Finite Group Databasebeta

← C3×#33086 #10651693

Subgroups — C3×#33086 #10651693

Order 768.

804 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2644C211yesmaximal, characteristic, complemented
2C3×#2275C211yesmaximal, characteristic, complemented
3C3×#1926C211yesmaximal, characteristic, complemented
4C3×#1926C211yesmaximal, characteristic, complemented
5C3×#1925C211yesmaximal, characteristic, complemented
6C3×#1920C211yesmaximal, characteristic, complemented
7C3×#1919C211yesmaximal, characteristic, complemented
8C3×#1918C211yesmaximal, characteristic, complemented
9C3×#1879C211yesmaximal, characteristic
10C3×#1879C211yesmaximal, characteristic
11C3×#1879C211yesmaximal, characteristic
12C3×#1864C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1840C211yesmaximal, characteristic, complemented
16#33086C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×#107C2211yescharacteristic
22C2×C3×#106C2211yescharacteristic
23C2×C3×#106C2211yescharacteristic
24C2×C3×#102C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C3×#397—21no—
31C3×#397—21no—
32C3×#397—21no—
33C3×#396—21no—
34C3×#390C2211yescharacteristic
35C3×#390C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×C4×C4⋊C4C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C3×C4×C4⋊C4C2211yescharacteristic
43C3×C4×C22⋊C4—21no—
44C3×C4×C22⋊C4—21no—
45C3×C4×C22⋊C4—21no—
46C3×#376C2211yescharacteristic
47C2×C3×#95—21no—
48C3×#340C2211yescharacteristic
49C3×#340C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#336C2211yescharacteristic
55C3×#336C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2644C2×C311yescharacteristic, complemented
61#2275C2×C311yescharacteristic, complemented
62#1926C2×C311yescharacteristic, complemented
63#1926C2×C311yescharacteristic, complemented
64#1925C2×C311yescharacteristic, complemented
65#1920C2×C311yescharacteristic, complemented
66#1919C2×C311yescharacteristic, complemented
67#1918C2×C311yescharacteristic, complemented
68#1879C2×C311yescharacteristic
69#1879C2×C311yescharacteristic
70#1879C2×C311yescharacteristic
71#1864C2×C311yescharacteristic, complemented
72#1864C2×C311yescharacteristic, complemented
73#1862C2×C311yescharacteristic, complemented
74#1840C2×C311yescharacteristic, complemented
75C22×C3×D4C2311yescharacteristic
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C2×C3×D8—22no—
81C2×C3×D8—22no—
82C2×C3×D8—22no—
83C22×C3×C8C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42—21no—
112C2×C3×C42—21no—
113C2×C3×C42—21no—
114C2×C3×C42C2311yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C3×#107—22no—
118C3×#106—22no—
119C3×#106—22no—
120C3×#102—22no—
121C3×#102—22no—
122C3×#102—22no—
123C3×#102—22no—
124C3×#102—22no—
125C3×#102—22no—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C3×#95—21no—
130C3×#95—21no—
131C3×#95—21no—
132C3×#95D411yescharacteristic
133C3×#95D411yescharacteristic
134C3×#95D411yescharacteristic
135C3×#95D411yescharacteristic
136C22×D8C22×C311yescharacteristic
137C2×C4×D4C22×C311yescharacteristic
138C2×C4×D4C22×C311yescharacteristic
139C2×C4×D4C22×C311yescharacteristic
140C2×#107C22×C311yescharacteristic
141C2×#106C22×C311yescharacteristic
142C2×#106C22×C311yescharacteristic
143C2×#102C22×C311yescharacteristic
144C2×#102C22×C311yescharacteristic
145C2×#102C22×C311yescharacteristic
146C2×#102C22×C311yescharacteristic
147C2×#102C22×C311yescharacteristic
148C2×#102C22×C311yescharacteristic
149#397—21no—
150#397—21no—
151#397—21no—
152#396—21no—
153#390C22×C311yescharacteristic
154#390C22×C311yescharacteristic
155#390C22×C311yescharacteristic
156#389C22×C311yescharacteristic
157#389C22×C311yescharacteristic
158#389C22×C311yescharacteristic
159C4×C4⋊C4C22×C311yescharacteristic
160C4×C4⋊C4C22×C311yescharacteristic
161C4×C4⋊C4C22×C311yescharacteristic
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—21no—
165#376C22×C311yescharacteristic
166C2×#95—21no—
167#340C22×C311yescharacteristic
168#340C22×C311yescharacteristic
169#340C22×C311yescharacteristic
170#340C22×C311yescharacteristic
171#340C22×C311yescharacteristic
172#340C22×C311yescharacteristic
173#336C22×C311yescharacteristic
174#336C22×C311yescharacteristic
175#336C22×C311yescharacteristic
176#336C22×C311yescharacteristic
177#336C22×C311yescharacteristic
178#336C22×C311yescharacteristic
179C24×C3—21no—
180C24×C3—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4#4112yes—
191C2×C3×D4#4112yes—
192C2×C3×D4#4112yes—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—24no—
197C22×C3×C4—24no—
198C22×C3×C4—24no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—81no—
203C22×C3×C4—81no—
204C22×C3×C4—81no—
205C22×C3×C4—81no—
206C22×C3×C4—81no—
207C22×C3×C4—81no—
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2411yescharacteristic
215C3×D8—44no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—81no—
238C3×C4⋊C4—81no—
239C3×C4⋊C4—81no—
240C3×C4⋊C4#4112yes—
241C3×C4⋊C4#4112yes—
242C3×C4⋊C4#4112yes—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—81no—
247C3×C22⋊C4—81no—
248C3×C22⋊C4—81no—
249C3×C22⋊C4—81no—
250C3×C22⋊C4—81no—
251C3×C22⋊C4—81no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—81no—
259C3×C42—81no—
260C3×C42—81no—
261C22×D4C23×C311yescharacteristic
262C22×D4C23×C311yescharacteristic
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C2×D8—22no—
267C2×D8—22no—
268C2×D8—22no—
269C22×C8C23×C311yescharacteristic
270C22×C8C23×C311yescharacteristic
271C22×C8C23×C311yescharacteristic
272C22×C8C23×C311yescharacteristic
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—22no—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4C23×C311yescharacteristic
283C2×C4⋊C4C23×C311yescharacteristic
284C2×C4⋊C4C23×C311yescharacteristic
285C2×C4⋊C4C23×C311yescharacteristic
286C2×C4⋊C4C23×C311yescharacteristic
287C2×C4⋊C4C23×C311yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42C23×C311yescharacteristic
301C2×C42C23×C311yescharacteristic
302C2×C42C23×C311yescharacteristic
303#107—22no—
304#106—22no—
305#106—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311#102—22no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95C3×D411yescharacteristic
319#95C3×D411yescharacteristic
320#95C3×D411yescharacteristic
321#95C3×D411yescharacteristic
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3C22×D411yescharacteristic
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C3×D4#12614yes—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
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—84no—
382C2×C3×C4—84no—
383C2×C3×C4—84no—
384C2×C3×C4C2×#4111yescharacteristic
385C2×C3×C4C2×#4111yescharacteristic
386C2×C3×C4C2×#4111yescharacteristic
387C2×C3×C4C2×#4111yescharacteristic
388C2×C3×C4C2×#4111yescharacteristic
389C2×C3×C4C2×#4111yescharacteristic
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—41no—
393C3×C8—41no—
394C24—21no—
395C24—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4C3×#4112yes—
406C2×D4C3×#4112yes—
407C2×D4C3×#4112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—81no—
418C22×C4—81no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4C2×C3×D411yescharacteristic
424C22×C4C2×C3×D411yescharacteristic
425C22×C4C2×C3×D411yescharacteristic
426C22×C4C2×C3×D411yescharacteristic
427C22×C4C2×C3×D411yescharacteristic
428C22×C4C2×C3×D411yescharacteristic
429C22×C4C24×C311yescharacteristic
430D8—44no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4C3×#4112yes—
456C4⋊C4C3×#4112yes—
457C4⋊C4C3×#4112yes—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C22⋊C4—81no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—81no—
475C42—81no—
476C22×C3—24no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3#52511yescharacteristic
491C22×C3#52511yescharacteristic
492C22×C3#52511yescharacteristic
493C22×C3#57611yescharacteristic
494C22×C3#57611yescharacteristic
495C22×C3#57711yescharacteristic
496C22×C3#57711yescharacteristic
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—81no—
507C3×C4—81no—
508C3×C4—81no—
509C3×C4C2×#12611yescharacteristic
510C3×C4#52911yescharacteristic
511C3×C4#52911yescharacteristic
512C3×C4#52911yescharacteristic
513C23—22no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C22×C3×D411yescharacteristic
528D4—22no—
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4C3×#12614yes—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—84no—
574C2×C4—84no—
575C2×C4C2×C3×#4111yescharacteristic
576C2×C4C2×C3×#4111yescharacteristic
577C2×C4C2×C3×#4111yescharacteristic
578C2×C4C2×C3×#4111yescharacteristic
579C2×C4C2×C3×#4111yescharacteristic
580C2×C4C2×C3×#4111yescharacteristic
581C8—41no—
582C8—41no—
583C8—41no—
584C8—41no—
585C2×C3—44no—
586C2×C3—161no—
587C2×C3#285211yescharacteristic
588C2×C3#311811yescharacteristic
589C2×C3#311811yescharacteristic
590C2×C3#311911yescharacteristic
591C2×C3#311911yescharacteristic
592C2×C3#312211yescharacteristic
593C2×C3#312511yescharacteristic
594C22—24no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22C3×#52511yescharacteristic
609C22C3×#52511yescharacteristic
610C22C3×#52511yescharacteristic
611C22C3×#57611yescharacteristic
612C22C3×#57611yescharacteristic
613C22C3×#57711yescharacteristic
614C22C3×#57711yescharacteristic
615C4—41no—
616C4—41no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4C2×C3×#12611yescharacteristic
628C4C3×#52911yescharacteristic
629C4C3×#52911yescharacteristic
630C4C3×#52911yescharacteristic
631C3#3308611yescharacteristic, direct product factor, Sylow
632C2—44no—
633C2—161no—
634C2C3×#285211yescharacteristic
635C2C3×#311811yescharacteristic
636C2C3×#311811yescharacteristic
637C2C3×#311911yescharacteristic
638C2C3×#311911yescharacteristic
639C2C3×#312211yescharacteristic
640C2C3×#312511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2644C2semidirect
2. C3×#2275C2semidirect
3. C3×#1926C2semidirect
4. C3×#1926C2semidirect
5. C3×#1925C2semidirect
6. C3×#1920C2semidirect
7. C3×#1919C2semidirect
8. C3×#1918C2semidirect
12. C3×#1864C2semidirect
13. C3×#1864C2semidirect
14. C3×#1862C2semidirect
15. C3×#1840C2semidirect
16. #33086C3direct (N × H)
60. #2644C2×C3semidirect
61. #2275C2×C3semidirect
62. #1926C2×C3semidirect
63. #1926C2×C3semidirect
64. #1925C2×C3semidirect
65. #1920C2×C3semidirect
66. #1919C2×C3semidirect
67. #1918C2×C3semidirect
71. #1864C2×C3semidirect
72. #1864C2×C3semidirect
73. #1862C2×C3semidirect
74. #1840C2×C3semidirect
631. C3#33086direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#26442
C3×#22752
C3×#19262
C3×#19252
C3×#19202
C3×#19192
C3×#19182
C3×#18792
C3×#18642
C3×#18622
C3×#18402
#330863