Finite Group Databasebeta

← C3×#29542 #10648149

Subgroups — C3×#29542 #10648149

Order 768.

746 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2319C211yesmaximal, characteristic, complemented
2C3×#2319C211yesmaximal, characteristic, complemented
3C3×#2088C211yesmaximal, characteristic, complemented
4C3×#2067C211yesmaximal, characteristic, complemented
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2054C211yesmaximal, characteristic
7C3×#1926C211yesmaximal, characteristic, complemented
8C3×#1926C211yesmaximal, characteristic, complemented
9C3×#1920C211yesmaximal, characteristic, complemented
10C3×#1918C211yesmaximal, characteristic, complemented
11C3×#1879C211yesmaximal, characteristic
12C3×#1879C211yesmaximal, characteristic
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1832C211yesmaximal, characteristic, complemented
16#29542C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#107C2211yescharacteristic
21C2×C3×#106C2211yescharacteristic
22C2×C3×#106C2211yescharacteristic
23C2×C3×C4⋊C8C2211yescharacteristic
24C2×C3×C4⋊C8C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C3×#390C2211yescharacteristic
32C3×#390C2211yescharacteristic
33C3×#390C2211yescharacteristic
34C3×#390C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#388—21no—
40C3×#388—21no—
41C3×#388—21no—
42C3×#388—21no—
43C3×#381—21no—
44C3×#381—21no—
45C3×#380—21no—
46C3×#380—21no—
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×#376C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2319C2×C311yescharacteristic, complemented
61#2319C2×C311yescharacteristic, complemented
62#2088C2×C311yescharacteristic, complemented
63#2067C2×C311yescharacteristic, complemented
64#2065C2×C311yescharacteristic, complemented
65#2054C2×C311yescharacteristic
66#1926C2×C311yescharacteristic, complemented
67#1926C2×C311yescharacteristic, complemented
68#1920C2×C311yescharacteristic, complemented
69#1918C2×C311yescharacteristic, complemented
70#1879C2×C311yescharacteristic
71#1879C2×C311yescharacteristic
72#1864C2×C311yescharacteristic, complemented
73#1862C2×C311yescharacteristic, complemented
74#1832C2×C311yescharacteristic, complemented
75C22×C3×D4C2311yescharacteristic
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C2×C3×D8—22no—
80C2×C3×D8—22no—
81C2×C3×D8—41no—
82C22×C3×C8C2311yescharacteristic
83C22×C3×C8C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
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×C42—21no—
111C2×C3×C42—21no—
112C2×C3×C42C2311yescharacteristic
113C2×C3×C42C2311yescharacteristic
114C2×C3×C42C2311yescharacteristic
115C3×#107—22no—
116C3×#106—22no—
117C3×#106—41no—
118C3×C4⋊C8—41no—
119C3×C4⋊C8—41no—
120C3×#102—22no—
121C3×#102—22no—
122C3×#102—22no—
123C3×#102—22no—
124C3×#102—41no—
125C3×#102—41no—
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×#107C22×C311yescharacteristic
140C2×#106C22×C311yescharacteristic
141C2×#106C22×C311yescharacteristic
142C2×C4⋊C8C22×C311yescharacteristic
143C2×C4⋊C8C22×C311yescharacteristic
144C2×#102C22×C311yescharacteristic
145C2×#102C22×C311yescharacteristic
146C2×#102C22×C311yescharacteristic
147C2×#102C22×C311yescharacteristic
148C2×#102C22×C311yescharacteristic
149C2×#102C22×C311yescharacteristic
150#390C22×C311yescharacteristic
151#390C22×C311yescharacteristic
152#390C22×C311yescharacteristic
153#390C22×C311yescharacteristic
154#389C22×C311yescharacteristic
155#389C22×C311yescharacteristic
156#389C22×C311yescharacteristic
157#389C22×C311yescharacteristic
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#381—21no—
163#381—21no—
164#380—21no—
165#380—21no—
166C4×C4⋊C4C22×C311yescharacteristic
167C4×C4⋊C4C22×C311yescharacteristic
168#376C22×C311yescharacteristic
169#340C22×C311yescharacteristic
170#340C22×C311yescharacteristic
171#340C22×C311yescharacteristic
172#340C22×C311yescharacteristic
173#340C22×C311yescharacteristic
174#340C22×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—21no—
191C2×C3×D4#4112yes—
192C2×C3×D4#4112yes—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—24no—
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—81no—
202C22×C3×C4—81no—
203C22×C3×C4—81no—
204C22×C3×C4—81no—
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2411yescharacteristic
212C3×D8—44no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
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—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—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—81no—
236C3×C4⋊C4—81no—
237C3×C4⋊C4—81no—
238C3×C4⋊C4—81no—
239C3×C4⋊C4#4112yes—
240C3×C4⋊C4#4112yes—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—24no—
243C3×C22⋊C4—81no—
244C3×C22⋊C4—81no—
245C3×C22⋊C4—81no—
246C3×C22⋊C4—81no—
247C3×C22⋊C4—81no—
248C3×C22⋊C4—81no—
249C3×C22⋊C4—81no—
250C3×C22⋊C4—81no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—81no—
258C3×C42—81no—
259C22×D4C23×C311yescharacteristic
260C22×D4C23×C311yescharacteristic
261C23×C4—21no—
262C23×C4—21no—
263C2×D8—22no—
264C2×D8—22no—
265C2×D8—41no—
266C22×C8C23×C311yescharacteristic
267C22×C8C23×C311yescharacteristic
268C22×C8C23×C311yescharacteristic
269C22×C8C23×C311yescharacteristic
270C4×D4—22no—
271C4×D4—22no—
272C4×D4—22no—
273C4×D4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C23×C311yescharacteristic
279C2×C4⋊C4C23×C311yescharacteristic
280C2×C4⋊C4C23×C311yescharacteristic
281C2×C4⋊C4C23×C311yescharacteristic
282C2×C4⋊C4C23×C311yescharacteristic
283C2×C4⋊C4C23×C311yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
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×C42—21no—
295C2×C42—21no—
296C2×C42C23×C311yescharacteristic
297C2×C42C23×C311yescharacteristic
298C2×C42C23×C311yescharacteristic
299#107—22no—
300#106—22no—
301#106—41no—
302C4⋊C8—41no—
303C4⋊C8—41no—
304#102—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308#102—41no—
309#102—41no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—21no—
316#95C3×D411yescharacteristic
317#95C3×D411yescharacteristic
318#95C3×D411yescharacteristic
319#95C3×D411yescharacteristic
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
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×C3C22×D411yescharacteristic
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
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—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
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—84no—
380C2×C3×C4—84no—
381C2×C3×C4C2×#4111yescharacteristic
382C2×C3×C4C2×#4111yescharacteristic
383C2×C3×C4C2×#4111yescharacteristic
384C2×C3×C4C2×#4111yescharacteristic
385C2×C3×C4H(5,𝔽2)11yescharacteristic
386C2×C3×C42−1+411yescharacteristic
387C3×C8—41no—
388C3×C8—41no—
389C3×C8—41no—
390C3×C8—41no—
391C24—21no—
392C24—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4C3×#4112yes—
404C2×D4C3×#4112yes—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—81no—
414C22×C4—81no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×C3×D411yescharacteristic
418C22×C4C2×C3×D411yescharacteristic
419C22×C4C2×C3×D411yescharacteristic
420C22×C4C2×C3×D411yescharacteristic
421C22×C4C2×C3×D411yescharacteristic
422C22×C4C2×C3×D411yescharacteristic
423C22×C4C24×C311yescharacteristic
424D8—44no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—81no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4—81no—
451C4⋊C4C3×#4112yes—
452C4⋊C4C3×#4112yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C22⋊C4—81no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—81no—
470C42—81no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—81no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3#52511yescharacteristic
486C22×C3#52511yescharacteristic
487C22×C3#53711yescharacteristic
488C22×C3#57611yescharacteristic
489C22×C3#57611yescharacteristic
490C22×C3#57711yescharacteristic
491C22×C3#57711yescharacteristic
492C3×C4—41no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—81no—
501C3×C4—81no—
502C3×C4—81no—
503C3×C4—81no—
504C3×C4#55111yescharacteristic
505C3×C4#55211yescharacteristic
506C3×C4#55211yescharacteristic
507C3×C4#55511yescharacteristic
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23C22×C3×D411yescharacteristic
523D4—22no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
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—84no—
568C2×C4—84no—
569C2×C4C2×C3×#4111yescharacteristic
570C2×C4C2×C3×#4111yescharacteristic
571C2×C4C2×C3×#4111yescharacteristic
572C2×C4C2×C3×#4111yescharacteristic
573C2×C4C3×H(5,𝔽2)11yescharacteristic
574C2×C4C3×2−1+411yescharacteristic
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C2×C3—82no—
580C2×C3—82no—
581C2×C3#260911yescharacteristic
582C2×C3#311811yescharacteristic
583C2×C3#311911yescharacteristic
584C2×C3#312211yescharacteristic
585C2×C3#312511yescharacteristic
586C2×C3#325711yescharacteristic
587C2×C3#325711yescharacteristic
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22C3×#52511yescharacteristic
603C22C3×#52511yescharacteristic
604C22C3×#53711yescharacteristic
605C22C3×#57611yescharacteristic
606C22C3×#57611yescharacteristic
607C22C3×#57711yescharacteristic
608C22C3×#57711yescharacteristic
609C4—41no—
610C4—41no—
611C4—41no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4C3×#55111yescharacteristic
622C4C3×#55211yescharacteristic
623C4C3×#55211yescharacteristic
624C4C3×#55511yescharacteristic
625C3#2954211yescharacteristic, direct product factor, Sylow
626C2—82no—
627C2—82no—
628C2C3×#260911yescharacteristic
629C2C3×#311811yescharacteristic
630C2C3×#311911yescharacteristic
631C2C3×#312211yescharacteristic
632C2C3×#312511yescharacteristic
633C2C3×#325711yescharacteristic
634C2C3×#325711yescharacteristic
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×#2319C2semidirect
2. C3×#2319C2semidirect
3. C3×#2088C2semidirect
4. C3×#2067C2semidirect
5. C3×#2065C2semidirect
7. C3×#1926C2semidirect
8. C3×#1926C2semidirect
9. C3×#1920C2semidirect
10. C3×#1918C2semidirect
13. C3×#1864C2semidirect
14. C3×#1862C2semidirect
15. C3×#1832C2semidirect
16. #29542C3direct (N × H)
60. #2319C2×C3semidirect
61. #2319C2×C3semidirect
62. #2088C2×C3semidirect
63. #2067C2×C3semidirect
64. #2065C2×C3semidirect
66. #1926C2×C3semidirect
67. #1926C2×C3semidirect
68. #1920C2×C3semidirect
69. #1918C2×C3semidirect
72. #1864C2×C3semidirect
73. #1862C2×C3semidirect
74. #1832C2×C3semidirect
625. C3#29542direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#23192
C3×#20882
C3×#20672
C3×#20652
C3×#20542
C3×#19262
C3×#19202
C3×#19182
C3×#18792
C3×#18642
C3×#18622
C3×#18322
#295423