Finite Group Databasebeta

← C3×#14758 #10633365

Subgroups — C3×#14758 #10633365

Order 768.

2242 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic
4C2×C3×#380C212yesmaximal
5C22×C3×#95C211yesmaximal, characteristic
6C3×#1446C211yesmaximal, characteristic, complemented
7C3×#1444C212yesmaximal, complemented
8C3×#1444C211yesmaximal, characteristic, complemented
9C3×#1441C212yesmaximal, complemented
10C3×#1441C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal
12#14758C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2212yes—
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—28no—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2212yes—
22C22×C3×C4⋊C4C2212yes—
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C3×#395—24no—
28C3×#385—24no—
29C3×#380—28no—
30C2×C3×#95—24no—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C22×C22⋊Q8C2×C311yescharacteristic
43C2×#395C2×C311yescharacteristic, complemented
44C2×#385C2×C311yescharacteristic
45C2×#380C2×C312yes—
46C22×#95C2×C311yescharacteristic
47#1446C2×C311yescharacteristic, complemented
48#1444C2×C312yescomplemented
49#1444C2×C311yescharacteristic, complemented
50#1441C2×C311yescharacteristic, complemented
51#1441C2×C312yescomplemented
52C22⋊#95C2×C312yes—
53C25×C3C2311yescharacteristic
54C22×C3×Q8—24no—
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—42no—
59C23×C3×C4—24no—
60C23×C3×C4—24no—
61C23×C3×C4—24no—
62C23×C3×C4—22no—
63C23×C3×C4—24no—
64C23×C3×C4—22no—
65C23×C3×C4—24no—
66C23×C3×C4—42no—
67C23×C3×C4—42no—
68C23×C3×C4—42no—
69C23×C3×C4D414yes—
70C23×C3×C4Q818yescomplemented
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2312yes—
75C23×C3×C4C2312yes—
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2312yes—
81C3×C22⋊Q8—232no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—42no—
96C2×C3×C4⋊C4—42no—
97C2×C3×C4⋊C4—42no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4D418yes—
105C2×C3×C22⋊C4Q814yescomplemented
106C3×#95—22no—
107C3×#95—24no—
108C3×#95—24no—
109C3×#95—24no—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—24no—
113C3×#95—24no—
114C3×#95—42no—
115C3×#95—42no—
116C3×#95D414yes—
117C23×Q8C22×C311yescharacteristic
118C24×C4C22×C311yescharacteristic
119C24×C4C22×C312yes—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—28no—
122C22×C4⋊C4C22×C311yescharacteristic
123C22×C4⋊C4C22×C311yescharacteristic
124C22×C4⋊C4C22×C312yes—
125C22×C4⋊C4C22×C312yes—
126C22×C4⋊C4C22×C312yes—
127C22×C4⋊C4C22×C311yescharacteristic
128C22×C22⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C311yescharacteristic
131#395—24no—
132#385—24no—
133#380—28no—
134C2×#95—24no—
135C2×#95C22×C312yes—
136C2×#95C22×C312yes—
137C2×#95C22×C311yescharacteristic
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C312yes—
142C2×#95C22×C311yescharacteristic
143C2×#95C22×C312yes—
144C2×#95C22×C312yes—
145C2×#95C22×C311yescharacteristic
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3C2×D412yes—
153C24×C3C2×D414yes—
154C24×C3C2×Q812yes—
155C24×C3C2×Q814yes—
156C24×C3#4112yes—
157C24×C3C2411yescharacteristic
158C2×C3×Q8—28no—
159C2×C3×Q8—48no—
160C2×C3×Q8—48no—
161C2×C3×Q8—44no—
162C2×C3×Q8—44no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—28no—
170C22×C3×C4—216no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—28no—
204C22×C3×C4—216no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—44no—
216C22×C3×C4—48no—
217C22×C3×C4—48no—
218C22×C3×C4—48no—
219C22×C3×C4—48no—
220C22×C3×C4—48no—
221C22×C3×C4—48no—
222C22×C3×C4—48no—
223C22×C3×C4C2×D414yes—
224C22×C3×C4C2×D414yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×Q812yes—
230C22×C3×C4C2×Q812yes—
231C22×C3×C4C2×Q814yes—
232C22×C3×C4C2×Q814yes—
233C22×C3×C4#4112yes—
234C22×C3×C4#4114yes—
235C3×C4⋊C4—28no—
236C3×C4⋊C4—216no—
237C3×C4⋊C4—48no—
238C3×C4⋊C4—48no—
239C3×C4⋊C4—44no—
240C3×C4⋊C4—44no—
241C3×C22⋊C4—216no—
242C3×C22⋊C4—28no—
243C3×C22⋊C4—44no—
244C25C23×C311yescharacteristic
245C22×Q8—24no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—42no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4C3×D414yes—
261C23×C4C3×Q818yescomplemented
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C311yescharacteristic
264C23×C4C23×C312yes—
265C23×C4C23×C312yes—
266C23×C4C23×C311yescharacteristic
267C23×C4C23×C311yescharacteristic
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C312yes—
270C23×C4C23×C311yescharacteristic
271C23×C4C23×C312yes—
272C22⋊Q8—232no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4C3×D418yes—
296C2×C22⋊C4C3×Q814yescomplemented
297#95—22no—
298#95—24no—
299#95—24no—
300#95—24no—
301#95—22no—
302#95—22no—
303#95—24no—
304#95—24no—
305#95—42no—
306#95—42no—
307#95C3×D414yes—
308C23×C3—22no—
309C23×C3—24no—
310C23×C3—22no—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—22no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—22no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3#12014yes—
327C23×C3C22⋊Q814yes—
328C23×C3C22⋊Q818yes—
329C23×C3C4⋊Q814yes—
330C23×C3C4⋊Q818yes—
331C23×C3C22×D411yescharacteristic
332C23×C3C22×D412yes—
333C23×C3C22×D411yescharacteristic
334C23×C3C22×Q812yes—
335C23×C3C22×Q811yescharacteristic
336C23×C3C2×#4111yescharacteristic
337C23×C3C2×#4111yescharacteristic
338C23×C3C2×#4112yes—
339C23×C3H(5,𝔽2)12yes—
340C23×C3H(5,𝔽2)11yescharacteristic
341C23×C32−1+411yescharacteristic
342C3×Q8—416no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—416no—
371C2×C3×C4—432no—
372C2×C3×C4—41no—
373C2×C3×C4—42no—
374C2×C3×C4—41no—
375C2×C3×C4—42no—
376C2×C3×C4—41no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4#12114yes—
404C2×C3×C4C22⋊Q818yescomplemented
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24C2×C3×D412yes—
412C24C2×C3×D414yes—
413C24C2×C3×Q812yes—
414C24C2×C3×Q814yes—
415C24C3×#4112yes—
416C24C24×C311yescharacteristic
417C2×Q8—28no—
418C2×Q8—48no—
419C2×Q8—48no—
420C2×Q8—44no—
421C2×Q8—44no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—216no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—28no—
463C22×C4—216no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—44no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4C2×C3×D414yes—
483C22×C4C2×C3×D414yes—
484C22×C4C2×C3×D412yes—
485C22×C4C2×C3×D412yes—
486C22×C4C2×C3×D412yes—
487C22×C4C2×C3×D414yes—
488C22×C4C2×C3×Q812yes—
489C22×C4C2×C3×Q812yes—
490C22×C4C2×C3×Q814yes—
491C22×C4C2×C3×Q814yes—
492C22×C4C3×#4112yes—
493C22×C4C3×#4114yes—
494C4⋊C4—28no—
495C4⋊C4—216no—
496C4⋊C4—48no—
497C4⋊C4—48no—
498C4⋊C4—44no—
499C4⋊C4—44no—
500C22⋊C4—216no—
501C22⋊C4—28no—
502C22⋊C4—44no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—28no—
510C22×C3—28no—
511C22×C3—28no—
512C22×C3—28no—
513C22×C3#39518yescomplemented
514C22×C3C2×#12011yescharacteristic
515C22×C3C2×#12111yescharacteristic
516C22×C3C2×C22⋊Q811yescharacteristic
517C22×C3C2×C22⋊Q812yes—
518C22×C3C2×C22⋊Q812yes—
519C22×C3C2×C4⋊Q811yescharacteristic
520C22×C3C2×C4⋊Q812yes—
521C22×C3#53211yescharacteristic
522C22×C3#53312yes—
523C22×C3#53411yescharacteristic
524C22×C3#53711yescharacteristic
525C22×C3#54312yes—
526C22×C3#54412yes—
527C22×C3D4212yes—
528C22×C3#54612yes—
529C22×C3#54611yescharacteristic
530C22×C3#54612yes—
531C22×C3#54712yes—
532C22×C3D4×Q811yescharacteristic
533C22×C3#55112yes—
534C22×C3#55211yescharacteristic
535C22×C3#55412yes—
536C22×C3#55411yescharacteristic
537C3×C4—24no—
538C3×C4—28no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—44no—
542C3×C4—42no—
543C3×C4—44no—
544C3×C4—44no—
545C3×C4—81no—
546C3×C4—81no—
547C23—22no—
548C23—24no—
549C23—22no—
550C23—24no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—22no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—22no—
561C23—24no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23C3×#12014yes—
566C23C3×C22⋊Q814yes—
567C23C3×C22⋊Q818yes—
568C23C3×C4⋊Q814yes—
569C23C3×C4⋊Q818yes—
570C23C22×C3×D411yescharacteristic
571C23C22×C3×D412yes—
572C23C22×C3×D411yescharacteristic
573C23C22×C3×Q812yes—
574C23C22×C3×Q811yescharacteristic
575C23C2×C3×#4111yescharacteristic
576C23C2×C3×#4111yescharacteristic
577C23C2×C3×#4112yes—
578C23C3×H(5,𝔽2)12yes—
579C23C3×H(5,𝔽2)11yescharacteristic
580C23C3×2−1+411yescharacteristic
581Q8—416no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—416no—
610C2×C4—432no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4C3×#12114yes—
643C2×C4C3×C22⋊Q818yescomplemented
644C2×C3—28no—
645C2×C3C2×#39511yescharacteristic
646C2×C3#241011yescharacteristic
647C2×C3#241711yescharacteristic
648C2×C3#243011yescharacteristic
649C2×C3#243712yes—
650C2×C3#243812yes—
651C2×C3#244012yes—
652C2×C3#254912yes—
653C2×C3#256411yescharacteristic
654C2×C3#265911yescharacteristic
655C2×C3#285711yescharacteristic
656C22—24no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—28no—
662C22—28no—
663C22—28no—
664C22—24no—
665C22—24no—
666C22C3×#39518yescomplemented
667C22C2×C3×#12011yescharacteristic
668C22C2×C3×#12111yescharacteristic
669C22C2×C3×C22⋊Q811yescharacteristic
670C22C2×C3×C22⋊Q812yes—
671C22C2×C3×C22⋊Q812yes—
672C22C2×C3×C4⋊Q811yescharacteristic
673C22C2×C3×C4⋊Q812yes—
674C22C3×#53211yescharacteristic
675C22C3×#53312yes—
676C22C3×#53411yescharacteristic
677C22C3×#53711yescharacteristic
678C22C3×#54312yes—
679C22C3×#54412yes—
680C22C3×D4212yes—
681C22C3×#54612yes—
682C22C3×#54611yescharacteristic
683C22C3×#54612yes—
684C22C3×#54712yes—
685C22C3×D4×Q811yescharacteristic
686C22C3×#55112yes—
687C22C3×#55211yescharacteristic
688C22C3×#55411yescharacteristic
689C22C3×#55412yes—
690C4—24no—
691C4—28no—
692C4—42no—
693C4—44no—
694C4—42no—
695C4—44no—
696C4—44no—
697C4—42no—
698C4—81no—
699C4—81no—
700C3#1475811yescharacteristic, direct product factor, Sylow
701C2—28no—
702C2C2×C3×#39511yescharacteristic
703C2C3×#241011yescharacteristic
704C2C3×#241711yescharacteristic
705C2C3×#243011yescharacteristic
706C2C3×#243712yes—
707C2C3×#243812yes—
708C2C3×#244012yes—
709C2C3×#254912yes—
710C2C3×#256411yescharacteristic
711C2C3×#265911yescharacteristic
712C2C3×#285711yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#395C2semidirect
6. C3×#1446C2semidirect
7. C3×#1444C2semidirect
8. C3×#1444C2semidirect
9. C3×#1441C2semidirect
10. C3×#1441C2semidirect
12. #14758C3direct (N × H)
43. C2×#395C2×C3semidirect
47. #1446C2×C3semidirect
48. #1444C2×C3semidirect
49. #1444C2×C3semidirect
50. #1441C2×C3semidirect
51. #1441C2×C3semidirect
70. C23×C3×C4Q8semidirect
105. C2×C3×C22⋊C4Q8semidirect
261. C23×C4C3×Q8semidirect
296. C2×C22⋊C4C3×Q8semidirect
404. C2×C3×C4C22⋊Q8semidirect
513. C22×C3#395semidirect
643. C2×C4C3×C22⋊Q8semidirect
666. C22C3×#395semidirect
700. C3#14758direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#3952
C2×C3×#3852
C2×C3×#3802
C22×C3×#952
C3×#14462
C3×#14442
C3×#14412
C3×C22⋊#952
#147583