Finite Group Databasebeta

← C3×#25791 #10644398

Subgroups — C3×#25791 #10644398

Order 768.

1760 conjugacy classes of subgroups.

The subgroup lattice has 866 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×#496C211yesmaximal, characteristic, complemented
3C2×C3×#492C211yesmaximal, characteristic, complemented
4C2×C3×#468C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#450C211yesmaximal, characteristic, complemented
7C3×#2433C211yesmaximal, characteristic, complemented
8C3×#2432C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2013C211yesmaximal, characteristic, complemented
11C3×#2012C211yesmaximal, characteristic, complemented
12C3×#2011C211yesmaximal, characteristic, complemented
13C3×#1973C211yesmaximal, characteristic, complemented
14C3×#1970C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25791C311yesmaximal, 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×SD16C2211yescharacteristic, complemented
27C22×C3×SD16C2211yescharacteristic, complemented
28C22×C3×D8C2211yescharacteristic
29C22×C3×D8C2211yescharacteristic
30C22×C3×D8C2211yescharacteristic, complemented
31C22×C3×M16C2211yescharacteristic
32C2×C3×C4⋊Q8C2211yescharacteristic, complemented
33C2×C3×#127C2211yescharacteristic
34C2×C3×#127C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic, complemented
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C2×C3×#120—22no—
39C3×#496—24no—
40C3×#492—24no—
41C3×#468—24no—
42C3×#450—24no—
43C3×#449—24no—
44C2×C3×#107C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×#102C2211yescharacteristic, complemented
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×#97C2211yescharacteristic, complemented
53C2×C3×C4×C8C2211yescharacteristic, complemented
54C3×#394—22no—
55C3×#392—22no—
56C3×#391C2211yescharacteristic, complemented
57C3×#390C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#390C2211yescharacteristic, complemented
60C3×#385—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
65C2×#496C2×C311yescharacteristic, complemented
66C2×#492C2×C311yescharacteristic, complemented
67C2×#468C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#450C2×C311yescharacteristic, complemented
70#2433C2×C311yescharacteristic, complemented
71#2432C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2013C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1973C2×C311yescharacteristic, complemented
77#1970C2×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×D4—22no—
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—21no—
95C22×C3×D4—22no—
96C22×C3×D4—22no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
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—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×SD16D414yescomplemented
124C2×C3×D8—22no—
125C2×C3×D8—22no—
126C2×C3×D8—22no—
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8—22no—
130C2×C3×D8—22no—
131C2×C3×D8—41no—
132C2×C3×D8D414yescomplemented
133C2×C3×M16—22no—
134C2×C3×M16—22no—
135C2×C3×M16D414yescomplemented
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2311yescharacteristic
140C3×C4⋊Q8—22no—
141C3×C4⋊Q8—41no—
142C3×#127—22no—
143C3×#127—22no—
144C3×#127—41no—
145C3×#127—41no—
146C3×#124—22no—
147C3×#124—41no—
148C3×C22⋊Q8—22no—
149C3×C22⋊Q8—22no—
150C3×#121—22no—
151C3×#121—22no—
152C3×#120—48no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4—22no—
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4D412yes—
164C2×C3×C42C2311yescharacteristic
165C2×C3×C42C2311yescharacteristic
166C3×#107—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×C22⋊C8D414yescomplemented
174C3×#97—22no—
175C3×C4×C8—22no—
176C3×#95—22no—
177C3×#95D412yes—
178C22×#41C22×C311yescharacteristic
179C23×D4C22×C311yescharacteristic
180C2×AGL(1,ℤ/8)—24no—
181C2×AGL(1,ℤ/8)—24no—
182C2×AGL(1,ℤ/8)—24no—
183C22×SD16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic, complemented
188C22×SD16C22×C311yescharacteristic, complemented
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×D8C22×C311yescharacteristic, complemented
192C22×M16C22×C311yescharacteristic
193C2×C4⋊Q8C22×C311yescharacteristic, complemented
194C2×#127C22×C311yescharacteristic
195C2×#127C22×C311yescharacteristic
196C2×#124C22×C311yescharacteristic, complemented
197C2×C22⋊Q8C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#120—22no—
200#496—24no—
201#492—24no—
202#468—24no—
203#450—24no—
204#449—24no—
205C2×#107C22×C311yescharacteristic, complemented
206C2×#103C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×#102C22×C311yescharacteristic, complemented
211C2×#102C22×C311yescharacteristic, complemented
212C2×C22⋊C8C22×C311yescharacteristic
213C2×#97C22×C311yescharacteristic, complemented
214C2×C4×C8C22×C311yescharacteristic, complemented
215#394—22no—
216#392—22no—
217#391C22×C311yescharacteristic, complemented
218#390C22×C311yescharacteristic
219#390C22×C311yescharacteristic
220#390C22×C311yescharacteristic, complemented
221#385—22no—
222C4×C22⋊C4C22×C311yescharacteristic
223#336C22×C311yescharacteristic, complemented
224#336C22×C311yescharacteristic, complemented
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—42no—
230C24×C3—42no—
231C24×C3—44no—
232C24×C3—42no—
233C24×C3—82no—
234C24×C3C2×D411yescharacteristic
235C3×#41—28no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
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×Q8C2×D412yes—
251C2×C3×D4—28no—
252C2×C3×D4—21no—
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—21no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—44no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—44no—
288C2×C3×D4—82no—
289C2×C3×D4—82no—
290C2×C3×D4C2×D412yes—
291C2×C3×D4C2×D412yes—
292C2×C3×D4C2×D412yes—
293C22×C3×C4—21no—
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—42no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2411yescharacteristic
310C3×SD16—28no—
311C3×SD16—28no—
312C3×SD16—44no—
313C3×SD16—44no—
314C3×SD16—44no—
315C3×SD16—44no—
316C3×D8—28no—
317C3×D8—28no—
318C3×D8—44no—
319C3×M16—28no—
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×C8C2×D412yes—
327C2×C3×C8C2×D412yes—
328C2×C3×C8C2×D412yes—
329C2×C3×C8C2×D412yes—
330C2×C3×C8C2×D412yes—
331C2×C3×C8C2×D412yes—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—44no—
337C3×C4⋊C4—42no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—42no—
343C3×C22⋊C4—44no—
344C3×C22⋊C4—44no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C25—21no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—41no—
355C2×#41—41no—
356C22×Q8C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—21no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4C23×C311yescharacteristic
370C22×D4C23×C311yescharacteristic
371C22×D4C23×C311yescharacteristic
372C22×D4C23×C311yescharacteristic
373C23×C4—21no—
374C23×C4C23×C311yescharacteristic
375AGL(1,ℤ/8)—232no—
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—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—41no—
391C2×SD16—41no—
392C2×SD16—41no—
393C2×SD16C3×D414yescomplemented
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8—22no—
401C2×D8—41no—
402C2×D8C3×D414yescomplemented
403C2×M16—22no—
404C2×M16—22no—
405C2×M16C3×D414yescomplemented
406C22×C8C23×C311yescharacteristic
407C22×C8C23×C311yescharacteristic
408C22×C8C23×C311yescharacteristic
409C22×C8C23×C311yescharacteristic
410C4⋊Q8—22no—
411C4⋊Q8—41no—
412#127—22no—
413#127—22no—
414#127—41no—
415#127—41no—
416#124—22no—
417#124—41no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420#121—22no—
421#121—22no—
422#120—48no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4C23×C311yescharacteristic
426C2×C4⋊C4C23×C311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4C3×D412yes—
434C2×C42C23×C311yescharacteristic
435C2×C42C23×C311yescharacteristic
436#107—22no—
437#103—22no—
438#103—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442#102—22no—
443C22⋊C8C3×D414yescomplemented
444#97—22no—
445C4×C8—22no—
446#95—22no—
447#95C3×D412yes—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—48no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—42no—
472C23×C3—42no—
473C23×C3—84no—
474C23×C3—84no—
475C23×C3—88no—
476C23×C3—88no—
477C23×C3#12712yes—
478C23×C3C22×D411yescharacteristic
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4—48no—
494C3×D4—48no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—88no—
506C3×D4—88no—
507C3×D4—84no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—48no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4#12712yes—
531C2×C3×C4AGL(1,ℤ/8)14yescomplemented
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537C2×C3×C4H(5,𝔽2)11yescharacteristic
538C3×C8—22no—
539C3×C8—22no—
540C3×C8—22no—
541C3×C8#12014yescomplemented
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—44no—
549C24—42no—
550C24—82no—
551C24C2×C3×D411yescharacteristic
552#41—28no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C3×D412yes—
568C2×D4—28no—
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—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—44no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4C2×C3×D412yes—
608C2×D4C2×C3×D412yes—
609C2×D4C2×C3×D412yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4C2×C3×D412yes—
622C22×C4C2×C3×D411yescharacteristic
623C22×C4C2×C3×D412yes—
624C22×C4C2×C3×D412yes—
625C22×C4C2×C3×D412yes—
626C22×C4C24×C311yescharacteristic
627SD16—28no—
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632SD16—44no—
633D8—28no—
634D8—28no—
635D8—44no—
636M16—28no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8C2×C3×D412yes—
644C2×C8C2×C3×D412yes—
645C2×C8C2×C3×D412yes—
646C2×C8C2×C3×D412yes—
647C2×C8C2×C3×D412yes—
648C2×C8C2×C3×D412yes—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—44no—
654C4⋊C4—42no—
655C22⋊C4—24no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—816no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—82no—
685C22×C3—82no—
686C22×C3—82no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—82no—
691C22×C3—82no—
692C22×C3C2×#12711yescharacteristic
693C22×C3D4211yescharacteristic
694C22×C3D4211yescharacteristic
695C22×C3C2×AGL(1,ℤ/8)12yes—
696C22×C3#57712yes—
697C3×C4—22no—
698C3×C4—24no—
699C3×C4—42no—
700C3×C4—42no—
701C3×C4—81no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4C2×#12011yescharacteristic
705C3×C4#53511yescharacteristic
706C3×C4D4211yescharacteristic
707C3×C4D4211yescharacteristic
708C23—22no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—48no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—88no—
736C23—88no—
737C23C3×#12712yes—
738C23C22×C3×D411yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—48no—
754D4—48no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—88no—
766D4—88no—
767D4—84no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—48no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4C3×#12712yes—
791C2×C4C3×AGL(1,ℤ/8)14yescomplemented
792C2×C4C22×C3×D411yescharacteristic
793C2×C4C22×C3×D411yescharacteristic
794C2×C4C22×C3×D411yescharacteristic
795C2×C4C22×C3×D411yescharacteristic
796C2×C4C3×H(5,𝔽2)11yescharacteristic
797C2×C4C3×H(5,𝔽2)11yescharacteristic
798C8—22no—
799C8—22no—
800C8—22no—
801C8C3×#12014yescomplemented
802C2×C3—42no—
803C2×C3—82no—
804C2×C3—82no—
805C2×C3—82no—
806C2×C3—161no—
807C2×C3#243311yescharacteristic
808C2×C3#315111yescharacteristic
809C2×C3#315411yescharacteristic
810C2×C3#326512yes—
811C2×C3#327212yes—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—816no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22C2×C3×#12711yescharacteristic
839C22C3×D4211yescharacteristic
840C22C3×D4211yescharacteristic
841C22C2×C3×AGL(1,ℤ/8)12yes—
842C22C3×#57712yes—
843C4—22no—
844C4—24no—
845C4—42no—
846C4—42no—
847C4—81no—
848C4—81no—
849C4—81no—
850C4C2×C3×#12011yescharacteristic
851C4C3×#53511yescharacteristic
852C4C3×D4211yescharacteristic
853C4C3×D4211yescharacteristic
854C3#2579111yescharacteristic, direct product factor, Sylow
855C2—42no—
856C2—82no—
857C2—82no—
858C2—82no—
859C2—161no—
860C2C3×#243311yescharacteristic
861C2C3×#315111yescharacteristic
862C2C3×#315411yescharacteristic
863C2C3×#326512yes—
864C2C3×#327212yes—
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×#496C2semidirect
3. C2×C3×#492C2semidirect
4. C2×C3×#468C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#450C2semidirect
7. C3×#2433C2semidirect
8. C3×#2432C2semidirect
9. C3×#2014C2semidirect
10. C3×#2013C2semidirect
11. C3×#2012C2semidirect
12. C3×#2011C2semidirect
13. C3×#1973C2semidirect
14. C3×#1970C2semidirect
15. C3×#1753C2semidirect
16. #25791C3direct (N × H)
26. C22×C3×SD16C22semidirect
27. C22×C3×SD16C22semidirect
30. C22×C3×D8C22semidirect
32. C2×C3×C4⋊Q8C22semidirect
35. C2×C3×#124C22semidirect
44. C2×C3×#107C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#103C22semidirect
49. C2×C3×#102C22semidirect
50. C2×C3×#102C22semidirect
52. C2×C3×#97C22semidirect
53. C2×C3×C4×C8C22semidirect
56. C3×#391C22semidirect
59. C3×#390C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C22×AGL(1,ℤ/8)C2×C3semidirect
65. C2×#496C2×C3semidirect
66. C2×#492C2×C3semidirect
67. C2×#468C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#450C2×C3semidirect
70. #2433C2×C3semidirect
71. #2432C2×C3semidirect
72. #2014C2×C3semidirect
73. #2013C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1973C2×C3semidirect
77. #1970C2×C3semidirect
78. #1753C2×C3semidirect
123. C2×C3×SD16D4semidirect
132. C2×C3×D8D4semidirect
135. C2×C3×M16D4semidirect
173. C3×C22⋊C8D4semidirect
187. C22×SD16C22×C3semidirect
188. C22×SD16C22×C3semidirect
191. C22×D8C22×C3semidirect
193. C2×C4⋊Q8C22×C3semidirect
196. C2×#124C22×C3semidirect
205. C2×#107C22×C3semidirect
206. C2×#103C22×C3semidirect
207. C2×#103C22×C3semidirect
210. C2×#102C22×C3semidirect
211. C2×#102C22×C3semidirect
213. C2×#97C22×C3semidirect
214. C2×C4×C8C22×C3semidirect
217. #391C22×C3semidirect
220. #390C22×C3semidirect
223. #336C22×C3semidirect
224. #336C22×C3semidirect
393. C2×SD16C3×D4semidirect
402. C2×D8C3×D4semidirect
405. C2×M16C3×D4semidirect
443. C22⋊C8C3×D4semidirect
531. C2×C3×C4AGL(1,ℤ/8)semidirect
541. C3×C8#120semidirect
791. C2×C4C3×AGL(1,ℤ/8)semidirect
801. C8C3×#120semidirect
854. C3#25791direct (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×#4962
C2×C3×#4922
C2×C3×#4682
C2×C3×#4492
C2×C3×#4502
C3×#24332
C3×#24322
C3×#20142
C3×#20132
C3×#20122
C3×#20112
C3×#19732
C3×#19702
C3×#17532
#257913