Finite Group Databasebeta

← Dic3×#4038 #14319511

Subgroups — Dic3×#4038 #14319511

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×C4×D5×Dic3C211yesmaximal, characteristic
3C2×#91358C211yesmaximal, characteristic
4C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
5C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#11748884C212yesmaximal
7Dic3×#685C212yesmaximal
8#11748699C211yesmaximal, characteristic, complemented
9Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
10#11748635C212yesmaximal, complemented
11C4×Dic3×Dic5C212yesmaximal, complemented
12C4×#4038—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×#685C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2212yes—
26C3×#4038C418yescomplemented
27C2×#6665C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2212yes—
33C4×D5×Dic3C418yescomplemented
34#91358C418yescomplemented
35#91115C2212yes—
36C5×C3⋊#95C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39Dic3×#117—51nomaximal, Hall
40C2×#4038—31no—
41C2×#4038D311yescharacteristic
42C2×C42×D5—31no—
43C4×C5×C4⋊C4—31no—
44C4⋊C4×Dic5—31no—
45C4⋊C4×Dic5—31no—
46C4×#685—32no—
47C4×C4⋊Dic5—31no—
48C42×Dic5—32no—
49#64955—32no—
50#64937—32no—
51C23×C3×D5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5C2×C414yes—
63C2×C3×C4×D5C2×C414yes—
64C2×C3×C4×D5C2×C414yes—
65C2×D5×Dic3—22no—
66C2×D5×Dic3—22no—
67C2×D5×Dic3—22no—
68C2×D5×Dic3—22no—
69C2×D5×Dic3C2×C414yes—
70C2×D5×Dic3C2×C414yes—
71C3×C5×C4⋊C4C2×C414yescomplemented
72C4⋊Dic15C2×C414yescomplemented
73C4×Dic15—24no—
74C4×Dic15C2×C414yes—
75C5×C4⋊Dic3C2×C414yescomplemented
76C4×C5×Dic3—24no—
77C4×C5×Dic3C2×C414yes—
78C3×#685C2×C418yes—
79C3×C4⋊Dic5C2×C414yescomplemented
80C3×C4×Dic5C2×C418yescomplemented
81#6665C2×C418yes—
82Dic3×Dic5—24no—
83Dic3×Dic5—24no—
84Dic3×Dic5C2×C414yes—
85Dic3×Dic5C2×C414yes—
86Dic3×Dic5C2×C418yescomplemented
87C2×C3×#117—51no—
88C2×#926—51no—
89C22×C4×Dic3—51no—
90Dic3×C4⋊C4—51no—
91Dic3×C4⋊C4—51no—
92Dic3×C4⋊C4—51no—
93Dic3×C4⋊C4D511yescharacteristic, complemented
94Dic3×C22⋊C4—52no—
95Dic3×C22⋊C4—52no—
96#4932—52no—
97C42×Dic3—52no—
98C22×C4×D5—31no—
99C22×C4×D5—31no—
100C22×C4×D5C2×D311yescharacteristic
101C2×C5×C4⋊C4—31no—
102C2×C5×C4⋊C4C2×D311yescharacteristic
103C2×C42×C5—31no—
104C2×C42×C5—32no—
105C2×#685—32no—
106C2×#685C2×D312yes—
107C2×C4⋊Dic5—31no—
108C2×C4⋊Dic5C2×D311yescharacteristic
109C2×C4×Dic5—31no—
110C2×C4×Dic5—31no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5C2×D312yes—
117#4038—38no—
118#4038Dic318yesdirect product factor
119C42×D5—38no—
120C5×#95—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124C4×#117—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C3×D5—21no—
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C22×C3×D5—21no—
130C22×C3×D5C22×C412yes—
131C22×C3×D5C22×C412yes—
132C22×C3×D5C22×C412yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C22×C414yes—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C22×C412yes—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C414yes—
145C2×Dic15C22×C412yes—
146C2×Dic15#4112yes—
147C2×Dic15#4112yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3C22×C412yes—
153C2×C5×Dic3C22×C414yes—
154C2×C5×Dic3C22×C412yes—
155C2×C5×Dic3#4112yes—
156C2×C5×Dic3#4112yes—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5C22×C414yes—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5C22×C412yes—
163C3×C4×D5C42116yescomplemented
164D5×Dic3—28no—
165D5×Dic3—28no—
166C23×C3×C4—51no—
167C23×Dic3—51no—
168C23×Dic3—51no—
169C3×#117—58no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C4⋊C4C2×D511yescharacteristic
172C2×C3×C22⋊C4—52no—
173C2×C3×C42—52no—
174C2×#217—52no—
175#926—58no—
176C2×C4⋊Dic3—51no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178C2×C4×Dic3—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—58no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3—52no—
185C2×C4×Dic3—52no—
186C2×C4×Dic3C2×D512yes—
187C2×C4×Dic3C2×D511yescharacteristic
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C3⋊#95C2×D512yes—
192C23×D5C22×D311yescharacteristic
193C22×C4×C5—31no—
194C22×C4×C5—32no—
195C22×C4×C5—31no—
196C22×C4×C5C22×D312yes—
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—31no—
199C22×Dic5—31no—
200C22×Dic5—32no—
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C2×C4×D5—34no—
204C2×C4×D5—34no—
205C2×C4×D5—62no—
206C2×C4×D5—62no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C2×C4×D5C4×D314yes—
210C2×C4×D5C4×D314yes—
211C2×C4×D5C2×Dic314yes—
212C5×C4⋊C4—34no—
213C5×C4⋊C4C2×Dic314yescomplemented
214C42×C5—34no—
215C42×C5—64no—
216#685—38no—
217#685C2×Dic318yes—
218C4⋊Dic5—34no—
219C4⋊Dic5C2×Dic314yescomplemented
220C4×Dic5—34no—
221C4×Dic5—34no—
222C4×Dic5—34no—
223C4×Dic5—38no—
224C4×Dic5—64no—
225C4×Dic5—64no—
226C4×Dic5—64no—
227C4×Dic5C2×Dic318yescomplemented
228C2×#117—51no—
229C2×#117—151no—
230C22×C42—151no—
231C4×C4⋊C4—31no—
232C4×C4⋊C4—151no—
233C4×C4⋊C4—151no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—152no—
236C4×C22⋊C4—152no—
237#376—152no—
238C43—152no—
239C22×C3×C5C23×C411yescharacteristic
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C23×C411yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5C2×#4111yescharacteristic
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—22no—
251C2×C3×D5—22no—
252C2×C3×D5C2×C4214yes—
253C3×C4×C5—24no—
254C3×C4×C5C2×C4214yes—
255Dic15—22no—
256Dic15—24no—
257Dic15#11714yescomplemented
258C3×Dic5—24no—
259C3×Dic5C2×C4214yes—
260C5×Dic3—22no—
261C5×Dic3—24no—
262C5×Dic3#11714yescomplemented
263C24×C3—51no—
264C22×C3×C4—51no—
265C22×C3×C4—54no—
266C22×C3×C4—54no—
267C22×C3×C4—54no—
268C22×C3×C4—52no—
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C22×Dic3—51no—
272C22×Dic3—51no—
273C22×Dic3—52no—
274C22×Dic3—54no—
275C22×Dic3—54no—
276C22×Dic3—102no—
277C22×Dic3—102no—
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3C22×D511yescharacteristic
281C22×Dic3C22×D512yes—
282C22×Dic3C22×D511yescharacteristic
283C3×C4⋊C4—54no—
284C3×C4⋊C4C4×D514yescomplemented
285C3×C22⋊C4—58no—
286C3×C42—58no—
287#217—58no—
288C4⋊Dic3—54no—
289C4⋊Dic3C4×D514yescomplemented
290C4×Dic3—24no—
291C4×Dic3—54no—
292C4×Dic3—54no—
293C4×Dic3—54no—
294C4×Dic3—58no—
295C4×Dic3—104no—
296C4×Dic3—104no—
297C4×Dic3—104no—
298C4×Dic3C4×D514yes—
299C23×C5C23×D311yescharacteristic
300C22×D5—21no—
301C22×D5—21no—
302C22×D5—21no—
303C22×D5—21no—
304C22×D5C2×C4×D312yes—
305C22×D5C2×C4×D312yes—
306C22×D5C22×Dic312yes—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—32no—
310C2×C4×C5—32no—
311C2×C4×C5—32no—
312C2×C4×C5—34no—
313C2×C4×C5—32no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—61no—
317C2×C4×C5—61no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5C22×Dic314yes—
321C2×C4×C5C22×Dic312yes—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—32no—
327C2×Dic5—32no—
328C2×Dic5—34no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—61no—
333C2×Dic5C2×C4×D312yes—
334C2×Dic5C2×C4×D312yes—
335C2×Dic5C22×Dic314yes—
336C2×Dic5C22×Dic312yes—
337C4×D5—68no—
338C4×D5—68no—
339C4×D5C4×Dic3116yescomplemented
340C23×C4—51no—
341C23×C4—151no—
342C23×C4—151no—
343#117—58no—
344#117—158no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—151no—
348C2×C4⋊C4D3×D511yescharacteristic
349C2×C22⋊C4—52no—
350C2×C22⋊C4—152no—
351C2×C42—31no—
352C2×C42—32no—
353C2×C42—52no—
354C2×C42—158no—
355C2×C42—152no—
356C2×C42—151no—
357C2×C42—151no—
358C2×C42—151no—
359C2×C42—152no—
360C2×C42—152no—
361C2×C42—152no—
362#95—32no—
363#95—152no—
364#95—152no—
365#95—152no—
366C2×C3×C5C22×C4211yescharacteristic
367C2×C3×C5C2×#11711yescharacteristic
368C2×C3×C5C2×#11711yescharacteristic
369C2×C3×C5C4×#4111yescharacteristic
370C2×C3×C5C4×#4111yescharacteristic
371C2×C3×C5C4×#4111yescharacteristic
372C2×C3×C5C4×#4111yescharacteristic
373C3×D5—24no—
374C23×C3—52no—
375C23×C3—52no—
376C23×C3—52no—
377C23×C3—101no—
378C23×C3—101no—
379C23×C3—101no—
380C23×C3—101no—
381C23×C3C23×D511yescharacteristic
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—516no—
388C2×C3×C4—54no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4C2×C4×D512yes—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4C2×C4×D514yes—
394C2×C3×C4C2×C4×D512yes—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—52no—
400C2×Dic3—52no—
401C2×Dic3—52no—
402C2×Dic3—52no—
403C2×Dic3—54no—
404C2×Dic3—108no—
405C2×Dic3—101no—
406C2×Dic3—102no—
407C2×Dic3—101no—
408C2×Dic3—102no—
409C2×Dic3—108no—
410C2×Dic3C2×C4×D512yes—
411C2×Dic3C2×C4×D514yes—
412C2×Dic3C2×C4×D512yes—
413C2×Dic3#71112yes—
414C2×Dic3#71312yes—
415C22×C5C22×C4×D311yescharacteristic
416C22×C5C22×C4×D311yescharacteristic
417C22×C5D3×#4111yescharacteristic
418C22×C5D3×#4111yescharacteristic
419C22×C5D3×#4111yescharacteristic
420C22×C5D3×#4111yescharacteristic
421C22×C5C23×Dic311yescharacteristic
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—22no—
425C2×D5—22no—
426C2×D5—22no—
427C2×D5—22no—
428C2×D5C2×C4×Dic314yes—
429C4×C5—24no—
430C4×C5—34no—
431C4×C5—62no—
432C4×C5—64no—
433C4×C5C2×C4×Dic314yes—
434Dic5—24no—
435Dic5—34no—
436Dic5—62no—
437Dic5—64no—
438Dic5C2×C4×Dic314yes—
439C24—51no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—32no—
443C22×C4—51no—
444C22×C4—54no—
445C22×C4—54no—
446C22×C4—54no—
447C22×C4—52no—
448C22×C4—154no—
449C22×C4—154no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—152no—
453C22×C4—302no—
454C22×C4—302no—
455C22×C4—302no—
456C22×C4—302no—
457C22×C4C2×D3×D512yes—
458C22×C4C2×D3×D511yescharacteristic
459C4⋊C4—34no—
460C4⋊C4—54no—
461C4⋊C4—154no—
462C4⋊C4D5×Dic314yescomplemented
463C22⋊C4—58no—
464C22⋊C4—158no—
465C42—34no—
466C42—58no—
467C42—64no—
468C42—154no—
469C42—154no—
470C42—158no—
471C42—154no—
472C42—304no—
473C42—304no—
474C42—304no—
475C3×C5C4×#11711yescharacteristic, complemented, Hall
476C22×C3—54no—
477C22×C3—102no—
478C22×C3—102no—
479C22×C3—102no—
480C22×C3—102no—
481C22×C3—102no—
482C22×C3—102no—
483C22×C3C22×C4×D511yescharacteristic
484C22×C3C22×C4×D511yescharacteristic
485C22×C3C22×C4×D511yescharacteristic
486C22×C3C2×#71111yescharacteristic
487C22×C3C2×#71311yescharacteristic
488C22×C3D5×#4111yescharacteristic
489C22×C3D5×#4111yescharacteristic
490C3×C4—24no—
491C3×C4—54no—
492C3×C4—104no—
493C3×C4C42×D514yes—
494Dic3—22no—
495Dic3—24no—
496Dic3—54no—
497Dic3—102no—
498Dic3—104no—
499Dic3#403814yesdirect product factor
500C2×C5D3×#11711yescharacteristic
501C2×C5D3×#11711yescharacteristic
502C2×C5#552211yescharacteristic
503C2×C5#552211yescharacteristic
504C2×C5C22×C4×Dic311yescharacteristic
505C2×C5Dic3×#4111yescharacteristic
506C2×C5Dic3×#4111yescharacteristic
507D5—24no—
508C23—52no—
509C23—52no—
510C23—52no—
511C23—101no—
512C23—101no—
513C23—101no—
514C23—101no—
515C23C22×D3×D511yescharacteristic
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—34no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—52no—
526C2×C4—516no—
527C2×C4—54no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—152no—
535C2×C4—152no—
536C2×C4—152no—
537C2×C4—152no—
538C2×C4—154no—
539C2×C4—308no—
540C2×C4—308no—
541C2×C4—301no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—301no—
545C2×C4C4×D3×D512yes—
546C2×C4C4×D3×D512yes—
547C2×C4C2×D5×Dic314yes—
548C2×C4C2×D5×Dic312yes—
549C2×C3—104no—
550C2×C3C2×C42×D511yescharacteristic
551C2×C3C2×#403811yescharacteristic
552C2×C3D5×#11711yescharacteristic
553C2×C3C4×#71111yescharacteristic
554C2×C3C4×#71111yescharacteristic
555C2×C3C4×#71311yescharacteristic
556C2×C3C4×#71311yescharacteristic
557C5Dic3×#11711yescharacteristic, complemented, Sylow
558C22—54no—
559C22—102no—
560C22—102no—
561C22—102no—
562C22—102no—
563C22—102no—
564C22—102no—
565C22C2×C4×D3×D511yescharacteristic
566C22C2×C4×D3×D511yescharacteristic
567C22D3×#71111yescharacteristic
568C22#9202411yescharacteristic
569C22D3×#71311yescharacteristic
570C22#9203411yescharacteristic
571C22C22×D5×Dic311yescharacteristic
572C4—24no—
573C4—34no—
574C4—54no—
575C4—62no—
576C4—64no—
577C4—104no—
578C4—154no—
579C4—302no—
580C4—304no—
581C4C4×D5×Dic314yes—
582C3C4×#403811yescharacteristic, complemented, Sylow
583C2—104no—
584C2#1175340211yescharacteristic
585C2#1175340311yescharacteristic
586C2D3×#403811yescharacteristic
587C2#1175383511yescharacteristic
588C2C2×C4×D5×Dic311yescharacteristic
589C2Dic3×#71111yescharacteristic
590C2Dic3×#71311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic15C2semidirect
5. C5×Dic3×C4⋊C4C2semidirect
8. #11748699C2semidirect
9. Dic3×C4⋊Dic5C2semidirect
10. #11748635C2semidirect
11. C4×Dic3×Dic5C2semidirect
26. C3×#4038C4semidirect
33. C4×D5×Dic3C4semidirect
34. #91358C4semidirect
71. C3×C5×C4⋊C4C2×C4semidirect
72. C4⋊Dic15C2×C4semidirect
75. C5×C4⋊Dic3C2×C4semidirect
79. C3×C4⋊Dic5C2×C4semidirect
80. C3×C4×Dic5C2×C4semidirect
86. Dic3×Dic5C2×C4semidirect
93. Dic3×C4⋊C4D5semidirect
118. #4038Dic3direct (N × H)
163. C3×C4×D5C42semidirect
213. C5×C4⋊C4C2×Dic3semidirect
219. C4⋊Dic5C2×Dic3semidirect
227. C4×Dic5C2×Dic3semidirect
257. Dic15#117semidirect
262. C5×Dic3#117semidirect
284. C3×C4⋊C4C4×D5semidirect
289. C4⋊Dic3C4×D5semidirect
339. C4×D5C4×Dic3semidirect
462. C4⋊C4D5×Dic3semidirect
475. C3×C5C4×#117semidirect
499. Dic3#4038direct (N × H)
557. C5Dic3×#117semidirect
582. C3C4×#4038semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×C4×D5×Dic32
C2×#913582
C4⋊C4×Dic152
C5×Dic3×C4⋊C42
#117488842
Dic3×#6852
#117486992
Dic3×C4⋊Dic52
#117486352
C4×Dic3×Dic52
C4×#40383
Dic3×#1175