Finite Group Databasebeta

← C3×#14921 #10633528

Subgroups — C3×#14921 #10633528

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#385C211yesmaximal, characteristic, complemented
5C2×C3×#380C211yesmaximal, characteristic, complemented
6C22×C3×#95C211yesmaximal, characteristic, complemented
7C3×#1443C212yesmaximal, complemented
8C3×#1441C212yesmaximal, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1439C212yesmaximal, complemented
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#14921C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2211yescharacteristic
26C3×#386—24no—
27C3×#386—24no—
28C3×#386—24no—
29C3×#385—24no—
30C3×#380—24no—
31C2×C3×#95—24no—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×#386C2×C311yescharacteristic
43C2×#386C2×C311yescharacteristic
44C2×#386C2×C311yescharacteristic
45C2×#385C2×C311yescharacteristic, complemented
46C2×#380C2×C311yescharacteristic, complemented
47C22×#95C2×C311yescharacteristic, complemented
48#1443C2×C312yescomplemented
49#1441C2×C312yescomplemented
50#1439C2×C312yescomplemented
51#1439C2×C312yescomplemented
52C22⋊#95C2×C311yescharacteristic, complemented
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4Q814yes—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—24no—
68C23×C3×C4—24no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—42no—
72C23×C3×C4—42no—
73C23×C3×C4—42no—
74C23×C3×C4—42no—
75C23×C3×C4D414yes—
76C23×C3×C4D414yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2312yes—
82C23×C3×C4C2312yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2312yes—
85C23×C3×C4C2311yescharacteristic
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—42no—
90C2×C3×C4⋊C4—42no—
91C2×C3×C4⋊C4—42no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4—42no—
109C2×C3×C22⋊C4—42no—
110C2×C3×C22⋊C4D414yes—
111C3×#95—24no—
112C3×#95—24no—
113C3×#95—24no—
114C3×#95—24no—
115C3×#95—24no—
116C3×#95—22no—
117C3×#95—24no—
118C3×#95—22no—
119C3×#95—24no—
120C3×#95—42no—
121C23×D4C22×C311yescharacteristic
122C24×C4C22×C311yescharacteristic
123C24×C4C22×C311yescharacteristic
124C24×C4C22×C311yescharacteristic
125C22×C4⋊C4C22×C312yes—
126C22×C4⋊C4C22×C312yes—
127C22×C22⋊C4C22×C311yescharacteristic
128C22×C22⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C311yescharacteristic
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C311yescharacteristic
132C22×C22⋊C4C22×C311yescharacteristic
133C22×C22⋊C4C22×C312yes—
134#386—24no—
135#386—24no—
136#386—24no—
137#385—24no—
138#380—24no—
139C2×#95—24no—
140C2×#95C22×C312yes—
141C2×#95C22×C312yes—
142C2×#95C22×C312yes—
143C2×#95C22×C312yes—
144C2×#95C22×C312yes—
145C2×#95C22×C311yescharacteristic
146C2×#95C22×C312yes—
147C2×#95C22×C312yes—
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3C2×D412yes—
165C24×C3C2×D412yes—
166C24×C3C2×D412yes—
167C24×C3C2×Q812yes—
168C24×C3C2×Q812yes—
169C24×C3#4112yes—
170C24×C3#4112yes—
171C24×C3#4112yes—
172C24×C3C2411yescharacteristic
173C2×C3×D4—28no—
174C2×C3×D4—28no—
175C2×C3×D4—28no—
176C2×C3×D4—44no—
177C2×C3×D4—44no—
178C2×C3×D4—44no—
179C2×C3×D4—44no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—28no—
184C22×C3×C4—28no—
185C22×C3×C4—28no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—28no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—44no—
233C22×C3×C4—48no—
234C22×C3×C4—48no—
235C22×C3×C4—48no—
236C22×C3×C4—48no—
237C22×C3×C4—48no—
238C22×C3×C4—44no—
239C22×C3×C4—44no—
240C22×C3×C4—44no—
241C22×C3×C4—48no—
242C22×C3×C4—44no—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D414yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×Q812yes—
248C22×C3×C4#4114yes—
249C22×C3×C4#4114yes—
250C3×C4⋊C4—48no—
251C3×C4⋊C4—48no—
252C3×C22⋊C4—28no—
253C3×C22⋊C4—48no—
254C3×C22⋊C4—48no—
255C3×C22⋊C4—44no—
256C3×C22⋊C4—44no—
257C3×C22⋊C4—44no—
258C3×C22⋊C4—44no—
259C25C23×C311yescharacteristic
260C25C23×C311yescharacteristic
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4C3×Q814yes—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C3×D414yes—
282C23×C4C3×D414yes—
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C312yes—
285C23×C4C23×C311yescharacteristic
286C23×C4C23×C312yes—
287C23×C4C23×C312yes—
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C311yescharacteristic
290C23×C4C23×C312yes—
291C23×C4C23×C311yescharacteristic
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4C3×D414yes—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—22no—
323#95—24no—
324#95—22no—
325#95—24no—
326#95—42no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3#12114yes—
367C23×C3#12114yes—
368C23×C3#12114yes—
369C23×C3C22⋊Q814yes—
370C23×C3C22⋊Q814yes—
371C23×C3C22⋊Q814yes—
372C23×C3#12614yes—
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×Q811yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4112yes—
381C23×C3C2×#4112yes—
382C23×C3H(5,𝔽2)12yes—
383C23×C3H(5,𝔽2)12yes—
384C3×D4—416no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—416no—
405C2×C3×C4—416no—
406C2×C3×C4—416no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—41no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4#12314yes—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24C2×C3×D412yes—
458C24C2×C3×D412yes—
459C24C2×C3×D412yes—
460C24C2×C3×Q812yes—
461C24C2×C3×Q812yes—
462C24C3×#4112yes—
463C24C3×#4112yes—
464C24C3×#4112yes—
465C24C24×C311yescharacteristic
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4C2×C3×D412yes—
537C22×C4C2×C3×D414yes—
538C22×C4C2×C3×D414yes—
539C22×C4C2×C3×D412yes—
540C22×C4C2×C3×Q812yes—
541C22×C4C3×#4114yes—
542C22×C4C3×#4114yes—
543C4⋊C4—48no—
544C4⋊C4—48no—
545C22⋊C4—28no—
546C22⋊C4—48no—
547C22⋊C4—48no—
548C22⋊C4—44no—
549C22⋊C4—44no—
550C22⋊C4—44no—
551C22⋊C4—44no—
552C22×C3—28no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—28no—
559C22×C3—24no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—44no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—44no—
566C22×C3—42no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3—82no—
572C22×C3—82no—
573C22×C3#39618yes—
574C22×C3C2×#12111yescharacteristic
575C22×C3C2×#12111yescharacteristic
576C22×C3C2×#12111yescharacteristic
577C22×C3C2×C22⋊Q811yescharacteristic
578C22×C3C2×C22⋊Q811yescharacteristic
579C22×C3C2×C22⋊Q811yescharacteristic
580C22×C3C2×#12311yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3C2×#12611yescharacteristic
583C22×C3#52912yes—
584C22×C3#53212yes—
585C22×C3#53412yes—
586C22×C3#53411yescharacteristic
587C22×C3#53511yescharacteristic
588C22×C3#53812yes—
589C22×C3#54612yes—
590C22×C3#54612yes—
591C22×C3#55112yes—
592C22×C3#55112yes—
593C22×C3#55312yes—
594C22×C3#55312yes—
595C22×C3#55412yes—
596C22×C3#55412yes—
597C3×C4—24no—
598C3×C4—44no—
599C3×C4—42no—
600C3×C4—44no—
601C3×C4—42no—
602C3×C4—44no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4—82no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C3×#12114yes—
646C23C3×#12114yes—
647C23C3×#12114yes—
648C23C3×C22⋊Q814yes—
649C23C3×C22⋊Q814yes—
650C23C3×C22⋊Q814yes—
651C23C3×#12614yes—
652C23C22×C3×D411yescharacteristic
653C23C22×C3×D411yescharacteristic
654C23C22×C3×D411yescharacteristic
655C23C22×C3×Q811yescharacteristic
656C23C2×C3×#4111yescharacteristic
657C23C2×C3×#4111yescharacteristic
658C23C2×C3×#4111yescharacteristic
659C23C2×C3×#4112yes—
660C23C2×C3×#4112yes—
661C23C3×H(5,𝔽2)12yes—
662C23C3×H(5,𝔽2)12yes—
663D4—416no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—416no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C3×#12314yes—
722C2×C3—28no—
723C2×C3—82no—
724C2×C3C2×#39611yescharacteristic
725C2×C3#241111yescharacteristic
726C2×C3#241211yescharacteristic
727C2×C3#245012yes—
728C2×C3#248711yescharacteristic
729C2×C3#251012yes—
730C2×C3#254312yes—
731C2×C3#256412yes—
732C2×C3#257911yescharacteristic
733C2×C3#261711yescharacteristic
734C2×C3#285411yescharacteristic
735C22—24no—
736C22—24no—
737C22—24no—
738C22—28no—
739C22—24no—
740C22—28no—
741C22—28no—
742C22—28no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—44no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—82no—
754C22—82no—
755C22—81no—
756C22C3×#39618yes—
757C22C2×C3×#12111yescharacteristic
758C22C2×C3×#12111yescharacteristic
759C22C2×C3×#12111yescharacteristic
760C22C2×C3×C22⋊Q811yescharacteristic
761C22C2×C3×C22⋊Q811yescharacteristic
762C22C2×C3×C22⋊Q811yescharacteristic
763C22C2×C3×#12311yescharacteristic
764C22C3×#52511yescharacteristic
765C22C2×C3×#12611yescharacteristic
766C22C3×#52912yes—
767C22C3×#53212yes—
768C22C3×#53411yescharacteristic
769C22C3×#53412yes—
770C22C3×#53511yescharacteristic
771C22C3×#53812yes—
772C22C3×#54612yes—
773C22C3×#54612yes—
774C22C3×#55112yes—
775C22C3×#55112yes—
776C22C3×#55312yes—
777C22C3×#55312yes—
778C22C3×#55412yes—
779C22C3×#55412yes—
780C4—24no—
781C4—44no—
782C4—42no—
783C4—44no—
784C4—42no—
785C4—44no—
786C4—81no—
787C4—82no—
788C4—81no—
789C3#1492111yescharacteristic, direct product factor, Sylow
790C2—28no—
791C2—82no—
792C2C2×C3×#39611yescharacteristic
793C2C3×#241111yescharacteristic
794C2C3×#241211yescharacteristic
795C2C3×#245012yes—
796C2C3×#248711yescharacteristic
797C2C3×#251012yes—
798C2C3×#254312yes—
799C2C3×#256412yes—
800C2C3×#257911yescharacteristic
801C2C3×#261711yescharacteristic
802C2C3×#285411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C3×#385C2semidirect
5. C2×C3×#380C2semidirect
6. C22×C3×#95C2semidirect
7. C3×#1443C2semidirect
8. C3×#1441C2semidirect
9. C3×#1439C2semidirect
10. C3×#1439C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14921C3direct (N × H)
45. C2×#385C2×C3semidirect
46. C2×#380C2×C3semidirect
47. C22×#95C2×C3semidirect
48. #1443C2×C3semidirect
49. #1441C2×C3semidirect
50. #1439C2×C3semidirect
51. #1439C2×C3semidirect
52. C22⋊#95C2×C3semidirect
789. C3#14921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×C3×#3852
C2×C3×#3802
C22×C3×#952
C3×#14432
C3×#14412
C3×#14392
C3×C22⋊#952
#149213