Finite Group Databasebeta

← C3×#24142 #10642749

Subgroups — C3×#24142 #10642749

Order 768.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic, complemented
2C3×#2626C211yesmaximal, characteristic, complemented
3C3×#2617C211yesmaximal, characteristic, complemented
4C3×#2321C211yesmaximal, characteristic, complemented
5C3×#2044C212yesmaximal, complemented
6C3×#2021C212yesmaximal, complemented
7C3×#1996C211yesmaximal, characteristic, complemented
8C3×#1964C211yesmaximal, characteristic, complemented
9C3×#1889C212yesmaximal, complemented
10C3×#1867C212yesmaximal, complemented
11C3×#1799C211yesmaximal, characteristic, complemented
12#24142C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#553—22no—
14C3×#553—21no—
15C3×#552—21no—
16C3×#551—22no—
17C3×#548—21no—
18C3×#546—21no—
19C3×#539—21no—
20C3×#538—21no—
21C3×#534C2212yes—
22C3×#529—21no—
23C3×#525—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×#120C2211yescharacteristic
27C2×C3×#120C2212yes—
28C3×#518C2212yes—
29C2×C3×C4×D4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C2×C3×#99C2212yes—
32C2×C3×#99C2212yes—
33C2×C3×#99C2212yes—
34C3×#399—21no—
35C3×#397—21no—
36C3×#396—22no—
37C3×#394—22no—
38C3×#393—21no—
39C3×#392—21no—
40C3×#390—21no—
41C3×#388—21no—
42C3×#388—21no—
43C3×#386—21no—
44C3×#386C2212yes—
45C3×#386C2211yescharacteristic
46C3×#385C2212yes—
47C3×#385C2211yescharacteristic
48C3×#380C2211yescharacteristic
49C3×#380C2211yescharacteristic
50C3×#379C2212yes—
51C3×#379C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#342C2212yes—
54C3×#342C2212yes—
55C3×#342C2212yes—
56#3505C2×C311yescharacteristic, complemented
57#2626C2×C311yescharacteristic, complemented
58#2617C2×C311yescharacteristic, complemented
59#2321C2×C311yescharacteristic, complemented
60#2044C2×C312yescomplemented
61#2021C2×C312yescomplemented
62#1996C2×C311yescharacteristic, complemented
63#1964C2×C311yescharacteristic, complemented
64#1889C2×C312yescomplemented
65#1867C2×C312yescomplemented
66#1799C2×C311yescharacteristic, complemented
67C25×C3C2311yescharacteristic
68C2×C3×#41—21no—
69C22×C3×Q8D411yescharacteristic, complemented
70C22×C3×D4—21no—
71C22×C3×D4—22no—
72C22×C3×D4D411yescharacteristic, complemented
73C22×C3×D4C2311yescharacteristic
74C22×C3×D4C2312yes—
75C23×C3×C4D411yescharacteristic, complemented
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C3×#126—22no—
79C3×#126—22no—
80C3×#126—22no—
81C3×#125—21no—
82C3×#125—22no—
83C3×#124—21no—
84C3×#124—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×#123—22no—
88C3×#123—22no—
89C3×#123—22no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—21no—
93C3×C22⋊Q8—21no—
94C3×C22⋊Q8—21no—
95C3×C22⋊Q8—21no—
96C3×#121—21no—
97C3×#121—22no—
98C3×#121—21no—
99C3×#121—21no—
100C3×#121—21no—
101C3×#121—21no—
102C3×#121—22no—
103C3×#121—22no—
104C3×#120—22no—
105C3×#120—22no—
106C3×#120—22no—
107C3×#120—22no—
108C3×#120—24no—
109C3×#120—42no—
110C3×C4×Q8—21no—
111C3×C4×D4—22no—
112C3×C4×D4—21no—
113C3×C4×D4—21no—
114C3×C4×D4—21no—
115C3×C4×D4—21no—
116C3×C4×D4—21no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×#117—21no—
122C3×#117—22no—
123C3×#117—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4D411yescharacteristic, complemented
129C2×C3×C4⋊C4D412yescomplemented
130C2×C3×C4⋊C4D411yescharacteristic, complemented
131C2×C3×C4⋊C4D411yescharacteristic, complemented
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4D411yescharacteristic, complemented
148C2×C3×C22⋊C4D412yescomplemented
149C2×C3×C22⋊C4C2311yescharacteristic
150C2×C3×C22⋊C4C2312yes—
151C2×C3×C22⋊C4C2312yes—
152C2×C3×C22⋊C4C2311yescharacteristic
153C2×C3×C22⋊C4C2312yes—
154C2×C3×C22⋊C4C2311yescharacteristic
155C2×C3×C42—21no—
156C2×C3×C42D411yescharacteristic, complemented
157C3×#99—24no—
158C3×#99—42no—
159C3×#99—42no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—22no—
165C3×#95—21no—
166C3×#95—22no—
167#553—22no—
168#553—21no—
169#552—21no—
170#551—22no—
171#548—21no—
172#546—21no—
173#539—21no—
174#538—21no—
175#534C22×C312yes—
176#529—21no—
177#525—21no—
178C2×C22⋊Q8C22×C311yescharacteristic
179C2×#121C22×C311yescharacteristic
180C2×#120C22×C311yescharacteristic
181C2×#120C22×C312yes—
182#518C22×C312yes—
183C2×C4×D4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C2×#99C22×C312yes—
186C2×#99C22×C312yes—
187C2×#99C22×C312yes—
188#399—21no—
189#397—21no—
190#396—22no—
191#394—22no—
192#393—21no—
193#392—21no—
194#390—21no—
195#388—21no—
196#388—21no—
197#386—21no—
198#386C22×C311yescharacteristic
199#386C22×C312yes—
200#385C22×C311yescharacteristic
201#385C22×C312yes—
202#380C22×C311yescharacteristic
203#380C22×C311yescharacteristic
204#379C22×C311yescharacteristic
205#379C22×C312yes—
206C4×C22⋊C4C22×C311yescharacteristic
207#342C22×C312yes—
208#342C22×C312yes—
209#342C22×C312yes—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—81no—
217C24×C3—81no—
218C24×C3C2×D412yes—
219C24×C3C2×D411yescharacteristic
220C24×C3#4112yescomplemented
221C24×C3C2411yescharacteristic
222C3×#41—82no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—81no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—21no—
229C2×C3×D4—22no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—21no—
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—22no—
240C2×C3×D4—24no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—44no—
244C2×C3×D4—81no—
245C2×C3×D4—81no—
246C2×C3×D4—81no—
247C2×C3×D4—82no—
248C2×C3×D4—82no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4—81no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D412yes—
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4—81no—
289C3×C4⋊C4—81no—
290C3×C4⋊C4—82no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—24no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—21no—
313C3×C22⋊C4—44no—
314C3×C22⋊C4—41no—
315C3×C22⋊C4—41no—
316C3×C22⋊C4—41no—
317C3×C22⋊C4—41no—
318C3×C22⋊C4—81no—
319C3×C22⋊C4—82no—
320C3×C22⋊C4—81no—
321C3×C22⋊C4—82no—
322C3×C22⋊C4—81no—
323C3×C22⋊C4—82no—
324C3×C22⋊C4#4112yescomplemented
325C3×C42—22no—
326C3×C42—22no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42—81no—
330C25C23×C311yescharacteristic
331C2×#41—21no—
332C22×Q8C3×D411yescharacteristic, complemented
333C22×D4—21no—
334C22×D4—22no—
335C22×D4C3×D411yescharacteristic, complemented
336C22×D4C23×C311yescharacteristic
337C22×D4C23×C312yes—
338C23×C4C3×D411yescharacteristic, complemented
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341#126—22no—
342#126—22no—
343#126—22no—
344#125—21no—
345#125—22no—
346#124—21no—
347#124—22no—
348#123—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352#123—22no—
353C22⋊Q8—21no—
354C22⋊Q8—22no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359#121—21no—
360#121—22no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—22no—
366#121—22no—
367#120—22no—
368#120—22no—
369#120—22no—
370#120—22no—
371#120—24no—
372#120—42no—
373C4×Q8—21no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384#117—21no—
385#117—22no—
386#117—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4C3×D411yescharacteristic, complemented
392C2×C4⋊C4C3×D411yescharacteristic, complemented
393C2×C4⋊C4C3×D412yescomplemented
394C2×C4⋊C4C3×D411yescharacteristic, complemented
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4C3×D411yescharacteristic, complemented
411C2×C22⋊C4C3×D412yescomplemented
412C2×C22⋊C4C23×C312yes—
413C2×C22⋊C4C23×C311yescharacteristic
414C2×C22⋊C4C23×C312yes—
415C2×C22⋊C4C23×C311yescharacteristic
416C2×C22⋊C4C23×C312yes—
417C2×C22⋊C4C23×C311yescharacteristic
418C2×C42—21no—
419C2×C42C3×D411yescharacteristic, complemented
420#99—24no—
421#99—42no—
422#99—42no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—22no—
428#95—21no—
429#95—22no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—42no—
444C23×C3—41no—
445C23×C3—42no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—41no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—82no—
458C23×C3—82no—
459C23×C3—82no—
460C23×C3—82no—
461C23×C3C22×D411yescharacteristic
462C23×C3C22×D411yescharacteristic
463C23×C3C22×D411yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3H(5,𝔽2)11yescharacteristic
467C23×C32−1+411yescharacteristic
468C3×Q8—42no—
469C3×Q8—81no—
470C3×D4—42no—
471C3×D4—42no—
472C3×D4—42no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—42no—
477C3×D4—42no—
478C3×D4—41no—
479C3×D4—81no—
480C3×D4—82no—
481C3×D4—84no—
482C3×D4—82no—
483C3×D4—88no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—41no—
507C2×C3×C4—42no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—41no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—81no—
523C2×C3×C4—82no—
524C2×C3×C4—82no—
525C2×C3×C4#12011yescharacteristic
526C2×C3×C4#12011yescharacteristic
527C2×C3×C4#12011yescharacteristic
528C2×C3×C4#12011yescharacteristic
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—81no—
536C24—81no—
537C24C2×C3×D412yes—
538C24C2×C3×D411yescharacteristic
539C24C3×#4112yescomplemented
540C24C24×C311yescharacteristic
541#41—82no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—81no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—44no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—82no—
567C2×D4—82no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4C2×C3×D411yescharacteristic
583C22×C4C2×C3×D412yes—
584C22×C4C2×C3×D411yescharacteristic
585C22×C4C2×C3×D412yes—
586C22×C4C2×C3×D411yescharacteristic
587C22×C4C2×C3×D412yes—
588C22×C4C2×C3×D411yescharacteristic
589C22×C4C2×C3×D411yescharacteristic
590C22×C4C2×C3×D411yescharacteristic
591C22×C4C2×C3×D411yescharacteristic
592C22×C4C2×C3×D411yescharacteristic
593C22×C4C2×C3×D411yescharacteristic
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—81no—
607C4⋊C4—81no—
608C4⋊C4—81no—
609C4⋊C4—82no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—24no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—44no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C22⋊C4—81no—
638C22⋊C4—82no—
639C22⋊C4—81no—
640C22⋊C4—82no—
641C22⋊C4—81no—
642C22⋊C4—82no—
643C22⋊C4C3×#4112yescomplemented
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—81no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—44no—
662C22×C3—42no—
663C22×C3—44no—
664C22×C3—41no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—82no—
672C22×C3—81no—
673C22×C3—82no—
674C22×C3—82no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—82no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3C2×#12011yescharacteristic
681C22×C3#52511yescharacteristic
682C22×C3#53711yescharacteristic
683C22×C3#54611yescharacteristic
684C22×C3#54711yescharacteristic
685C22×C3#54811yescharacteristic
686C22×C3#55011yescharacteristic
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—42no—
692C3×C4—41no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—42no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—82no—
699C3×C4—81no—
700C3×C4—82no—
701C3×C4—81no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—82no—
730C23—82no—
731C23—82no—
732C23—82no—
733C23C22×C3×D411yescharacteristic
734C23C22×C3×D411yescharacteristic
735C23C22×C3×D411yescharacteristic
736C23C2×C3×#4111yescharacteristic
737C23C2×C3×#4111yescharacteristic
738C23C3×H(5,𝔽2)11yescharacteristic
739C23C3×2−1+411yescharacteristic
740Q8—42no—
741Q8—81no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—42no—
749D4—42no—
750D4—41no—
751D4—81no—
752D4—84no—
753D4—82no—
754D4—82no—
755D4—88no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—81no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4C3×#12011yescharacteristic
798C2×C4C3×#12011yescharacteristic
799C2×C4C3×#12011yescharacteristic
800C2×C4C3×#12011yescharacteristic
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—82no—
808C2×C3—81no—
809C2×C3—82no—
810C2×C3#240711yescharacteristic
811C2×C3#302611yescharacteristic
812C2×C3#302711yescharacteristic
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—41no—
835C22—82no—
836C22—81no—
837C22—82no—
838C22—82no—
839C22—81no—
840C22—81no—
841C22—82no—
842C22—81no—
843C22—81no—
844C22C2×C3×#12011yescharacteristic
845C22C3×#52511yescharacteristic
846C22C3×#53711yescharacteristic
847C22C3×#54611yescharacteristic
848C22C3×#54711yescharacteristic
849C22C3×#54811yescharacteristic
850C22C3×#55011yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—42no—
856C4—41no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—41no—
861C4—42no—
862C4—82no—
863C4—82no—
864C4—81no—
865C4—81no—
866C3#2414211yescharacteristic, direct product factor, Sylow
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C3×#240711yescharacteristic
877C2C3×#302611yescharacteristic
878C2C3×#302711yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3505C2semidirect
2. C3×#2626C2semidirect
3. C3×#2617C2semidirect
4. C3×#2321C2semidirect
5. C3×#2044C2semidirect
6. C3×#2021C2semidirect
7. C3×#1996C2semidirect
8. C3×#1964C2semidirect
9. C3×#1889C2semidirect
10. C3×#1867C2semidirect
11. C3×#1799C2semidirect
12. #24142C3direct (N × H)
56. #3505C2×C3semidirect
57. #2626C2×C3semidirect
58. #2617C2×C3semidirect
59. #2321C2×C3semidirect
60. #2044C2×C3semidirect
61. #2021C2×C3semidirect
62. #1996C2×C3semidirect
63. #1964C2×C3semidirect
64. #1889C2×C3semidirect
65. #1867C2×C3semidirect
66. #1799C2×C3semidirect
69. C22×C3×Q8D4semidirect
72. C22×C3×D4D4semidirect
75. C23×C3×C4D4semidirect
128. C2×C3×C4⋊C4D4semidirect
129. C2×C3×C4⋊C4D4semidirect
130. C2×C3×C4⋊C4D4semidirect
131. C2×C3×C4⋊C4D4semidirect
147. C2×C3×C22⋊C4D4semidirect
148. C2×C3×C22⋊C4D4semidirect
156. C2×C3×C42D4semidirect
220. C24×C3#41semidirect
324. C3×C22⋊C4#41semidirect
332. C22×Q8C3×D4semidirect
335. C22×D4C3×D4semidirect
338. C23×C4C3×D4semidirect
391. C2×C4⋊C4C3×D4semidirect
392. C2×C4⋊C4C3×D4semidirect
393. C2×C4⋊C4C3×D4semidirect
394. C2×C4⋊C4C3×D4semidirect
410. C2×C22⋊C4C3×D4semidirect
411. C2×C22⋊C4C3×D4semidirect
419. C2×C42C3×D4semidirect
539. C24C3×#41semidirect
643. C22⋊C4C3×#41semidirect
866. C3#24142direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35052
C3×#26262
C3×#26172
C3×#23212
C3×#20442
C3×#20212
C3×#19962
C3×#19642
C3×#18892
C3×#18672
C3×#17992
#241423