Finite Group Databasebeta

← C3×#33076 #10651683

Subgroups — C3×#33076 #10651683

Order 768.

760 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2647C211yesmaximal, characteristic, complemented
2C3×#2275C211yesmaximal, characteristic
3C3×#1949C211yesmaximal, characteristic, complemented
4C3×#1948C211yesmaximal, characteristic, complemented
5C3×#1920C211yesmaximal, characteristic, complemented
6C3×#1919C211yesmaximal, characteristic, complemented
7C3×#1919C211yesmaximal, characteristic, complemented
8C3×#1918C211yesmaximal, characteristic, complemented
9C3×#1864C211yesmaximal, characteristic
10C3×#1864C211yesmaximal, characteristic
11C3×#1864C211yesmaximal, characteristic
12C3×#1862C211yesmaximal, characteristic
13C3×#1832C211yesmaximal, characteristic, complemented
14C3×#1804C211yesmaximal, characteristic
15C3×#1802C211yesmaximal, characteristic
16#33076C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#107C2211yescharacteristic
21C2×C3×#106C2211yescharacteristic
22C2×C3×#106C2211yescharacteristic
23C2×C3×#106C2211yescharacteristic
24C2×C3×C4⋊C8C2211yescharacteristic
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C3×#400—21no—
31C3×#400—21no—
32C3×#398—21no—
33C3×#398—21no—
34C3×#389C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#384C2211yescharacteristic
39C3×#382C2211yescharacteristic
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×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2647C2×C311yescharacteristic, complemented
61#2275C2×C311yescharacteristic
62#1949C2×C311yescharacteristic, complemented
63#1948C2×C311yescharacteristic, complemented
64#1920C2×C311yescharacteristic, complemented
65#1919C2×C311yescharacteristic, complemented
66#1919C2×C311yescharacteristic, complemented
67#1918C2×C311yescharacteristic, complemented
68#1864C2×C311yescharacteristic
69#1864C2×C311yescharacteristic
70#1864C2×C311yescharacteristic
71#1862C2×C311yescharacteristic
72#1832C2×C311yescharacteristic, complemented
73#1804C2×C311yescharacteristic
74#1802C2×C311yescharacteristic
75C22×C3×D4C2311yescharacteristic
76C23×C3×C4—21no—
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C22×C3×C8C2311yescharacteristic
80C22×C3×C8C2311yescharacteristic
81C22×C3×C8C2311yescharacteristic
82C22×C3×C8C2311yescharacteristic
83C3×C4×D4—22no—
84C3×C4×D4—22no—
85C3×C4×D4—22no—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C3×C4×D4Q814yes—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
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×C42—21no—
106C2×C3×C42—21no—
107C2×C3×C42—21no—
108C2×C3×C42C2311yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C3×#107—22no—
112C3×#106—22no—
113C3×#106—22no—
114C3×#106—22no—
115C3×C4⋊C8—22no—
116C3×C4⋊C8—22no—
117C3×#102—22no—
118C3×#102—22no—
119C3×#102—22no—
120C3×#102—22no—
121C3×#95—21no—
122C3×#95—21no—
123C3×#95—21no—
124C3×#95—21no—
125C3×#95—21no—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C3×#95—21no—
130C3×#95D411yescharacteristic
131C3×#95D411yescharacteristic
132C3×#95D411yescharacteristic
133C3×#95D411yescharacteristic
134C2×C4×D4C22×C311yescharacteristic
135C2×C4×D4C22×C311yescharacteristic
136C2×C4×D4C22×C311yescharacteristic
137C2×#107C22×C311yescharacteristic
138C2×#106C22×C311yescharacteristic
139C2×#106C22×C311yescharacteristic
140C2×#106C22×C311yescharacteristic
141C2×C4⋊C8C22×C311yescharacteristic
142C2×C4⋊C8C22×C311yescharacteristic
143C2×#102C22×C311yescharacteristic
144C2×#102C22×C311yescharacteristic
145C2×#102C22×C311yescharacteristic
146C2×#102C22×C311yescharacteristic
147#400—21no—
148#400—21no—
149#398—21no—
150#398—21no—
151#389C22×C311yescharacteristic
152#389C22×C311yescharacteristic
153#389C22×C311yescharacteristic
154#389C22×C311yescharacteristic
155#384C22×C311yescharacteristic
156#382C22×C311yescharacteristic
157C4×C4⋊C4C22×C311yescharacteristic
158C4×C4⋊C4C22×C311yescharacteristic
159C4×C4⋊C4C22×C311yescharacteristic
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163#376C22×C311yescharacteristic
164C2×#95—21no—
165#340C22×C311yescharacteristic
166#340C22×C311yescharacteristic
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
177C24×C3—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4C2×Q812yes—
182C2×C3×D4#4112yes—
183C2×C3×D4#4112yes—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—24no—
188C22×C3×C4—24no—
189C22×C3×C4—24no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—81no—
195C22×C3×C4—81no—
196C22×C3×C4—81no—
197C22×C3×C4—81no—
198C22×C3×C4—81no—
199C22×C3×C4—81no—
200C22×C3×C4C2×D411yescharacteristic
201C22×C3×C4C2×D411yescharacteristic
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2411yescharacteristic
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—81no—
231C3×C4⋊C4—81no—
232C3×C4⋊C4—81no—
233C3×C4⋊C4—81no—
234C3×C4⋊C4—81no—
235C3×C4⋊C4—81no—
236C3×C4⋊C4C2×Q812yes—
237C3×C4⋊C4#4112yes—
238C3×C4⋊C4#4112yes—
239C3×C22⋊C4—24no—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—24no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—81no—
247C3×C42—81no—
248C3×C42—81no—
249C3×C42C2×Q812yes—
250C3×C42#4112yes—
251C22×D4C23×C311yescharacteristic
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C22×C8C23×C311yescharacteristic
256C22×C8C23×C311yescharacteristic
257C22×C8C23×C311yescharacteristic
258C22×C8C23×C311yescharacteristic
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4C3×Q814yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C23×C311yescharacteristic
272C2×C4⋊C4C23×C311yescharacteristic
273C2×C4⋊C4C23×C311yescharacteristic
274C2×C4⋊C4C23×C311yescharacteristic
275C2×C4⋊C4C23×C311yescharacteristic
276C2×C4⋊C4C23×C311yescharacteristic
277C2×C4⋊C4C23×C311yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42C23×C311yescharacteristic
285C2×C42C23×C311yescharacteristic
286C2×C42C23×C311yescharacteristic
287#107—22no—
288#106—22no—
289#106—22no—
290#106—22no—
291C4⋊C8—22no—
292C4⋊C8—22no—
293#102—22no—
294#102—22no—
295#102—22no—
296#102—22no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95C3×D411yescharacteristic
307#95C3×D411yescharacteristic
308#95C3×D411yescharacteristic
309#95C3×D411yescharacteristic
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3C22×D411yescharacteristic
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—22no—
321C3×D4#12514yes—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—84no—
360C2×C3×C4—84no—
361C2×C3×C4—84no—
362C2×C3×C4C22⋊Q812yes—
363C2×C3×C4C22⋊Q812yes—
364C2×C3×C4C22×Q811yescharacteristic
365C2×C3×C4C2×#4111yescharacteristic
366C2×C3×C4C2×#4111yescharacteristic
367C2×C3×C4C2×#4111yescharacteristic
368C2×C3×C4C2×#4111yescharacteristic
369C2×C3×C4C2×#4111yescharacteristic
370C3×C8—41no—
371C3×C8—41no—
372C3×C8—41no—
373C3×C8—41no—
374C24—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4C2×C3×Q812yes—
379C2×D4C3×#4112yes—
380C2×D4C3×#4112yes—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—81no—
392C22×C4—81no—
393C22×C4—81no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4—81no—
397C22×C4C2×C3×D411yescharacteristic
398C22×C4C2×C3×D411yescharacteristic
399C22×C4C2×C3×D411yescharacteristic
400C22×C4C2×C3×D411yescharacteristic
401C22×C4C2×C3×D411yescharacteristic
402C22×C4C2×C3×D411yescharacteristic
403C22×C4C24×C311yescharacteristic
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—81no—
428C4⋊C4—81no—
429C4⋊C4—81no—
430C4⋊C4—81no—
431C4⋊C4—81no—
432C4⋊C4—81no—
433C4⋊C4C2×C3×Q812yes—
434C4⋊C4C3×#4112yes—
435C4⋊C4C3×#4112yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42—21no—
443C42—81no—
444C42—81no—
445C42—81no—
446C42C2×C3×Q812yes—
447C42C3×#4112yes—
448C22×C3—24no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3C2×C22⋊Q811yescharacteristic
456C22×C3#52511yescharacteristic
457C22×C3#52511yescharacteristic
458C22×C3#57611yescharacteristic
459C22×C3#57711yescharacteristic
460C22×C3#57711yescharacteristic
461C22×C3#57711yescharacteristic
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—42no—
465C3×C4—41no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—81no—
472C3×C4—81no—
473C3×C4—81no—
474C3×C4—81no—
475C3×C4C2×#12511yescharacteristic
476C3×C4#52911yescharacteristic
477C3×C4#52911yescharacteristic
478C3×C4#53311yescharacteristic
479C23—22no—
480C23—22no—
481C23—22no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23C22×C3×D411yescharacteristic
487D4—22no—
488D4—22no—
489D4—22no—
490D4C3×#12514yes—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—84no—
529C2×C4—84no—
530C2×C4—84no—
531C2×C4C3×C22⋊Q812yes—
532C2×C4C3×C22⋊Q812yes—
533C2×C4C22×C3×Q811yescharacteristic
534C2×C4C2×C3×#4111yescharacteristic
535C2×C4C2×C3×#4111yescharacteristic
536C2×C4C2×C3×#4111yescharacteristic
537C2×C4C2×C3×#4111yescharacteristic
538C2×C4C2×C3×#4111yescharacteristic
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C2×C3—44no—
544C2×C3#285111yescharacteristic
545C2×C3#308111yescharacteristic
546C2×C3#308411yescharacteristic
547C2×C3#311811yescharacteristic
548C2×C3#311911yescharacteristic
549C2×C3#312311yescharacteristic
550C2×C3#312511yescharacteristic
551C22—24no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22C2×C3×C22⋊Q811yescharacteristic
559C22C3×#52511yescharacteristic
560C22C3×#52511yescharacteristic
561C22C3×#57611yescharacteristic
562C22C3×#57711yescharacteristic
563C22C3×#57711yescharacteristic
564C22C3×#57711yescharacteristic
565C4—22no—
566C4—22no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4C2×C3×#12511yescharacteristic
579C4C3×#52911yescharacteristic
580C4C3×#52911yescharacteristic
581C4C3×#53311yescharacteristic
582C3#3307611yescharacteristic, direct product factor, Sylow
583C2—44no—
584C2C3×#285111yescharacteristic
585C2C3×#308111yescharacteristic
586C2C3×#308411yescharacteristic
587C2C3×#311811yescharacteristic
588C2C3×#311911yescharacteristic
589C2C3×#312311yescharacteristic
590C2C3×#312511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
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×#2647C2semidirect
3. C3×#1949C2semidirect
4. C3×#1948C2semidirect
5. C3×#1920C2semidirect
6. C3×#1919C2semidirect
7. C3×#1919C2semidirect
8. C3×#1918C2semidirect
13. C3×#1832C2semidirect
16. #33076C3direct (N × H)
60. #2647C2×C3semidirect
62. #1949C2×C3semidirect
63. #1948C2×C3semidirect
64. #1920C2×C3semidirect
65. #1919C2×C3semidirect
66. #1919C2×C3semidirect
67. #1918C2×C3semidirect
72. #1832C2×C3semidirect
582. C3#33076direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#26472
C3×#22752
C3×#19492
C3×#19482
C3×#19202
C3×#19192
C3×#19182
C3×#18642
C3×#18622
C3×#18322
C3×#18042
C3×#18022
#330763