Finite Group Databasebeta

← C3×#24366 #10642973

Subgroups — C3×#24366 #10642973

Order 768.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#459C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic, complemented
6C3×D4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2054C211yesmaximal, characteristic, complemented
9C3×#2012C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1851C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24366C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)—24no—
20C2×C3×AGL(1,ℤ/8)—24no—
21C2×C3×AGL(1,ℤ/8)—24no—
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×D8C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29C2×C3×#127C2211yescharacteristic, complemented
30C2×C3×#124C2211yescharacteristic, complemented
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C22×C3×C22⋊C4—21no—
35C3×#463—24no—
36C3×#459—24no—
37C3×#447—24no—
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×C4⋊C8C2211yescharacteristic, complemented
40C2×C3×#103C2211yescharacteristic, complemented
41C2×C3×#103C2211yescharacteristic, complemented
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#392—21no—
50C3×#392—21no—
51C3×#391C2211yescharacteristic, complemented
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic, complemented
55C3×#386—21no—
56C3×#386—21no—
57C3×#386—21no—
58C3×#386—21no—
59C3×#380C2211yescharacteristic
60C3×#379—21no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C3×#336C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
67C2×#463C2×C311yescharacteristic, complemented
68C2×#459C2×C311yescharacteristic, complemented
69C2×#447C2×C311yescharacteristic, complemented
70#2431C2×C311yescharacteristic, complemented
71D4×C22⋊C4C2×C311yescharacteristic, complemented
72#2055C2×C311yescharacteristic, complemented
73#2054C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1895C2×C311yescharacteristic, complemented
77#1879C2×C311yescharacteristic, complemented
78#1877C2×C311yescharacteristic, complemented
79#1851C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—22no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4D414yescomplemented
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4—21no—
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C3×AGL(1,ℤ/8)—232no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16D414yescomplemented
115C2×C3×D8—22no—
116C2×C3×D8—22no—
117C2×C3×D8—22no—
118C2×C3×D8—22no—
119C2×C3×D8—22no—
120C2×C3×D8—22no—
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8—22no—
124C2×C3×D8—41no—
125C2×C3×D8—41no—
126C2×C3×D8D414yescomplemented
127C2×C3×M16—22no—
128C2×C3×M16—22no—
129C2×C3×M16—22no—
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2311yescharacteristic
133C22×C3×C8C2311yescharacteristic
134C3×#127—22no—
135C3×#127—41no—
136C3×#124—22no—
137C3×#124—41no—
138C3×#121—22no—
139C3×#121—22no—
140C3×C4×D4—22no—
141C3×C4×D4—22no—
142C3×C4×D4—41no—
143C3×C4×D4—41no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—44no—
160C2×C3×C22⋊C4D411yescharacteristic
161C2×C3×C22⋊C4D411yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C3×C4⋊C8—22no—
165C3×C4⋊C8—22no—
166C3×#103—22no—
167C3×#103—41no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—41no—
174C3×C22⋊C8—22no—
175C3×#95—21no—
176C3×#95—21no—
177C3×#95—21no—
178C3×#95D411yescharacteristic
179C3×#95D411yescharacteristic
180C22×#41C22×C311yescharacteristic
181C23×D4C22×C311yescharacteristic
182C2×AGL(1,ℤ/8)—24no—
183C2×AGL(1,ℤ/8)—24no—
184C2×AGL(1,ℤ/8)—24no—
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic
188C22×D8C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×#127C22×C311yescharacteristic, complemented
193C2×#124C22×C311yescharacteristic, complemented
194C2×#121C22×C311yescharacteristic
195C2×C4×D4C22×C311yescharacteristic
196C2×C4×D4C22×C311yescharacteristic
197C22×C22⋊C4—21no—
198#463—24no—
199#459—24no—
200#447—24no—
201C2×C4⋊C8C22×C311yescharacteristic, complemented
202C2×C4⋊C8C22×C311yescharacteristic, complemented
203C2×#103C22×C311yescharacteristic, complemented
204C2×#103C22×C311yescharacteristic, complemented
205C2×#102C22×C311yescharacteristic
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic, complemented
208C2×#102C22×C311yescharacteristic, complemented
209C2×#102C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic, complemented
211C2×C22⋊C8C22×C311yescharacteristic
212#392—21no—
213#392—21no—
214#391C22×C311yescharacteristic, complemented
215#390C22×C311yescharacteristic
216#390C22×C311yescharacteristic
217#390C22×C311yescharacteristic, complemented
218#386—21no—
219#386—21no—
220#386—21no—
221#386—21no—
222#380C22×C311yescharacteristic
223#379—21no—
224C4×C22⋊C4C22×C311yescharacteristic
225#340C22×C311yescharacteristic, complemented
226#340C22×C311yescharacteristic, complemented
227#336C22×C311yescharacteristic, complemented
228#336C22×C311yescharacteristic, complemented
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—24no—
233C24×C3—21no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3C2×D411yescharacteristic
241C3×#41—28no—
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8C2×D412yes—
251C2×C3×D4—28no—
252C2×C3×D4—24no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—81no—
286C2×C3×D4—81no—
287C2×C3×D4—81no—
288C2×C3×D4—81no—
289C2×C3×D4C2×D412yes—
290C2×C3×D4C2×D412yes—
291C2×C3×D4C2×D412yes—
292C2×C3×D4C2×D412yes—
293C2×C3×D4C2×D412yes—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4—81no—
310C22×C3×C4—81no—
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4#4112yes—
318C22×C3×C4C2411yescharacteristic
319C3×SD16—28no—
320C3×SD16—28no—
321C3×D8—28no—
322C3×D8—28no—
323C3×D8—44no—
324C3×D8—44no—
325C3×M16—28no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8C2×D412yes—
337C2×C3×C8C2×D412yes—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—42no—
347C3×C22⋊C4—42no—
348C3×C22⋊C4—42no—
349C3×C22⋊C4—42no—
350C3×C22⋊C4—42no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—42no—
353C3×C22⋊C4—42no—
354C3×C22⋊C4—81no—
355C3×C22⋊C4—81no—
356C3×C22⋊C4—81no—
357C3×C22⋊C4—81no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—21no—
361C3×C42—21no—
362C25—21no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—41no—
368C2×#41—41no—
369C22×Q8C23×C311yescharacteristic
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—22no—
378C22×D4—41no—
379C22×D4—41no—
380C22×D4C3×D414yescomplemented
381C22×D4C23×C311yescharacteristic
382C22×D4C23×C311yescharacteristic
383C22×D4C23×C311yescharacteristic
384C22×D4C23×C311yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—21no—
388C23×C4C23×C311yescharacteristic
389AGL(1,ℤ/8)—232no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16C3×D414yescomplemented
396C2×D8—22no—
397C2×D8—22no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8—22no—
401C2×D8—22no—
402C2×D8—22no—
403C2×D8—22no—
404C2×D8—22no—
405C2×D8—41no—
406C2×D8—41no—
407C2×D8C3×D414yescomplemented
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—22no—
411C22×C8C23×C311yescharacteristic
412C22×C8C23×C311yescharacteristic
413C22×C8C23×C311yescharacteristic
414C22×C8C23×C311yescharacteristic
415#127—22no—
416#127—41no—
417#124—22no—
418#124—41no—
419#121—22no—
420#121—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—41no—
425C2×C4⋊C4C23×C311yescharacteristic
426C2×C4⋊C4C23×C311yescharacteristic
427C2×C4⋊C4C23×C311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4C3×D411yescharacteristic
442C2×C22⋊C4C3×D411yescharacteristic
443C2×C42C23×C311yescharacteristic
444C2×C42C23×C311yescharacteristic
445C4⋊C8—22no—
446C4⋊C8—22no—
447#103—22no—
448#103—41no—
449#102—22no—
450#102—22no—
451#102—22no—
452#102—22no—
453#102—22no—
454#102—41no—
455C22⋊C8—22no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95C3×D411yescharacteristic
460#95C3×D411yescharacteristic
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—48no—
473C23×C3—48no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—84no—
498C23×C3—84no—
499C23×C3—84no—
500C23×C3—84no—
501C23×C3—84no—
502C23×C3#12112yes—
503C23×C3C22×D411yescharacteristic
504C3×Q8—22no—
505C3×Q8—22no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—48no—
516C3×D4—48no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—84no—
526C3×D4—84no—
527C3×D4—84no—
528C3×D4#12014yes—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—48no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—84no—
560C2×C3×C4—84no—
561C2×C3×C4#12112yes—
562C2×C3×C4AGL(1,ℤ/8)12yescomplemented
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C2×#4111yescharacteristic
567C2×C3×C4H(5,𝔽2)11yescharacteristic
568C2×C3×C4H(5,𝔽2)11yescharacteristic
569C3×C8—22no—
570C3×C8—22no—
571C3×C8—41no—
572C3×C8—41no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—24no—
577C24—21no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×C3×D411yescharacteristic
585#41—28no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8C2×C3×D412yes—
595C2×D4—28no—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×C3×D412yes—
634C2×D4C2×C3×D412yes—
635C2×D4C2×C3×D412yes—
636C2×D4C2×C3×D412yes—
637C2×D4C2×C3×D412yes—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4C2×C3×D411yescharacteristic
656C22×C4C2×C3×D411yescharacteristic
657C22×C4C2×C3×D411yescharacteristic
658C22×C4C2×C3×D411yescharacteristic
659C22×C4C2×C3×D412yes—
660C22×C4C2×C3×D411yescharacteristic
661C22×C4C3×#4112yes—
662C22×C4C24×C311yescharacteristic
663SD16—28no—
664SD16—28no—
665D8—28no—
666D8—28no—
667D8—44no—
668D8—44no—
669M16—28no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8C2×C3×D412yes—
681C2×C8C2×C3×D412yes—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—41no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—42no—
714C22×C3—41no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—816no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3C2×#12111yescharacteristic
743C22×C3D4211yescharacteristic
744C22×C3D4211yescharacteristic
745C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
746C22×C3#57511yescharacteristic
747C22×C3#57611yescharacteristic
748C22×C3#57611yescharacteristic
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4C2×#12011yescharacteristic
759C3×C4#53411yescharacteristic
760C3×C4#54611yescharacteristic
761C3×C4#54611yescharacteristic
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—21no—
770C23—21no—
771C23—22no—
772C23—22no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23C3×#12112yes—
804C23C22×C3×D411yescharacteristic
805Q8—22no—
806Q8—22no—
807Q8—41no—
808Q8—41no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—48no—
817D4—48no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4—84no—
828D4—84no—
829D4C3×#12014yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—48no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—84no—
861C2×C4—84no—
862C2×C4C3×#12112yes—
863C2×C4C3×AGL(1,ℤ/8)12yescomplemented
864C2×C4C22×C3×D411yescharacteristic
865C2×C4C22×C3×D411yescharacteristic
866C2×C4C22×C3×D411yescharacteristic
867C2×C4C2×C3×#4111yescharacteristic
868C2×C4C3×H(5,𝔽2)11yescharacteristic
869C2×C4C3×H(5,𝔽2)11yescharacteristic
870C8—22no—
871C8—22no—
872C8—41no—
873C8—41no—
874C2×C3—42no—
875C2×C3—44no—
876C2×C3—82no—
877C2×C3—82no—
878C2×C3—161no—
879C2×C3#241011yescharacteristic
880C2×C3#303611yescharacteristic
881C2×C3#304111yescharacteristic
882C2×C3#326411yescharacteristic
883C2×C3#326811yescharacteristic
884C2×C3#327311yescharacteristic
885C2×C3#327411yescharacteristic
886C22—22no—
887C22—24no—
888C22—22no—
889C22—22no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—816no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22C2×C3×#12111yescharacteristic
923C22C3×D4211yescharacteristic
924C22C3×D4211yescharacteristic
925C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
926C22C3×#57511yescharacteristic
927C22C3×#57611yescharacteristic
928C22C3×#57611yescharacteristic
929C4—22no—
930C4—22no—
931C4—42no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—81no—
936C4—81no—
937C4—81no—
938C4C2×C3×#12011yescharacteristic
939C4C3×#53411yescharacteristic
940C4C3×#54611yescharacteristic
941C4C3×#54611yescharacteristic
942C3#2436611yescharacteristic, direct product factor, Sylow
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C3×#241011yescharacteristic
949C2C3×#303611yescharacteristic
950C2C3×#304111yescharacteristic
951C2C3×#326411yescharacteristic
952C2C3×#326811yescharacteristic
953C2C3×#327311yescharacteristic
954C2C3×#327411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#459C2semidirect
4. C2×C3×#447C2semidirect
5. C3×#2431C2semidirect
6. C3×D4×C22⋊C4C2semidirect
7. C3×#2055C2semidirect
8. C3×#2054C2semidirect
9. C3×#2012C2semidirect
10. C3×#2011C2semidirect
11. C3×#1895C2semidirect
12. C3×#1879C2semidirect
13. C3×#1877C2semidirect
14. C3×#1851C2semidirect
15. C3×#1788C2semidirect
16. #24366C3direct (N × H)
29. C2×C3×#127C22semidirect
30. C2×C3×#124C22semidirect
38. C2×C3×C4⋊C8C22semidirect
39. C2×C3×C4⋊C8C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#103C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
51. C3×#391C22semidirect
54. C3×#390C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C3×#336C22semidirect
65. C3×#336C22semidirect
66. C22×AGL(1,ℤ/8)C2×C3semidirect
67. C2×#463C2×C3semidirect
68. C2×#459C2×C3semidirect
69. C2×#447C2×C3semidirect
70. #2431C2×C3semidirect
71. D4×C22⋊C4C2×C3semidirect
72. #2055C2×C3semidirect
73. #2054C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1895C2×C3semidirect
77. #1879C2×C3semidirect
78. #1877C2×C3semidirect
79. #1851C2×C3semidirect
80. #1788C2×C3semidirect
99. C22×C3×D4D4semidirect
114. C2×C3×SD16D4semidirect
126. C2×C3×D8D4semidirect
192. C2×#127C22×C3semidirect
193. C2×#124C22×C3semidirect
201. C2×C4⋊C8C22×C3semidirect
202. C2×C4⋊C8C22×C3semidirect
203. C2×#103C22×C3semidirect
204. C2×#103C22×C3semidirect
207. C2×#102C22×C3semidirect
208. C2×#102C22×C3semidirect
209. C2×#102C22×C3semidirect
210. C2×#102C22×C3semidirect
214. #391C22×C3semidirect
217. #390C22×C3semidirect
225. #340C22×C3semidirect
226. #340C22×C3semidirect
227. #336C22×C3semidirect
228. #336C22×C3semidirect
380. C22×D4C3×D4semidirect
395. C2×SD16C3×D4semidirect
407. C2×D8C3×D4semidirect
562. C2×C3×C4AGL(1,ℤ/8)semidirect
863. C2×C4C3×AGL(1,ℤ/8)semidirect
942. C3#24366direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
C2×C3×#4632
C2×C3×#4592
C2×C3×#4472
C3×#24312
C3×D4×C22⋊C42
C3×#20552
C3×#20542
C3×#20122
C3×#20112
C3×#18952
C3×#18792
C3×#18772
C3×#18512
C3×#17882
#243663