Finite Group Databasebeta

← C3×#15132 #10633739

Subgroups — C3×#15132 #10633739

Order 768.

1626 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
1C2×C3×#397C212yesmaximal
2C2×C3×#389C211yesmaximal, characteristic, complemented
3C2×C3×#380C211yesmaximal, characteristic
4C2×C3×#380C211yesmaximal, characteristic
5C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
6C3×#1443C212yesmaximal, complemented
7C3×#1442C212yesmaximal, complemented
8C3×#1440C212yesmaximal
9C3×C4⋊#95C211yesmaximal, characteristic, complemented
10C3×C4⋊#95C211yesmaximal, characteristic, complemented
11C3×C4⋊#95C211yesmaximal, characteristic, complemented
12#15132C311yesmaximal, characteristic, direct product factor, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C3×#397—28no—
26C3×#389—24no—
27C3×#380—24no—
28C3×#380—24no—
29C3×C4×C22⋊C4—24no—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×#397C2×C312yes—
42C2×#389C2×C311yescharacteristic, complemented
43C2×#380C2×C311yescharacteristic
44C2×#380C2×C311yescharacteristic
45C2×C4×C22⋊C4C2×C311yescharacteristic
46#1443C2×C312yescomplemented
47#1442C2×C312yescomplemented
48#1440C2×C312yes—
49C4⋊#95C2×C311yescharacteristic, complemented
50C4⋊#95C2×C311yescharacteristic, complemented
51C4⋊#95C2×C311yescharacteristic, complemented
52C25×C3C2311yescharacteristic
53C23×C3×C4—22no—
54C23×C3×C4—22no—
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4D414yes—
60C23×C3×C4C2312yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C4⋊C4D414yes—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4D414yes—
97C2×C3×C42—22no—
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42—22no—
103C3×#95—22no—
104C3×#95—22no—
105C3×#95—24no—
106C3×#95—24no—
107C3×#95—24no—
108C3×#95—24no—
109C3×#95—24no—
110C3×#95—24no—
111C3×#95—24no—
112C3×#95—24no—
113C3×#95—42no—
114C24×C4C22×C311yescharacteristic
115C22×C4⋊C4C22×C311yescharacteristic
116C22×C4⋊C4C22×C311yescharacteristic
117C22×C4⋊C4C22×C311yescharacteristic
118C22×C4⋊C4C22×C312yes—
119C22×C4⋊C4C22×C311yescharacteristic
120C22×C22⋊C4C22×C312yes—
121C22×C22⋊C4C22×C311yescharacteristic
122C22×C22⋊C4C22×C312yes—
123C22×C22⋊C4C22×C311yescharacteristic
124C22×C42C22×C311yescharacteristic
125C22×C42C22×C311yescharacteristic
126#397—28no—
127#389—24no—
128#380—24no—
129#380—24no—
130C4×C22⋊C4—24no—
131C2×#95C22×C312yes—
132C2×#95C22×C312yes—
133C2×#95C22×C312yes—
134C2×#95C22×C312yes—
135C2×#95C22×C312yes—
136C2×#95C22×C312yes—
137C2×#95C22×C311yescharacteristic
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C312yes—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—21no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3C2×D412yes—
155C24×C3C2×D412yes—
156C24×C3#4112yes—
157C24×C3C2411yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—22no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—28no—
195C22×C3×C4—28no—
196C22×C3×C4—28no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
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—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—44no—
219C22×C3×C4—44no—
220C22×C3×C4—44no—
221C22×C3×C4—44no—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D414yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4#4112yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4112yes—
231C22×C3×C4#4112yes—
232C22×C3×C4#4112yes—
233C22×C3×C4#4112yes—
234C22×C3×C4#4112yes—
235C3×C4⋊C4—28no—
236C3×C4⋊C4—48no—
237C3×C4⋊C4—44no—
238C3×C4⋊C4—44no—
239C3×C4⋊C4—44no—
240C3×C22⋊C4—28no—
241C3×C22⋊C4—28no—
242C3×C22⋊C4—48no—
243C3×C22⋊C4—48no—
244C3×C42—44no—
245C3×C42—44no—
246C25C23×C311yescharacteristic
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4C3×D414yes—
254C23×C4C23×C312yes—
255C23×C4C23×C312yes—
256C23×C4C23×C312yes—
257C23×C4C23×C312yes—
258C23×C4C23×C311yescharacteristic
259C23×C4C23×C311yescharacteristic
260C23×C4C23×C311yescharacteristic
261C23×C4C23×C311yescharacteristic
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C311yescharacteristic
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4C3×D414yes—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4C3×D414yes—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297#95—22no—
298#95—22no—
299#95—24no—
300#95—24no—
301#95—24no—
302#95—24no—
303#95—24no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—42no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3#12114yes—
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D411yescharacteristic
345C23×C3C22×D411yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3C2×#4111yescharacteristic
352C23×C3C2×#4111yescharacteristic
353C23×C3C2×#4111yescharacteristic
354C23×C3H(5,𝔽2)11yescharacteristic
355C23×C32−1+411yescharacteristic
356C23×C32−1+411yescharacteristic
357C23×C32−1+411yescharacteristic
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—24no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—416no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
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#12114yes—
423C2×C3×C4#12314yes—
424C2×C3×C4#12314yes—
425C2×C3×C4#12314yes—
426C2×C3×C4#12414yes—
427C2×C3×C4#12614yes—
428C2×C3×C4#12614yes—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24C2×C3×D412yes—
442C24C2×C3×D412yes—
443C24C3×#4112yes—
444C24C24×C311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4C2×C3×D412yes—
510C22×C4C2×C3×D412yes—
511C22×C4C2×C3×D414yes—
512C22×C4C2×C3×D412yes—
513C22×C4C2×C3×D412yes—
514C22×C4C2×C3×D412yes—
515C22×C4C3×#4112yes—
516C22×C4C3×#4112yes—
517C22×C4C3×#4112yes—
518C22×C4C3×#4112yes—
519C22×C4C3×#4112yes—
520C22×C4C3×#4112yes—
521C22×C4C3×#4112yes—
522C4⋊C4—28no—
523C4⋊C4—48no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C22⋊C4—28no—
528C22⋊C4—28no—
529C22⋊C4—48no—
530C22⋊C4—48no—
531C42—44no—
532C42—44no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3C2×#12111yescharacteristic
549C22×C3C2×#12111yescharacteristic
550C22×C3C2×#12311yescharacteristic
551C22×C3C2×#12311yescharacteristic
552C22×C3C2×#12311yescharacteristic
553C22×C3#52511yescharacteristic
554C22×C3C2×#12411yescharacteristic
555C22×C3C2×#12611yescharacteristic
556C22×C3C2×#12611yescharacteristic
557C22×C3#52911yescharacteristic
558C22×C3#52911yescharacteristic
559C22×C3#53211yescharacteristic
560C22×C3#53211yescharacteristic
561C22×C3#53611yescharacteristic
562C22×C3#53711yescharacteristic
563C22×C3#54111yescharacteristic
564C22×C3#54111yescharacteristic
565C22×C3#54211yescharacteristic
566C22×C3#54211yescharacteristic
567C22×C3D4211yescharacteristic
568C22×C3#54711yescharacteristic
569C22×C3#54711yescharacteristic
570C22×C3#54711yescharacteristic
571C22×C3#54711yescharacteristic
572C22×C3#54811yescharacteristic
573C22×C3#54811yescharacteristic
574C22×C3#55211yescharacteristic
575C22×C3#55211yescharacteristic
576C22×C3#55211yescharacteristic
577C22×C3#55211yescharacteristic
578C22×C3#55311yescharacteristic
579C22×C3#55311yescharacteristic
580C22×C3#55511yescharacteristic
581C22×C3#55611yescharacteristic
582C22×C3#55611yescharacteristic
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—44no—
587C3×C4—42no—
588C3×C4—42no—
589C3×C4—82no—
590C3×C4—82no—
591C3×C4—82no—
592C3×C4#39718yescomplemented
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23C3×#12114yes—
628C23C22×C3×D411yescharacteristic
629C23C22×C3×D411yescharacteristic
630C23C22×C3×D411yescharacteristic
631C23C2×C3×#4111yescharacteristic
632C23C2×C3×#4111yescharacteristic
633C23C2×C3×#4111yescharacteristic
634C23C2×C3×#4111yescharacteristic
635C23C2×C3×#4111yescharacteristic
636C23C2×C3×#4111yescharacteristic
637C23C2×C3×#4111yescharacteristic
638C23C2×C3×#4111yescharacteristic
639C23C3×H(5,𝔽2)11yescharacteristic
640C23C3×2−1+411yescharacteristic
641C23C3×2−1+411yescharacteristic
642C23C3×2−1+411yescharacteristic
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—416no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
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—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4C3×#12114yes—
708C2×C4C3×#12314yes—
709C2×C4C3×#12314yes—
710C2×C4C3×#12314yes—
711C2×C4C3×#12414yes—
712C2×C4C3×#12614yes—
713C2×C4C3×#12614yes—
714C2×C3—44no—
715C2×C3C2×#39711yescharacteristic
716C2×C3#241511yescharacteristic
717C2×C3#241611yescharacteristic
718C2×C3#242111yescharacteristic
719C2×C3#242211yescharacteristic
720C2×C3#248511yescharacteristic
721C2×C3#248611yescharacteristic
722C2×C3#248911yescharacteristic
723C2×C3#249111yescharacteristic
724C2×C3#249411yescharacteristic
725C2×C3#249511yescharacteristic
726C2×C3#249611yescharacteristic
727C2×C3#249611yescharacteristic
728C2×C3#262511yescharacteristic
729C2×C3#285411yescharacteristic
730C22—24no—
731C22—24no—
732C22—24no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22C2×C3×#12111yescharacteristic
746C22C2×C3×#12111yescharacteristic
747C22C2×C3×#12311yescharacteristic
748C22C2×C3×#12311yescharacteristic
749C22C2×C3×#12311yescharacteristic
750C22C3×#52511yescharacteristic
751C22C2×C3×#12411yescharacteristic
752C22C2×C3×#12611yescharacteristic
753C22C2×C3×#12611yescharacteristic
754C22C3×#52911yescharacteristic
755C22C3×#52911yescharacteristic
756C22C3×#53211yescharacteristic
757C22C3×#53211yescharacteristic
758C22C3×#53611yescharacteristic
759C22C3×#53711yescharacteristic
760C22C3×#54111yescharacteristic
761C22C3×#54111yescharacteristic
762C22C3×#54211yescharacteristic
763C22C3×#54211yescharacteristic
764C22C3×D4211yescharacteristic
765C22C3×#54711yescharacteristic
766C22C3×#54711yescharacteristic
767C22C3×#54711yescharacteristic
768C22C3×#54711yescharacteristic
769C22C3×#54811yescharacteristic
770C22C3×#54811yescharacteristic
771C22C3×#55211yescharacteristic
772C22C3×#55211yescharacteristic
773C22C3×#55211yescharacteristic
774C22C3×#55211yescharacteristic
775C22C3×#55311yescharacteristic
776C22C3×#55311yescharacteristic
777C22C3×#55511yescharacteristic
778C22C3×#55611yescharacteristic
779C22C3×#55611yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—44no—
784C4—42no—
785C4—42no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4C3×#39718yescomplemented
790C3#1513211yescharacteristic, direct product factor, Sylow
791C2—44no—
792C2C2×C3×#39711yescharacteristic
793C2C3×#241511yescharacteristic
794C2C3×#241611yescharacteristic
795C2C3×#242111yescharacteristic
796C2C3×#242211yescharacteristic
797C2C3×#248511yescharacteristic
798C2C3×#248611yescharacteristic
799C2C3×#248911yescharacteristic
800C2C3×#249111yescharacteristic
801C2C3×#249411yescharacteristic
802C2C3×#249511yescharacteristic
803C2C3×#249611yescharacteristic
804C2C3×#249611yescharacteristic
805C2C3×#262511yescharacteristic
806C2C3×#285411yescharacteristic
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×#389C2semidirect
6. C3×#1443C2semidirect
7. C3×#1442C2semidirect
9. C3×C4⋊#95C2semidirect
10. C3×C4⋊#95C2semidirect
11. C3×C4⋊#95C2semidirect
12. #15132C3direct (N × H)
42. C2×#389C2×C3semidirect
46. #1443C2×C3semidirect
47. #1442C2×C3semidirect
49. C4⋊#95C2×C3semidirect
50. C4⋊#95C2×C3semidirect
51. C4⋊#95C2×C3semidirect
592. C3×C4#397semidirect
789. C4C3×#397semidirect
790. C3#15132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3892
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14432
C3×#14422
C3×#14402
C3×C4⋊#952
#151323