Finite Group Databasebeta

← C3×#11042 #10629649

Subgroups — C3×#11042 #10629649

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊C8C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊C8C212yesmaximal
3C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
4C2×C3×#336C212yesmaximal, complemented
5C2×C3×#336C211yesmaximal, characteristic, complemented
6#11042C311yesmaximal, characteristic, direct product factor, Sylow
7C24×C3×C4C2211yescharacteristic
8C23×C3×C8C2212yes—
9C23×C3×C8C2212yes—
10C22×C3×C22⋊C4C411yescharacteristic
11C22×C3×C22⋊C4C411yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C22×C3×C42C2211yescharacteristic
14C2×C3×C4⋊C8—24no—
15C2×C3×C4⋊C8—22no—
16C2×C3×C22⋊C8—24no—
17C2×C3×C22⋊C8—24no—
18C2×C3×C22⋊C8—24no—
19C3×C4×C22⋊C4—22no—
20C3×C4×C22⋊C4—22no—
21C2×C3×#95C411yescharacteristic
22C2×C3×#95C411yescharacteristic
23C3×#336—24no—
24C3×#336—22no—
25C22×C4⋊C8C2×C311yescharacteristic, complemented
26C22×C22⋊C8C2×C312yes—
27C2×C4×C22⋊C4C2×C311yescharacteristic
28C2×#336C2×C312yescomplemented
29C2×#336C2×C311yescharacteristic, complemented
30C25×C3C2×C411yescharacteristic
31C23×C3×C4—21no—
32C23×C3×C4—21no—
33C23×C3×C4—22no—
34C23×C3×C4—22no—
35C23×C3×C4—21no—
36C23×C3×C4—21no—
37C23×C3×C4—22no—
38C23×C3×C4—22no—
39C23×C3×C4C2×C411yescharacteristic
40C23×C3×C4C2×C411yescharacteristic
41C23×C3×C4C2×C411yescharacteristic
42C23×C3×C4C2×C411yescharacteristic
43C23×C3×C4C2×C411yescharacteristic
44C23×C3×C4D412yes—
45C23×C3×C4Q812yes—
46C23×C3×C4C2311yescharacteristic
47C22×C3×C8—22no—
48C22×C3×C8—22no—
49C22×C3×C8—22no—
50C22×C3×C8—22no—
51C22×C3×C8—22no—
52C22×C3×C8—22no—
53C22×C3×C8—22no—
54C22×C3×C8—22no—
55C22×C3×C8—22no—
56C22×C3×C8—22no—
57C22×C3×C8—22no—
58C22×C3×C8—22no—
59C22×C3×C8D414yes—
60C22×C3×C8D414yes—
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4—22no—
63C2×C3×C22⋊C4—22no—
64C2×C3×C22⋊C4—22no—
65C2×C3×C22⋊C4—22no—
66C2×C3×C22⋊C4C814yescomplemented
67C2×C3×C42—22no—
68C2×C3×C42—22no—
69C2×C3×C42—21no—
70C2×C3×C42—21no—
71C2×C3×C42—22no—
72C2×C3×C42—22no—
73C2×C3×C42D412yes—
74C2×C3×C42D412yes—
75C3×C4⋊C8—28no—
76C3×C22⋊C8—216no—
77C3×#95—22no—
78C3×#95—22no—
79C24×C4C22×C311yescharacteristic
80C23×C8C22×C312yes—
81C23×C8C22×C312yes—
82C22×C22⋊C4C3×C411yescharacteristic
83C22×C22⋊C4C3×C411yescharacteristic
84C22×C42C22×C311yescharacteristic
85C22×C42C22×C311yescharacteristic
86C2×C4⋊C8—24no—
87C2×C4⋊C8—22no—
88C2×C22⋊C8—24no—
89C2×C22⋊C8—24no—
90C2×C22⋊C8—24no—
91C4×C22⋊C4—22no—
92C4×C22⋊C4—22no—
93C2×#95C3×C411yescharacteristic
94C2×#95C3×C411yescharacteristic
95#336—24no—
96#336—22no—
97C24×C3—21no—
98C24×C3—21no—
99C24×C3—22no—
100C24×C3—22no—
101C24×C3—21no—
102C24×C3—21no—
103C24×C3—22no—
104C24×C3—22no—
105C24×C3C4⋊C412yes—
106C24×C3C2×C812yes—
107C24×C3M1612yes—
108C24×C3C22×C411yescharacteristic
109C22×C3×C4—22no—
110C22×C3×C4—22no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—24no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—41no—
136C22×C3×C4—42no—
137C22×C3×C4—42no—
138C22×C3×C4—42no—
139C22×C3×C4—41no—
140C22×C3×C4—42no—
141C22×C3×C4—42no—
142C22×C3×C4—41no—
143C22×C3×C4—42no—
144C22×C3×C4—41no—
145C22×C3×C4C22⋊C412yes—
146C22×C3×C4C22⋊C412yes—
147C22×C3×C4C4⋊C412yes—
148C22×C3×C4C2×C812yes—
149C22×C3×C4C2×C812yes—
150C22×C3×C4M1612yes—
151C22×C3×C4M1612yes—
152C22×C3×C4C2×D412yes—
153C22×C3×C4C2×D411yescharacteristic
154C22×C3×C4C2×D412yes—
155C22×C3×C4C2×D411yescharacteristic
156C22×C3×C4C2×D411yescharacteristic
157C22×C3×C4C2×Q811yescharacteristic
158C22×C3×C4#4111yescharacteristic
159C22×C3×C4#4112yes—
160C22×C3×C4#4111yescharacteristic
161C22×C3×C4#4112yes—
162C2×C3×C8—24no—
163C2×C3×C8—24no—
164C2×C3×C8—24no—
165C2×C3×C8—24no—
166C2×C3×C8—24no—
167C2×C3×C8—24no—
168C2×C3×C8—42no—
169C2×C3×C8—42no—
170C2×C3×C8—42no—
171C2×C3×C8—42no—
172C2×C3×C8—42no—
173C2×C3×C8—42no—
174C2×C3×C8—42no—
175C2×C3×C8—42no—
176C3×C22⋊C4—28no—
177C3×C22⋊C4—28no—
178C3×C42—22no—
179C3×C42—24no—
180C3×C42—22no—
181C3×C42—42no—
182C3×C42—41no—
183C3×C42—41no—
184C25C2×C3×C411yescharacteristic
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4C2×C3×C411yescharacteristic
194C23×C4C2×C3×C411yescharacteristic
195C23×C4C2×C3×C411yescharacteristic
196C23×C4C2×C3×C411yescharacteristic
197C23×C4C2×C3×C411yescharacteristic
198C23×C4C3×D412yes—
199C23×C4C3×Q812yes—
200C23×C4C23×C311yescharacteristic
201C22×C8—22no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—22no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8—22no—
213C22×C8C3×D414yes—
214C22×C8C3×D414yes—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4C3×C814yescomplemented
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—22no—
227C2×C42C3×D412yes—
228C2×C42C3×D412yes—
229C4⋊C8—28no—
230C22⋊C8—216no—
231#95—22no—
232#95—22no—
233C23×C3—22no—
234C23×C3—24no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—24no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—24no—
242C23×C3—24no—
243C23×C3—24no—
244C23×C3—24no—
245C23×C3—41no—
246C23×C3—42no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—42no—
251C23×C3—42no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3C4⋊C814yescomplemented
256C23×C3C2×C22⋊C411yescharacteristic
257C23×C3C2×C4⋊C411yescharacteristic
258C23×C3#11711yescharacteristic
259C23×C3C4×D412yes—
260C23×C3C4×D412yes—
261C23×C3C22×C811yescharacteristic
262C23×C3C2×M1611yescharacteristic
263C23×C3C2×M1611yescharacteristic
264C23×C3C2×M1611yescharacteristic
265C23×C3#13112yes—
266C23×C3#13112yes—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—44no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4C22⋊C814yescomplemented
298C2×C3×C4#12011yescharacteristic
299C2×C3×C4#12012yes—
300C2×C3×C4#12112yes—
301C2×C3×C4#12111yescharacteristic
302C2×C3×C4#12111yescharacteristic
303C2×C3×C4#12112yes—
304C2×C3×C4#12112yes—
305C2×C3×C4C22⋊Q812yes—
306C2×C3×C4C22⋊Q811yescharacteristic
307C2×C3×C4C22⋊Q811yescharacteristic
308C2×C3×C4C22⋊Q812yes—
309C2×C3×C4#12312yes—
310C2×C3×C4#12312yes—
311C2×C3×C4#12311yescharacteristic
312C2×C3×C4#12412yes—
313C2×C3×C4#12411yescharacteristic
314C2×C3×C4#12612yes—
315C2×C3×C4#12711yescharacteristic
316C3×C8—44no—
317C3×C8—44no—
318C24—21no—
319C24—21no—
320C24—22no—
321C24—22no—
322C24—21no—
323C24—21no—
324C24—22no—
325C24—22no—
326C24C3×C4⋊C412yes—
327C24C2×C3×C812yes—
328C24C3×M1612yes—
329C24C22×C3×C411yescharacteristic
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—41no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—41no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4C3×C22⋊C412yes—
367C22×C4C3×C22⋊C412yes—
368C22×C4C3×C4⋊C412yes—
369C22×C4C2×C3×C812yes—
370C22×C4C2×C3×C812yes—
371C22×C4C3×M1612yes—
372C22×C4C3×M1612yes—
373C22×C4C2×C3×D412yes—
374C22×C4C2×C3×D411yescharacteristic
375C22×C4C2×C3×D412yes—
376C22×C4C2×C3×D411yescharacteristic
377C22×C4C2×C3×D411yescharacteristic
378C22×C4C2×C3×Q811yescharacteristic
379C22×C4C3×#4111yescharacteristic
380C22×C4C3×#4112yes—
381C22×C4C3×#4111yescharacteristic
382C22×C4C3×#4112yes—
383C2×C8—24no—
384C2×C8—24no—
385C2×C8—24no—
386C2×C8—24no—
387C2×C8—24no—
388C2×C8—24no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—42no—
396C2×C8—42no—
397C22⋊C4—28no—
398C22⋊C4—28no—
399C42—22no—
400C42—24no—
401C42—22no—
402C42—42no—
403C42—41no—
404C42—41no—
405C22×C3—24no—
406C22×C3—28no—
407C22×C3—42no—
408C22×C3—44no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—44no—
412C22×C3—44no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3#38011yescharacteristic
417C22×C3#38512yes—
418C22×C3#38611yescharacteristic
419C22×C3#38812yes—
420C22×C3#39011yescharacteristic
421C22×C3C2×C22⋊C811yescharacteristic
422C22×C3#40711yescharacteristic
423C22×C3#40811yescharacteristic
424C22×C3#40811yescharacteristic
425C22×C3C2×C4⋊C811yescharacteristic
426C22×C3#42311yescharacteristic
427C22×C3#42412yes—
428C22×C3#43111yescharacteristic
429C22×C3#43211yescharacteristic
430C22×C3#43312yes—
431C22×C3C8×D412yes—
432C22×C3C8×D412yes—
433C22×C3#43512yes—
434C22×C3#43512yes—
435C22×C3#43512yes—
436C22×C3#43512yes—
437C22×C3#43612yes—
438C22×C3#43612yes—
439C3×C4—24no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4#39211yescharacteristic
445C3×C4#39311yescharacteristic
446C3×C4#39412yes—
447C3×C4#39612yes—
448C3×C4#39711yescharacteristic
449C3×C4#39911yescharacteristic
450C23—22no—
451C23—24no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—24no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—41no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23C3×C4⋊C814yescomplemented
473C23C2×C3×C22⋊C411yescharacteristic
474C23C2×C3×C4⋊C411yescharacteristic
475C23C3×#11711yescharacteristic
476C23C3×C4×D412yes—
477C23C3×C4×D412yes—
478C23C22×C3×C811yescharacteristic
479C23C2×C3×M1611yescharacteristic
480C23C2×C3×M1611yescharacteristic
481C23C2×C3×M1611yescharacteristic
482C23C3×#13112yes—
483C23C3×#13112yes—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4C3×C22⋊C814yescomplemented
515C2×C4C3×#12011yescharacteristic
516C2×C4C3×#12012yes—
517C2×C4C3×#12112yes—
518C2×C4C3×#12111yescharacteristic
519C2×C4C3×#12111yescharacteristic
520C2×C4C3×#12112yes—
521C2×C4C3×#12112yes—
522C2×C4C3×C22⋊Q812yes—
523C2×C4C3×C22⋊Q811yescharacteristic
524C2×C4C3×C22⋊Q811yescharacteristic
525C2×C4C3×C22⋊Q812yes—
526C2×C4C3×#12312yes—
527C2×C4C3×#12312yes—
528C2×C4C3×#12311yescharacteristic
529C2×C4C3×#12412yes—
530C2×C4C3×#12411yescharacteristic
531C2×C4C3×#12612yes—
532C2×C4C3×#12711yescharacteristic
533C8—44no—
534C8—44no—
535C2×C3—44no—
536C2×C3#143911yescharacteristic
537C2×C3#179711yescharacteristic
538C2×C3#179811yescharacteristic
539C2×C3#185012yes—
540C2×C3#185112yes—
541C2×C3#186911yescharacteristic
542C2×C3#187011yescharacteristic
543C2×C3#192312yes—
544C2×C3#192412yes—
545C2×C3#195411yescharacteristic
546C2×C3#195511yescharacteristic
547C22—24no—
548C22—28no—
549C22—42no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—44no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22C3×#38011yescharacteristic
559C22C3×#38512yes—
560C22C3×#38611yescharacteristic
561C22C3×#38812yes—
562C22C3×#39011yescharacteristic
563C22C2×C3×C22⋊C811yescharacteristic
564C22C3×#40711yescharacteristic
565C22C3×#40811yescharacteristic
566C22C3×#40811yescharacteristic
567C22C2×C3×C4⋊C811yescharacteristic
568C22C3×#42311yescharacteristic
569C22C3×#42412yes—
570C22C3×#43111yescharacteristic
571C22C3×#43211yescharacteristic
572C22C3×#43312yes—
573C22C3×C8×D412yes—
574C22C3×C8×D412yes—
575C22C3×#43512yes—
576C22C3×#43512yes—
577C22C3×#43512yes—
578C22C3×#43512yes—
579C22C3×#43612yes—
580C22C3×#43612yes—
581C4—24no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—42no—
586C4C3×#39211yescharacteristic
587C4C3×#39311yescharacteristic
588C4C3×#39412yes—
589C4C3×#39612yes—
590C4C3×#39711yescharacteristic
591C4C3×#39911yescharacteristic
592C3#1104211yescharacteristic, direct product factor, Sylow
593C2—44no—
594C2C3×#143911yescharacteristic
595C2C3×#179711yescharacteristic
596C2C3×#179811yescharacteristic
597C2C3×#185012yes—
598C2C3×#185112yes—
599C2C3×#186911yescharacteristic
600C2C3×#187011yescharacteristic
601C2C3×#192312yes—
602C2C3×#192412yes—
603C2C3×#195411yescharacteristic
604C2C3×#195511yescharacteristic
subgroupG/H
centerC23×C3×C4C23
commutatorC23C22×C3×C8
Frattini, cosocleC23×C4C23×C3
socleC24×C3C22×C4
prime radicalC25×C3C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊C8C2semidirect
4. C2×C3×#336C2semidirect
5. C2×C3×#336C2semidirect
6. #11042C3direct (N × H)
25. C22×C4⋊C8C2×C3semidirect
28. C2×#336C2×C3semidirect
29. C2×#336C2×C3semidirect
66. C2×C3×C22⋊C4C8semidirect
220. C2×C22⋊C4C3×C8semidirect
255. C23×C3C4⋊C8semidirect
297. C2×C3×C4C22⋊C8semidirect
472. C23C3×C4⋊C8semidirect
514. C2×C4C3×C22⋊C8semidirect
592. C3#11042direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊C82
C22×C3×C22⋊C82
C2×C3×C4×C22⋊C42
C2×C3×#3362
#110423