2×C3—82no—
550C2×C3—82no—
551C2×C3#516211yescharacteristic
552C2×C3#516311yescharacteristic
553C2×C3#516511yescharacteristic
554C2×C3#516611yescharacteristic
555C2×C3#517111yescharacteristic
556C2×C3#517411yescharacteristic
557C2×C3#522211yescharacteristic
558C2×C3C3×#39411yescharacteristic
559C2×C3C3×#46011yescharacteristic
560C2×C3C3×#46111yescharacteristic
561C2×C3C3×#46311yescharacteristic
562C2×C3C3×#46411yescharacteristic
563C2×C3C3×#46511yescharacteristic
564C2×C3C3×#46811yescharacteristic
565C22—42no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22C3×D3×SD1611yescharacteristic
573C22C3×#91411yescharacteristic
574C22C3×#91511yescharacteristic
575C22C3×#91611yescharacteristic
576C22C3×#93811yescharacteristic
577C22C3×#93911yescharacteristic
578C22C3×#93911yescharacteristic
579C4—42no—
580C4—62no—
581C4—121no—
582C4—241no—
583C4—241no—
584C4C3×#93511yescharacteristic
585C4C3×#93511yescharacteristic
586C4C3×#93611yescharacteristic
587C4C3×#95311yescharacteristic
588C3—21no—
589C3#7205111yescharacteristic, direct product factor
590C3C3×#205511yescharacteristic, complemented
591C2—82no—
592C2C3×#516211yescharacteristic
593C2C3×#516311yescharacteristic
594C2C3×#516511yescharacteristic
595C2C3×#516611yescharacteristic
596C2C3×#517111yescharacteristic
597C2C3×#517411yescharacteristic
598C2C3×#522211yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC22×C32×SD16C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC22×C3×SD16D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
2. C3×#5229C2semidirect
3. C2×C3×#835C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C3×#4551C2semidirect
9. #72051C3direct (N × H)
35. #5229C2×C3semidirect
36. C2×#835C2×C3semidirect
39. C2×Dic3⋊C8C2×C3semidirect
41. #4551C2×C3semidirect
153. C2×C3×Dic3SD16semidirect
388. C2×Dic3C3×SD16semidirect
501. C32#2055semidirect
589. C3#72051direct (N × H)
590. C3C3×#2055semidirect

Maximal subgroups

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

subgroupindex
C22×C32×SD162
C3×#52292
C2×C3×#8352
C3×#52212
C2×C3×#8322
C2×C3×Dic3⋊C82
C3×#45512
C3×#20553
#720513