Finite Group Databasebeta

← C3×#24638 #10643245

Subgroups — C3×#24638 #10643245

Order 768.

982 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#463C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C3×#2544C211yesmaximal, characteristic, complemented
4C3×#2354C211yesmaximal, characteristic, complemented
5C3×#2055C211yesmaximal, characteristic, complemented
6C3×#2054C211yesmaximal, characteristic, complemented
7C3×#2012C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1982C211yesmaximal, characteristic, complemented
11C3×#1959C211yesmaximal, characteristic, complemented
12C3×#1940C211yesmaximal, characteristic, complemented
13C3×#1927C211yesmaximal, characteristic, complemented
14C3×#1926C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#24638C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#127C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×#117—21no—
26C3×#463—24no—
27C3×#442—24no—
28C2×C3×#106C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
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×#102C2211yescharacteristic
42C2×C3×#97C2211yescharacteristic
43C3×#394—21no—
44C3×#394—21no—
45C3×#391C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#388—21no—
50C3×#388—21no—
51C3×#386—21no—
52C3×#386—21no—
53C3×#384C2211yescharacteristic
54C3×#380—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#463C2×C311yescharacteristic, complemented
63C2×#442C2×C311yescharacteristic, complemented
64#2544C2×C311yescharacteristic, complemented
65#2354C2×C311yescharacteristic, complemented
66#2055C2×C311yescharacteristic, complemented
67#2054C2×C311yescharacteristic, complemented
68#2012C2×C311yescharacteristic, complemented
69#2011C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1982C2×C311yescharacteristic, complemented
72#1959C2×C311yescharacteristic, complemented
73#1940C2×C311yescharacteristic, complemented
74#1927C2×C311yescharacteristic, complemented
75#1926C2×C311yescharacteristic, complemented
76#1802C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C2×C3×SD16—22no—
86C2×C3×SD16—41no—
87C2×C3×SD16—41no—
88C2×C3×D8—22no—
89C2×C3×D8—22no—
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—41no—
93C2×C3×D8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#127—22no—
99C3×#127—41no—
100C3×#124—22no—
101C3×#124—22no—
102C3×#124—22no—
103C3×#124—41no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4D414yescomplemented
108C3×#117—44no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C42—21no—
130C2×C3×C42—21no—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C3×#106—22no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8—41no—
137C3×C4⋊C8—41no—
138C3×#103—22no—
139C3×#103—22no—
140C3×#103—41no—
141C3×#102—22no—
142C3×#102—22no—
143C3×#102—22no—
144C3×#102—22no—
145C3×#102—41no—
146C3×#102—41no—
147C3×#102—41no—
148C3×#97—22no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95D411yescharacteristic
154C3×#95D411yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C22×D8C22×C311yescharacteristic
157C22×D8C22×C311yescharacteristic
158C2×#127C22×C311yescharacteristic
159C2×#124C22×C311yescharacteristic
160C2×#124C22×C311yescharacteristic
161C2×C4×D4C22×C311yescharacteristic
162C2×C4×D4C22×C311yescharacteristic
163C2×#117—21no—
164#463—24no—
165#442—24no—
166C2×#106C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×C4⋊C8C22×C311yescharacteristic
169C2×C4⋊C8C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#103C22×C311yescharacteristic
173C2×#102C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×#102C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#97C22×C311yescharacteristic
181#394—21no—
182#394—21no—
183#391C22×C311yescharacteristic
184#390C22×C311yescharacteristic
185#390C22×C311yescharacteristic
186#390C22×C311yescharacteristic
187#388—21no—
188#388—21no—
189#386—21no—
190#386—21no—
191#384C22×C311yescharacteristic
192#380—21no—
193C4×C4⋊C4C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195C4×C4⋊C4C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#336C22×C311yescharacteristic
199#336C22×C311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—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×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
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—21no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4C2×D412yes—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—42no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4—81no—
243C22×C3×C4—81no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C3×SD16—44no—
252C3×D8—28no—
253C3×D8—44no—
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—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8#4112yes—
266C3×C4⋊C4—22no—
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—41no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—81no—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—81no—
287C3×C22⋊C4—81no—
288C3×C22⋊C4—81no—
289C3×C22⋊C4—81no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—42no—
295C3×C42—42no—
296C3×C42C2×D412yes—
297C3×C42#4112yes—
298C22×Q8C23×C311yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C23×C311yescharacteristic
302C22×D4C23×C311yescharacteristic
303C22×D4C23×C311yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C2×SD16—22no—
307C2×SD16—41no—
308C2×SD16—41no—
309C2×D8—22no—
310C2×D8—22no—
311C2×D8—22no—
312C2×D8—22no—
313C2×D8—41no—
314C2×D8—41no—
315C22×C8C23×C311yescharacteristic
316C22×C8C23×C311yescharacteristic
317C22×C8C23×C311yescharacteristic
318C22×C8C23×C311yescharacteristic
319#127—22no—
320#127—41no—
321#124—22no—
322#124—22no—
323#124—22no—
324#124—41no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4C3×D414yescomplemented
329#117—44no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C3×D411yescharacteristic
333C2×C4⋊C4C3×D411yescharacteristic
334C2×C4⋊C4C23×C311yescharacteristic
335C2×C4⋊C4C23×C311yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42C23×C311yescharacteristic
353C2×C42C23×C311yescharacteristic
354C2×C42C23×C311yescharacteristic
355#106—22no—
356C4⋊C8—22no—
357C4⋊C8—41no—
358C4⋊C8—41no—
359#103—22no—
360#103—22no—
361#103—41no—
362#102—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366#102—41no—
367#102—41no—
368#102—41no—
369#97—22no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95C3×D411yescharacteristic
375#95C3×D411yescharacteristic
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3C22×D411yescharacteristic
398C3×Q8—41no—
399C3×Q8—41no—
400C3×Q8—41no—
401C3×Q8—41no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—41no—
407C3×D4—41no—
408C3×D4—41no—
409C3×D4—41no—
410C3×D4—41no—
411C3×D4—41no—
412C3×D4—41no—
413C3×D4—41no—
414C3×D4—84no—
415C3×D4—84no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—48no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—84no—
448C2×C3×C4#12112yes—
449C2×C3×C4#12112yes—
450C2×C3×C4AGL(1,ℤ/8)12yes—
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4H(5,𝔽2)11yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C3×C8—22no—
458C3×C8—41no—
459C3×C8—41no—
460C3×C8—41no—
461C24—21no—
462C24—21no—
463C24—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—81no—
491C2×D4—81no—
492C2×D4C2×C3×D412yes—
493C2×D4C3×#4112yes—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×C3×D411yescharacteristic
506C22×C4C2×C3×D411yescharacteristic
507C22×C4C2×C3×D411yescharacteristic
508C22×C4C2×C3×D411yescharacteristic
509C22×C4C2×C3×D411yescharacteristic
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C24×C311yescharacteristic
512SD16—44no—
513D8—28no—
514D8—44no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8C3×#4112yes—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—41no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4C2×C3×D412yes—
539C22⋊C4—24no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—42no—
557C42C2×C3×D412yes—
558C42C3×#4112yes—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—81no—
566C22×C3—81no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—81no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3—81no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3C2×#12111yescharacteristic
581C22×C3#54611yescharacteristic
582C22×C3#55011yescharacteristic
583C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
584C22×C3#57511yescharacteristic
585C22×C3#57611yescharacteristic
586C22×C3#57711yescharacteristic
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—81no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4—81no—
598C3×C4#52511yescharacteristic
599C3×C4#53511yescharacteristic
600C3×C4#55311yescharacteristic
601C3×C4#55511yescharacteristic
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C22×C3×D411yescharacteristic
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—84no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—48no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4C3×#12112yes—
675C2×C4C3×#12112yes—
676C2×C4C3×AGL(1,ℤ/8)12yes—
677C2×C4C22×C3×D411yescharacteristic
678C2×C4C2×C3×#4111yescharacteristic
679C2×C4C2×C3×#4111yescharacteristic
680C2×C4C2×C3×#4111yescharacteristic
681C2×C4C3×H(5,𝔽2)11yescharacteristic
682C2×C4C3×H(5,𝔽2)11yescharacteristic
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C2×C3—82no—
688C2×C3—82no—
689C2×C3—161no—
690C2×C3#241411yescharacteristic
691C2×C3#303611yescharacteristic
692C2×C3#304511yescharacteristic
693C2×C3#330611yescharacteristic
694C2×C3#331911yescharacteristic
695C2×C3#339911yescharacteristic
696C2×C3#340111yescharacteristic
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22C2×C3×#12111yescharacteristic
719C22C3×#54611yescharacteristic
720C22C3×#55011yescharacteristic
721C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
722C22C3×#57511yescharacteristic
723C22C3×#57611yescharacteristic
724C22C3×#57711yescharacteristic
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4C3×#52511yescharacteristic
737C4C3×#53511yescharacteristic
738C4C3×#55311yescharacteristic
739C4C3×#55511yescharacteristic
740C3#2463811yescharacteristic, direct product factor, Sylow
741C2—82no—
742C2—82no—
743C2—161no—
744C2C3×#241411yescharacteristic
745C2C3×#303611yescharacteristic
746C2C3×#304511yescharacteristic
747C2C3×#330611yescharacteristic
748C2C3×#331911yescharacteristic
749C2C3×#339911yescharacteristic
750C2C3×#340111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
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×#463C2semidirect
2. C2×C3×#442C2semidirect
3. C3×#2544C2semidirect
4. C3×#2354C2semidirect
5. C3×#2055C2semidirect
6. C3×#2054C2semidirect
7. C3×#2012C2semidirect
9. C3×#1983C2semidirect
10. C3×#1982C2semidirect
11. C3×#1959C2semidirect
12. C3×#1940C2semidirect
13. C3×#1927C2semidirect
14. C3×#1926C2semidirect
15. C3×#1802C2semidirect
16. #24638C3direct (N × H)
62. C2×#463C2×C3semidirect
63. C2×#442C2×C3semidirect
64. #2544C2×C3semidirect
65. #2354C2×C3semidirect
66. #2055C2×C3semidirect
67. #2054C2×C3semidirect
68. #2012C2×C3semidirect
70. #1983C2×C3semidirect
71. #1982C2×C3semidirect
72. #1959C2×C3semidirect
73. #1940C2×C3semidirect
74. #1927C2×C3semidirect
75. #1926C2×C3semidirect
76. #1802C2×C3semidirect
107. C3×C4×D4D4semidirect
328. C4×D4C3×D4semidirect
740. C3#24638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4632
C2×C3×#4422
C3×#25442
C3×#23542
C3×#20552
C3×#20542
C3×#20122
C3×#20112
C3×#19832
C3×#19822
C3×#19592
C3×#19402
C3×#19272
C3×#19262
C3×#18022
#246383