Finite Group Databasebeta

← C3×#21383 #10639990

Subgroups — C3×#21383 #10639990

Order 768.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3444C211yesmaximal, characteristic
2C2×C3×C4×M16C211yesmaximal, characteristic, complemented
3C3×#2283C211yesmaximal, characteristic, complemented
4C3×#1986C212yesmaximal, complemented
5C3×#1980C212yesmaximal, complemented
6C3×#1871C214yesmaximal, complemented
7C3×#1759C214yesmaximal, complemented
8#21383C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×M16C2212yes—
10C3×#533C411yescharacteristic, complemented
11C3×#533C411yescharacteristic, complemented
12C3×#533C2211yescharacteristic
13C3×#532C411yescharacteristic, complemented
14C3×#532C411yescharacteristic, complemented
15C3×#532C2211yescharacteristic
16C3×#529—21no—
17C3×#529—21no—
18C3×#529—21no—
19C3×#529—21no—
20C3×#529C412yescomplemented
21C3×#529C412yescomplemented
22C3×#525—21no—
23C3×#525—21no—
24C3×#525C2212yes—
25C3×C4×#41—21no—
26C3×C4×#41—21no—
27C3×C4×#41C2212yes—
28C22×C3×C42C2211yescharacteristic
29C2×C3×#104C2218yes—
30C3×C4×M16—21no—
31C3×C4×M16—21no—
32C3×C4×M16C2212yes—
33C3×C4×M16C2212yes—
34C2×C3×#97—21no—
35C2×C3×C4×C8—21no—
36C3×#383—21no—
37C3×#382—21no—
38C3×#381—21no—
39C3×#380—21no—
40C3×C4×C4⋊C4C2212yes—
41C3×C4×C22⋊C4C2212yes—
42C3×#376C2212yes—
43C3×#339C2218yes—
44#3444C2×C311yescharacteristic
45C2×C4×M16C2×C311yescharacteristic, complemented
46#2283C2×C311yescharacteristic, complemented
47#1986C2×C312yescomplemented
48#1980C2×C312yescomplemented
49#1871C2×C314yescomplemented
50#1759C2×C314yescomplemented
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41C2312yes—
54C23×C3×C4D411yescharacteristic
55C23×C3×C4D411yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C2×C3×M16—22no—
58C2×C3×M16—28no—
59C2×C3×M16C2314yes—
60C22×C3×C8—22no—
61C3×C4⋊Q8C2×C411yescharacteristic
62C3×C4⋊Q8C2×C411yescharacteristic
63C3×C4⋊Q8C2×C411yescharacteristic
64C3×#127C2×C411yescharacteristic
65C3×#126—22no—
66C3×#126—22no—
67C3×#125—21no—
68C3×#125—21no—
69C3×#125C2×C412yes—
70C3×#124—21no—
71C3×#124—21no—
72C3×#124C2×C412yes—
73C3×#123—22no—
74C3×#123—22no—
75C3×#123—22no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—21no—
79C3×C22⋊Q8—21no—
80C3×C22⋊Q8C2×C412yes—
81C3×C22⋊Q8C2×C412yes—
82C3×#121—21no—
83C3×#121—21no—
84C3×#121—21no—
85C3×#121—21no—
86C3×#121C2×C412yes—
87C3×#121C2×C412yes—
88C3×#120—22no—
89C3×C4×Q8—21no—
90C3×C4×Q8—21no—
91C3×C4×Q8—21no—
92C3×C4×Q8—21no—
93C3×C4×Q8C2×C412yes—
94C3×C4×Q8C2×C412yes—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—21no—
102C3×C4×D4—21no—
103C3×C4×D4—21no—
104C3×C4×D4—21no—
105C3×C4×D4C2×C412yes—
106C3×C4×D4C2×C412yes—
107C3×#117—21no—
108C3×#117—21no—
109C3×#117—22no—
110C3×#117—22no—
111C3×#117—22no—
112C3×#117C2312yes—
113C2×C3×C4⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C42—22no—
116C2×C3×C42C2×C411yescharacteristic
117C2×C3×C42C2×C411yescharacteristic
118C2×C3×C42C2×C411yescharacteristic
119C2×C3×C42C2×C411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42D411yescharacteristic
122C2×C3×C42D411yescharacteristic
123C2×C3×C42D411yescharacteristic
124C2×C3×C42D411yescharacteristic
125C2×C3×C42D411yescharacteristic
126C2×C3×C42C2314yes—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#104—216no—
130C3×#97—22no—
131C3×#97—22no—
132C3×C4×C8—22no—
133C3×C4×C8—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138C22×M16C22×C312yes—
139#533C3×C411yescharacteristic, complemented
140#533C3×C411yescharacteristic, complemented
141#533C22×C311yescharacteristic
142#532C3×C411yescharacteristic, complemented
143#532C3×C411yescharacteristic, complemented
144#532C22×C311yescharacteristic
145#529—21no—
146#529—21no—
147#529—21no—
148#529—21no—
149#529C3×C412yescomplemented
150#529C3×C412yescomplemented
151#525—21no—
152#525—21no—
153#525C22×C312yes—
154C4×#41—21no—
155C4×#41—21no—
156C4×#41C22×C312yes—
157C22×C42C22×C311yescharacteristic
158C2×#104C22×C318yes—
159C4×M16—21no—
160C4×M16—21no—
161C4×M16C22×C312yes—
162C4×M16C22×C312yes—
163C2×#97—21no—
164C2×C4×C8—21no—
165#383—21no—
166#382—21no—
167#381—21no—
168#380—21no—
169C4×C4⋊C4C22×C312yes—
170C4×C22⋊C4C22×C312yes—
171#376C22×C312yes—
172#339C22×C318yes—
173C24×C3C2×D411yescharacteristic
174C3×#41—28no—
175C3×#41—44no—
176C3×#41—44no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8C22×C412yes—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4C22×C412yes—
186C22×C3×C4—24no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—24no—
191C22×C3×C4—42no—
192C22×C3×C4—42no—
193C22×C3×C4C22⋊C411yescharacteristic
194C22×C3×C4C22⋊C411yescharacteristic
195C22×C3×C4C22⋊C411yescharacteristic
196C22×C3×C4C22⋊C411yescharacteristic
197C22×C3×C4C22⋊C411yescharacteristic
198C22×C3×C4C22⋊C411yescharacteristic
199C22×C3×C4C22⋊C411yescharacteristic
200C22×C3×C4C22⋊C411yescharacteristic
201C22×C3×C4C22×C411yescharacteristic
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2411yescharacteristic
211C3×M16—28no—
212C3×M16—24no—
213C3×M16#4118yescomplemented
214C2×C3×C8—28no—
215C2×C3×C8—24no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—44no—
227C3×C4⋊C4C22×C412yes—
228C3×C4⋊C4C22×C412yes—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—22no—
238C3×C22⋊C4—44no—
239C3×C42—22no—
240C3×C42—22no—
241C3×C42—22no—
242C3×C42—28no—
243C3×C42C22⋊C411yescharacteristic
244C3×C42C22⋊C411yescharacteristic
245C3×C42C22⋊C411yescharacteristic
246C3×C42C22⋊C411yescharacteristic
247C3×C42C22⋊C411yescharacteristic
248C3×C42C22⋊C411yescharacteristic
249C3×C42C22⋊C411yescharacteristic
250C3×C42C22⋊C411yescharacteristic
251C3×C42C22×C411yescharacteristic
252C3×C42C22×C411yescharacteristic
253C3×C42C22×C411yescharacteristic
254C3×C42C22×C411yescharacteristic
255C3×C42C2×D411yescharacteristic
256C3×C42C2×D411yescharacteristic
257C3×C42C2×D411yescharacteristic
258C3×C42C2×D411yescharacteristic
259C2×#41—21no—
260C2×#41—21no—
261C2×#41C23×C312yes—
262C23×C4C3×D411yescharacteristic
263C23×C4C3×D411yescharacteristic
264C23×C4C23×C311yescharacteristic
265C2×M16—22no—
266C2×M16—28no—
267C2×M16C23×C314yes—
268C22×C8—22no—
269C4⋊Q8C2×C3×C411yescharacteristic
270C4⋊Q8C2×C3×C411yescharacteristic
271C4⋊Q8C2×C3×C411yescharacteristic
272#127C2×C3×C411yescharacteristic
273#126—22no—
274#126—22no—
275#125—21no—
276#125—21no—
277#125C2×C3×C412yes—
278#124—21no—
279#124—21no—
280#124C2×C3×C412yes—
281#123—22no—
282#123—22no—
283#123—22no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8C2×C3×C412yes—
289C22⋊Q8C2×C3×C412yes—
290#121—21no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121C2×C3×C412yes—
295#121C2×C3×C412yes—
296#120—22no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8C2×C3×C412yes—
302C4×Q8C2×C3×C412yes—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4C2×C3×C412yes—
314C4×D4C2×C3×C412yes—
315#117—21no—
316#117—21no—
317#117—22no—
318#117—22no—
319#117—22no—
320#117C23×C312yes—
321C2×C4⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C42—22no—
324C2×C42C2×C3×C411yescharacteristic
325C2×C42C2×C3×C411yescharacteristic
326C2×C42C2×C3×C411yescharacteristic
327C2×C42C2×C3×C411yescharacteristic
328C2×C42C3×D411yescharacteristic
329C2×C42C3×D411yescharacteristic
330C2×C42C3×D411yescharacteristic
331C2×C42C3×D411yescharacteristic
332C2×C42C3×D411yescharacteristic
333C2×C42C3×D411yescharacteristic
334C2×C42C23×C314yes—
335C2×C42C23×C311yescharacteristic
336C2×C42C23×C311yescharacteristic
337#104—216no—
338#97—22no—
339#97—22no—
340C4×C8—22no—
341C4×C8—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—41no—
350C23×C3C2×C22⋊C411yescharacteristic
351C23×C3C2×C22⋊C411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C3×Q8—24no—
354C3×Q8—42no—
355C3×Q8—42no—
356C3×D4—24no—
357C3×D4—42no—
358C3×D4—44no—
359C3×D4—44no—
360C3×D4—44no—
361C3×D4—42no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—44no—
383C2×C3×C4—44no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—44no—
387C2×C3×C4—44no—
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4C2×C22⋊C411yescharacteristic
390C2×C3×C4C2×C22⋊C411yescharacteristic
391C2×C3×C4C2×C22⋊C411yescharacteristic
392C2×C3×C4C2×C22⋊C411yescharacteristic
393C2×C3×C4C2×C22⋊C411yescharacteristic
394C2×C3×C4C2×C22⋊C411yescharacteristic
395C2×C3×C4C2×C22⋊C411yescharacteristic
396C2×C3×C4C2×C22⋊C411yescharacteristic
397C2×C3×C4C2×C22⋊C411yescharacteristic
398C2×C3×C4C23×C411yescharacteristic
399C2×C3×C4C22×D411yescharacteristic
400C2×C3×C4C2×#4114yes—
401C3×C8—28no—
402C24C2×C3×D411yescharacteristic
403#41—28no—
404#41—44no—
405#41—44no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C22×C3×C412yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C22×C3×C412yes—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4C3×C22⋊C411yescharacteristic
423C22×C4C3×C22⋊C411yescharacteristic
424C22×C4C3×C22⋊C411yescharacteristic
425C22×C4C3×C22⋊C411yescharacteristic
426C22×C4C3×C22⋊C411yescharacteristic
427C22×C4C3×C22⋊C411yescharacteristic
428C22×C4C3×C22⋊C411yescharacteristic
429C22×C4C3×C22⋊C411yescharacteristic
430C22×C4C22×C3×C411yescharacteristic
431C22×C4C22×C3×C411yescharacteristic
432C22×C4C2×C3×D411yescharacteristic
433C22×C4C2×C3×D411yescharacteristic
434C22×C4C2×C3×D411yescharacteristic
435C22×C4C2×C3×D411yescharacteristic
436C22×C4C2×C3×D411yescharacteristic
437C22×C4C2×C3×D411yescharacteristic
438C22×C4C2×C3×D411yescharacteristic
439C22×C4C24×C311yescharacteristic
440M16—28no—
441M16—24no—
442M16C3×#4118yescomplemented
443C2×C8—28no—
444C2×C8—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—44no—
456C4⋊C4C22×C3×C412yes—
457C4⋊C4C22×C3×C412yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—44no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—28no—
472C42C3×C22⋊C411yescharacteristic
473C42C3×C22⋊C411yescharacteristic
474C42C3×C22⋊C411yescharacteristic
475C42C3×C22⋊C411yescharacteristic
476C42C3×C22⋊C411yescharacteristic
477C42C3×C22⋊C411yescharacteristic
478C42C3×C22⋊C411yescharacteristic
479C42C3×C22⋊C411yescharacteristic
480C42C22×C3×C411yescharacteristic
481C42C22×C3×C411yescharacteristic
482C42C22×C3×C411yescharacteristic
483C42C22×C3×C411yescharacteristic
484C42C2×C3×D411yescharacteristic
485C42C2×C3×D411yescharacteristic
486C42C2×C3×D411yescharacteristic
487C42C2×C3×D411yescharacteristic
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—44no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3#42112yes—
500C22×C3C22×C22⋊C411yescharacteristic
501C22×C3#53212yes—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—84no—
515C3×C4#42112yes—
516C3×C4C4×#4112yes—
517C3×C4#52512yes—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—41no—
522C23C2×C3×C22⋊C411yescharacteristic
523C23C2×C3×C22⋊C411yescharacteristic
524C23C22×C3×D411yescharacteristic
525Q8—24no—
526Q8—42no—
527Q8—42no—
528D4—24no—
529D4—42no—
530D4—44no—
531D4—44no—
532D4—44no—
533D4—42no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4C2×C3×C22⋊C411yescharacteristic
561C2×C4C2×C3×C22⋊C411yescharacteristic
562C2×C4C2×C3×C22⋊C411yescharacteristic
563C2×C4C2×C3×C22⋊C411yescharacteristic
564C2×C4C2×C3×C22⋊C411yescharacteristic
565C2×C4C2×C3×C22⋊C411yescharacteristic
566C2×C4C2×C3×C22⋊C411yescharacteristic
567C2×C4C2×C3×C22⋊C411yescharacteristic
568C2×C4C2×C3×C22⋊C411yescharacteristic
569C2×C4C2×C3×C22⋊C411yescharacteristic
570C2×C4C23×C3×C411yescharacteristic
571C2×C4C22×C3×D411yescharacteristic
572C2×C4C2×C3×#4114yes—
573C8—28no—
574C2×C3—22no—
575C2×C3—22no—
576C2×C3—41no—
577C2×C3—82no—
578C2×C3#229711yescharacteristic
579C2×C3C2×#42111yescharacteristic
580C2×C3C2×#42111yescharacteristic
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22C3×#42112yes—
593C22C22×C3×C22⋊C411yescharacteristic
594C22C3×#53212yes—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4—84no—
608C4C3×#42112yes—
609C4C3×C4×#4112yes—
610C4C3×#52512yes—
611C3#2138311yescharacteristic, direct product factor, Sylow
612C2—22no—
613C2—22no—
614C2—41no—
615C2—82no—
616C2C3×#229711yescharacteristic
617C2C2×C3×#42111yescharacteristic
618C2C2×C3×#42111yescharacteristic
subgroupG/H
centerC2×C3×C4C22×D4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
socleC22×C3C22×C22⋊C4
prime radicalC3×#3444C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×M16C2semidirect
3. C3×#2283C2semidirect
4. C3×#1986C2semidirect
5. C3×#1980C2semidirect
6. C3×#1871C2semidirect
7. C3×#1759C2semidirect
8. #21383C3direct (N × H)
10. C3×#533C4semidirect
11. C3×#533C4semidirect
13. C3×#532C4semidirect
14. C3×#532C4semidirect
20. C3×#529C4semidirect
21. C3×#529C4semidirect
45. C2×C4×M16C2×C3semidirect
46. #2283C2×C3semidirect
47. #1986C2×C3semidirect
48. #1980C2×C3semidirect
49. #1871C2×C3semidirect
50. #1759C2×C3semidirect
139. #533C3×C4semidirect
140. #533C3×C4semidirect
142. #532C3×C4semidirect
143. #532C3×C4semidirect
149. #529C3×C4semidirect
150. #529C3×C4semidirect
213. C3×M16#41semidirect
442. M16C3×#41semidirect
611. C3#21383direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34442
C2×C3×C4×M162
C3×#22832
C3×#19862
C3×#19802
C3×#18712
C3×#17592
#213833