Finite Group Databasebeta

← C3×#25587 #10644194

Subgroups — C3×#25587 #10644194

Order 768.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic, complemented
2C3×#2561C211yesmaximal, characteristic, complemented
3C3×#2539C211yesmaximal, characteristic, complemented
4C3×#2534C211yesmaximal, characteristic, complemented
5C3×#2022C212yesmaximal, complemented
6C3×#2021C212yesmaximal, complemented
7C3×#1996C211yesmaximal, characteristic, complemented
8C3×#1964C211yesmaximal, characteristic, complemented
9C3×#1890C212yesmaximal, complemented
10C3×#1889C212yesmaximal, complemented
11C3×C4×#99C211yesmaximal, characteristic, complemented
12#25587C311yesmaximal, 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×#123C2212yes—
25C2×C3×#123C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#120C2212yes—
29C2×C3×#120C2211yescharacteristic
30C3×#518C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C2×C3×#99C2212yes—
34C2×C3×#99C2212yes—
35C2×C3×#99C2212yes—
36C3×#399—21no—
37C3×#397—21no—
38C3×#396—21no—
39C3×#394—21no—
40C3×#393—21no—
41C3×#392—21no—
42C3×#390—22no—
43C3×#388—22no—
44C3×#388—21no—
45C3×#386—21no—
46C3×#381C2212yes—
47C3×#381C2211yescharacteristic
48C3×#380C2211yescharacteristic
49C3×#379C2212yes—
50C3×#379C2211yescharacteristic
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#342C2212yes—
54C3×#342C2212yes—
55C3×#342C2212yes—
56#3505C2×C311yescharacteristic, complemented
57#2561C2×C311yescharacteristic, complemented
58#2539C2×C311yescharacteristic, complemented
59#2534C2×C311yescharacteristic, complemented
60#2022C2×C312yescomplemented
61#2021C2×C312yescomplemented
62#1996C2×C311yescharacteristic, complemented
63#1964C2×C311yescharacteristic, complemented
64#1890C2×C312yescomplemented
65#1889C2×C312yescomplemented
66C4×#99C2×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×#123—24no—
91C3×#123—42no—
92C3×#123—42no—
93C3×C22⋊Q8—21no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—21no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8—21no—
98C3×C22⋊Q8—21no—
99C3×#121—21no—
100C3×#121—22no—
101C3×#121—21no—
102C3×#121—21no—
103C3×#121—21no—
104C3×#121—21no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#120—22no—
108C3×#120—22no—
109C3×#120—24no—
110C3×#120—42no—
111C3×#120—42no—
112C3×C4×Q8—21no—
113C3×C4×D4—22no—
114C3×C4×D4—21no—
115C3×C4×D4—21no—
116C3×C4×D4—21no—
117C3×C4×D4—21no—
118C3×C4×D4—21no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×C4×D4—22no—
123C3×#117—21no—
124C3×#117—22no—
125C3×#117—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4D412yescomplemented
130C2×C3×C4⋊C4D411yescharacteristic, complemented
131C2×C3×C4⋊C4D411yescharacteristic, complemented
132C2×C3×C4⋊C4D411yescharacteristic, complemented
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
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—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4D412yescomplemented
149C2×C3×C22⋊C4D411yescharacteristic, complemented
150C2×C3×C22⋊C4C2312yes—
151C2×C3×C22⋊C4C2311yescharacteristic
152C2×C3×C22⋊C4C2311yescharacteristic
153C2×C3×C22⋊C4C2311yescharacteristic
154C2×C3×C22⋊C4C2312yes—
155C2×C3×C22⋊C4C2312yes—
156C2×C3×C42—21no—
157C2×C3×C42—21no—
158C2×C3×C42D411yescharacteristic, complemented
159C3×#99—24no—
160C3×#99—42no—
161C3×#99—42no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—22no—
167C3×#95—21no—
168C3×#95—22no—
169#553—22no—
170#553—21no—
171#552—21no—
172#551—22no—
173#548—21no—
174#546—21no—
175#539—21no—
176#538—21no—
177#534C22×C312yes—
178#529—21no—
179#525—21no—
180C2×#123C22×C312yes—
181C2×#123C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184C2×#120C22×C312yes—
185C2×#120C22×C311yescharacteristic
186#518C22×C312yes—
187C2×C4×D4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C2×#99C22×C312yes—
190C2×#99C22×C312yes—
191C2×#99C22×C312yes—
192#399—21no—
193#397—21no—
194#396—21no—
195#394—21no—
196#393—21no—
197#392—21no—
198#390—22no—
199#388—22no—
200#388—21no—
201#386—21no—
202#381C22×C312yes—
203#381C22×C311yescharacteristic
204#380C22×C311yescharacteristic
205#379C22×C312yes—
206#379C22×C311yescharacteristic
207C4×C22⋊C4C22×C311yescharacteristic
208C4×C22⋊C4C22×C311yescharacteristic
209#342C22×C312yes—
210#342C22×C312yes—
211#342C22×C312yes—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—42no—
218C24×C3—81no—
219C24×C3C2×D412yes—
220C24×C3C2×D411yescharacteristic
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—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—44no—
241C2×C3×D4—42no—
242C2×C3×D4—44no—
243C2×C3×D4—42no—
244C2×C3×D4—81no—
245C2×C3×D4—82no—
246C2×C3×D4—81no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—22no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—44no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4—81no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—21no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—44no—
309C3×C22⋊C4—44no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—44no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
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#4114yescomplemented
321C3×C42—22no—
322C3×C42—22no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—81no—
326C3×C42—81no—
327C25C23×C311yescharacteristic
328C2×#41—21no—
329C22×Q8C3×D411yescharacteristic, complemented
330C22×D4—21no—
331C22×D4—22no—
332C22×D4C3×D411yescharacteristic, complemented
333C22×D4C23×C311yescharacteristic
334C22×D4C23×C312yes—
335C23×C4C3×D411yescharacteristic, complemented
336C23×C4C23×C311yescharacteristic
337C23×C4C23×C311yescharacteristic
338#126—22no—
339#126—22no—
340#126—22no—
341#125—21no—
342#125—22no—
343#124—21no—
344#124—22no—
345#123—22no—
346#123—22no—
347#123—22no—
348#123—22no—
349#123—22no—
350#123—24no—
351#123—42no—
352#123—42no—
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—24no—
370#120—42no—
371#120—42no—
372C4×Q8—21no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383#117—21no—
384#117—22no—
385#117—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C3×D411yescharacteristic, complemented
390C2×C4⋊C4C3×D411yescharacteristic, complemented
391C2×C4⋊C4C3×D412yescomplemented
392C2×C4⋊C4C3×D411yescharacteristic, complemented
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
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—22no—
408C2×C22⋊C4C3×D411yescharacteristic, complemented
409C2×C22⋊C4C3×D412yescomplemented
410C2×C22⋊C4C23×C311yescharacteristic
411C2×C22⋊C4C23×C311yescharacteristic
412C2×C22⋊C4C23×C312yes—
413C2×C22⋊C4C23×C311yescharacteristic
414C2×C22⋊C4C23×C312yes—
415C2×C22⋊C4C23×C312yes—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42C3×D411yescharacteristic, complemented
419#99—24no—
420#99—42no—
421#99—42no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—22no—
427#95—21no—
428#95—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—42no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—42no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—42no—
455C23×C3—42no—
456C23×C3—84no—
457C23×C3—84no—
458C23×C3C22×D411yescharacteristic
459C23×C3C22×D411yescharacteristic
460C23×C3C22×D411yescharacteristic
461C23×C3C2×#4112yes—
462C23×C3H(5,𝔽2)12yes—
463C3×Q8—42no—
464C3×Q8—81no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—42no—
468C3×D4—42no—
469C3×D4—42no—
470C3×D4—42no—
471C3×D4—42no—
472C3×D4—81no—
473C3×D4—82no—
474C3×D4—82no—
475C3×D4—88no—
476C3×D4—84no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—81no—
516C2×C3×C4—82no—
517C2×C3×C4—82no—
518C2×C3×C4#12011yescharacteristic
519C2×C3×C4#12011yescharacteristic
520C2×C3×C4#12011yescharacteristic
521C2×C3×C4#12011yescharacteristic
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—42no—
528C24—81no—
529C24C2×C3×D412yes—
530C24C2×C3×D411yescharacteristic
531C24C24×C311yescharacteristic
532#41—82no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—81no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—82no—
556C2×D4—81no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—81no—
571C22×C4—81no—
572C22×C4C2×C3×D411yescharacteristic
573C22×C4C2×C3×D412yes—
574C22×C4C2×C3×D411yescharacteristic
575C22×C4C2×C3×D412yes—
576C22×C4C2×C3×D411yescharacteristic
577C22×C4C2×C3×D412yes—
578C22×C4C2×C3×D411yescharacteristic
579C22×C4C2×C3×D411yescharacteristic
580C22×C4C2×C3×D411yescharacteristic
581C22×C4C2×C3×D411yescharacteristic
582C22×C4C2×C3×D411yescharacteristic
583C22×C4C2×C3×D411yescharacteristic
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—81no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—22no—
607C22⋊C4—21no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—44no—
623C22⋊C4—42no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—81no—
629C22⋊C4—82no—
630C22⋊C4C3×#4114yescomplemented
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—81no—
636C42—81no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—44no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—82no—
658C22×C3—82no—
659C22×C3—81no—
660C22×C3—82no—
661C22×C3—81no—
662C22×C3—82no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3C2×#12011yescharacteristic
667C22×C3#53211yescharacteristic
668C22×C3#53511yescharacteristic
669C22×C3#54612yes—
670C22×C3#55012yes—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—44no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—42no—
682C3×C4—81no—
683C3×C4—82no—
684C3×C4—81no—
685C3×C4—81no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—84no—
714C23—84no—
715C23C22×C3×D411yescharacteristic
716C23C22×C3×D411yescharacteristic
717C23C22×C3×D411yescharacteristic
718C23C2×C3×#4112yes—
719C23C3×H(5,𝔽2)12yes—
720Q8—42no—
721Q8—81no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—81no—
730D4—82no—
731D4—82no—
732D4—88no—
733D4—84no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4C3×#12011yescharacteristic
776C2×C4C3×#12011yescharacteristic
777C2×C4C3×#12011yescharacteristic
778C2×C4C3×#12011yescharacteristic
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—22no—
782C2×C3—21no—
783C2×C3—82no—
784C2×C3—81no—
785C2×C3—82no—
786C2×C3#243111yescharacteristic
787C2×C3#302511yescharacteristic
788C2×C3#302611yescharacteristic
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—82no—
810C22—82no—
811C22—81no—
812C22—82no—
813C22—81no—
814C22—82no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22C2×C3×#12011yescharacteristic
819C22C3×#53211yescharacteristic
820C22C3×#53511yescharacteristic
821C22C3×#54612yes—
822C22C3×#55012yes—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—44no—
828C4—41no—
829C4—42no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—81no—
835C4—81no—
836C4—82no—
837C4—81no—
838C3#2558711yescharacteristic, direct product factor, Sylow
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C3×#243111yescharacteristic
847C2C3×#302511yescharacteristic
848C2C3×#302611yescharacteristic
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×#2561C2semidirect
3. C3×#2539C2semidirect
4. C3×#2534C2semidirect
5. C3×#2022C2semidirect
6. C3×#2021C2semidirect
7. C3×#1996C2semidirect
8. C3×#1964C2semidirect
9. C3×#1890C2semidirect
10. C3×#1889C2semidirect
11. C3×C4×#99C2semidirect
12. #25587C3direct (N × H)
56. #3505C2×C3semidirect
57. #2561C2×C3semidirect
58. #2539C2×C3semidirect
59. #2534C2×C3semidirect
60. #2022C2×C3semidirect
61. #2021C2×C3semidirect
62. #1996C2×C3semidirect
63. #1964C2×C3semidirect
64. #1890C2×C3semidirect
65. #1889C2×C3semidirect
66. C4×#99C2×C3semidirect
69. C22×C3×Q8D4semidirect
72. C22×C3×D4D4semidirect
75. C23×C3×C4D4semidirect
129. C2×C3×C4⋊C4D4semidirect
130. C2×C3×C4⋊C4D4semidirect
131. C2×C3×C4⋊C4D4semidirect
132. C2×C3×C4⋊C4D4semidirect
148. C2×C3×C22⋊C4D4semidirect
149. C2×C3×C22⋊C4D4semidirect
158. C2×C3×C42D4semidirect
320. C3×C22⋊C4#41semidirect
329. C22×Q8C3×D4semidirect
332. C22×D4C3×D4semidirect
335. C23×C4C3×D4semidirect
389. C2×C4⋊C4C3×D4semidirect
390. C2×C4⋊C4C3×D4semidirect
391. C2×C4⋊C4C3×D4semidirect
392. C2×C4⋊C4C3×D4semidirect
408. C2×C22⋊C4C3×D4semidirect
409. C2×C22⋊C4C3×D4semidirect
418. C2×C42C3×D4semidirect
630. C22⋊C4C3×#41semidirect
838. C3#25587direct (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×#25612
C3×#25392
C3×#25342
C3×#20222
C3×#20212
C3×#19962
C3×#19642
C3×#18902
C3×#18892
C3×C4×#992
#255873