Finite Group Databasebeta

← C3×#82839 #11807518

Subgroups — C3×#82839 #11807518

Order 1152.

1275 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic
4C3×C4×#217C212yesmaximal, complemented
5C3×#4980C212yesmaximal, complemented
6C3×Dic3×C4⋊C4C212yesmaximal, complemented
7C3×#4951C212yesmaximal, complemented
8C3×#4951C212yesmaximal, complemented
9C3×Dic3×C22⋊C4C212yesmaximal, complemented
10C3×#2374—31nomaximal
11#82839C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C32×#123C418yescomplemented
16C2×C32×C4⋊C4C2212yes—
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×C3×#217C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C2×C3×#123—21no—
35C2×C3×#123D311yescharacteristic
36C2×C3×#123C2×C311yescharacteristic
37C3×#390—31no—
38C3×#388—32no—
39C3×#388—32no—
40C3×#387—32no—
41C3×#386—31no—
42C3×C4×C4⋊C4—32no—
43C3×C4×C22⋊C4—32no—
44C3×C4×C22⋊C4—32no—
45#5221C2×C311yescharacteristic
46#5220C2×C311yescharacteristic
47C4×#217C2×C312yescomplemented
48#4980C2×C312yescomplemented
49Dic3×C4⋊C4C2×C312yescomplemented
50#4951C2×C312yescomplemented
51#4951C2×C312yescomplemented
52Dic3×C22⋊C4C2×C312yescomplemented
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C2×C32×D4—41no—
56C2×C32×D4—41no—
57C2×C32×D4C2×C414yes—
58C22×C32×C4—41no—
59C22×C32×C4—41no—
60C22×C32×C4C2×C414yescomplemented
61C22×C32×C4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C3×Dic3—24no—
65C22×C3×Dic3—41no—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C32×C4⋊C4C2×C418yescomplemented
71C32×C22⋊C4C2×C418yes—
72C32×C22⋊C4C2×C414yescomplemented
73C3×#217—24no—
74C3×#217—24no—
75C3×#217—24no—
76C3×#217—41no—
77C3×C4⋊Dic3—24no—
78C3×C4⋊Dic3—41no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3—41no—
81C3×C4×Dic3—42no—
82C3×C4×Dic3—42no—
83#2374—31noSylow
84C22×C3×D4—21no—
85C22×C3×D4C2×D311yescharacteristic
86C22×C3×D4C22×C311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—31no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C23×Dic3C22×C311yescharacteristic
92C3×#123—28no—
93C3×#123Dic318yescomplemented
94C3×#123C3×C418yescomplemented
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4C2×D312yes—
99C2×C3×C4⋊C4C22×C312yes—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4C2×D312yes—
107C2×C3×C22⋊C4C2×D311yescharacteristic
108C2×C3×C22⋊C4C22×C312yes—
109C2×C3×C22⋊C4C22×C311yescharacteristic
110C2×C3×C42—32no—
111C2×C3×C42—32no—
112C2×C3×C42—32no—
113C2×C3×C42—31no—
114C2×#217C22×C312yes—
115C2×#217C22×C312yes—
116C2×#217C22×C312yes—
117C2×#217C22×C311yescharacteristic
118C2×C4⋊Dic3C22×C312yes—
119C2×C4⋊Dic3C22×C311yescharacteristic
120C2×C4×Dic3C22×C312yes—
121C2×C4×Dic3C22×C312yes—
122C2×C4×Dic3C22×C312yes—
123C2×C4×Dic3C22×C311yescharacteristic
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—32no—
127C3×#95—32no—
128C3×#95—32no—
129C3⋊#95C22×C312yes—
130C3⋊#95C22×C312yes—
131C3⋊#95C22×C312yes—
132C3⋊#95C22×C312yes—
133C3⋊#95C22×C312yes—
134C23×C32—21no—
135C23×C32—21no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32—22no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32C22×C412yes—
143C23×C32C22×C412yes—
144C23×C32C2411yescharacteristic
145C32×D4—44no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—44no—
153C2×C32×C4C22×C414yes—
154C2×C32×C4C22×C414yes—
155C2×C32×C4C22×C412yes—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—44no—
167C2×C3×Dic3#4114yes—
168C2×C3×Dic3#4114yes—
169C2×#123C3×D311yescharacteristic
170#390—31no—
171#388—32no—
172#388—32no—
173#387—32no—
174#386—31no—
175C4×C4⋊C4—32no—
176C4×C22⋊C4—32no—
177C4×C22⋊C4—32no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3C22×D311yescharacteristic
181C24×C3C22×D311yescharacteristic
182C24×C3C23×C311yescharacteristic
183C24×C3C23×C311yescharacteristic
184C2×C3×D4—24no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—42no—
190C2×C3×D4—42no—
191C2×C3×D4C2×Dic314yes—
192C2×C3×D4C2×C3×C414yes—
193C22×C3×C4—24no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—41no—
202C22×C3×C4—41no—
203C22×C3×C4—41no—
204C22×C3×C4—41no—
205C22×C3×C4—42no—
206C22×C3×C4—42no—
207C22×C3×C4—64no—
208C22×C3×C4—121no—
209C22×C3×C4C2×Dic314yescomplemented
210C22×C3×C4C2×C3×C414yescomplemented
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C23×C312yes—
215C22×C3×C4C23×C312yes—
216C22×C3×C4C23×C311yescharacteristic
217C22×Dic3—24no—
218C22×Dic3—41no—
219C22×Dic3C23×C312yes—
220C22×Dic3C23×C312yes—
221C22×Dic3C23×C312yes—
222C22×Dic3C23×C312yes—
223C3×C4⋊C4—28no—
224C3×C4⋊C4—64no—
225C3×C4⋊C4—121no—
226C3×C4⋊C4C2×Dic318yescomplemented
227C3×C4⋊C4C2×C3×C418yescomplemented
228C3×C22⋊C4—28no—
229C3×C22⋊C4—24no—
230C3×C22⋊C4—64no—
231C3×C22⋊C4—64no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—121no—
234C3×C22⋊C4C2×Dic318yes—
235C3×C22⋊C4C2×Dic314yescomplemented
236C3×C22⋊C4C2×C3×C418yes—
237C3×C22⋊C4C2×C3×C414yescomplemented
238C3×C42—64no—
239C3×C42—122no—
240C3×C42—122no—
241C3×C42—121no—
242#217—24no—
243#217—24no—
244#217—24no—
245#217—41no—
246C4⋊Dic3—24no—
247C4⋊Dic3—41no—
248C4×Dic3—24no—
249C4×Dic3—41no—
250C4×Dic3—42no—
251C4×Dic3—42no—
252C22×C32—22no—
253C22×C32—24no—
254C22×C32—24no—
255C22×C32—22no—
256C22×C32—41no—
257C22×C32—42no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32—41no—
262C22×C32C23×C411yescharacteristic
263C22×C32C2×#4112yes—
264C22×C32C2×#4112yes—
265C22×C32H(5,𝔽2)11yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C32×C4—24no—
268C32×C4—24no—
269C32×C4—22no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×D4C2×C3×D311yescharacteristic
275C23×C4—31no—
276C23×C4C2×C3×D311yescharacteristic
277#123C3×Dic318yescomplemented
278C2×C4⋊C4—32no—
279C2×C4⋊C4—31no—
280C2×C4⋊C4C2×C3×D312yes—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—32no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—31no—
285C2×C22⋊C4C2×C3×D312yes—
286C2×C22⋊C4C2×C3×D311yescharacteristic
287C2×C42—32no—
288C2×C42—32no—
289C2×C42—32no—
290C2×C42—31no—
291#95—32no—
292#95—32no—
293#95—32no—
294#95—32no—
295#95—32no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3C22×Dic312yes—
324C23×C3C22×Dic312yes—
325C23×C3C22×C3×C412yes—
326C23×C3C22×C3×C412yes—
327C23×C3C23×D311yescharacteristic
328C23×C3C24×C311yescharacteristic
329C3×D4—44no—
330C3×D4—44no—
331C3×D4—48no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—34no—
348C2×C3×C4—34no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—44no—
356C2×C3×C4—44no—
357C2×C3×C4—48no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—124no—
369C2×C3×C4C22×Dic314yes—
370C2×C3×C4C22×Dic314yes—
371C2×C3×C4C22×Dic312yes—
372C2×C3×C4C22×C3×C414yes—
373C2×C3×C4C22×C3×C414yes—
374C2×C3×C4C22×C3×C412yes—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—44no—
386C2×Dic3C3×#4114yes—
387C2×Dic3C3×#4114yes—
388C2×C32—42no—
389C2×C32—42no—
390C2×C32C4×#4112yes—
391C2×C32#51811yescharacteristic
392C2×C32#55111yescharacteristic
393C2×C32#55312yes—
394C2×C32#55911yescharacteristic
395C24C22×C3×D311yescharacteristic
396C24C22×C3×D311yescharacteristic
397C2×D4—41no—
398C2×D4—41no—
399C2×D4C2×C3×Dic314yes—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—64no—
407C22×C4—121no—
408C22×C4C2×C3×Dic314yescomplemented
409C22×C4C22×C3×D312yes—
410C22×C4C22×C3×D312yes—
411C22×C4C22×C3×D311yescharacteristic
412C4⋊C4—64no—
413C4⋊C4—121no—
414C4⋊C4C2×C3×Dic318yescomplemented
415C22⋊C4—64no—
416C22⋊C4—64no—
417C22⋊C4—64no—
418C22⋊C4—121no—
419C22⋊C4C2×C3×Dic318yes—
420C22⋊C4C2×C3×Dic314yescomplemented
421C42—64no—
422C42—122no—
423C42—122no—
424C42—121no—
425C22×C3—24no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—44no—
440C22×C3—42no—
441C22×C3—44no—
442C22×C3—42no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—81no—
458C22×C3—82no—
459C22×C3—81no—
460C22×C3#100411yescharacteristic
461C22×C3#100411yescharacteristic
462C22×C3D3×#4112yes—
463C22×C3D3×#4112yes—
464C22×C3C23×Dic311yescharacteristic
465C22×C3C23×C3×C411yescharacteristic
466C22×C3C2×C3×#4112yes—
467C22×C3C2×C3×#4112yes—
468C22×C3C3×H(5,𝔽2)11yescharacteristic
469C22×C3C3×H(5,𝔽2)11yescharacteristic
470C3×C4—24no—
471C3×C4—22no—
472C3×C4—24no—
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—22no—
476C3×C4—44no—
477C3×C4—42no—
478C3×C4—44no—
479C3×C4—64no—
480C3×C4—64no—
481C3×C4—122no—
482C3×C4—122no—
483Dic3—24no—
484Dic3—24no—
485Dic3—42no—
486Dic3—42no—
487C32#237411yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23C22×C3×Dic312yes—
497C23C22×C3×Dic312yes—
498C23C23×C3×D311yescharacteristic
499D4—44no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—44no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—124no—
520C2×C4C22×C3×Dic314yes—
521C2×C4C22×C3×Dic314yes—
522C2×C4C22×C3×Dic312yes—
523C2×C3—21no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—44no—
529C2×C3—42no—
530C2×C3—42no—
531C2×C3—42no—
532C2×C3—42no—
533C2×C3—82no—
534C2×C3#565911yescharacteristic
535C2×C3#566112yes—
536C2×C3#566411yescharacteristic
537C2×C3#579811yescharacteristic
538C2×C3Dic3×#4112yes—
539C2×C3C3×C4×#4112yes—
540C2×C3C3×#51811yescharacteristic
541C2×C3C3×#55111yescharacteristic
542C2×C3C3×#55312yes—
543C2×C3C3×#55911yescharacteristic
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—41no—
553C22—41no—
554C22C3×#100411yescharacteristic
555C22C3×#100411yescharacteristic
556C22C3×D3×#4112yes—
557C22C3×D3×#4112yes—
558C22C23×C3×Dic311yescharacteristic
559C4—24no—
560C4—22no—
561C4—24no—
562C4—64no—
563C4—64no—
564C4—122no—
565C4—122no—
566C3—21no—
567C3#8283911yescharacteristic, direct product factor
568C3C3×#237411yescharacteristic, complemented
569C2—42no—
570C2—42no—
571C2C3×#565911yescharacteristic
572C2C3×#566112yes—
573C2C3×#566411yescharacteristic
574C2C3×#579811yescharacteristic
575C2C3×Dic3×#4112yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#123C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#123D3
hypocenterC3C3×#2374
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
4. C3×C4×#217C2semidirect
5. C3×#4980C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C3×#4951C2semidirect
8. C3×#4951C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
11. #82839C3direct (N × H)
15. C32×#123C4semidirect
47. C4×#217C2×C3semidirect
48. #4980C2×C3semidirect
49. Dic3×C4⋊C4C2×C3semidirect
50. #4951C2×C3semidirect
51. #4951C2×C3semidirect
52. Dic3×C22⋊C4C2×C3semidirect
60. C22×C32×C4C2×C4semidirect
70. C32×C4⋊C4C2×C4semidirect
72. C32×C22⋊C4C2×C4semidirect
93. C3×#123Dic3semidirect
94. C3×#123C3×C4semidirect
209. C22×C3×C4C2×Dic3semidirect
210. C22×C3×C4C2×C3×C4semidirect
226. C3×C4⋊C4C2×Dic3semidirect
227. C3×C4⋊C4C2×C3×C4semidirect
235. C3×C22⋊C4C2×Dic3semidirect
237. C3×C22⋊C4C2×C3×C4semidirect
277. #123C3×Dic3semidirect
408. C22×C4C2×C3×Dic3semidirect
414. C4⋊C4C2×C3×Dic3semidirect
420. C22⋊C4C2×C3×Dic3semidirect
487. C32#2374semidirect
567. C3#82839direct (N × H)
568. C3C3×#2374semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C3×#52212
C3×#52202
C3×C4×#2172
C3×#49802
C3×Dic3×C4⋊C42
C3×#49512
C3×Dic3×C22⋊C42
C3×#23743
#828393