Finite Group Databasebeta

← C2×C3×#8453 #72276657

Subgroups — C2×C3×#8453 #72276657

Order 1536.

9348 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3484C211yesmaximal, characteristic
2C2×C3×#1783C211yesmaximal, characteristic, complemented
3C2×C3×#1504C214yesmaximal, complemented
4C2×C3×#1438C211yesmaximal, characteristic, complemented
5C3×#8453C218yesmaximal, direct product factor
6C2×#8453C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×H(5,𝔽2)C411yescharacteristic, complemented
8C24×C3×D4C2211yescharacteristic
9C3×#3484—28no—
10C3×#3484—22no—
11C3×#3484—22no—
12C3×#3484C414yescomplemented
13C3×#3484C2214yes—
14C2×C3×#546—24no—
15C2×C3×D42—24no—
16C2×C3×#535C412yescomplemented
17C2×C3×#534—22no—
18C2×C3×#525C2212yes—
19C22×C3×#120—22no—
20C2×C3×#518C411yescharacteristic, complemented
21C23×C3×C22⋊C4—22no—
22C22×C3×#100—22no—
23C2×C3×#407C2212yescomplemented
24C22×C3×#95C2212yescomplemented
25C3×#1783—22no—
26C3×#1783C2214yescomplemented
27C3×#1504—28no—
28C3×#1504C22116yescomplemented
29C2×C3×#328—24no—
30C2×C3×#327—24no—
31C3×#1438—22no—
32C3×#1438C2214yescomplemented
33C2×#3484C2×C311yescharacteristic
34C2×#1783C2×C311yescharacteristic, complemented
35C2×#1504C2×C314yescomplemented
36C2×#1438C2×C311yescharacteristic, complemented
37#8453C2×C318yesdirect product factor
38C26×C3D412yes—
39C2×C3×H(5,𝔽2)—24no—
40C2×C3×H(5,𝔽2)—22no—
41C2×C3×H(5,𝔽2)—48no—
42C2×C3×H(5,𝔽2)C2×C414yescomplemented
43C22×C3×#41—22no—
44C22×C3×#41C2×C412yes—
45C23×C3×D4—24no—
46C23×C3×D4—22no—
47C23×C3×D4—24no—
48C23×C3×D4—24no—
49C23×C3×D4—22no—
50C23×C3×D4—48no—
51C23×C3×D4C2×C411yescharacteristic
52C23×C3×D4C2×C411yescharacteristic
53C23×C3×D4C2×C412yes—
54C23×C3×D4D412yes—
55C23×C3×D4D412yes—
56C23×C3×D4D412yes—
57C23×C3×D4C2312yes—
58C24×C3×C4—22no—
59C24×C3×C4C2311yescharacteristic
60C22×C3×M16—22no—
61C3×#546—216no—
62C3×#546—216no—
63C3×#546—216no—
64C3×#546—216no—
65C3×D42—216no—
66C3×D42—216no—
67C3×D42—216no—
68C3×D42—216no—
69C3×#535—24no—
70C3×#535—24no—
71C3×#535—24no—
72C3×#535C2×C418yescomplemented
73C3×#534—216no—
74C3×#534—28no—
75C3×#534—28no—
76C2×C3×#127—22no—
77C2×C3×#124—22no—
78C3×#525—24no—
79C3×#525—22no—
80C3×#525—22no—
81C3×#525C2×C414yes—
82C3×#525D418yes—
83C3×#525C2314yes—
84C2×C3×#123—24no—
85C2×C3×#123—22no—
86C2×C3×C22⋊Q8D414yes—
87C2×C3×#121—28no—
88C2×C3×#121—24no—
89C2×C3×#121D414yes—
90C2×C3×#120—28no—
91C2×C3×#120—216no—
92C2×C3×#120—24no—
93C2×C3×#120—24no—
94C2×C3×#120—28no—
95C2×C3×#120—22no—
96C2×C3×#120—28no—
97C3×#518—22no—
98C3×#518—24no—
99C3×#518C2×C414yescomplemented
100C2×C3×C4×D4—24no—
101C2×C3×C4×D4—24no—
102C2×C3×#117C2×C412yes—
103C22×C3×C22⋊C4—24no—
104C22×C3×C22⋊C4—22no—
105C22×C3×C22⋊C4—28no—
106C22×C3×C22⋊C4—48no—
107C22×C3×C22⋊C4—416no—
108C2×C3×#100—28no—
109C2×C3×#100—48no—
110C3×#407—24no—
111C3×#407—22no—
112C3×#407C2314yescomplemented
113C2×C3×C22⋊C8—24no—
114C2×C3×#95—24no—
115C2×C3×#95—24no—
116C2×C3×#95—22no—
117C2×C3×#95C2314yescomplemented
118C3×#328—216no—
119C3×#327—216no—
120C22×H(5,𝔽2)C3×C411yescharacteristic, complemented
121C24×D4C22×C311yescharacteristic
122#3484—22no—
123#3484—22no—
124#3484—28no—
125#3484C3×C414yescomplemented
126#3484C22×C314yes—
127C2×#546—24no—
128C2×D42—24no—
129C2×#535C3×C412yescomplemented
130C2×#534—22no—
131C2×#525C22×C312yes—
132C22×#120—22no—
133C2×#518C3×C411yescharacteristic, complemented
134C23×C22⋊C4—22no—
135C22×#100—22no—
136C2×#407C22×C312yescomplemented
137C22×#95C22×C312yescomplemented
138#1783—22no—
139#1783C22×C314yescomplemented
140#1504—28no—
141#1504C22×C3116yescomplemented
142C2×#328—24no—
143C2×#327—24no—
144#1438—22no—
145#1438C22×C314yescomplemented
146C25×C3—22no—
147C25×C3—28no—
148C25×C3—24no—
149C25×C3—24no—
150C25×C3—44no—
151C25×C3—48no—
152C25×C3—48no—
153C25×C3C22⋊C412yes—
154C25×C3C22⋊C414yes—
155C25×C3C22⋊C412yes—
156C25×C3C2×D411yescharacteristic
157C25×C3C2×D414yes—
158C3×H(5,𝔽2)—432no—
159C3×H(5,𝔽2)—416no—
160C3×H(5,𝔽2)—416no—
161C2×C3×#41—28no—
162C2×C3×#41—28no—
163C2×C3×#41—22no—
164C2×C3×#41—22no—
165C2×C3×#41—48no—
166C2×C3×#41—416no—
167C2×C3×#41C22⋊C414yescomplemented
168C2×C3×#41C22×C414yes—
169C22×C3×Q8C22⋊C412yescomplemented
170C22×C3×D4—28no—
171C22×C3×D4—24no—
172C22×C3×D4—28no—
173C22×C3×D4—28no—
174C22×C3×D4—28no—
175C22×C3×D4—22no—
176C22×C3×D4—28no—
177C22×C3×D4—24no—
178C22×C3×D4—28no—
179C22×C3×D4—216no—
180C22×C3×D4—216no—
181C22×C3×D4—28no—
182C22×C3×D4—22no—
183C22×C3×D4—22no—
184C22×C3×D4—22no—
185C22×C3×D4—22no—
186C22×C3×D4—28no—
187C22×C3×D4—24no—
188C22×C3×D4—24no—
189C22×C3×D4—28no—
190C22×C3×D4—28no—
191C22×C3×D4—28no—
192C22×C3×D4—44no—
193C22×C3×D4—44no—
194C22×C3×D4—48no—
195C22×C3×D4—48no—
196C22×C3×D4—48no—
197C22×C3×D4—48no—
198C22×C3×D4—432no—
199C22×C3×D4—432no—
200C22×C3×D4—416no—
201C22×C3×D4—48no—
202C22×C3×D4—48no—
203C22×C3×D4—88no—
204C22×C3×D4—88no—
205C22×C3×D4C22⋊C412yes—
206C22×C3×D4C22⋊C414yes—
207C22×C3×D4C22⋊C412yes—
208C22×C3×D4C22⋊C412yescomplemented
209C22×C3×D4C22×C412yes—
210C22×C3×D4C22×C412yes—
211C22×C3×D4C2×D414yes—
212C23×C3×C4—22no—
213C23×C3×C4—24no—
214C23×C3×C4—22no—
215C23×C3×C4—28no—
216C23×C3×C4—24no—
217C23×C3×C4—44no—
218C23×C3×C4—44no—
219C23×C3×C4—48no—
220C23×C3×C4—48no—
221C23×C3×C4—42no—
222C23×C3×C4—42no—
223C23×C3×C4C22×C411yescharacteristic
224C23×C3×C4C22×C411yescharacteristic
225C23×C3×C4C2×D411yescharacteristic
226C23×C3×C4C2×D411yescharacteristic
227C23×C3×C4C2×D414yes—
228C23×C3×C4C2×D414yes—
229C23×C3×C4C2×D411yescharacteristic
230C23×C3×C4C2411yescharacteristic
231C2×C3×M16—24no—
232C2×C3×M16—42no—
233C2×C3×M16—48no—
234C22×C3×C8—42no—
235C3×#127—28no—
236C3×#127—28no—
237C3×#124—28no—
238C3×#124—28no—
239C3×#123—216no—
240C3×#123—216no—
241C3×#123—24no—
242C3×#123—28no—
243C3×#123—24no—
244C3×C22⋊Q8—24no—
245C3×C22⋊Q8—24no—
246C3×C22⋊Q8C22⋊C418yescomplemented
247C3×C22⋊Q8C2×D418yes—
248C3×#121—232no—
249C3×#121—232no—
250C3×#121—216no—
251C3×#121—24no—
252C3×#121—24no—
253C3×#121—216no—
254C3×#121C22⋊C418yescomplemented
255C3×#121C2×D418yes—
256C3×#120—216no—
257C3×#120—232no—
258C3×#120—232no—
259C3×#120—216no—
260C3×#120—216no—
261C3×#120—24no—
262C3×#120—216no—
263C3×#120—28no—
264C3×#120—24no—
265C3×C4×D4—216no—
266C3×C4×D4—28no—
267C3×C4×D4—28no—
268C3×C4×D4—28no—
269C3×C4×D4—28no—
270C3×C4×D4—216no—
271C3×#117—22no—
272C3×#117—22no—
273C3×#117C22⋊C414yescomplemented
274C3×#117C22×C414yes—
275C2×C3×C4⋊C4—24no—
276C2×C3×C4⋊C4C22⋊C414yescomplemented
277C2×C3×C22⋊C4—24no—
278C2×C3×C22⋊C4—28no—
279C2×C3×C22⋊C4—28no—
280C2×C3×C22⋊C4—216no—
281C2×C3×C22⋊C4—216no—
282C2×C3×C22⋊C4—22no—
283C2×C3×C22⋊C4—28no—
284C2×C3×C22⋊C4—24no—
285C2×C3×C22⋊C4—24no—
286C2×C3×C22⋊C4—432no—
287C2×C3×C22⋊C4—416no—
288C2×C3×C22⋊C4—464no—
289C2×C3×C42—22no—
290C3×#100—416no—
291C3×C22⋊C8—28no—
292C3×C22⋊C8—44no—
293C3×#95—28no—
294C3×#95—44no—
295C26C3×D412yes—
296C2×H(5,𝔽2)—24no—
297C2×H(5,𝔽2)—22no—
298C2×H(5,𝔽2)—48no—
299C2×H(5,𝔽2)C2×C3×C414yescomplemented
300C22×#41—22no—
301C22×#41C2×C3×C412yes—
302C23×D4—22no—
303C23×D4—24no—
304C23×D4—22no—
305C23×D4—24no—
306C23×D4—24no—
307C23×D4—48no—
308C23×D4C2×C3×C411yescharacteristic
309C23×D4C2×C3×C411yescharacteristic
310C23×D4C2×C3×C412yes—
311C23×D4C3×D412yes—
312C23×D4C3×D412yes—
313C23×D4C3×D412yes—
314C23×D4C23×C312yes—
315C24×C4—22no—
316C24×C4C23×C311yescharacteristic
317C22×M16—22no—
318#546—216no—
319#546—216no—
320#546—216no—
321#546—216no—
322D42—216no—
323D42—216no—
324D42—216no—
325D42—216no—
326#535—24no—
327#535—24no—
328#535—24no—
329#535C2×C3×C418yescomplemented
330#534—216no—
331#534—28no—
332#534—28no—
333C2×#127—22no—
334C2×#124—22no—
335#525—24no—
336#525—22no—
337#525—22no—
338#525C2×C3×C414yes—
339#525C3×D418yes—
340#525C23×C314yes—
341C2×#123—24no—
342C2×#123—22no—
343C2×C22⋊Q8C3×D414yes—
344C2×#121—28no—
345C2×#121—24no—
346C2×#121C3×D414yes—
347C2×#120—28no—
348C2×#120—216no—
349C2×#120—24no—
350C2×#120—24no—
351C2×#120—28no—
352C2×#120—22no—
353C2×#120—28no—
354#518—22no—
355#518—24no—
356#518C2×C3×C414yescomplemented
357C2×C4×D4—24no—
358C2×C4×D4—24no—
359C2×#117C2×C3×C412yes—
360C22×C22⋊C4—24no—
361C22×C22⋊C4—22no—
362C22×C22⋊C4—28no—
363C22×C22⋊C4—416no—
364C22×C22⋊C4—48no—
365C2×#100—28no—
366C2×#100—48no—
367#407—24no—
368#407—22no—
369#407C23×C314yescomplemented
370C2×C22⋊C8—24no—
371C2×#95—24no—
372C2×#95—24no—
373C2×#95—22no—
374C2×#95C23×C314yescomplemented
375#328—216no—
376#327—216no—
377C24×C3—24no—
378C24×C3—24no—
379C24×C3—24no—
380C24×C3—22no—
381C24×C3—22no—
382C24×C3—24no—
383C24×C3—28no—
384C24×C3—22no—
385C24×C3—22no—
386C24×C3—28no—
387C24×C3—24no—
388C24×C3—28no—
389C24×C3—28no—
390C24×C3—28no—
391C24×C3—22no—
392C24×C3—24no—
393C24×C3—44no—
394C24×C3—44no—
395C24×C3—416no—
396C24×C3—416no—
397C24×C3—48no—
398C24×C3—48no—
399C24×C3—416no—
400C24×C3—48no—
401C24×C3—48no—
402C24×C3—432no—
403C24×C3—416no—
404C24×C3—416no—
405C24×C3—48no—
406C24×C3—48no—
407C24×C3—48no—
408C24×C3—88no—
409C24×C3—88no—
410C24×C3—84no—
411C24×C3—84no—
412C24×C3—88no—
413C24×C3—816no—
414C24×C3—88no—
415C24×C3—88no—
416C24×C3#9918yes—
417C24×C3C2×C22⋊C411yescharacteristic
418C24×C3C2×C22⋊C411yescharacteristic
419C24×C3C2×C22⋊C414yes—
420C24×C3C2×C22⋊C414yes—
421C24×C3#12012yes—
422C24×C3#12012yes—
423C24×C3C22×D411yescharacteristic
424C3×#41—48no—
425C3×#41—48no—
426C3×#41—48no—
427C3×#41—48no—
428C3×#41—432no—
429C3×#41—432no—
430C2×C3×Q8—22no—
431C2×C3×Q8—44no—
432C2×C3×Q8C2×C22⋊C414yescomplemented
433C2×C3×D4—216no—
434C2×C3×D4—216no—
435C2×C3×D4—28no—
436C2×C3×D4—28no—
437C2×C3×D4—216no—
438C2×C3×D4—24no—
439C2×C3×D4—28no—
440C2×C3×D4—28no—
441C2×C3×D4—24no—
442C2×C3×D4—28no—
443C2×C3×D4—28no—
444C2×C3×D4—232no—
445C2×C3×D4—24no—
446C2×C3×D4—24no—
447C2×C3×D4—28no—
448C2×C3×D4—24no—
449C2×C3×D4—28no—
450C2×C3×D4—24no—
451C2×C3×D4—22no—
452C2×C3×D4—44no—
453C2×C3×D4—44no—
454C2×C3×D4—44no—
455C2×C3×D4—44no—
456C2×C3×D4—416no—
457C2×C3×D4—416no—
458C2×C3×D4—44no—
459C2×C3×D4—48no—
460C2×C3×D4—48no—
461C2×C3×D4—432no—
462C2×C3×D4—432no—
463C2×C3×D4—432no—
464C2×C3×D4—432no—
465C2×C3×D4—432no—
466C2×C3×D4—432no—
467C2×C3×D4—416no—
468C2×C3×D4—416no—
469C2×C3×D4—432no—
470C2×C3×D4—48no—
471C2×C3×D4—416no—
472C2×C3×D4—48no—
473C2×C3×D4—48no—
474C2×C3×D4—816no—
475C2×C3×D4—832no—
476C2×C3×D4—816no—
477C2×C3×D4—816no—
478C2×C3×D4C2×C22⋊C414yescomplemented
479C22×C3×C4—24no—
480C22×C3×C4—24no—
481C22×C3×C4—28no—
482C22×C3×C4—24no—
483C22×C3×C4—22no—
484C22×C3×C4—216no—
485C22×C3×C4—24no—
486C22×C3×C4—24no—
487C22×C3×C4—28no—
488C22×C3×C4—42no—
489C22×C3×C4—42no—
490C22×C3×C4—42no—
491C22×C3×C4—48no—
492C22×C3×C4—48no—
493C22×C3×C4—42no—
494C22×C3×C4—48no—
495C22×C3×C4—48no—
496C22×C3×C4—432no—
497C22×C3×C4—48no—
498C22×C3×C4—48no—
499C22×C3×C4—48no—
500C22×C3×C4—48no—
501C22×C3×C4—44no—
502C22×C3×C4—44no—
503C22×C3×C4—88no—
504C22×C3×C4—816no—
505C22×C3×C4—84no—
506C22×C3×C4—84no—
507C22×C3×C4—84no—
508C22×C3×C4—84no—
509C22×C3×C4C2×C22⋊C412yes—
510C22×C3×C4C2×C22⋊C412yes—
511C22×C3×C4C2×C22⋊C411yescharacteristic
512C22×C3×C4C2×C22⋊C411yescharacteristic
513C22×C3×C4C2×C22⋊C414yes—
514C22×C3×C4#12012yes—
515C22×C3×C4#12012yes—
516C22×C3×C4#12014yes—
517C22×C3×C4#12014yes—
518C22×C3×C4C23×C411yescharacteristic
519C22×C3×C4C22×D411yescharacteristic
520C22×C3×C4C22×D414yes—
521C3×M16—48no—
522C3×M16—84no—
523C2×C3×C8—44no—
524C2×C3×C8—84no—
525C3×C4⋊C4—28no—
526C3×C4⋊C4—28no—
527C3×C4⋊C4—24no—
528C3×C4⋊C4C2×C22⋊C418yescomplemented
529C3×C22⋊C4—216no—
530C3×C22⋊C4—232no—
531C3×C22⋊C4—24no—
532C3×C22⋊C4—28no—
533C3×C22⋊C4—24no—
534C3×C22⋊C4—28no—
535C3×C22⋊C4—28no—
536C3×C22⋊C4—28no—
537C3×C22⋊C4—464no—
538C3×C42—24no—
539C3×C42—24no—
540C25—22no—
541C25—28no—
542C25—24no—
543C25—24no—
544C25—44no—
545C25—48no—
546C25—48no—
547C25C3×C22⋊C412yes—
548C25C3×C22⋊C414yes—
549C25C3×C22⋊C412yes—
550C25C2×C3×D411yescharacteristic
551C25C2×C3×D414yes—
552H(5,𝔽2)—432no—
553H(5,𝔽2)—416no—
554H(5,𝔽2)—416no—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—48no—
560C2×#41—416no—
561C2×#41C3×C22⋊C414yescomplemented
562C2×#41C22×C3×C414yes—
563C22×Q8C3×C22⋊C412yescomplemented
564C22×D4—28no—
565C22×D4—24no—
566C22×D4—28no—
567C22×D4—28no—
568C22×D4—28no—
569C22×D4—22no—
570C22×D4—28no—
571C22×D4—24no—
572C22×D4—28no—
573C22×D4—216no—
574C22×D4—216no—
575C22×D4—28no—
576C22×D4—22no—
577C22×D4—22no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—28no—
581C22×D4—24no—
582C22×D4—24no—
583C22×D4—28no—
584C22×D4—28no—
585C22×D4—28no—
586C22×D4—44no—
587C22×D4—44no—
588C22×D4—48no—
589C22×D4—48no—
590C22×D4—48no—
591C22×D4—48no—
592C22×D4—432no—
593C22×D4—432no—
594C22×D4—416no—
595C22×D4—48no—
596C22×D4—48no—
597C22×D4—88no—
598C22×D4—88no—
599C22×D4C3×C22⋊C412yes—
600C22×D4C3×C22⋊C414yes—
601C22×D4C3×C22⋊C412yes—
602C22×D4C3×C22⋊C412yescomplemented
603C22×D4C22×C3×C412yes—
604C22×D4C22×C3×C412yes—
605C22×D4C2×C3×D414yes—
606C23×C4—22no—
607C23×C4—24no—
608C23×C4—22no—
609C23×C4—28no—
610C23×C4—24no—
611C23×C4—44no—
612C23×C4—48no—
613C23×C4—48no—
614C23×C4—44no—
615C23×C4—42no—
616C23×C4—42no—
617C23×C4C22×C3×C411yescharacteristic
618C23×C4C22×C3×C411yescharacteristic
619C23×C4C2×C3×D411yescharacteristic
620C23×C4C2×C3×D411yescharacteristic
621C23×C4C2×C3×D414yes—
622C23×C4C2×C3×D414yes—
623C23×C4C2×C3×D411yescharacteristic
624C23×C4C24×C311yescharacteristic
625C2×M16—24no—
626C2×M16—42no—
627C2×M16—48no—
628C22×C8—42no—
629#127—28no—
630#127—28no—
631#124—28no—
632#124—28no—
633#123—216no—
634#123—216no—
635#123—24no—
636#123—28no—
637#123—24no—
638C22⋊Q8—24no—
639C22⋊Q8—24no—
640C22⋊Q8C3×C22⋊C418yescomplemented
641C22⋊Q8C2×C3×D418yes—
642#121—232no—
643#121—232no—
644#121—216no—
645#121—24no—
646#121—24no—
647#121—216no—
648#121C3×C22⋊C418yescomplemented
649#121C2×C3×D418yes—
650#120—216no—
651#120—232no—
652#120—232no—
653#120—216no—
654#120—216no—
655#120—24no—
656#120—216no—
657#120—28no—
658#120—24no—
659C4×D4—216no—
660C4×D4—28no—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—28no—
664C4×D4—216no—
665#117—22no—
666#117—22no—
667#117C3×C22⋊C414yescomplemented
668#117C22×C3×C414yes—
669C2×C4⋊C4—24no—
670C2×C4⋊C4C3×C22⋊C414yescomplemented
671C2×C22⋊C4—24no—
672C2×C22⋊C4—28no—
673C2×C22⋊C4—28no—
674C2×C22⋊C4—216no—
675C2×C22⋊C4—216no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—28no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—24no—
680C2×C22⋊C4—432no—
681C2×C22⋊C4—416no—
682C2×C22⋊C4—464no—
683C2×C42—22no—
684#100—416no—
685C22⋊C8—28no—
686C22⋊C8—44no—
687#95—28no—
688#95—44no—
689C23×C3—28no—
690C23×C3—216no—
691C23×C3—28no—
692C23×C3—24no—
693C23×C3—24no—
694C23×C3—24no—
695C23×C3—24no—
696C23×C3—22no—
697C23×C3—22no—
698C23×C3—22no—
699C23×C3—22no—
700C23×C3—22no—
701C23×C3—22no—
702C23×C3—24no—
703C23×C3—24no—
704C23×C3—24no—
705C23×C3—28no—
706C23×C3—24no—
707C23×C3—28no—
708C23×C3—24no—
709C23×C3—24no—
710C23×C3—24no—
711C23×C3—24no—
712C23×C3—416no—
713C23×C3—416no—
714C23×C3—416no—
715C23×C3—48no—
716C23×C3—48no—
717C23×C3—48no—
718C23×C3—416no—
719C23×C3—432no—
720C23×C3—48no—
721C23×C3—416no—
722C23×C3—416no—
723C23×C3—48no—
724C23×C3—48no—
725C23×C3—416no—
726C23×C3—48no—
727C23×C3—48no—
728C23×C3—48no—
729C23×C3—44no—
730C23×C3—44no—
731C23×C3—44no—
732C23×C3—88no—
733C23×C3—88no—
734C23×C3—84no—
735C23×C3—88no—
736C23×C3—84no—
737C23×C3—832no—
738C23×C3—832no—
739C23×C3—88no—
740C23×C3—84no—
741C23×C3—88no—
742C23×C3—832no—
743C23×C3—816no—
744C23×C3—84no—
745C23×C3—832no—
746C23×C3—816no—
747C23×C3—1616no—
748C23×C3#37912yes—
749C23×C3#37911yescharacteristic
750C23×C3#37911yescharacteristic
751C23×C3C2×#9914yes—
752C23×C3C2×#9918yes—
753C23×C3#45314yes—
754C23×C3#45514yes—
755C23×C3C22×C22⋊C411yescharacteristic
756C23×C3C2×#12012yes—
757C3×Q8—44no—
758C3×Q8—44no—
759C3×D4—216no—
760C3×D4—216no—
761C3×D4—416no—
762C3×D4—416no—
763C3×D4—44no—
764C3×D4—48no—
765C3×D4—48no—
766C3×D4—44no—
767C3×D4—432no—
768C3×D4—416no—
769C3×D4—48no—
770C3×D4—48no—
771C3×D4—48no—
772C3×D4—48no—
773C3×D4—832no—
774C2×C3×C4—22no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—24no—
779C2×C3×C4—24no—
780C2×C3×C4—24no—
781C2×C3×C4—24no—
782C2×C3×C4—28no—
783C2×C3×C4—24no—
784C2×C3×C4—44no—
785C2×C3×C4—44no—
786C2×C3×C4—44no—
787C2×C3×C4—44no—
788C2×C3×C4—48no—
789C2×C3×C4—48no—
790C2×C3×C4—416no—
791C2×C3×C4—48no—
792C2×C3×C4—44no—
793C2×C3×C4—416no—
794C2×C3×C4—48no—
795C2×C3×C4—816no—
796C2×C3×C4—88no—
797C2×C3×C4—816no—
798C2×C3×C4—816no—
799C2×C3×C4—84no—
800C2×C3×C4—84no—
801C2×C3×C4#37912yes—
802C2×C3×C4#37912yes—
803C2×C3×C4C22×C22⋊C412yes—
804C2×C3×C4C2×#12012yes—
805C3×C8—84no—
806C24—24no—
807C24—24no—
808C24—24no—
809C24—22no—
810C24—22no—
811C24—24no—
812C24—28no—
813C24—22no—
814C24—22no—
815C24—28no—
816C24—28no—
817C24—24no—
818C24—28no—
819C24—28no—
820C24—22no—
821C24—24no—
822C24—44no—
823C24—44no—
824C24—416no—
825C24—416no—
826C24—48no—
827C24—48no—
828C24—48no—
829C24—416no—
830C24—48no—
831C24—416no—
832C24—432no—
833C24—416no—
834C24—48no—
835C24—48no—
836C24—48no—
837C24—88no—
838C24—88no—
839C24—84no—
840C24—84no—
841C24—88no—
842C24—816no—
843C24—88no—
844C24—88no—
845C24C3×#9918yes—
846C24C2×C3×C22⋊C411yescharacteristic
847C24C2×C3×C22⋊C411yescharacteristic
848C24C2×C3×C22⋊C414yes—
849C24C2×C3×C22⋊C414yes—
850C24C3×#12012yes—
851C24C3×#12012yes—
852C24C22×C3×D411yescharacteristic
853#41—48no—
854#41—48no—
855#41—48no—
856#41—48no—
857#41—432no—
858#41—432no—
859C2×Q8—22no—
860C2×Q8—44no—
861C2×Q8C2×C3×C22⋊C414yescomplemented
862C2×D4—216no—
863C2×D4—216no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—216no—
867C2×D4—28no—
868C2×D4—24no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—24no—
872C2×D4—28no—
873C2×D4—232no—
874C2×D4—24no—
875C2×D4—28no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—28no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—416no—
886C2×D4—416no—
887C2×D4—44no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—432no—
891C2×D4—432no—
892C2×D4—432no—
893C2×D4—432no—
894C2×D4—432no—
895C2×D4—432no—
896C2×D4—416no—
897C2×D4—416no—
898C2×D4—432no—
899C2×D4—48no—
900C2×D4—416no—
901C2×D4—48no—
902C2×D4—48no—
903C2×D4—816no—
904C2×D4—832no—
905C2×D4—816no—
906C2×D4—816no—
907C2×D4C2×C3×C22⋊C414yescomplemented
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—28no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—216no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—42no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—432no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—88no—
933C22×C4—816no—
934C22×C4—84no—
935C22×C4—84no—
936C22×C4—84no—
937C22×C4—84no—
938C22×C4C2×C3×C22⋊C411yescharacteristic
939C22×C4C2×C3×C22⋊C411yescharacteristic
940C22×C4C2×C3×C22⋊C412yes—
941C22×C4C2×C3×C22⋊C412yes—
942C22×C4C2×C3×C22⋊C414yes—
943C22×C4C3×#12012yes—
944C22×C4C3×#12012yes—
945C22×C4C3×#12014yes—
946C22×C4C3×#12014yes—
947C22×C4C23×C3×C411yescharacteristic
948C22×C4C22×C3×D411yescharacteristic
949C22×C4C22×C3×D414yes—
950M16—48no—
951M16—84no—
952C2×C8—44no—
953C2×C8—84no—
954C4⋊C4—28no—
955C4⋊C4—24no—
956C4⋊C4—28no—
957C4⋊C4C2×C3×C22⋊C418yescomplemented
958C22⋊C4—216no—
959C22⋊C4—232no—
960C22⋊C4—24no—
961C22⋊C4—28no—
962C22⋊C4—24no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—464no—
967C42—24no—
968C42—24no—
969C22×C3—22no—
970C22×C3—24no—
971C22×C3—28no—
972C22×C3—28no—
973C22×C3—22no—
974C22×C3—28no—
975C22×C3—28no—
976C22×C3—28no—
977C22×C3—28no—
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—22no—
983C22×C3—22no—
984C22×C3—28no—
985C22×C3—48no—
986C22×C3—48no—
987C22×C3—416no—
988C22×C3—48no—
989C22×C3—44no—
990C22×C3—44no—
991C22×C3—48no—
992C22×C3—48no—
993C22×C3—84no—
994C22×C3—88no—
995C22×C3—816no—
996C22×C3—832no—
997C22×C3—816no—
998C22×C3—84no—
999C22×C3—88no—
1000C22×C3—88no—
1001C22×C3—88no—
1002C22×C3—1616no—
1003C22×C3#178112yes—
1004C22×C3#178112yes—
1005C22×C3#179214yes—
1006C22×C3#179214yes—
1007C22×C3C2×#37911yescharacteristic
1008C22×C3C22×#9912yes—
1009C22×C3C2×#45312yes—
1010C22×C3C2×#45512yes—
1011C3×C4—22no—
1012C3×C4—22no—
1013C3×C4—22no—
1014C3×C4—22no—
1015C3×C4—44no—
1016C3×C4—48no—
1017C3×C4—88no—
1018C23—28no—
1019C23—216no—
1020C23—28no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—28no—
1034C23—24no—
1035C23—24no—
1036C23—28no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—416no—
1042C23—416no—
1043C23—416no—
1044C23—48no—
1045C23—48no—
1046C23—48no—
1047C23—416no—
1048C23—48no—
1049C23—432no—
1050C23—416no—
1051C23—416no—
1052C23—48no—
1053C23—44no—
1054C23—44no—
1055C23—44no—
1056C23—48no—
1057C23—416no—
1058C23—48no—
1059C23—48no—
1060C23—48no—
1061C23—88no—
1062C23—84no—
1063C23—88no—
1064C23—84no—
1065C23—88no—
1066C23—832no—
1067C23—832no—
1068C23—88no—
1069C23—84no—
1070C23—88no—
1071C23—832no—
1072C23—816no—
1073C23—84no—
1074C23—832no—
1075C23—816no—
1076C23—1616no—
1077C23C3×#37911yescharacteristic
1078C23C3×#37912yes—
1079C23C3×#37911yescharacteristic
1080C23C2×C3×#9914yes—
1081C23C2×C3×#9918yes—
1082C23C3×#45314yes—
1083C23C3×#45514yes—
1084C23C22×C3×C22⋊C411yescharacteristic
1085C23C2×C3×#12012yes—
1086Q8—44no—
1087Q8—44no—
1088D4—216no—
1089D4—216no—
1090D4—416no—
1091D4—416no—
1092D4—44no—
1093D4—48no—
1094D4—48no—
1095D4—44no—
1096D4—432no—
1097D4—48no—
1098D4—48no—
1099D4—416no—
1100D4—48no—
1101D4—48no—
1102D4—832no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—48no—
1118C2×C4—48no—
1119C2×C4—416no—
1120C2×C4—44no—
1121C2×C4—48no—
1122C2×C4—416no—
1123C2×C4—48no—
1124C2×C4—816no—
1125C2×C4—88no—
1126C2×C4—816no—
1127C2×C4—84no—
1128C2×C4—816no—
1129C2×C4—84no—
1130C2×C4C3×#37912yes—
1131C2×C4C3×#37912yes—
1132C2×C4C22×C3×C22⋊C412yes—
1133C2×C4C2×C3×#12012yes—
1134C8—84no—
1135C2×C3—22no—
1136C2×C3—22no—
1137C2×C3—24no—
1138C2×C3—22no—
1139C2×C3—22no—
1140C2×C3—48no—
1141C2×C3—84no—
1142C2×C3—84no—
1143C2×C3#845314yesdirect product factor
1144C2×C3C2×#178111yescharacteristic
1145C2×C3C2×#179212yes—
1146C22—22no—
1147C22—24no—
1148C22—28no—
1149C22—28no—
1150C22—22no—
1151C22—28no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—28no—
1159C22—28no—
1160C22—28no—
1161C22—28no—
1162C22—48no—
1163C22—48no—
1164C22—48no—
1165C22—416no—
1166C22—44no—
1167C22—44no—
1168C22—48no—
1169C22—48no—
1170C22—84no—
1171C22—88no—
1172C22—816no—
1173C22—832no—
1174C22—816no—
1175C22—84no—
1176C22—88no—
1177C22—88no—
1178C22—88no—
1179C22—1616no—
1180C22C3×#178112yes—
1181C22C3×#178112yes—
1182C22C3×#179214yes—
1183C22C3×#179214yes—
1184C22C2×C3×#37911yescharacteristic
1185C22C22×C3×#9912yes—
1186C22C2×C3×#45312yes—
1187C22C2×C3×#45512yes—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—44no—
1193C4—48no—
1194C4—88no—
1195C3C2×#845311yescharacteristic, direct product factor, Sylow
1196C2—22no—
1197C2—22no—
1198C2—22no—
1199C2—24no—
1200C2—22no—
1201C2—48no—
1202C2—84no—
1203C2—84no—
1204C2C3×#845314yesdirect product factor
1205C2C2×C3×#178111yescharacteristic
1206C2C2×C3×#179212yes—
subgroupG/H
center, socleC23×C3#379
commutatorC22×C4C23×C3×C4
Frattini, cosocleC23×C4C24×C3
prime radicalC2×C3×#3484C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#1783C2semidirect
3. C2×C3×#1504C2semidirect
4. C2×C3×#1438C2semidirect
5. C3×#8453C2direct (N × H)
6. C2×#8453C3direct (N × H)
7. C22×C3×H(5,𝔽2)C4semidirect
12. C3×#3484C4semidirect
16. C2×C3×#535C4semidirect
20. C2×C3×#518C4semidirect
23. C2×C3×#407C22semidirect
24. C22×C3×#95C22semidirect
26. C3×#1783C22semidirect
28. C3×#1504C22semidirect
32. C3×#1438C22semidirect
34. C2×#1783C2×C3semidirect
35. C2×#1504C2×C3semidirect
36. C2×#1438C2×C3semidirect
37. #8453C2×C3direct (N × H)
42. C2×C3×H(5,𝔽2)C2×C4semidirect
72. C3×#535C2×C4semidirect
99. C3×#518C2×C4semidirect
112. C3×#407C23semidirect
117. C2×C3×#95C23semidirect
120. C22×H(5,𝔽2)C3×C4semidirect
125. #3484C3×C4semidirect
129. C2×#535C3×C4semidirect
133. C2×#518C3×C4semidirect
136. C2×#407C22×C3semidirect
137. C22×#95C22×C3semidirect
139. #1783C22×C3semidirect
141. #1504C22×C3semidirect
145. #1438C22×C3semidirect
167. C2×C3×#41C22⋊C4semidirect
169. C22×C3×Q8C22⋊C4semidirect
208. C22×C3×D4C22⋊C4semidirect
246. C3×C22⋊Q8C22⋊C4semidirect
254. C3×#121C22⋊C4semidirect
273. C3×#117C22⋊C4semidirect
276. C2×C3×C4⋊C4C22⋊C4semidirect
299. C2×H(5,𝔽2)C2×C3×C4semidirect
329. #535C2×C3×C4semidirect
356. #518C2×C3×C4semidirect
369. #407C23×C3semidirect
374. C2×#95C23×C3semidirect
432. C2×C3×Q8C2×C22⋊C4semidirect
478. C2×C3×D4C2×C22⋊C4semidirect
528. C3×C4⋊C4C2×C22⋊C4semidirect
561. C2×#41C3×C22⋊C4semidirect
563. C22×Q8C3×C22⋊C4semidirect
602. C22×D4C3×C22⋊C4semidirect
640. C22⋊Q8C3×C22⋊C4semidirect
648. #121C3×C22⋊C4semidirect
667. #117C3×C22⋊C4semidirect
670. C2×C4⋊C4C3×C22⋊C4semidirect
861. C2×Q8C2×C3×C22⋊C4semidirect
907. C2×D4C2×C3×C22⋊C4semidirect
957. C4⋊C4C2×C3×C22⋊C4semidirect
1143. C2×C3#8453direct (N × H)
1195. C3C2×#8453direct (N × H)
1204. C2C3×#8453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#34842
C2×C3×#17832
C2×C3×#15042
C2×C3×#14382
C3×#84532
C2×#84533