Finite Group Databasebeta

← C3×#10941 #10629548

Subgroups — C3×#10941 #10629548

Order 768.

904 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#413C211yesmaximal, characteristic
2C2×C3×#410C211yesmaximal, characteristic
3C3×#2879C211yesmaximal, characteristic
4C3×#2873C211yesmaximal, characteristic, complemented
5C2×C3×#344C211yesmaximal, characteristic, complemented
6C2×C3×#344C211yesmaximal, characteristic, complemented
7C3×#1742C211yesmaximal, characteristic, complemented
8#10941C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C22×C3×M16C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C2×C3×#117C2211yescharacteristic
16C3×#413—22no—
17C3×#413—22no—
18C2×C3×#101C412yescomplemented
19C2×C3×#100C412yescomplemented
20C3×#410—22no—
21C3×#410—22no—
22C2×C3×#99C414yes—
23C3×#408—22no—
24C3×#408—22no—
25C3×#407C414yescomplemented
26C3×#405—22no—
27C3×#405—22no—
28C3×C4×M16—22no—
29C3×#344—22no—
30C3×#344—22no—
31C3×#343—22no—
32C2×#413C2×C311yescharacteristic
33C2×#410C2×C311yescharacteristic
34#2879C2×C311yescharacteristic
35#2873C2×C311yescharacteristic, complemented
36C2×#344C2×C311yescharacteristic, complemented
37C2×#344C2×C311yescharacteristic, complemented
38#1742C2×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×#41—21no—
50C2×C3×#41—21no—
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4C2×C412yes—
53C22×C3×D4C2×C411yescharacteristic
54C23×C3×C4C2×C412yes—
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×M16—21no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16—21no—
71C2×C3×M16—21no—
72C2×C3×M16—21no—
73C2×C3×M16C2×C412yes—
74C2×C3×M16C2×C412yes—
75C2×C3×M16C2×C412yes—
76C2×C3×M16C2×C412yes—
77C2×C3×M16D412yes—
78C2×C3×M16D412yes—
79C2×C3×M16D412yes—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8D412yes—
84C3×#117—21no—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117—21no—
88C3×#117—21no—
89C3×#117—21no—
90C3×#117D412yes—
91C3×#117D412yes—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C22⋊C4C2×C412yes—
95C2×C3×C22⋊C4C2×C412yes—
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C3×#101—24no—
99C3×#100—24no—
100C3×#99—28no—
101C3×C22⋊C8—28no—
102C3×#97—24no—
103C3×C4×C8—24no—
104C22×#41C22×C311yescharacteristic
105C22×M16C22×C311yescharacteristic
106C22×M16C22×C311yescharacteristic
107C22×M16C22×C311yescharacteristic
108C22×M16C22×C311yescharacteristic
109C2×#117C22×C311yescharacteristic
110C2×#117C22×C311yescharacteristic
111#413—22no—
112#413—22no—
113C2×#101C3×C412yescomplemented
114C2×#100C3×C412yescomplemented
115#410—22no—
116#410—22no—
117C2×#99C3×C414yes—
118#408—22no—
119#408—22no—
120#407C3×C414yescomplemented
121#405—22no—
122#405—22no—
123C4×M16—22no—
124#344—22no—
125#344—22no—
126#343—22no—
127C24×C3C4212yes—
128C24×C3C22×C411yescharacteristic
129C3×#41—41no—
130C3×#41—41no—
131C3×#41—41no—
132C3×#41—41no—
133C3×#41—41no—
134C3×#41—41no—
135C3×#41—41no—
136C3×#41—41no—
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×Q8—21no—
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4C4212yes—
172C22×C3×C4C22×C411yescharacteristic
173C22×C3×C4C22×C411yescharacteristic
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4#4111yescharacteristic
181C22×C3×C4#4111yescharacteristic
182C22×C3×C4#4111yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C3×M16—22no—
187C3×M16—22no—
188C3×M16—22no—
189C3×M16—22no—
190C3×M16—22no—
191C3×M16—22no—
192C3×M16—22no—
193C3×M16—22no—
194C3×M16—22no—
195C3×M16—22no—
196C3×M16—22no—
197C3×M16—41no—
198C3×M16—41no—
199C3×M16—41no—
200C3×M16—41no—
201C3×M16C22⋊C414yes—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—22no—
209C2×C3×C8—41no—
210C2×C3×C8—41no—
211C2×C3×C8—41no—
212C2×C3×C8—41no—
213C2×C3×C8C22⋊C414yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—41no—
217C3×C4⋊C4—41no—
218C3×C22⋊C4—22no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C22⋊C4C22⋊C414yes—
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×#41—21no—
237C2×#41—21no—
238C22×Q8C2×C3×C411yescharacteristic
239C22×D4C2×C3×C412yes—
240C22×D4C2×C3×C411yescharacteristic
241C23×C4C2×C3×C412yes—
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×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16C2×C3×C412yes—
261C2×M16C2×C3×C412yes—
262C2×M16C2×C3×C412yes—
263C2×M16C2×C3×C412yes—
264C2×M16C3×D412yes—
265C2×M16C3×D412yes—
266C2×M16C3×D412yes—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8C3×D412yes—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277#117C3×D412yes—
278#117C3×D412yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C22⋊C4C2×C3×C412yes—
282C2×C22⋊C4C2×C3×C412yes—
283C2×C42—21no—
284C2×C42—21no—
285#101—24no—
286#100—24no—
287#99—28no—
288C22⋊C8—28no—
289#97—24no—
290C4×C8—24no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—81no—
295C23×C3—82no—
296C23×C3C2×C4211yescharacteristic
297C23×C3C2×C22⋊C411yescharacteristic
298C23×C3#11711yescharacteristic
299C23×C3C4×D411yescharacteristic
300C23×C3C4×D411yescharacteristic
301C23×C3C4×D411yescharacteristic
302C23×C3C4×D411yescharacteristic
303C3×Q8—41no—
304C3×Q8—41no—
305C3×Q8—41no—
306C3×Q8—41no—
307C3×D4—42no—
308C3×D4—42no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—82no—
325C2×C3×C4—82no—
326C2×C3×C4C2×C22⋊C411yescharacteristic
327C2×C3×C4C2×C22⋊C411yescharacteristic
328C2×C3×C4#11711yescharacteristic
329C2×C3×C4#11711yescharacteristic
330C2×C3×C4C4×D411yescharacteristic
331C2×C3×C4C4×D411yescharacteristic
332C2×C3×C4C4×D411yescharacteristic
333C2×C3×C4C4×D411yescharacteristic
334C2×C3×C4C4×D411yescharacteristic
335C2×C3×C4C4×D411yescharacteristic
336C2×C3×C4C4×D411yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4#12011yescharacteristic
339C2×C3×C4#12111yescharacteristic
340C2×C3×C4#12111yescharacteristic
341C2×C3×C4#12111yescharacteristic
342C2×C3×C4#12111yescharacteristic
343C2×C3×C4#12111yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12311yescharacteristic
346C2×C3×C4#12311yescharacteristic
347C2×C3×C4#12311yescharacteristic
348C2×C3×C4#12411yescharacteristic
349C2×C3×C4#12411yescharacteristic
350C2×C3×C4#12411yescharacteristic
351C2×C3×C4#12611yescharacteristic
352C2×C3×C4#12611yescharacteristic
353C2×C3×C4#12711yescharacteristic
354C3×C8—24no—
355C3×C8—24no—
356C3×C8—42no—
357C3×C8—42no—
358C24C3×C4212yes—
359C24C22×C3×C411yescharacteristic
360#41—41no—
361#41—41no—
362#41—41no—
363#41—41no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—41no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4C3×C4212yes—
403C22×C4C22×C3×C411yescharacteristic
404C22×C4C22×C3×C411yescharacteristic
405C22×C4C2×C3×D411yescharacteristic
406C22×C4C2×C3×D411yescharacteristic
407C22×C4C2×C3×D411yescharacteristic
408C22×C4C2×C3×D411yescharacteristic
409C22×C4C2×C3×D411yescharacteristic
410C22×C4C2×C3×D411yescharacteristic
411C22×C4C3×#4111yescharacteristic
412C22×C4C3×#4111yescharacteristic
413C22×C4C3×#4111yescharacteristic
414C22×C4C3×#4111yescharacteristic
415C22×C4C3×#4111yescharacteristic
416C22×C4C3×#4111yescharacteristic
417M16—22no—
418M16—22no—
419M16—22no—
420M16—22no—
421M16—22no—
422M16—22no—
423M16—22no—
424M16—22no—
425M16—22no—
426M16—22no—
427M16—22no—
428M16—41no—
429M16—41no—
430M16—41no—
431M16—41no—
432M16C3×C22⋊C414yes—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8C3×C22⋊C414yes—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4C3×C22⋊C414yes—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—44no—
465C22×C3—42no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3C4×C22⋊C411yescharacteristic
469C22×C3C4×C22⋊C411yescharacteristic
470C22×C3C4×C22⋊C411yescharacteristic
471C22×C3#38611yescharacteristic
472C22×C3#38811yescharacteristic
473C22×C3#38811yescharacteristic
474C22×C3#39011yescharacteristic
475C3×C4—44no—
476C3×C4—42no—
477C3×C4—82no—
478C3×C4#38611yescharacteristic
479C3×C4#38611yescharacteristic
480C3×C4#38811yescharacteristic
481C3×C4#38811yescharacteristic
482C3×C4#38811yescharacteristic
483C3×C4#38811yescharacteristic
484C3×C4#39011yescharacteristic
485C3×C4#39011yescharacteristic
486C23—22no—
487C23—22no—
488C23—22no—
489C23—81no—
490C23—82no—
491C23C2×C3×C4211yescharacteristic
492C23C2×C3×C22⋊C411yescharacteristic
493C23C3×#11711yescharacteristic
494C23C3×C4×D411yescharacteristic
495C23C3×C4×D411yescharacteristic
496C23C3×C4×D411yescharacteristic
497C23C3×C4×D411yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—42no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C2×C3×C22⋊C411yescharacteristic
522C2×C4C2×C3×C22⋊C411yescharacteristic
523C2×C4C3×#11711yescharacteristic
524C2×C4C3×#11711yescharacteristic
525C2×C4C3×C4×D411yescharacteristic
526C2×C4C3×C4×D411yescharacteristic
527C2×C4C3×C4×D411yescharacteristic
528C2×C4C3×C4×D411yescharacteristic
529C2×C4C3×C4×D411yescharacteristic
530C2×C4C3×C4×D411yescharacteristic
531C2×C4C3×C4×D411yescharacteristic
532C2×C4C3×C4×D411yescharacteristic
533C2×C4C3×#12011yescharacteristic
534C2×C4C3×#12111yescharacteristic
535C2×C4C3×#12111yescharacteristic
536C2×C4C3×#12111yescharacteristic
537C2×C4C3×#12111yescharacteristic
538C2×C4C3×#12111yescharacteristic
539C2×C4C3×#12111yescharacteristic
540C2×C4C3×#12311yescharacteristic
541C2×C4C3×#12311yescharacteristic
542C2×C4C3×#12311yescharacteristic
543C2×C4C3×#12411yescharacteristic
544C2×C4C3×#12411yescharacteristic
545C2×C4C3×#12411yescharacteristic
546C2×C4C3×#12611yescharacteristic
547C2×C4C3×#12611yescharacteristic
548C2×C4C3×#12711yescharacteristic
549C8—24no—
550C8—24no—
551C8—42no—
552C8—42no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—82no—
561C2×C3#143711yescharacteristic
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22C3×C4×C22⋊C411yescharacteristic
574C22C3×C4×C22⋊C411yescharacteristic
575C22C3×C4×C22⋊C411yescharacteristic
576C22C3×#38611yescharacteristic
577C22C3×#38811yescharacteristic
578C22C3×#38811yescharacteristic
579C22C3×#39011yescharacteristic
580C4—44no—
581C4—42no—
582C4—82no—
583C4C3×#38611yescharacteristic
584C4C3×#38611yescharacteristic
585C4C3×#38811yescharacteristic
586C4C3×#38811yescharacteristic
587C4C3×#38811yescharacteristic
588C4C3×#38811yescharacteristic
589C4C3×#39011yescharacteristic
590C4C3×#39011yescharacteristic
591C3#1094111yescharacteristic, direct product factor, Sylow
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—82no—
600C2C3×#143711yescharacteristic
subgroupG/H
centerC3×C4#386
commutatorC23C2×C3×C42
Frattini, cosocleC23×C4C23×C3
socleC2×C3#1437
prime radicalC22×C3×#41C22
LCSG ▷ C23 ▷ 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. C2×C3×#344C2semidirect
6. C2×C3×#344C2semidirect
7. C3×#1742C2semidirect
8. #10941C3direct (N × H)
18. C2×C3×#101C4semidirect
19. C2×C3×#100C4semidirect
25. C3×#407C4semidirect
35. #2873C2×C3semidirect
36. C2×#344C2×C3semidirect
37. C2×#344C2×C3semidirect
38. #1742C2×C3semidirect
113. C2×#101C3×C4semidirect
114. C2×#100C3×C4semidirect
120. #407C3×C4semidirect
591. C3#10941direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4132
C2×C3×#4102
C3×#28792
C3×#28732
C2×C3×#3442
C3×#17422
#109413