Finite Group Databasebeta

← C3×#24349 #10642956

Subgroups — C3×#24349 #10642956

Order 768.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic
2C2×C3×#479C211yesmaximal, characteristic, complemented
3C2×C3×#440C211yesmaximal, characteristic
4C3×#2582C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2026C211yesmaximal, characteristic, complemented
8C3×#2024C211yesmaximal, characteristic, complemented
9C3×#1992C211yesmaximal, characteristic, complemented
10C3×#1985C211yesmaximal, characteristic, complemented
11C3×#1877C211yesmaximal, characteristic
12C3×#1877C211yesmaximal, characteristic
13C3×#1864C211yesmaximal, characteristic
14C3×#1862C211yesmaximal, characteristic
15C3×#1802C211yesmaximal, characteristic
16#24349C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C3×#554—24no—
19C3×#554—24no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#125C2211yescharacteristic
22C2×C3×#125C2211yescharacteristic
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C22×C3×C4⋊C4—21no—
32C3×#479—24no—
33C3×#440—24no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#97C2211yescharacteristic
45C3×#398—21no—
46C3×#398—21no—
47C3×#391—21no—
48C3×#391C2211yescharacteristic
49C3×#391C2211yescharacteristic
50C3×#389—21no—
51C3×#389C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#384C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic
65C2×#479C2×C311yescharacteristic, complemented
66C2×#440C2×C311yescharacteristic
67#2582C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2057C2×C311yescharacteristic, complemented
70#2026C2×C311yescharacteristic, complemented
71#2024C2×C311yescharacteristic, complemented
72#1992C2×C311yescharacteristic, complemented
73#1985C2×C311yescharacteristic, complemented
74#1877C2×C311yescharacteristic
75#1877C2×C311yescharacteristic
76#1864C2×C311yescharacteristic
77#1862C2×C311yescharacteristic
78#1802C2×C311yescharacteristic
79C22×C3×Q8—21no—
80C22×C3×Q8D411yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16Q814yescomplemented
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—22no—
95C3×#125—22no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125D414yes—
99C3×C22⋊Q8—28no—
100C3×C22⋊Q8—28no—
101C3×C22⋊Q8—28no—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C3×C4×Q8—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4D414yes—
112C2×C3×C4⋊C4—28no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42—21no—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C3×#107—22no—
140C3×#107—22no—
141C3×#106—22no—
142C3×C4⋊C8—22no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#97—22no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C22×SD16C22×C311yescharacteristic
157#554—24no—
158#554—24no—
159C2×C4⋊Q8C22×C311yescharacteristic
160C2×#125C22×C311yescharacteristic
161C2×#125C22×C311yescharacteristic
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C4×Q8C22×C311yescharacteristic
166C2×C4×Q8C22×C311yescharacteristic
167C2×C4×D4C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170C22×C4⋊C4—21no—
171#479—24no—
172#440—24no—
173C2×#107C22×C311yescharacteristic
174C2×#107C22×C311yescharacteristic
175C2×#106C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#97C22×C311yescharacteristic
184#398—21no—
185#398—21no—
186#391—21no—
187#391C22×C311yescharacteristic
188#391C22×C311yescharacteristic
189#389—21no—
190#389C22×C311yescharacteristic
191#389C22×C311yescharacteristic
192#384C22×C311yescharacteristic
193#340C22×C311yescharacteristic
194#340C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#336C22×C311yescharacteristic
200#336C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203C24×C3—21no—
204C2×C3×Q8—24no—
205C2×C3×Q8—22no—
206C2×C3×Q8—22no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—41no—
213C2×C3×Q8—81no—
214C2×C3×Q8—81no—
215C2×C3×Q8C2×Q812yes—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4C2×D412yes—
220C2×C3×D4C2×Q812yes—
221C2×C3×D4#4112yes—
222C22×C3×C4—24no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—24no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—81no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C3×SD16—28no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8C2×Q812yes—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4—81no—
278C3×C4⋊C4—81no—
279C3×C4⋊C4—81no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—42no—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293C22×Q8—21no—
294C22×Q8C3×D411yescharacteristic
295C22×Q8C23×C311yescharacteristic
296C22×D4C23×C311yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×SD16C3×Q814yescomplemented
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#125—22no—
310#125—22no—
311#125—22no—
312#125C3×D414yes—
313C22⋊Q8—28no—
314C22⋊Q8—28no—
315C22⋊Q8—28no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4C3×D414yes—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4C3×D411yescharacteristic
338C2×C4⋊C4C3×D411yescharacteristic
339C2×C4⋊C4C3×D411yescharacteristic
340C2×C4⋊C4C23×C311yescharacteristic
341C2×C4⋊C4C23×C311yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C4⋊C4C23×C311yescharacteristic
344C2×C4⋊C4C23×C311yescharacteristic
345C2×C4⋊C4C23×C311yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C42—21no—
350C2×C42C23×C311yescharacteristic
351C2×C42C23×C311yescharacteristic
352C2×C42C23×C311yescharacteristic
353#107—22no—
354#107—22no—
355#106—22no—
356C4⋊C8—22no—
357#103—22no—
358#103—22no—
359#103—22no—
360#102—22no—
361#102—22no—
362#102—22no—
363#97—22no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3C22×D411yescharacteristic
378C3×Q8—22no—
379C3×Q8—22no—
380C3×Q8—44no—
381C3×Q8—41no—
382C3×Q8—41no—
383C3×Q8—84no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4C22⋊Q814yes—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—48no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—84no—
426C2×C3×C4—84no—
427C2×C3×C4#12012yes—
428C2×C3×C4#12012yes—
429C2×C3×C4#13712yes—
430C2×C3×C4C22×D411yescharacteristic
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C22×Q811yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434C2×C3×C42−1+411yescharacteristic
435C2×C3×C42−1+411yescharacteristic
436C3×C8—22no—
437C3×C8—41no—
438C3×C8—41no—
439C3×C8—41no—
440C24—21no—
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—81no—
451C2×Q8—81no—
452C2×Q8C2×C3×Q812yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C2×C3×D412yes—
457C2×D4C2×C3×Q812yes—
458C2×D4C3×#4112yes—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4C2×C3×D411yescharacteristic
476C22×C4C2×C3×D411yescharacteristic
477C22×C4C2×C3×D411yescharacteristic
478C22×C4C2×C3×D411yescharacteristic
479C22×C4C2×C3×D411yescharacteristic
480C22×C4C2×C3×D411yescharacteristic
481C22×C4C24×C311yescharacteristic
482SD16—28no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8C2×C3×Q812yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—81no—
517C4⋊C4C2×C3×D412yes—
518C4⋊C4C2×C3×D412yes—
519C4⋊C4C2×C3×D412yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42C2×C3×D412yes—
529C42C2×C3×D412yes—
530C22×C3—24no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3C2×#12011yescharacteristic
538C22×C3#54811yescharacteristic
539C22×C3D4×Q811yescharacteristic
540C22×C3C2×#13711yescharacteristic
541C22×C3#57511yescharacteristic
542C22×C3#57611yescharacteristic
543C22×C3#57711yescharacteristic
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—81no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4C2×C22⋊Q811yescharacteristic
558C3×C4#53611yescharacteristic
559C3×C4#54811yescharacteristic
560C3×C4D4×Q811yescharacteristic
561C23—22no—
562C23—22no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23C22×C3×D411yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—44no—
572Q8—41no—
573Q8—41no—
574Q8—84no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4C3×C22⋊Q814yes—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—48no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4—84no—
618C2×C4C3×#12012yes—
619C2×C4C3×#12012yes—
620C2×C4C3×#13712yes—
621C2×C4C22×C3×D411yescharacteristic
622C2×C4C22×C3×D411yescharacteristic
623C2×C4C22×C3×Q811yescharacteristic
624C2×C4C2×C3×#4111yescharacteristic
625C2×C4C3×2−1+411yescharacteristic
626C2×C4C3×2−1+411yescharacteristic
627C8—22no—
628C8—41no—
629C8—41no—
630C8—41no—
631C2×C3—44no—
632C2×C3#240911yescharacteristic
633C2×C3#300711yescharacteristic
634C2×C3#301211yescharacteristic
635C2×C3#337011yescharacteristic
636C2×C3#337211yescharacteristic
637C2×C3#338511yescharacteristic
638C2×C3#338811yescharacteristic
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22C2×C3×#12011yescharacteristic
647C22C3×#54811yescharacteristic
648C22C3×D4×Q811yescharacteristic
649C22C2×C3×#13711yescharacteristic
650C22C3×#57511yescharacteristic
651C22C3×#57611yescharacteristic
652C22C3×#57711yescharacteristic
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C2×C3×C22⋊Q811yescharacteristic
667C4C3×#53611yescharacteristic
668C4C3×#54811yescharacteristic
669C4C3×D4×Q811yescharacteristic
670C3#2434911yescharacteristic, direct product factor, Sylow
671C2—44no—
672C2C3×#240911yescharacteristic
673C2C3×#300711yescharacteristic
674C2C3×#301211yescharacteristic
675C2C3×#337011yescharacteristic
676C2C3×#337211yescharacteristic
677C2C3×#338511yescharacteristic
678C2C3×#338811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#479C2semidirect
4. C3×#2582C2semidirect
5. C3×#2059C2semidirect
6. C3×#2057C2semidirect
7. C3×#2026C2semidirect
8. C3×#2024C2semidirect
9. C3×#1992C2semidirect
10. C3×#1985C2semidirect
16. #24349C3direct (N × H)
65. C2×#479C2×C3semidirect
67. #2582C2×C3semidirect
68. #2059C2×C3semidirect
69. #2057C2×C3semidirect
70. #2026C2×C3semidirect
71. #2024C2×C3semidirect
72. #1992C2×C3semidirect
73. #1985C2×C3semidirect
88. C2×C3×SD16Q8semidirect
302. C2×SD16C3×Q8semidirect
670. C3#24349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4792
C2×C3×#4402
C3×#25822
C3×#20592
C3×#20572
C3×#20262
C3×#20242
C3×#19922
C3×#19852
C3×#18772
C3×#18642
C3×#18622
C3×#18022
#243493