Finite Group Databasebeta

← C3×#10951 #10629558

Subgroups — C3×#10951 #10629558

Order 768.

916 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#421C211yesmaximal, characteristic
2C3×#2896C211yesmaximal, characteristic
3C2×C3×#410C211yesmaximal, characteristic
4C3×#2873C211yesmaximal, characteristic, complemented
5C3×#1740C211yesmaximal, characteristic, complemented
6C3×#1733C211yesmaximal, characteristic, complemented
7C2×C3×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8#10951C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C2×C3×#117C2211yescharacteristic
13C2×C3×#117C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C2×C3×#117C2211yescharacteristic
16C3×#421—22no—
17C3×#421—22no—
18C2×C3×#104C414yescomplemented
19C3×#419C412yescomplemented
20C3×#418C412yescomplemented
21C3×#417—22no—
22C3×#416—22no—
23C3×#410—22no—
24C3×#410C414yescomplemented
25C2×C3×#99—22no—
26C3×#405—22no—
27C3×#405—22no—
28C3×C4×M16—22no—
29C3×#342—22no—
30C3×#339—22no—
31C3×H(3,ℤ/4)—22no—
32C2×#421C2×C311yescharacteristic
33#2896C2×C311yescharacteristic
34C2×#410C2×C311yescharacteristic
35#2873C2×C311yescharacteristic, complemented
36#1740C2×C311yescharacteristic, complemented
37#1733C2×C311yescharacteristic, complemented
38C2×H(3,ℤ/4)C2×C311yescharacteristic, complemented
39C2×C3×#41—21no—
40C2×C3×#41—21no—
41C2×C3×#41—21no—
42C2×C3×#41—21no—
43C2×C3×#41—21no—
44C2×C3×#41—21no—
45C2×C3×#41—21no—
46C2×C3×#41—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41C2×C412yes—
50C2×C3×#41C2×C412yes—
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4—21no—
53C22×C3×D4C2×C411yescharacteristic
54C23×C3×C4—21no—
55C23×C3×C4C2311yescharacteristic
56C2×C3×M16—21no—
57C2×C3×M16—21no—
58C2×C3×M16—21no—
59C2×C3×M16—21no—
60C2×C3×M16—21no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C2×C3×M16C2×C412yes—
64C2×C3×M16C2×C412yes—
65C2×C3×M16D412yes—
66C2×C3×M16D412yes—
67C2×C3×M16D412yes—
68C22×C3×C8—21no—
69C22×C3×C8D412yes—
70C3×#117—21no—
71C3×#117—21no—
72C3×#117—21no—
73C3×#117—21no—
74C3×#117—21no—
75C3×#117—21no—
76C3×#117—21no—
77C3×#117—21no—
78C3×#117—21no—
79C3×#117—21no—
80C3×#117—21no—
81C3×#117—21no—
82C3×#117C2×C412yes—
83C3×#117C2×C412yes—
84C3×#117C2×C412yes—
85C3×#117D412yes—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—21no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4D412yes—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2×C412yes—
98C3×#104—28no—
99C3×#103—24no—
100C3×#102—24no—
101C3×#99—28no—
102C3×#97—24no—
103C3×C4×C8—24no—
104C22×#41C22×C311yescharacteristic
105C22×M16C22×C311yescharacteristic
106C22×M16C22×C311yescharacteristic
107C2×#117C22×C311yescharacteristic
108C2×#117C22×C311yescharacteristic
109C2×#117C22×C311yescharacteristic
110C2×#117C22×C311yescharacteristic
111#421—22no—
112#421—22no—
113C2×#104C3×C414yescomplemented
114#419C3×C412yescomplemented
115#418C3×C412yescomplemented
116#417—22no—
117#416—22no—
118#410—22no—
119#410C3×C414yescomplemented
120C2×#99—22no—
121#405—22no—
122#405—22no—
123C4×M16—22no—
124#342—22no—
125#339—22no—
126H(3,ℤ/4)—22no—
127C24×C3—21no—
128C24×C3C2×D411yescharacteristic
129C3×#41—22no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—41no—
138C3×#41—41no—
139C3×#41—41no—
140C3×#41—41no—
141C3×#41—41no—
142C3×#41—41no—
143C3×#41—41no—
144C3×#41—41no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×Q8—21no—
150C2×C3×Q8C4212yes—
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—41no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4C4212yes—
163C22×C3×C4—21no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4C22×C411yescharacteristic
175C22×C3×C4C22×C411yescharacteristic
176C22×C3×C4C22×C411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4#4111yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C3×M16—22no—
189C3×M16—22no—
190C3×M16—22no—
191C3×M16—22no—
192C3×M16—22no—
193C3×M16—22no—
194C3×M16—22no—
195C3×M16C22⋊C414yes—
196C2×C3×C8—22no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
200C2×C3×C8—22no—
201C2×C3×C8C22⋊C414yes—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—41no—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—22no—
213C3×C22⋊C4—41no—
214C3×C22⋊C4—41no—
215C3×C22⋊C4—41no—
216C3×C22⋊C4—41no—
217C3×C22⋊C4C22⋊C414yes—
218C3×C42—22no—
219C3×C42—22no—
220C3×C42—22no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—41no—
225C3×C42—41no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41—21no—
236C2×#41C2×C3×C412yes—
237C2×#41C2×C3×C412yes—
238C22×Q8C2×C3×C411yescharacteristic
239C22×D4—21no—
240C22×D4C2×C3×C411yescharacteristic
241C23×C4—21no—
242C23×C4C23×C311yescharacteristic
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16C2×C3×C412yes—
251C2×M16C2×C3×C412yes—
252C2×M16C3×D412yes—
253C2×M16C3×D412yes—
254C2×M16C3×D412yes—
255C22×C8—21no—
256C22×C8C3×D412yes—
257#117—21no—
258#117—21no—
259#117—21no—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267#117—21no—
268#117—21no—
269#117C2×C3×C412yes—
270#117C2×C3×C412yes—
271#117C2×C3×C412yes—
272#117C3×D412yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4C3×D412yes—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42C2×C3×C412yes—
285#104—28no—
286#103—24no—
287#102—24no—
288#99—28no—
289#97—24no—
290C4×C8—24no—
291C23×C3—22no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—81no—
295C23×C3—82no—
296C23×C3C2×C22⋊C411yescharacteristic
297C23×C3C4×D411yescharacteristic
298C23×C3C4×D411yescharacteristic
299C23×C3#12111yescharacteristic
300C23×C3#12111yescharacteristic
301C23×C3#12411yescharacteristic
302C23×C3#12711yescharacteristic
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—41no—
306C3×Q8—41no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—41no—
314C3×D4—41no—
315C2×C3×C4—22no—
316C2×C3×C4—24no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—82no—
327C2×C3×C4—82no—
328C2×C3×C4—82no—
329C2×C3×C4—82no—
330C2×C3×C4C2×C4211yescharacteristic
331C2×C3×C4C2×C22⋊C411yescharacteristic
332C2×C3×C4C2×C22⋊C411yescharacteristic
333C2×C3×C4#11711yescharacteristic
334C2×C3×C4#11711yescharacteristic
335C2×C3×C4#11711yescharacteristic
336C2×C3×C4C4×D411yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4C4×D411yescharacteristic
339C2×C3×C4C4×D411yescharacteristic
340C2×C3×C4C4×D411yescharacteristic
341C2×C3×C4C4×D411yescharacteristic
342C2×C3×C4C4×D411yescharacteristic
343C2×C3×C4C4×D411yescharacteristic
344C2×C3×C4C4×D411yescharacteristic
345C2×C3×C4C4×D411yescharacteristic
346C2×C3×C4#12011yescharacteristic
347C2×C3×C4#12111yescharacteristic
348C2×C3×C4#12111yescharacteristic
349C2×C3×C4#12111yescharacteristic
350C2×C3×C4#12111yescharacteristic
351C2×C3×C4#12311yescharacteristic
352C2×C3×C4#12311yescharacteristic
353C2×C3×C4#12311yescharacteristic
354C2×C3×C4#12411yescharacteristic
355C2×C3×C4#12411yescharacteristic
356C2×C3×C4#12611yescharacteristic
357C2×C3×C4#12611yescharacteristic
358C3×C8—24no—
359C3×C8—24no—
360C24—21no—
361C24C2×C3×D411yescharacteristic
362#41—22no—
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—22no—
368#41—22no—
369#41—22no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—41no—
376#41—41no—
377#41—41no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8C3×C4212yes—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4C3×C4212yes—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C22×C3×C411yescharacteristic
408C22×C4C22×C3×C411yescharacteristic
409C22×C4C22×C3×C411yescharacteristic
410C22×C4C2×C3×D411yescharacteristic
411C22×C4C2×C3×D411yescharacteristic
412C22×C4C2×C3×D411yescharacteristic
413C22×C4C2×C3×D411yescharacteristic
414C22×C4C2×C3×D411yescharacteristic
415C22×C4C3×#4111yescharacteristic
416C22×C4C3×#4111yescharacteristic
417C22×C4C3×#4111yescharacteristic
418C22×C4C3×#4111yescharacteristic
419C22×C4C3×#4111yescharacteristic
420C22×C4C3×#4111yescharacteristic
421M16—22no—
422M16—22no—
423M16—22no—
424M16—22no—
425M16—22no—
426M16—22no—
427M16—22no—
428M16C3×C22⋊C414yes—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8C3×C22⋊C414yes—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4C3×C22⋊C414yes—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—41no—
458C42—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—42no—
467C22×C3—82no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3C4×C22⋊C411yescharacteristic
471C22×C3#38611yescharacteristic
472C22×C3#38811yescharacteristic
473C22×C3#38811yescharacteristic
474C22×C3#39011yescharacteristic
475C22×C3#39011yescharacteristic
476C22×C3#39011yescharacteristic
477C3×C4—44no—
478C3×C4—42no—
479C3×C4—82no—
480C3×C4—82no—
481C3×C4—82no—
482C3×C4C4×C22⋊C411yescharacteristic
483C3×C4C4×C22⋊C411yescharacteristic
484C3×C4#38611yescharacteristic
485C3×C4#38611yescharacteristic
486C3×C4#38811yescharacteristic
487C3×C4#38811yescharacteristic
488C3×C4#38811yescharacteristic
489C3×C4#38811yescharacteristic
490C23—22no—
491C23—41no—
492C23—41no—
493C23—81no—
494C23—82no—
495C23C2×C3×C22⋊C411yescharacteristic
496C23C3×C4×D411yescharacteristic
497C23C3×C4×D411yescharacteristic
498C23C3×#12111yescharacteristic
499C23C3×#12111yescharacteristic
500C23C3×#12411yescharacteristic
501C23C3×#12711yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—41no—
513D4—41no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C2×C3×C4211yescharacteristic
530C2×C4C2×C3×C22⋊C411yescharacteristic
531C2×C4C2×C3×C22⋊C411yescharacteristic
532C2×C4C3×#11711yescharacteristic
533C2×C4C3×#11711yescharacteristic
534C2×C4C3×#11711yescharacteristic
535C2×C4C3×C4×D411yescharacteristic
536C2×C4C3×C4×D411yescharacteristic
537C2×C4C3×C4×D411yescharacteristic
538C2×C4C3×C4×D411yescharacteristic
539C2×C4C3×C4×D411yescharacteristic
540C2×C4C3×C4×D411yescharacteristic
541C2×C4C3×C4×D411yescharacteristic
542C2×C4C3×C4×D411yescharacteristic
543C2×C4C3×C4×D411yescharacteristic
544C2×C4C3×C4×D411yescharacteristic
545C2×C4C3×#12011yescharacteristic
546C2×C4C3×#12111yescharacteristic
547C2×C4C3×#12111yescharacteristic
548C2×C4C3×#12111yescharacteristic
549C2×C4C3×#12111yescharacteristic
550C2×C4C3×#12311yescharacteristic
551C2×C4C3×#12311yescharacteristic
552C2×C4C3×#12311yescharacteristic
553C2×C4C3×#12411yescharacteristic
554C2×C4C3×#12411yescharacteristic
555C2×C4C3×#12611yescharacteristic
556C2×C4C3×#12611yescharacteristic
557C8—24no—
558C8—24no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—82no—
567C2×C3#143711yescharacteristic
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—42no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22C3×C4×C22⋊C411yescharacteristic
580C22C3×#38611yescharacteristic
581C22C3×#38811yescharacteristic
582C22C3×#38811yescharacteristic
583C22C3×#39011yescharacteristic
584C22C3×#39011yescharacteristic
585C22C3×#39011yescharacteristic
586C4—44no—
587C4—42no—
588C4—82no—
589C4—82no—
590C4—82no—
591C4C3×C4×C22⋊C411yescharacteristic
592C4C3×C4×C22⋊C411yescharacteristic
593C4C3×#38611yescharacteristic
594C4C3×#38611yescharacteristic
595C4C3×#38811yescharacteristic
596C4C3×#38811yescharacteristic
597C4C3×#38811yescharacteristic
598C4C3×#38811yescharacteristic
599C3#1095111yescharacteristic, direct product factor, Sylow
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2C3×#143711yescharacteristic
subgroupG/H
centerC3×C4#386
commutatorC2×C4C2×C3×C42
Frattini, cosocleC23×C4C23×C3
socleC2×C3#1437
prime radicalC22×C3×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C3×C4 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#2873C2semidirect
5. C3×#1740C2semidirect
6. C3×#1733C2semidirect
7. C2×C3×H(3,ℤ/4)C2semidirect
8. #10951C3direct (N × H)
18. C2×C3×#104C4semidirect
19. C3×#419C4semidirect
20. C3×#418C4semidirect
24. C3×#410C4semidirect
35. #2873C2×C3semidirect
36. #1740C2×C3semidirect
37. #1733C2×C3semidirect
38. C2×H(3,ℤ/4)C2×C3semidirect
113. C2×#104C3×C4semidirect
114. #419C3×C4semidirect
115. #418C3×C4semidirect
119. #410C3×C4semidirect
599. C3#10951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4212
C3×#28962
C2×C3×#4102
C3×#28732
C3×#17402
C3×#17332
C2×C3×H(3,ℤ/4)2
#109513