Finite Group Databasebeta

← C3×#14911 #10633518

Subgroups — C3×#14911 #10633518

Order 768.

4146 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×C3×#120C211yesmaximal, characteristic
3C23×C3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#386C211yesmaximal, characteristic, complemented
5C2×C3×#381C211yesmaximal, characteristic, complemented
6C2×C3×#379C211yesmaximal, characteristic, complemented
7C3×#1439C214yesmaximal, complemented
8C3×#1438C214yesmaximal, complemented
9C3×C22⋊#95C211yesmaximal, characteristic, complemented
10#14911C311yesmaximal, characteristic, direct product factor, Sylow
11C26×C3C2211yescharacteristic
12C23×C3×D4C2211yescharacteristic
13C23×C3×D4C2212yes—
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C2×C3×#123—24no—
17C2×C3×#123—24no—
18C2×C3×#123—24no—
19C2×C3×#120—24no—
20C2×C3×#120—24no—
21C2×C3×#120—24no—
22C22×C3×C4⋊C4C2212yescomplemented
23C22×C3×C22⋊C4—24no—
24C22×C3×C22⋊C4—24no—
25C22×C3×C22⋊C4—24no—
26C22×C3×C22⋊C4C2214yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2214yes—
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2212yescomplemented
33C22×C3×C22⋊C4C2212yescomplemented
34C3×#386—24no—
35C3×#381—24no—
36C3×#379—24no—
37C2×C3×#95C2214yescomplemented
38C2×C3×#95C2212yescomplemented
39C2×C3×#95C2214yescomplemented
40C22×#123C2×C311yescharacteristic, complemented
41C22×#120C2×C311yescharacteristic
42C23×C22⋊C4C2×C311yescharacteristic, complemented
43C2×#386C2×C311yescharacteristic, complemented
44C2×#381C2×C311yescharacteristic, complemented
45C2×#379C2×C311yescharacteristic, complemented
46#1439C2×C314yescomplemented
47#1438C2×C314yescomplemented
48C22⋊#95C2×C311yescharacteristic, complemented
49C25×C3—22no—
50C25×C3—22no—
51C25×C3—28no—
52C25×C3—22no—
53C25×C3—22no—
54C25×C3—22no—
55C25×C3—22no—
56C25×C3—44no—
57C25×C3D414yes—
58C25×C3C2311yescharacteristic
59C25×C3C2312yes—
60C25×C3C2311yescharacteristic
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—28no—
70C22×C3×D4—24no—
71C22×C3×D4—44no—
72C22×C3×D4D414yes—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—44no—
82C23×C3×C4D414yescomplemented
83C23×C3×C4D414yescomplemented
84C23×C3×C4C2312yes—
85C23×C3×C4C2312yes—
86C23×C3×C4C2312yes—
87C23×C3×C4C2312yes—
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2312yes—
90C3×#123—232no—
91C3×#120—232no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C4⋊C4—24no—
95C2×C3×C22⋊C4—232no—
96C2×C3×C22⋊C4—28no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—28no—
104C2×C3×C22⋊C4—28no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—28no—
113C2×C3×C22⋊C4—28no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—44no—
116C2×C3×C22⋊C4—44no—
117C2×C3×C22⋊C4D414yes—
118C2×C3×C22⋊C4D414yescomplemented
119C3×#95—28no—
120C3×#95—24no—
121C3×#95—44no—
122C26C22×C311yescharacteristic
123C23×D4C22×C311yescharacteristic
124C23×D4C22×C312yes—
125C24×C4C22×C311yescharacteristic
126C24×C4C22×C311yescharacteristic
127C2×#123—24no—
128C2×#123—24no—
129C2×#123—24no—
130C2×#120—24no—
131C2×#120—24no—
132C2×#120—24no—
133C22×C4⋊C4C22×C312yescomplemented
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4C22×C314yes—
138C22×C22⋊C4C22×C312yes—
139C22×C22⋊C4C22×C311yescharacteristic
140C22×C22⋊C4C22×C314yes—
141C22×C22⋊C4C22×C311yescharacteristic
142C22×C22⋊C4C22×C311yescharacteristic
143C22×C22⋊C4C22×C312yescomplemented
144C22×C22⋊C4C22×C312yescomplemented
145#386—24no—
146#381—24no—
147#379—24no—
148C2×#95C22×C314yescomplemented
149C2×#95C22×C312yescomplemented
150C2×#95C22×C314yescomplemented
151C24×C3—24no—
152C24×C3—24no—
153C24×C3—216no—
154C24×C3—216no—
155C24×C3—28no—
156C24×C3—216no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—24no—
164C24×C3—24no—
165C24×C3—24no—
166C24×C3—28no—
167C24×C3—28no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—24no—
175C24×C3—24no—
176C24×C3—48no—
177C24×C3—416no—
178C24×C3—416no—
179C24×C3—416no—
180C24×C3—416no—
181C24×C3—48no—
182C24×C3—48no—
183C24×C3—44no—
184C24×C3—44no—
185C24×C3—44no—
186C24×C3—44no—
187C24×C3C2×D412yes—
188C24×C3C2×D414yes—
189C24×C3C2×D412yes—
190C24×C3C2×D412yes—
191C24×C3C2×D412yes—
192C24×C3C2×D412yes—
193C24×C3C2×D412yes—
194C24×C3C2×D412yes—
195C24×C3#4118yes—
196C24×C3#4112yes—
197C24×C3C2411yescharacteristic
198C2×C3×D4—216no—
199C2×C3×D4—28no—
200C2×C3×D4—28no—
201C2×C3×D4—28no—
202C2×C3×D4—416no—
203C2×C3×D4—416no—
204C2×C3×D4—48no—
205C2×C3×D4—44no—
206C2×C3×D4—44no—
207C2×C3×D4—44no—
208C2×C3×D4—48no—
209C2×C3×D4—44no—
210C22×C3×C4—28no—
211C22×C3×C4—28no—
212C22×C3×C4—28no—
213C22×C3×C4—28no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—24no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4—24no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—24no—
242C22×C3×C4—24no—
243C22×C3×C4—48no—
244C22×C3×C4—48no—
245C22×C3×C4—48no—
246C22×C3×C4—44no—
247C22×C3×C4—44no—
248C22×C3×C4—44no—
249C22×C3×C4—44no—
250C22×C3×C4C2×D414yes—
251C22×C3×C4C2×D414yes—
252C22×C3×C4C2×D414yes—
253C22×C3×C4C2×D414yes—
254C22×C3×C4C2×D412yes—
255C3×C4⋊C4—216no—
256C3×C22⋊C4—232no—
257C3×C22⋊C4—216no—
258C3×C22⋊C4—216no—
259C3×C22⋊C4—28no—
260C3×C22⋊C4—28no—
261C3×C22⋊C4—416no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—44no—
264C25—22no—
265C25—22no—
266C25—28no—
267C25—22no—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—44no—
272C25C3×D414yes—
273C25C23×C311yescharacteristic
274C25C23×C312yes—
275C25C23×C311yescharacteristic
276C22×D4—24no—
277C22×D4—24no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—28no—
285C22×D4—24no—
286C22×D4—44no—
287C22×D4C3×D414yes—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—44no—
297C23×C4C3×D414yescomplemented
298C23×C4C3×D414yescomplemented
299C23×C4C23×C312yes—
300C23×C4C23×C312yes—
301C23×C4C23×C312yes—
302C23×C4C23×C312yes—
303C23×C4C23×C311yescharacteristic
304C23×C4C23×C312yes—
305#123—232no—
306#120—232no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C22⋊C4—232no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4C3×D414yes—
333C2×C22⋊C4C3×D414yescomplemented
334#95—28no—
335#95—24no—
336#95—44no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—28no—
344C23×C3—28no—
345C23×C3—28no—
346C23×C3—28no—
347C23×C3—232no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—28no—
353C23×C3—28no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—28no—
357C23×C3—28no—
358C23×C3—28no—
359C23×C3—28no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—28no—
364C23×C3—432no—
365C23×C3—432no—
366C23×C3—416no—
367C23×C3—432no—
368C23×C3—432no—
369C23×C3—432no—
370C23×C3—432no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—44no—
376C23×C3—44no—
377C23×C3—44no—
378C23×C3—44no—
379C23×C3—44no—
380C23×C3—44no—
381C23×C3—416no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—41no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3#12014yes—
396C23×C3#12014yes—
397C23×C3#12014yes—
398C23×C3#12114yes—
399C23×C3#12114yes—
400C23×C3#12114yes—
401C23×C3#12318yescomplemented
402C23×C3#12714yes—
403C23×C3C22×D411yescharacteristic
404C23×C3C22×D411yescharacteristic
405C23×C3C22×D411yescharacteristic
406C23×C3C22×D411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C2×#4111yescharacteristic
410C23×C3C2×#4114yes—
411C23×C3H(5,𝔽2)14yes—
412C3×D4—432no—
413C3×D4—416no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—28no—
426C2×C3×C4—28no—
427C2×C3×C4—416no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—41no—
438C2×C3×C4—44no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4—416no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—44no—
449C2×C3×C4—44no—
450C24—24no—
451C24—24no—
452C24—216no—
453C24—216no—
454C24—28no—
455C24—216no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—24no—
464C24—24no—
465C24—28no—
466C24—28no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—24no—
474C24—24no—
475C24—48no—
476C24—416no—
477C24—416no—
478C24—416no—
479C24—416no—
480C24—48no—
481C24—48no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24C2×C3×D412yes—
487C24C2×C3×D414yes—
488C24C2×C3×D412yes—
489C24C2×C3×D412yes—
490C24C2×C3×D412yes—
491C24C2×C3×D412yes—
492C24C2×C3×D412yes—
493C24C2×C3×D412yes—
494C24C3×#4118yes—
495C24C3×#4112yes—
496C24C24×C311yescharacteristic
497C2×D4—216no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—416no—
502C2×D4—416no—
503C2×D4—48no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—44no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4C2×C3×D414yes—
550C22×C4C2×C3×D414yes—
551C22×C4C2×C3×D414yes—
552C22×C4C2×C3×D414yes—
553C22×C4C2×C3×D412yes—
554C4⋊C4—216no—
555C22⋊C4—232no—
556C22⋊C4—216no—
557C22⋊C4—216no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—416no—
561C22⋊C4—48no—
562C22⋊C4—44no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—28no—
572C22×C3—28no—
573C22×C3—28no—
574C22×C3—464no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—48no—
578C22×C3—44no—
579C22×C3—48no—
580C22×C3—44no—
581C22×C3—48no—
582C22×C3—48no—
583C22×C3—42no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3#39218yes—
593C22×C3C2×#12011yescharacteristic
594C22×C3C2×#12011yescharacteristic
595C22×C3C2×#12011yescharacteristic
596C22×C3C2×#12111yescharacteristic
597C22×C3C2×#12111yescharacteristic
598C22×C3C2×#12111yescharacteristic
599C22×C3C2×#12312yes—
600C22×C3#52512yes—
601C22×C3#52512yes—
602C22×C3C2×#12711yescharacteristic
603C22×C3#53412yes—
604C22×C3#53412yes—
605C22×C3#53512yes—
606C22×C3#54614yes—
607C22×C3#54614yes—
608C22×C3#54614yes—
609C22×C3#55114yes—
610C3×C4—44no—
611C3×C4—44no—
612C3×C4—42no—
613C3×C4—44no—
614C3×C4—44no—
615C3×C4—82no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—232no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—28no—
632C23—28no—
633C23—24no—
634C23—24no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—432no—
644C23—432no—
645C23—432no—
646C23—432no—
647C23—432no—
648C23—432no—
649C23—416no—
650C23—416no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23C3×#12014yes—
675C23C3×#12014yes—
676C23C3×#12014yes—
677C23C3×#12114yes—
678C23C3×#12114yes—
679C23C3×#12114yes—
680C23C3×#12318yescomplemented
681C23C3×#12714yes—
682C23C22×C3×D411yescharacteristic
683C23C22×C3×D411yescharacteristic
684C23C22×C3×D411yescharacteristic
685C23C22×C3×D411yescharacteristic
686C23C22×C3×D411yescharacteristic
687C23C22×C3×D411yescharacteristic
688C23C2×C3×#4111yescharacteristic
689C23C2×C3×#4114yes—
690C23C3×H(5,𝔽2)14yes—
691D4—432no—
692D4—416no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—416no—
707C2×C4—416no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C3—28no—
730C2×C3—48no—
731C2×C3—82no—
732C2×C3C2×#39211yescharacteristic
733C2×C3#240412yes—
734C2×C3#240512yes—
735C2×C3#241112yes—
736C2×C3#241212yes—
737C2×C3#253412yes—
738C2×C3#253912yes—
739C2×C3#261311yescharacteristic
740C2×C3#284911yescharacteristic
741C22—28no—
742C22—28no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—24no—
748C22—24no—
749C22—28no—
750C22—28no—
751C22—28no—
752C22—464no—
753C22—44no—
754C22—48no—
755C22—44no—
756C22—48no—
757C22—44no—
758C22—48no—
759C22—48no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—81no—
769C22—81no—
770C22C3×#39218yes—
771C22C2×C3×#12011yescharacteristic
772C22C2×C3×#12011yescharacteristic
773C22C2×C3×#12011yescharacteristic
774C22C2×C3×#12111yescharacteristic
775C22C2×C3×#12111yescharacteristic
776C22C2×C3×#12111yescharacteristic
777C22C2×C3×#12312yes—
778C22C3×#52512yes—
779C22C3×#52512yes—
780C22C2×C3×#12711yescharacteristic
781C22C3×#53412yes—
782C22C3×#53412yes—
783C22C3×#53512yes—
784C22C3×#54614yes—
785C22C3×#54614yes—
786C22C3×#54614yes—
787C22C3×#55114yes—
788C4—44no—
789C4—42no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4—82no—
794C3#1491111yescharacteristic, direct product factor, Sylow
795C2—28no—
796C2—48no—
797C2—82no—
798C2C2×C3×#39211yescharacteristic
799C2C3×#240412yes—
800C2C3×#240512yes—
801C2C3×#241112yes—
802C2C3×#241212yes—
803C2C3×#253412yes—
804C2C3×#253912yes—
805C2C3×#261311yescharacteristic
806C2C3×#284911yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC22×C3×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C23×C3×C22⋊C4C2semidirect
4. C2×C3×#386C2semidirect
5. C2×C3×#381C2semidirect
6. C2×C3×#379C2semidirect
7. C3×#1439C2semidirect
8. C3×#1438C2semidirect
9. C3×C22⋊#95C2semidirect
10. #14911C3direct (N × H)
22. C22×C3×C4⋊C4C22semidirect
32. C22×C3×C22⋊C4C22semidirect
33. C22×C3×C22⋊C4C22semidirect
37. C2×C3×#95C22semidirect
38. C2×C3×#95C22semidirect
39. C2×C3×#95C22semidirect
40. C22×#123C2×C3semidirect
42. C23×C22⋊C4C2×C3semidirect
43. C2×#386C2×C3semidirect
44. C2×#381C2×C3semidirect
45. C2×#379C2×C3semidirect
46. #1439C2×C3semidirect
47. #1438C2×C3semidirect
48. C22⋊#95C2×C3semidirect
82. C23×C3×C4D4semidirect
83. C23×C3×C4D4semidirect
118. C2×C3×C22⋊C4D4semidirect
133. C22×C4⋊C4C22×C3semidirect
143. C22×C22⋊C4C22×C3semidirect
144. C22×C22⋊C4C22×C3semidirect
148. C2×#95C22×C3semidirect
149. C2×#95C22×C3semidirect
150. C2×#95C22×C3semidirect
297. C23×C4C3×D4semidirect
298. C23×C4C3×D4semidirect
333. C2×C22⋊C4C3×D4semidirect
401. C23×C3#123semidirect
680. C23C3×#123semidirect
794. C3#14911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×#1202
C23×C3×C22⋊C42
C2×C3×#3862
C2×C3×#3812
C2×C3×#3792
C3×#14392
C3×#14382
C3×C22⋊#952
#149113