Finite Group Databasebeta

← C3×#25796 #10644403

Subgroups — C3×#25796 #10644403

Order 768.

1630 conjugacy classes of subgroups.

The subgroup lattice has 834 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×#497C211yesmaximal, characteristic, complemented
3C2×C3×#495C211yesmaximal, characteristic, complemented
4C2×C3×#470C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×C3×#450C211yesmaximal, characteristic, complemented
7C3×#2435C211yesmaximal, characteristic, complemented
8C3×#2432C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2013C211yesmaximal, characteristic, complemented
11C3×#2012C211yesmaximal, characteristic, complemented
12C3×#2012C211yesmaximal, characteristic, complemented
13C3×#1972C211yesmaximal, characteristic, complemented
14C3×#1968C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25796C311yesmaximal, 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×Q16C2211yescharacteristic, complemented
23C22×C3×Q16C2211yescharacteristic, complemented
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×SD16C2211yescharacteristic, complemented
29C22×C3×D8C2211yescharacteristic
30C22×C3×D8C2211yescharacteristic
31C22×C3×M16C2211yescharacteristic
32C2×C3×C4⋊Q8C2211yescharacteristic, complemented
33C2×C3×#124C2211yescharacteristic
34C2×C3×#124C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic, complemented
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×C22⋊Q8C2211yescharacteristic
38C3×#497—24no—
39C3×#495—24no—
40C3×#470—24no—
41C3×#452—24no—
42C3×#450—24no—
43C2×C3×#106C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic, complemented
52C2×C3×C4×C8C2211yescharacteristic, complemented
53C3×#394—22no—
54C3×#394—22no—
55C3×#391C2211yescharacteristic, complemented
56C3×#390C2211yescharacteristic
57C3×#390C2211yescharacteristic
58C3×#390C2211yescharacteristic, complemented
59C3×#385—22no—
60C3×#379—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C22×AGL(1,ℤ/8)C2×C311yescharacteristic
65C2×#497C2×C311yescharacteristic, complemented
66C2×#495C2×C311yescharacteristic, complemented
67C2×#470C2×C311yescharacteristic, complemented
68C2×#452C2×C311yescharacteristic, complemented
69C2×#450C2×C311yescharacteristic, complemented
70#2435C2×C311yescharacteristic, complemented
71#2432C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2013C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2012C2×C311yescharacteristic, complemented
76#1972C2×C311yescharacteristic, complemented
77#1968C2×C311yescharacteristic, complemented
78#1753C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—41no—
85C2×C3×#41—41no—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—21no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—21no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4C2311yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C3×AGL(1,ℤ/8)—232no—
103C2×C3×Q16—22no—
104C2×C3×Q16—22no—
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—41no—
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—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—41no—
121C2×C3×SD16—41no—
122C2×C3×SD16—41no—
123C2×C3×SD16D414yes—
124C2×C3×D8—22no—
125C2×C3×D8—22no—
126C2×C3×D8—22no—
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8D414yes—
130C2×C3×M16—22no—
131C2×C3×M16—22no—
132C2×C3×M16D414yes—
133C22×C3×C8C2311yescharacteristic
134C22×C3×C8C2311yescharacteristic
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C3×C4⋊Q8—22no—
138C3×C4⋊Q8—41no—
139C3×#124—22no—
140C3×#124—22no—
141C3×#124—22no—
142C3×#124—41no—
143C3×#124—41no—
144C3×#124—41no—
145C3×C22⋊Q8—22no—
146C3×C22⋊Q8—22no—
147C3×C22⋊Q8—22no—
148C3×C22⋊Q8—22no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4D412yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C3×#106—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×C22⋊C8D414yes—
173C3×#97—22no—
174C3×C4×C8—22no—
175C3×#95—22no—
176C3×#95D412yes—
177C22×#41C22×C311yescharacteristic
178C23×D4C22×C311yescharacteristic
179C2×AGL(1,ℤ/8)—24no—
180C2×AGL(1,ℤ/8)—24no—
181C2×AGL(1,ℤ/8)—24no—
182C22×Q16C22×C311yescharacteristic, complemented
183C22×Q16C22×C311yescharacteristic, complemented
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic, complemented
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×C4⋊Q8C22×C311yescharacteristic, complemented
193C2×#124C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic
195C2×#124C22×C311yescharacteristic, complemented
196C2×C22⋊Q8C22×C311yescharacteristic
197C2×C22⋊Q8C22×C311yescharacteristic
198#497—24no—
199#495—24no—
200#470—24no—
201#452—24no—
202#450—24no—
203C2×#106C22×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×C22⋊C8C22×C311yescharacteristic
211C2×#97C22×C311yescharacteristic, complemented
212C2×C4×C8C22×C311yescharacteristic, complemented
213#394—22no—
214#394—22no—
215#391C22×C311yescharacteristic, complemented
216#390C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#390C22×C311yescharacteristic, complemented
219#385—22no—
220#379—22no—
221C4×C22⋊C4C22×C311yescharacteristic
222#336C22×C311yescharacteristic, complemented
223#336C22×C311yescharacteristic, complemented
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—42no—
228C24×C3—42no—
229C24×C3—44no—
230C24×C3—42no—
231C24×C3—82no—
232C24×C3C2×D411yescharacteristic
233C3×#41—28no—
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
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×Q8C2×D412yes—
255C2×C3×D4—28no—
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—44no—
272C2×C3×D4—44no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—44no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4C2×D412yes—
281C2×C3×D4C2×D412yes—
282C2×C3×D4C2×D412yes—
283C22×C3×C4—21no—
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—42no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2411yescharacteristic
301C3×Q16—44no—
302C3×Q16—44no—
303C3×SD16—28no—
304C3×SD16—28no—
305C3×SD16—44no—
306C3×SD16—44no—
307C3×SD16—44no—
308C3×D8—28no—
309C3×D8—28no—
310C3×M16—28no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8C2×D412yes—
318C2×C3×C8C2×D412yes—
319C2×C3×C8C2×D412yes—
320C2×C3×C8C2×D412yes—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—44no—
328C3×C4⋊C4—42no—
329C3×C4⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—82no—
338C3×C22⋊C4—82no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C25—21no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—41no—
349C2×#41—41no—
350C22×Q8C23×C311yescharacteristic
351C22×Q8C23×C311yescharacteristic
352C22×Q8C23×C311yescharacteristic
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4C23×C311yescharacteristic
362C22×D4C23×C311yescharacteristic
363C22×D4C23×C311yescharacteristic
364C23×C4—21no—
365C23×C4C23×C311yescharacteristic
366AGL(1,ℤ/8)—232no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—41no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—41no—
385C2×SD16—41no—
386C2×SD16—41no—
387C2×SD16C3×D414yes—
388C2×D8—22no—
389C2×D8—22no—
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8C3×D414yes—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16C3×D414yes—
397C22×C8C23×C311yescharacteristic
398C22×C8C23×C311yescharacteristic
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401C4⋊Q8—22no—
402C4⋊Q8—41no—
403#124—22no—
404#124—22no—
405#124—22no—
406#124—41no—
407#124—41no—
408#124—41no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4C23×C311yescharacteristic
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4C3×D412yes—
427C2×C42C23×C311yescharacteristic
428C2×C42C23×C311yescharacteristic
429#106—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#102—22no—
434#102—22no—
435#102—22no—
436C22⋊C8C3×D414yes—
437#97—22no—
438C4×C8—22no—
439#95—22no—
440#95C3×D412yes—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—48no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—42no—
456C23×C3—42no—
457C23×C3—42no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3—42no—
461C23×C3—84no—
462C23×C3—84no—
463C23×C3—88no—
464C23×C3—88no—
465C23×C3#12712yes—
466C23×C3C22×D411yescharacteristic
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—48no—
486C3×D4—48no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—48no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4#12712yes—
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C3×C8—22no—
527C3×C8—22no—
528C3×C8—22no—
529C3×C8#12014yes—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—42no—
534C24—42no—
535C24—44no—
536C24—42no—
537C24—82no—
538C24C2×C3×D411yescharacteristic
539#41—28no—
540#41—44no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8C2×C3×D412yes—
561C2×D4—28no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×C3×D412yes—
587C2×D4C2×C3×D412yes—
588C2×D4C2×C3×D412yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4C2×C3×D412yes—
602C22×C4C2×C3×D412yes—
603C22×C4C2×C3×D411yescharacteristic
604C22×C4C2×C3×D412yes—
605C22×C4C2×C3×D412yes—
606C22×C4C24×C311yescharacteristic
607Q16—44no—
608Q16—44no—
609SD16—28no—
610SD16—28no—
611SD16—44no—
612SD16—44no—
613SD16—44no—
614D8—28no—
615D8—28no—
616M16—28no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×C3×D412yes—
624C2×C8C2×C3×D412yes—
625C2×C8C2×C3×D412yes—
626C2×C8C2×C3×D412yes—
627C2×C8C2×C3×D412yes—
628C2×C8C2×C3×D412yes—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—816no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—82no—
668C22×C3—82no—
669C22×C3—82no—
670C22×C3C2×#12711yescharacteristic
671C22×C3D4211yescharacteristic
672C22×C3D4211yescharacteristic
673C22×C3#57512yes—
674C22×C3#57712yes—
675C3×C4—22no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4C2×#12011yescharacteristic
684C3×C4#53511yescharacteristic
685C3×C4D4211yescharacteristic
686C3×C4D4211yescharacteristic
687C23—22no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—48no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—84no—
708C23—84no—
709C23—88no—
710C23—88no—
711C23C3×#12712yes—
712C23C22×C3×D411yescharacteristic
713Q8—22no—
714Q8—22no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—48no—
732D4—48no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4C3×#12712yes—
766C2×C4C22×C3×D411yescharacteristic
767C2×C4C22×C3×D411yescharacteristic
768C2×C4C22×C3×D411yescharacteristic
769C2×C4C22×C3×D411yescharacteristic
770C2×C4C3×H(5,𝔽2)11yescharacteristic
771C2×C4C3×H(5,𝔽2)11yescharacteristic
772C8—22no—
773C8—22no—
774C8—22no—
775C8C3×#12014yes—
776C2×C3—42no—
777C2×C3—82no—
778C2×C3—82no—
779C2×C3—82no—
780C2×C3#243311yescharacteristic
781C2×C3#315311yescharacteristic
782C2×C3#315411yescharacteristic
783C2×C3#326712yes—
784C2×C3#327512yes—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—816no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22C2×C3×#12711yescharacteristic
807C22C3×D4211yescharacteristic
808C22C3×D4211yescharacteristic
809C22C3×#57512yes—
810C22C3×#57712yes—
811C4—22no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4C2×C3×#12011yescharacteristic
820C4C3×#53511yescharacteristic
821C4C3×D4211yescharacteristic
822C4C3×D4211yescharacteristic
823C3#2579611yescharacteristic, direct product factor, Sylow
824C2—42no—
825C2—82no—
826C2—82no—
827C2—82no—
828C2C3×#243311yescharacteristic
829C2C3×#315311yescharacteristic
830C2C3×#315411yescharacteristic
831C2C3×#326712yes—
832C2C3×#327512yes—
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×#497C2semidirect
3. C2×C3×#495C2semidirect
4. C2×C3×#470C2semidirect
5. C2×C3×#452C2semidirect
6. C2×C3×#450C2semidirect
7. C3×#2435C2semidirect
8. C3×#2432C2semidirect
9. C3×#2015C2semidirect
10. C3×#2013C2semidirect
11. C3×#2012C2semidirect
12. C3×#2012C2semidirect
13. C3×#1972C2semidirect
14. C3×#1968C2semidirect
15. C3×#1753C2semidirect
16. #25796C3direct (N × H)
22. C22×C3×Q16C22semidirect
23. C22×C3×Q16C22semidirect
28. C22×C3×SD16C22semidirect
32. C2×C3×C4⋊Q8C22semidirect
35. C2×C3×#124C22semidirect
43. C2×C3×#106C22semidirect
44. C2×C3×#103C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#103C22semidirect
49. C2×C3×#102C22semidirect
51. C2×C3×#97C22semidirect
52. C2×C3×C4×C8C22semidirect
55. C3×#391C22semidirect
58. C3×#390C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
65. C2×#497C2×C3semidirect
66. C2×#495C2×C3semidirect
67. C2×#470C2×C3semidirect
68. C2×#452C2×C3semidirect
69. C2×#450C2×C3semidirect
70. #2435C2×C3semidirect
71. #2432C2×C3semidirect
72. #2015C2×C3semidirect
73. #2013C2×C3semidirect
74. #2012C2×C3semidirect
75. #2012C2×C3semidirect
76. #1972C2×C3semidirect
77. #1968C2×C3semidirect
78. #1753C2×C3semidirect
182. C22×Q16C22×C3semidirect
183. C22×Q16C22×C3semidirect
188. C22×SD16C22×C3semidirect
192. C2×C4⋊Q8C22×C3semidirect
195. C2×#124C22×C3semidirect
203. C2×#106C22×C3semidirect
204. C2×#103C22×C3semidirect
205. C2×#103C22×C3semidirect
206. C2×#103C22×C3semidirect
209. C2×#102C22×C3semidirect
211. C2×#97C22×C3semidirect
212. C2×C4×C8C22×C3semidirect
215. #391C22×C3semidirect
218. #390C22×C3semidirect
222. #336C22×C3semidirect
223. #336C22×C3semidirect
823. C3#25796direct (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×#4972
C2×C3×#4952
C2×C3×#4702
C2×C3×#4522
C2×C3×#4502
C3×#24352
C3×#24322
C3×#20152
C3×#20132
C3×#20122
C3×#19722
C3×#19682
C3×#17532
#257963