Finite Group Databasebeta

← C3×#24367 #10642974

Subgroups — C3×#24367 #10642974

Order 768.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#461C211yesmaximal, characteristic, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C3×#2432C211yesmaximal, characteristic, complemented
6C3×D4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2054C211yesmaximal, characteristic, complemented
9C3×#2013C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1851C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24367C311yesmaximal, 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×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29C2×C3×C4⋊Q8C2211yescharacteristic, complemented
30C2×C3×#124C2211yescharacteristic, complemented
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C22×C3×C22⋊C4—21no—
35C3×#463—24no—
36C3×#461—24no—
37C3×#450—24no—
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×C4⋊C8C2211yescharacteristic, complemented
40C2×C3×#103C2211yescharacteristic, complemented
41C2×C3×#103C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#394—21no—
50C3×#394—21no—
51C3×#391C2211yescharacteristic, complemented
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic, complemented
55C3×#386—21no—
56C3×#386—21no—
57C3×#385—21no—
58C3×#385—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
67C2×#463C2×C311yescharacteristic, complemented
68C2×#461C2×C311yescharacteristic, complemented
69C2×#450C2×C311yescharacteristic, complemented
70#2432C2×C311yescharacteristic, complemented
71D4×C22⋊C4C2×C311yescharacteristic, complemented
72#2055C2×C311yescharacteristic, complemented
73#2054C2×C311yescharacteristic, complemented
74#2013C2×C311yescharacteristic, complemented
75#2012C2×C311yescharacteristic, complemented
76#1894C2×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×Q8C2311yescharacteristic
90C22×C3×D4—22no—
91C22×C3×D4—22no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—22no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4D414yes—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C3×AGL(1,ℤ/8)—232no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—41no—
116C2×C3×SD16—41no—
117C2×C3×SD16D414yes—
118C2×C3×D8—22no—
119C2×C3×D8—22no—
120C2×C3×D8—22no—
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8D414yes—
124C2×C3×M16—22no—
125C2×C3×M16—22no—
126C2×C3×M16—22no—
127C22×C3×C8C2311yescharacteristic
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C4⋊Q8—22no—
132C3×C4⋊Q8—41no—
133C3×#124—22no—
134C3×#124—41no—
135C3×C22⋊Q8—22no—
136C3×C22⋊Q8—22no—
137C3×C4×D4—22no—
138C3×C4×D4—22no—
139C3×C4×D4—41no—
140C3×C4×D4—41no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
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—22no—
168C3×#103—22no—
169C3×#103—41no—
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×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×C4⋊Q8C22×C311yescharacteristic, complemented
193C2×#124C22×C311yescharacteristic, complemented
194C2×C22⋊Q8C22×C311yescharacteristic
195C2×C4×D4C22×C311yescharacteristic
196C2×C4×D4C22×C311yescharacteristic
197C22×C22⋊C4—21no—
198#463—24no—
199#461—24no—
200#450—24no—
201C2×C4⋊C8C22×C311yescharacteristic, complemented
202C2×C4⋊C8C22×C311yescharacteristic, complemented
203C2×#103C22×C311yescharacteristic, complemented
204C2×#103C22×C311yescharacteristic, complemented
205C2×#103C22×C311yescharacteristic, complemented
206C2×#103C22×C311yescharacteristic, complemented
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic, complemented
211C2×C22⋊C8C22×C311yescharacteristic
212#394—21no—
213#394—21no—
214#391C22×C311yescharacteristic, complemented
215#390C22×C311yescharacteristic
216#390C22×C311yescharacteristic
217#390C22×C311yescharacteristic, complemented
218#386—21no—
219#386—21no—
220#385—21no—
221#385—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—42no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—81no—
238C24×C3—81no—
239C24×C3C2×D411yescharacteristic
240C3×#41—28no—
241C3×#41—44no—
242C3×#41—44no—
243C3×#41—44no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8C2×D412yes—
256C2×C3×D4—28no—
257C2×C3×D4—24no—
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—44no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4C2×D412yes—
280C2×C3×D4C2×D412yes—
281C2×C3×D4C2×D412yes—
282C2×C3×D4C2×D412yes—
283C2×C3×D4C2×D412yes—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4—81no—
301C22×C3×C4—81no—
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4#4112yes—
309C22×C3×C4C2411yescharacteristic
310C3×SD16—28no—
311C3×SD16—28no—
312C3×SD16—44no—
313C3×SD16—44no—
314C3×D8—28no—
315C3×D8—28no—
316C3×M16—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8C2×D412yes—
328C2×C3×C8C2×D412yes—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—42no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4—42no—
338C3×C22⋊C4—22no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—42no—
343C3×C22⋊C4—42no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—42no—
347C3×C22⋊C4—42no—
348C3×C22⋊C4—42no—
349C3×C22⋊C4—42no—
350C3×C22⋊C4—81no—
351C3×C22⋊C4—81no—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C25—21no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—41no—
362C2×#41—41no—
363C22×Q8C23×C311yescharacteristic
364C22×Q8C23×C311yescharacteristic
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—22no—
370C22×D4—41no—
371C22×D4—41no—
372C22×D4C3×D414yes—
373C22×D4C23×C311yescharacteristic
374C22×D4C23×C311yescharacteristic
375C22×D4C23×C311yescharacteristic
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4C23×C311yescharacteristic
380AGL(1,ℤ/8)—232no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—41no—
391C2×SD16—41no—
392C2×SD16C3×D414yes—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8C3×D414yes—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—22no—
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404C22×C8C23×C311yescharacteristic
405C22×C8C23×C311yescharacteristic
406C4⋊Q8—22no—
407C4⋊Q8—41no—
408#124—22no—
409#124—41no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—41no—
415C4×D4—41no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C23×C311yescharacteristic
420C2×C4⋊C4C23×C311yescharacteristic
421C2×C4⋊C4C23×C311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
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—44no—
435C2×C22⋊C4C3×D411yescharacteristic
436C2×C22⋊C4C3×D411yescharacteristic
437C2×C42C23×C311yescharacteristic
438C2×C42C23×C311yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—22no—
441#103—22no—
442#103—22no—
443#103—22no—
444#103—41no—
445#102—22no—
446#102—22no—
447#102—22no—
448#102—41no—
449C22⋊C8—22no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C3×D411yescharacteristic
454#95C3×D411yescharacteristic
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—48no—
467C23×C3—48no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
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—84no—
485C23×C3—84no—
486C23×C3—84no—
487C23×C3—84no—
488C23×C3—84no—
489C23×C3#12112yes—
490C23×C3C22×D411yescharacteristic
491C3×Q8—22no—
492C3×Q8—22no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—48no—
507C3×D4—48no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4#12014yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—48no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—84no—
547C2×C3×C4—84no—
548C2×C3×C4#12112yes—
549C2×C3×C4AGL(1,ℤ/8)12yescomplemented
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C2×#4111yescharacteristic
554C2×C3×C4H(5,𝔽2)11yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C3×C8—22no—
557C3×C8—22no—
558C3×C8—41no—
559C3×C8—41no—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—24no—
564C24—42no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—81no—
569C24—81no—
570C24C2×C3×D411yescharacteristic
571#41—28no—
572#41—44no—
573#41—44no—
574#41—44no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×C3×D412yes—
587C2×D4—28no—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4C2×C3×D412yes—
611C2×D4C2×C3×D412yes—
612C2×D4C2×C3×D412yes—
613C2×D4C2×C3×D412yes—
614C2×D4C2×C3×D412yes—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4C2×C3×D411yescharacteristic
634C22×C4C2×C3×D411yescharacteristic
635C22×C4C2×C3×D411yescharacteristic
636C22×C4C2×C3×D411yescharacteristic
637C22×C4C2×C3×D412yes—
638C22×C4C2×C3×D411yescharacteristic
639C22×C4C3×#4112yes—
640C22×C4C24×C311yescharacteristic
641SD16—28no—
642SD16—28no—
643SD16—44no—
644SD16—44no—
645D8—28no—
646D8—28no—
647M16—28no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×C3×D412yes—
659C2×C8C2×C3×D412yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C22⋊C4—22no—
670C22⋊C4—41no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C22×C3—22no—
688C22×C3—24no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—816no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3C2×#12111yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3D4211yescharacteristic
719C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
720C22×C3#57511yescharacteristic
721C22×C3#57711yescharacteristic
722C22×C3#57711yescharacteristic
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—42no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4C2×#12011yescharacteristic
734C3×C4#53411yescharacteristic
735C3×C4#54611yescharacteristic
736C3×C4#54611yescharacteristic
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—48no—
749C23—48no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23C3×#12112yes—
772C23C22×C3×D411yescharacteristic
773Q8—22no—
774Q8—22no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—48no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4C3×#12014yes—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4C3×#12112yes—
831C2×C4C3×AGL(1,ℤ/8)12yescomplemented
832C2×C4C22×C3×D411yescharacteristic
833C2×C4C22×C3×D411yescharacteristic
834C2×C4C22×C3×D411yescharacteristic
835C2×C4C2×C3×#4111yescharacteristic
836C2×C4C3×H(5,𝔽2)11yescharacteristic
837C2×C4C3×H(5,𝔽2)11yescharacteristic
838C8—22no—
839C8—22no—
840C8—41no—
841C8—41no—
842C2×C3—42no—
843C2×C3—44no—
844C2×C3—82no—
845C2×C3—82no—
846C2×C3#241011yescharacteristic
847C2×C3#303611yescharacteristic
848C2×C3#304211yescharacteristic
849C2×C3#326511yescharacteristic
850C2×C3#326711yescharacteristic
851C2×C3#327211yescharacteristic
852C2×C3#327511yescharacteristic
853C22—22no—
854C22—24no—
855C22—22no—
856C22—22no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—816no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22C2×C3×#12111yescharacteristic
883C22C3×D4211yescharacteristic
884C22C3×D4211yescharacteristic
885C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
886C22C3×#57511yescharacteristic
887C22C3×#57711yescharacteristic
888C22C3×#57711yescharacteristic
889C4—22no—
890C4—22no—
891C4—42no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4C2×C3×#12011yescharacteristic
900C4C3×#53411yescharacteristic
901C4C3×#54611yescharacteristic
902C4C3×#54611yescharacteristic
903C3#2436711yescharacteristic, direct product factor, Sylow
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C3×#241011yescharacteristic
909C2C3×#303611yescharacteristic
910C2C3×#304211yescharacteristic
911C2C3×#326511yescharacteristic
912C2C3×#326711yescharacteristic
913C2C3×#327211yescharacteristic
914C2C3×#327511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×AGL(1,ℤ/8)C2
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
2. C2×C3×#463C2semidirect
3. C2×C3×#461C2semidirect
4. C2×C3×#450C2semidirect
5. C3×#2432C2semidirect
6. C3×D4×C22⋊C4C2semidirect
7. C3×#2055C2semidirect
8. C3×#2054C2semidirect
9. C3×#2013C2semidirect
10. C3×#2012C2semidirect
11. C3×#1894C2semidirect
12. C3×#1879C2semidirect
13. C3×#1877C2semidirect
14. C3×#1851C2semidirect
15. C3×#1788C2semidirect
16. #24367C3direct (N × H)
29. C2×C3×C4⋊Q8C22semidirect
30. C2×C3×#124C22semidirect
38. C2×C3×C4⋊C8C22semidirect
39. C2×C3×C4⋊C8C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#103C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
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
67. C2×#463C2×C3semidirect
68. C2×#461C2×C3semidirect
69. C2×#450C2×C3semidirect
70. #2432C2×C3semidirect
71. D4×C22⋊C4C2×C3semidirect
72. #2055C2×C3semidirect
73. #2054C2×C3semidirect
74. #2013C2×C3semidirect
75. #2012C2×C3semidirect
76. #1894C2×C3semidirect
77. #1879C2×C3semidirect
78. #1877C2×C3semidirect
79. #1851C2×C3semidirect
80. #1788C2×C3semidirect
192. C2×C4⋊Q8C22×C3semidirect
193. C2×#124C22×C3semidirect
201. C2×C4⋊C8C22×C3semidirect
202. C2×C4⋊C8C22×C3semidirect
203. C2×#103C22×C3semidirect
204. C2×#103C22×C3semidirect
205. C2×#103C22×C3semidirect
206. C2×#103C22×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
549. C2×C3×C4AGL(1,ℤ/8)semidirect
831. C2×C4C3×AGL(1,ℤ/8)semidirect
903. C3#24367direct (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×#4612
C2×C3×#4502
C3×#24322
C3×D4×C22⋊C42
C3×#20552
C3×#20542
C3×#20132
C3×#20122
C3×#18942
C3×#18792
C3×#18772
C3×#18512
C3×#17882
#243673