Finite Group Databasebeta

← C3×#14725 #10633332

Subgroups — C3×#14725 #10633332

Order 768.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#120C211yesmaximal, characteristic
2C23×C3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#394C212yesmaximal, complemented
4C2×C3×#386C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic, complemented
6C2×C3×#380C211yesmaximal, characteristic, complemented
7C2×C3×#379C211yesmaximal, characteristic, complemented
8C3×#1440C212yesmaximal, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1438C212yesmaximal, complemented
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#14725C311yesmaximal, characteristic, direct product factor, Sylow
13C26×C3C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2212yes—
16C24×C3×C4C2211yescharacteristic
17C24×C3×C4C2211yescharacteristic
18C2×C3×#120—24no—
19C2×C3×#120—24no—
20C2×C3×#120—24no—
21C22×C3×C4⋊C4C2212yescomplemented
22C22×C3×C22⋊C4—24no—
23C22×C3×C22⋊C4—28no—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C22⋊C4C2212yes—
32C22×C3×C22⋊C4C2211yescharacteristic, complemented
33C22×C3×C22⋊C4C2212yescomplemented
34C22×C3×C22⋊C4C2211yescharacteristic, complemented
35C3×#394—28no—
36C3×#386—24no—
37C3×#386—24no—
38C3×#380—24no—
39C3×#379—24no—
40C2×C3×#95C2212yescomplemented
41C2×C3×#95C2212yescomplemented
42C2×C3×#95C2211yescharacteristic, complemented
43C2×C3×#95C2212yescomplemented
44C2×C3×#95C2211yescharacteristic, complemented
45C2×C3×#95C2212yescomplemented
46C22×#120C2×C311yescharacteristic
47C23×C22⋊C4C2×C311yescharacteristic, complemented
48C2×#394C2×C312yescomplemented
49C2×#386C2×C311yescharacteristic, complemented
50C2×#386C2×C311yescharacteristic, complemented
51C2×#380C2×C311yescharacteristic, complemented
52C2×#379C2×C311yescharacteristic, complemented
53#1440C2×C312yescomplemented
54#1439C2×C312yescomplemented
55#1438C2×C312yescomplemented
56C22⋊#95C2×C311yescharacteristic, complemented
57C25×C3—24no—
58C25×C3—22no—
59C25×C3—24no—
60C25×C3—22no—
61C25×C3—22no—
62C25×C3—22no—
63C25×C3—22no—
64C25×C3—22no—
65C25×C3—42no—
66C25×C3—42no—
67C25×C3D414yes—
68C25×C3C2311yescharacteristic
69C25×C3C2312yes—
70C25×C3C2311yescharacteristic
71C22×C3×D4—22no—
72C22×C3×D4—24no—
73C22×C3×D4—24no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—24no—
80C22×C3×D4—24no—
81C22×C3×D4—24no—
82C22×C3×D4—42no—
83C22×C3×D4—42no—
84C22×C3×D4D414yes—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—24no—
89C23×C3×C4—24no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—42no—
93C23×C3×C4—42no—
94C23×C3×C4D414yescomplemented
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2312yes—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2312yes—
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2312yes—
102C23×C3×C4C2311yescharacteristic
103C3×#120—232no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4—24no—
106C2×C3×C4⋊C4—42no—
107C2×C3×C22⋊C4—232no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—24no—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—24no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—24no—
126C2×C3×C22⋊C4—24no—
127C2×C3×C22⋊C4—24no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—24no—
133C2×C3×C22⋊C4—42no—
134C2×C3×C22⋊C4—42no—
135C2×C3×C22⋊C4—42no—
136C2×C3×C22⋊C4—42no—
137C2×C3×C22⋊C4D414yes—
138C2×C3×C22⋊C4D418yescomplemented
139C3×#95—24no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—24no—
143C3×#95—24no—
144C3×#95—42no—
145C26C22×C311yescharacteristic
146C23×D4C22×C311yescharacteristic
147C23×D4C22×C312yes—
148C24×C4C22×C311yescharacteristic
149C24×C4C22×C311yescharacteristic
150C2×#120—24no—
151C2×#120—24no—
152C2×#120—24no—
153C22×C4⋊C4C22×C312yescomplemented
154C22×C22⋊C4—24no—
155C22×C22⋊C4—28no—
156C22×C22⋊C4C22×C312yes—
157C22×C22⋊C4C22×C312yes—
158C22×C22⋊C4C22×C312yes—
159C22×C22⋊C4C22×C311yescharacteristic
160C22×C22⋊C4C22×C311yescharacteristic
161C22×C22⋊C4C22×C311yescharacteristic
162C22×C22⋊C4C22×C312yes—
163C22×C22⋊C4C22×C312yes—
164C22×C22⋊C4C22×C311yescharacteristic, complemented
165C22×C22⋊C4C22×C312yescomplemented
166C22×C22⋊C4C22×C311yescharacteristic, complemented
167#394—28no—
168#386—24no—
169#386—24no—
170#380—24no—
171#379—24no—
172C2×#95C22×C312yescomplemented
173C2×#95C22×C312yescomplemented
174C2×#95C22×C311yescharacteristic, complemented
175C2×#95C22×C312yescomplemented
176C2×#95C22×C311yescharacteristic, complemented
177C2×#95C22×C312yescomplemented
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—28no—
183C24×C3—216no—
184C24×C3—28no—
185C24×C3—216no—
186C24×C3—28no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—22no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3—22no—
198C24×C3—22no—
199C24×C3—28no—
200C24×C3—28no—
201C24×C3—21no—
202C24×C3—22no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—22no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—48no—
212C24×C3—48no—
213C24×C3—48no—
214C24×C3—48no—
215C24×C3—48no—
216C24×C3—48no—
217C24×C3—48no—
218C24×C3—48no—
219C24×C3—48no—
220C24×C3—44no—
221C24×C3—44no—
222C24×C3—48no—
223C24×C3—44no—
224C24×C3—44no—
225C24×C3—44no—
226C24×C3—44no—
227C24×C3C2×D412yes—
228C24×C3C2×D414yes—
229C24×C3C2×D414yes—
230C24×C3C2×D412yes—
231C24×C3C2×D412yes—
232C24×C3C2×D412yes—
233C24×C3C2×D412yes—
234C24×C3#4114yes—
235C24×C3#4112yes—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C2×C3×D4—216no—
240C2×C3×D4—28no—
241C2×C3×D4—28no—
242C2×C3×D4—28no—
243C2×C3×D4—48no—
244C2×C3×D4—48no—
245C2×C3×D4—48no—
246C2×C3×D4—48no—
247C2×C3×D4—48no—
248C2×C3×D4—48no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—22no—
256C22×C3×C4—28no—
257C22×C3×C4—28no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—28no—
281C22×C3×C4—21no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—21no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—22no—
290C22×C3×C4—21no—
291C22×C3×C4—22no—
292C22×C3×C4—21no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—44no—
299C22×C3×C4—48no—
300C22×C3×C4—48no—
301C22×C3×C4—48no—
302C22×C3×C4—48no—
303C22×C3×C4—44no—
304C22×C3×C4—44no—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D414yes—
308C22×C3×C4C2×D414yes—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D414yes—
311C3×C4⋊C4—48no—
312C3×C22⋊C4—216no—
313C3×C22⋊C4—216no—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—216no—
316C3×C22⋊C4—48no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—48no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—48no—
321C3×C22⋊C4—44no—
322C3×C22⋊C4—44no—
323C25—24no—
324C25—22no—
325C25—24no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—22no—
331C25—42no—
332C25—42no—
333C25C3×D414yes—
334C25C23×C311yescharacteristic
335C25C23×C312yes—
336C25C23×C311yescharacteristic
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4C3×D414yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4C3×D414yescomplemented
361C23×C4C23×C312yes—
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C312yes—
366C23×C4C23×C312yes—
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369#120—232no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—42no—
373C2×C22⋊C4—232no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4C3×D414yes—
404C2×C22⋊C4C3×D418yescomplemented
405#95—24no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—42no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—22no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—232no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—432no—
452C23×C3—432no—
453C23×C3—416no—
454C23×C3—416no—
455C23×C3—416no—
456C23×C3—416no—
457C23×C3—432no—
458C23×C3—432no—
459C23×C3—416no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3—42no—
473C23×C3—42no—
474C23×C3—42no—
475C23×C3—42no—
476C23×C3—416no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—42no—
481C23×C3—41no—
482C23×C3—42no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—42no—
487C23×C3—41no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3#12014yes—
496C23×C3#12118yes—
497C23×C3#12114yes—
498C23×C3#12114yes—
499C23×C3#12114yes—
500C23×C3#12314yes—
501C23×C3#12314yes—
502C23×C3#12414yes—
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D411yescharacteristic
505C23×C3C22×D411yescharacteristic
506C23×C3C22×D412yes—
507C23×C3C22×D411yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4112yes—
512C23×C3H(5,𝔽2)12yes—
513C23×C3H(5,𝔽2)12yes—
514C3×D4—432no—
515C3×D4—416no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—24no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—24no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—416no—
533C2×C3×C4—416no—
534C2×C3×C4—42no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—42no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—42no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—42no—
547C2×C3×C4—42no—
548C2×C3×C4—41no—
549C2×C3×C4—42no—
550C2×C3×C4—41no—
551C2×C3×C4—42no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—41no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—41no—
558C2×C3×C4—42no—
559C2×C3×C4—41no—
560C2×C3×C4—42no—
561C2×C3×C4—42no—
562C2×C3×C4—42no—
563C2×C3×C4—42no—
564C2×C3×C4—42no—
565C2×C3×C4#12014yescomplemented
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—28no—
571C24—28no—
572C24—216no—
573C24—216no—
574C24—28no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—28no—
588C24—28no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—48no—
608C24—44no—
609C24—44no—
610C24—48no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24—44no—
615C24C2×C3×D412yes—
616C24C2×C3×D414yes—
617C24C2×C3×D414yes—
618C24C2×C3×D412yes—
619C24C2×C3×D412yes—
620C24C2×C3×D412yes—
621C24C2×C3×D412yes—
622C24C3×#4114yes—
623C24C3×#4112yes—
624C24C3×#4112yes—
625C24C3×#4112yes—
626C24C24×C311yescharacteristic
627C2×D4—216no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—44no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4C2×C3×D412yes—
694C22×C4C2×C3×D412yes—
695C22×C4C2×C3×D414yes—
696C22×C4C2×C3×D414yes—
697C22×C4C2×C3×D412yes—
698C22×C4C2×C3×D414yes—
699C4⋊C4—48no—
700C22⋊C4—216no—
701C22⋊C4—216no—
702C22⋊C4—28no—
703C22⋊C4—216no—
704C22⋊C4—48no—
705C22⋊C4—44no—
706C22⋊C4—48no—
707C22⋊C4—44no—
708C22⋊C4—48no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—24no—
717C22×C3—28no—
718C22×C3—28no—
719C22×C3—28no—
720C22×C3—24no—
721C22×C3—28no—
722C22×C3—28no—
723C22×C3—28no—
724C22×C3—464no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—44no—
730C22×C3—44no—
731C22×C3—44no—
732C22×C3—44no—
733C22×C3—44no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—44no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—44no—
740C22×C3—44no—
741C22×C3—42no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—82no—
747C22×C3—82no—
748C22×C3#39418yescomplemented
749C22×C3C2×#12011yescharacteristic
750C22×C3C2×#12011yescharacteristic
751C22×C3C2×#12111yescharacteristic
752C22×C3C2×#12112yes—
753C22×C3C2×#12111yescharacteristic
754C22×C3C2×#12111yescharacteristic
755C22×C3C2×#12311yescharacteristic
756C22×C3C2×#12311yescharacteristic
757C22×C3#52511yescharacteristic
758C22×C3#52512yes—
759C22×C3C2×#12411yescharacteristic
760C22×C3#53412yes—
761C22×C3#53411yescharacteristic
762C22×C3#53511yescharacteristic
763C22×C3#53812yes—
764C22×C3D4212yes—
765C22×C3D4212yes—
766C22×C3#54612yes—
767C22×C3#54612yes—
768C22×C3#54612yes—
769C22×C3#54612yes—
770C22×C3#55112yes—
771C22×C3#55112yes—
772C3×C4—24no—
773C3×C4—42no—
774C3×C4—44no—
775C3×C4—42no—
776C3×C4—44no—
777C3×C4—81no—
778C3×C4—81no—
779C3×C4—82no—
780C23—22no—
781C23—24no—
782C23—22no—
783C23—24no—
784C23—22no—
785C23—24no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—232no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—24no—
820C23—432no—
821C23—432no—
822C23—416no—
823C23—416no—
824C23—416no—
825C23—416no—
826C23—432no—
827C23—432no—
828C23—416no—
829C23—416no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23C3×#12014yes—
865C23C3×#12118yes—
866C23C3×#12114yes—
867C23C3×#12114yes—
868C23C3×#12114yes—
869C23C3×#12314yes—
870C23C3×#12314yes—
871C23C3×#12414yes—
872C23C22×C3×D411yescharacteristic
873C23C22×C3×D411yescharacteristic
874C23C22×C3×D411yescharacteristic
875C23C22×C3×D412yes—
876C23C22×C3×D411yescharacteristic
877C23C2×C3×#4111yescharacteristic
878C23C2×C3×#4111yescharacteristic
879C23C2×C3×#4111yescharacteristic
880C23C2×C3×#4112yes—
881C23C3×H(5,𝔽2)12yes—
882C23C3×H(5,𝔽2)12yes—
883D4—432no—
884D4—416no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—42no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—42no—
921C2×C4—41no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4C3×#12014yescomplemented
935C2×C3—28no—
936C2×C3—48no—
937C2×C3—82no—
938C2×C3C2×#39411yescharacteristic
939C2×C3#240811yescharacteristic
940C2×C3#241011yescharacteristic
941C2×C3#241012yes—
942C2×C3#241111yescharacteristic
943C2×C3#241212yes—
944C2×C3#241812yes—
945C2×C3#247212yes—
946C2×C3#253411yescharacteristic
947C2×C3#261711yescharacteristic
948C2×C3#284711yescharacteristic
949C22—24no—
950C22—24no—
951C22—24no—
952C22—28no—
953C22—24no—
954C22—28no—
955C22—28no—
956C22—28no—
957C22—24no—
958C22—24no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—464no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—42no—
976C22—42no—
977C22—44no—
978C22—44no—
979C22—42no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—82no—
984C22—82no—
985C22—81no—
986C22C3×#39418yescomplemented
987C22C2×C3×#12011yescharacteristic
988C22C2×C3×#12011yescharacteristic
989C22C2×C3×#12111yescharacteristic
990C22C2×C3×#12111yescharacteristic
991C22C2×C3×#12111yescharacteristic
992C22C2×C3×#12112yes—
993C22C2×C3×#12311yescharacteristic
994C22C2×C3×#12311yescharacteristic
995C22C3×#52511yescharacteristic
996C22C3×#52512yes—
997C22C2×C3×#12411yescharacteristic
998C22C3×#53412yes—
999C22C3×#53411yescharacteristic
1000C22C3×#53511yescharacteristic
1001C22C3×#53812yes—
1002C22C3×D4212yes—
1003C22C3×D4212yes—
1004C22C3×#54612yes—
1005C22C3×#54612yes—
1006C22C3×#54612yes—
1007C22C3×#54612yes—
1008C22C3×#55112yes—
1009C22C3×#55112yes—
1010C4—24no—
1011C4—42no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—81no—
1016C4—82no—
1017C4—81no—
1018C3#1472511yescharacteristic, direct product factor, Sylow
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C3×#39411yescharacteristic
1023C2C3×#240811yescharacteristic
1024C2C3×#241011yescharacteristic
1025C2C3×#241012yes—
1026C2C3×#241111yescharacteristic
1027C2C3×#241212yes—
1028C2C3×#241812yes—
1029C2C3×#247212yes—
1030C2C3×#253411yescharacteristic
1031C2C3×#261711yescharacteristic
1032C2C3×#284711yescharacteristic
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
2. C23×C3×C22⋊C4C2semidirect
3. C2×C3×#394C2semidirect
4. C2×C3×#386C2semidirect
5. C2×C3×#386C2semidirect
6. C2×C3×#380C2semidirect
7. C2×C3×#379C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
10. C3×#1438C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14725C3direct (N × H)
21. C22×C3×C4⋊C4C22semidirect
32. C22×C3×C22⋊C4C22semidirect
33. C22×C3×C22⋊C4C22semidirect
34. C22×C3×C22⋊C4C22semidirect
40. C2×C3×#95C22semidirect
41. C2×C3×#95C22semidirect
42. C2×C3×#95C22semidirect
43. C2×C3×#95C22semidirect
44. C2×C3×#95C22semidirect
45. C2×C3×#95C22semidirect
47. C23×C22⋊C4C2×C3semidirect
48. C2×#394C2×C3semidirect
49. C2×#386C2×C3semidirect
50. C2×#386C2×C3semidirect
51. C2×#380C2×C3semidirect
52. C2×#379C2×C3semidirect
53. #1440C2×C3semidirect
54. #1439C2×C3semidirect
55. #1438C2×C3semidirect
56. C22⋊#95C2×C3semidirect
94. C23×C3×C4D4semidirect
138. C2×C3×C22⋊C4D4semidirect
153. C22×C4⋊C4C22×C3semidirect
164. C22×C22⋊C4C22×C3semidirect
165. C22×C22⋊C4C22×C3semidirect
166. C22×C22⋊C4C22×C3semidirect
172. C2×#95C22×C3semidirect
173. C2×#95C22×C3semidirect
174. C2×#95C22×C3semidirect
175. C2×#95C22×C3semidirect
176. C2×#95C22×C3semidirect
177. C2×#95C22×C3semidirect
360. C23×C4C3×D4semidirect
404. C2×C22⋊C4C3×D4semidirect
565. C2×C3×C4#120semidirect
748. C22×C3#394semidirect
934. C2×C4C3×#120semidirect
986. C22C3×#394semidirect
1018. C3#14725direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1202
C23×C3×C22⋊C42
C2×C3×#3942
C2×C3×#3862
C2×C3×#3802
C2×C3×#3792
C3×#14402
C3×#14392
C3×#14382
C3×C22⋊#952
#147253