Finite Group Databasebeta

← C3×#26777 #10645384

Subgroups — C3×#26777 #10645384

Order 768.

698 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
1C3×#2508C211yesmaximal, characteristic, complemented
2C3×#2367C211yesmaximal, characteristic
3C3×#2073C211yesmaximal, characteristic
4C3×#2067C211yesmaximal, characteristic
5C3×#2042C211yesmaximal, characteristic
6C3×#2042C211yesmaximal, characteristic
7C3×#1935C211yesmaximal, characteristic, complemented
8C3×#1928C211yesmaximal, characteristic, complemented
9C3×#1921C211yesmaximal, characteristic, complemented
10C3×#1918C211yesmaximal, characteristic, complemented
11C3×#1917C211yesmaximal, characteristic, complemented
12C3×#1863C211yesmaximal, characteristic, complemented
13C3×#1862C211yesmaximal, characteristic
14C3×#1805C211yesmaximal, characteristic, complemented
15C3×#1762C211yesmaximal, characteristic
16#26777C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#107C2211yescharacteristic
21C2×C3×#107C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic
23C2×C3×#103C2211yescharacteristic
24C2×C3×#103C2211yescharacteristic
25C2×C3×#103C2211yescharacteristic
26C2×C3×#103C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#97C2211yescharacteristic
32C3×#400—21no—
33C3×#398—21no—
34C3×#391C2211yescharacteristic
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×#388—21no—
41C3×#388—21no—
42C3×#387—21no—
43C3×#385—21no—
44C3×#382—21no—
45C3×#382C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×C4×C22⋊C4—21no—
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2508C2×C311yescharacteristic, complemented
61#2367C2×C311yescharacteristic
62#2073C2×C311yescharacteristic
63#2067C2×C311yescharacteristic
64#2042C2×C311yescharacteristic
65#2042C2×C311yescharacteristic
66#1935C2×C311yescharacteristic, complemented
67#1928C2×C311yescharacteristic, complemented
68#1921C2×C311yescharacteristic, complemented
69#1918C2×C311yescharacteristic, complemented
70#1917C2×C311yescharacteristic, complemented
71#1863C2×C311yescharacteristic, complemented
72#1862C2×C311yescharacteristic
73#1805C2×C311yescharacteristic, complemented
74#1762C2×C311yescharacteristic
75C22×C3×Q8C2311yescharacteristic
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C22×C3×C8C2311yescharacteristic
79C22×C3×C8C2311yescharacteristic
80C22×C3×C8C2311yescharacteristic
81C22×C3×C8C2311yescharacteristic
82C3×#124—22no—
83C3×#124—22no—
84C3×C4×Q8—22no—
85C3×C4×Q8—41no—
86C3×C4×D4—22no—
87C3×C4×D4—41no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4D411yescharacteristic
94C2×C3×C4⋊C4D411yescharacteristic
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×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×C42—21no—
107C2×C3×C42—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×C3×C42C2311yescharacteristic
112C3×#107—22no—
113C3×#107—22no—
114C3×C4⋊C8—41no—
115C3×#103—22no—
116C3×#103—22no—
117C3×#103—22no—
118C3×#103—41no—
119C3×#102—22no—
120C3×#102—22no—
121C3×#102—22no—
122C3×#102—41no—
123C3×#97—41no—
124C3×#95—21no—
125C3×#95—21no—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C3×#95—21no—
130C3×#95—21no—
131C3×#95—21no—
132C3×#95—21no—
133C3×#95—21no—
134C3×#95D411yescharacteristic
135C3×#95D411yescharacteristic
136C2×#124C22×C311yescharacteristic
137C2×C4×Q8C22×C311yescharacteristic
138C2×C4×D4C22×C311yescharacteristic
139C2×#107C22×C311yescharacteristic
140C2×#107C22×C311yescharacteristic
141C2×C4⋊C8C22×C311yescharacteristic
142C2×#103C22×C311yescharacteristic
143C2×#103C22×C311yescharacteristic
144C2×#103C22×C311yescharacteristic
145C2×#103C22×C311yescharacteristic
146C2×#102C22×C311yescharacteristic
147C2×#102C22×C311yescharacteristic
148C2×#102C22×C311yescharacteristic
149C2×#102C22×C311yescharacteristic
150C2×#97C22×C311yescharacteristic
151#400—21no—
152#398—21no—
153#391C22×C311yescharacteristic
154#390C22×C311yescharacteristic
155#389C22×C311yescharacteristic
156#389C22×C311yescharacteristic
157#389C22×C311yescharacteristic
158#389C22×C311yescharacteristic
159#388—21no—
160#388—21no—
161#387—21no—
162#385—21no—
163#382—21no—
164#382C22×C311yescharacteristic
165C4×C4⋊C4C22×C311yescharacteristic
166C4×C4⋊C4C22×C311yescharacteristic
167C4×C4⋊C4C22×C311yescharacteristic
168C4×C22⋊C4—21no—
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—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8#4112yes—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4#4112yes—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—81no—
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2411yescharacteristic
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—
219C2×C3×C8—21no—
220C2×C3×C8—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—21no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—42no—
234C3×C4⋊C4—42no—
235C3×C4⋊C4—81no—
236C3×C4⋊C4—81no—
237C3×C4⋊C4—81no—
238C3×C4⋊C4#4112yes—
239C3×C4⋊C4#4112yes—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—42no—
243C3×C22⋊C4—42no—
244C3×C22⋊C4—81no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—42no—
252C3×C42—42no—
253C3×C42—81no—
254C22×Q8C23×C311yescharacteristic
255C22×D4C23×C311yescharacteristic
256C23×C4—21no—
257C22×C8C23×C311yescharacteristic
258C22×C8C23×C311yescharacteristic
259C22×C8C23×C311yescharacteristic
260C22×C8C23×C311yescharacteristic
261#124—22no—
262#124—22no—
263C4×Q8—22no—
264C4×Q8—41no—
265C4×D4—22no—
266C4×D4—41no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C3×D411yescharacteristic
273C2×C4⋊C4C3×D411yescharacteristic
274C2×C4⋊C4C23×C311yescharacteristic
275C2×C4⋊C4C23×C311yescharacteristic
276C2×C4⋊C4C23×C311yescharacteristic
277C2×C4⋊C4C23×C311yescharacteristic
278C2×C4⋊C4C23×C311yescharacteristic
279C2×C4⋊C4C23×C311yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42C23×C311yescharacteristic
289C2×C42C23×C311yescharacteristic
290C2×C42C23×C311yescharacteristic
291#107—22no—
292#107—22no—
293C4⋊C8—41no—
294#103—22no—
295#103—22no—
296#103—22no—
297#103—41no—
298#102—22no—
299#102—22no—
300#102—22no—
301#102—41no—
302#97—41no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95C3×D411yescharacteristic
314#95C3×D411yescharacteristic
315C23×C3—22no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3C22×D411yescharacteristic
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—41no—
326C3×Q8—41no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—41no—
330C3×D4—41no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
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—21no—
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—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
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—84no—
371C2×C3×C4C2×#4111yescharacteristic
372C2×C3×C4C2×#4111yescharacteristic
373C2×C3×C4C2×#4111yescharacteristic
374C2×C3×C4C2×#4111yescharacteristic
375C2×C3×C4H(5,𝔽2)11yescharacteristic
376C2×C3×C42−1+411yescharacteristic
377C3×C8—41no—
378C3×C8—41no—
379C3×C8—41no—
380C3×C8—41no—
381C24—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C3×#4112yes—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4C3×#4112yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C2×C3×D411yescharacteristic
405C22×C4C2×C3×D411yescharacteristic
406C22×C4C2×C3×D411yescharacteristic
407C22×C4C2×C3×D411yescharacteristic
408C22×C4C2×C3×D411yescharacteristic
409C22×C4C2×C3×D411yescharacteristic
410C22×C4C24×C311yescharacteristic
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—81no—
438C4⋊C4—81no—
439C4⋊C4—81no—
440C4⋊C4C3×#4112yes—
441C4⋊C4C3×#4112yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—81no—
447C42—21no—
448C42—21no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—42no—
454C42—42no—
455C42—81no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3#52511yescharacteristic
464C22×C3#54611yescharacteristic
465C22×C3#54811yescharacteristic
466C22×C3#57511yescharacteristic
467C22×C3#57511yescharacteristic
468C22×C3#57611yescharacteristic
469C22×C3#57811yescharacteristic
470C3×C4—41no—
471C3×C4—42no—
472C3×C4—41no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—81no—
480C3×C4—81no—
481C3×C4—81no—
482C3×C4—81no—
483C3×C4#52911yescharacteristic
484C3×C4#53911yescharacteristic
485C3×C4#55211yescharacteristic
486C3×C4#55311yescharacteristic
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×C3×D411yescharacteristic
495Q8—22no—
496Q8—22no—
497Q8—41no—
498Q8—41no—
499D4—22no—
500D4—22no—
501D4—41no—
502D4—41no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4C2×C3×#4111yescharacteristic
544C2×C4C2×C3×#4111yescharacteristic
545C2×C4C2×C3×#4111yescharacteristic
546C2×C4C2×C3×#4111yescharacteristic
547C2×C4C3×H(5,𝔽2)11yescharacteristic
548C2×C4C3×2−1+411yescharacteristic
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C2×C3—82no—
554C2×C3#246011yescharacteristic
555C2×C3#311111yescharacteristic
556C2×C3#312411yescharacteristic
557C2×C3#331911yescharacteristic
558C2×C3#332711yescharacteristic
559C2×C3#337011yescharacteristic
560C2×C3#337711yescharacteristic
561C22—42no—
562C22—42no—
563C22—42no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C3×#52511yescharacteristic
569C22C3×#54611yescharacteristic
570C22C3×#54811yescharacteristic
571C22C3×#57511yescharacteristic
572C22C3×#57511yescharacteristic
573C22C3×#57611yescharacteristic
574C22C3×#57811yescharacteristic
575C4—42no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4C3×#52911yescharacteristic
589C4C3×#53911yescharacteristic
590C4C3×#55211yescharacteristic
591C4C3×#55311yescharacteristic
592C3#2677711yescharacteristic, direct product factor, Sylow
593C2—82no—
594C2C3×#246011yescharacteristic
595C2C3×#311111yescharacteristic
596C2C3×#312411yescharacteristic
597C2C3×#331911yescharacteristic
598C2C3×#332711yescharacteristic
599C2C3×#337011yescharacteristic
600C2C3×#337711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2508C2semidirect
7. C3×#1935C2semidirect
8. C3×#1928C2semidirect
9. C3×#1921C2semidirect
10. C3×#1918C2semidirect
11. C3×#1917C2semidirect
12. C3×#1863C2semidirect
14. C3×#1805C2semidirect
16. #26777C3direct (N × H)
60. #2508C2×C3semidirect
66. #1935C2×C3semidirect
67. #1928C2×C3semidirect
68. #1921C2×C3semidirect
69. #1918C2×C3semidirect
70. #1917C2×C3semidirect
71. #1863C2×C3semidirect
73. #1805C2×C3semidirect
592. C3#26777direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#25082
C3×#23672
C3×#20732
C3×#20672
C3×#20422
C3×#19352
C3×#19282
C3×#19212
C3×#19182
C3×#19172
C3×#18632
C3×#18622
C3×#18052
C3×#17622
#267773