Finite Group Databasebeta

← C3×#24635 #10643242

Subgroups — C3×#24635 #10643242

Order 768.

904 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#464C211yesmaximal, characteristic, complemented
2C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
3C3×#2544C211yesmaximal, characteristic
4C3×#2356C211yesmaximal, characteristic, complemented
5C3×#2056C211yesmaximal, characteristic, complemented
6C3×#2055C211yesmaximal, characteristic, complemented
7C3×#2015C211yesmaximal, characteristic, complemented
8C3×#2014C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1982C211yesmaximal, characteristic
11C3×#1958C211yesmaximal, characteristic, complemented
12C3×#1939C211yesmaximal, characteristic, complemented
13C3×#1927C211yesmaximal, characteristic, complemented
14C3×#1926C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24635C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×#127C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4C2211yescharacteristic
25C3×#464—24no—
26C3×C4×SD16—24no—
27C2×C3×#106C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×C4×C8C2211yescharacteristic
42C3×#394—21no—
43C3×#394—21no—
44C3×#391C2211yescharacteristic
45C3×#391C2211yescharacteristic
46C3×#391C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#387—21no—
49C3×#387—21no—
50C3×#386—21no—
51C3×#386—21no—
52C3×#383—21no—
53C3×#382C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×#376—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#464C2×C311yescharacteristic, complemented
63C2×C4×SD16C2×C311yescharacteristic, complemented
64#2544C2×C311yescharacteristic
65#2356C2×C311yescharacteristic, complemented
66#2056C2×C311yescharacteristic, complemented
67#2055C2×C311yescharacteristic, complemented
68#2015C2×C311yescharacteristic, complemented
69#2014C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1982C2×C311yescharacteristic
72#1958C2×C311yescharacteristic, complemented
73#1939C2×C311yescharacteristic, complemented
74#1927C2×C311yescharacteristic, complemented
75#1926C2×C311yescharacteristic, complemented
76#1804C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C2×C3×Q16—22no—
85C2×C3×Q16—41no—
86C2×C3×Q16—41no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C2×C3×SD16—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#127—22no—
98C3×#127—41no—
99C3×#124—22no—
100C3×#124—22no—
101C3×#124—22no—
102C3×#124—41no—
103C3×C4×Q8—22no—
104C3×C4×Q8D414yescomplemented
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4D411yescharacteristic
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C42—21no—
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C3×#106—22no—
128C3×C4⋊C8—22no—
129C3×C4⋊C8—41no—
130C3×C4⋊C8—41no—
131C3×#103—22no—
132C3×#103—22no—
133C3×#103—22no—
134C3×#103—41no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—41no—
139C3×#102—41no—
140C3×#102—41no—
141C3×C4×C8—22no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95D411yescharacteristic
153C3×#95D411yescharacteristic
154C22×Q16C22×C311yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C22×SD16C22×C311yescharacteristic
157C2×#127C22×C311yescharacteristic
158C2×#124C22×C311yescharacteristic
159C2×#124C22×C311yescharacteristic
160C2×C4×Q8C22×C311yescharacteristic
161C2×C4×D4C22×C311yescharacteristic
162#464—24no—
163C4×SD16—24no—
164C2×#106C22×C311yescharacteristic
165C2×C4⋊C8C22×C311yescharacteristic
166C2×C4⋊C8C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×#103C22×C311yescharacteristic
169C2×#103C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#102C22×C311yescharacteristic
173C2×#102C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×#102C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×C4×C8C22×C311yescharacteristic
179#394—21no—
180#394—21no—
181#391C22×C311yescharacteristic
182#391C22×C311yescharacteristic
183#391C22×C311yescharacteristic
184#390C22×C311yescharacteristic
185#387—21no—
186#387—21no—
187#386—21no—
188#386—21no—
189#383—21no—
190#382C22×C311yescharacteristic
191C4×C4⋊C4C22×C311yescharacteristic
192C4×C4⋊C4C22×C311yescharacteristic
193C4×C4⋊C4C22×C311yescharacteristic
194#376—21no—
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#336C22×C311yescharacteristic
198#336C22×C311yescharacteristic
199C24×C3—21no—
200C24×C3—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8C2×D412yes—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4#4112yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—42no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C3×Q16—44no—
248C3×SD16—28no—
249C3×SD16—44no—
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×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8#4112yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—41no—
272C3×C4⋊C4C2×D412yes—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—81no—
279C3×C22⋊C4—81no—
280C3×C42—24no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—42no—
286C3×C42—42no—
287C3×C42C2×D412yes—
288C3×C42#4112yes—
289C22×Q8C23×C311yescharacteristic
290C22×Q8C23×C311yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C23×C311yescharacteristic
294C22×D4C23×C311yescharacteristic
295C23×C4—21no—
296C2×Q16—22no—
297C2×Q16—41no—
298C2×Q16—41no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×SD16—41no—
304C2×SD16—41no—
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307C22×C8C23×C311yescharacteristic
308C22×C8C23×C311yescharacteristic
309#127—22no—
310#127—41no—
311#124—22no—
312#124—22no—
313#124—22no—
314#124—41no—
315C4×Q8—22no—
316C4×Q8C3×D414yescomplemented
317C4×D4—22no—
318C4×D4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C3×D411yescharacteristic
321C2×C4⋊C4C3×D411yescharacteristic
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42C23×C311yescharacteristic
337C2×C42C23×C311yescharacteristic
338C2×C42C23×C311yescharacteristic
339#106—22no—
340C4⋊C8—22no—
341C4⋊C8—41no—
342C4⋊C8—41no—
343#103—22no—
344#103—22no—
345#103—22no—
346#103—41no—
347#102—22no—
348#102—22no—
349#102—22no—
350#102—41no—
351#102—41no—
352#102—41no—
353C4×C8—22no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95C3×D411yescharacteristic
365#95C3×D411yescharacteristic
366C23×C3—22no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3C22×D411yescharacteristic
381C3×Q8—22no—
382C3×Q8—22no—
383C3×Q8—41no—
384C3×Q8—41no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—84no—
398C3×D4—84no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
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—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—84no—
433C2×C3×C4#12112yes—
434C2×C3×C4#12112yes—
435C2×C3×C4#13512yes—
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C3×C8—22no—
443C3×C8—41no—
444C3×C8—41no—
445C3×C8—41no—
446C24—21no—
447C24—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8C2×C3×D412yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4C3×#4112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C24×C311yescharacteristic
494Q16—44no—
495SD16—28no—
496SD16—44no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8C3×#4112yes—
509C4⋊C4—24no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4C2×C3×D412yes—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—42no—
534C42C2×C3×D412yes—
535C42C3×#4112yes—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3—81no—
550C22×C3C2×#12111yescharacteristic
551C22×C3#54611yescharacteristic
552C22×C3#55011yescharacteristic
553C22×C3C2×#13511yescharacteristic
554C22×C3#57511yescharacteristic
555C22×C3#57711yescharacteristic
556C22×C3#57711yescharacteristic
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—41no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—81no—
566C3×C4—81no—
567C3×C4—81no—
568C3×C4—81no—
569C3×C4#52511yescharacteristic
570C3×C4#53511yescharacteristic
571C3×C4#55311yescharacteristic
572C3×C4#55511yescharacteristic
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C22×C3×D411yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605D4—84no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4C3×#12112yes—
641C2×C4C3×#12112yes—
642C2×C4C3×#13512yes—
643C2×C4C22×C3×D411yescharacteristic
644C2×C4C2×C3×#4111yescharacteristic
645C2×C4C2×C3×#4111yescharacteristic
646C2×C4C2×C3×#4111yescharacteristic
647C2×C4C3×H(5,𝔽2)11yescharacteristic
648C2×C4C3×H(5,𝔽2)11yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C2×C3—82no—
654C2×C3—161no—
655C2×C3#241411yescharacteristic
656C2×C3#303511yescharacteristic
657C2×C3#304311yescharacteristic
658C2×C3#329611yescharacteristic
659C2×C3#332311yescharacteristic
660C2×C3#339411yescharacteristic
661C2×C3#340111yescharacteristic
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22C2×C3×#12111yescharacteristic
677C22C3×#54611yescharacteristic
678C22C3×#55011yescharacteristic
679C22C2×C3×#13511yescharacteristic
680C22C3×#57511yescharacteristic
681C22C3×#57711yescharacteristic
682C22C3×#57711yescharacteristic
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C3×#52511yescharacteristic
696C4C3×#53511yescharacteristic
697C4C3×#55311yescharacteristic
698C4C3×#55511yescharacteristic
699C3#2463511yescharacteristic, direct product factor, Sylow
700C2—82no—
701C2—161no—
702C2C3×#241411yescharacteristic
703C2C3×#303511yescharacteristic
704C2C3×#304311yescharacteristic
705C2C3×#329611yescharacteristic
706C2C3×#332311yescharacteristic
707C2C3×#339411yescharacteristic
708C2C3×#340111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#127C22
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. C2×C3×#464C2semidirect
2. C2×C3×C4×SD16C2semidirect
4. C3×#2356C2semidirect
5. C3×#2056C2semidirect
6. C3×#2055C2semidirect
7. C3×#2015C2semidirect
9. C3×#1983C2semidirect
11. C3×#1958C2semidirect
12. C3×#1939C2semidirect
13. C3×#1927C2semidirect
14. C3×#1926C2semidirect
15. C3×#1804C2semidirect
16. #24635C3direct (N × H)
62. C2×#464C2×C3semidirect
63. C2×C4×SD16C2×C3semidirect
65. #2356C2×C3semidirect
66. #2056C2×C3semidirect
67. #2055C2×C3semidirect
68. #2015C2×C3semidirect
70. #1983C2×C3semidirect
72. #1958C2×C3semidirect
73. #1939C2×C3semidirect
74. #1927C2×C3semidirect
75. #1926C2×C3semidirect
76. #1804C2×C3semidirect
104. C3×C4×Q8D4semidirect
316. C4×Q8C3×D4semidirect
699. C3#24635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4642
C2×C3×C4×SD162
C3×#25442
C3×#23562
C3×#20562
C3×#20552
C3×#20152
C3×#20142
C3×#19832
C3×#19822
C3×#19582
C3×#19392
C3×#19272
C3×#19262
C3×#18042
#246353