Finite Group Databasebeta

← C3×#23954 #10642561

Subgroups — C3×#23954 #10642561

Order 768.

1482 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic, complemented
2C3×#3003C211yesmaximal, characteristic, complemented
3C2×C3×#418C211yesmaximal, characteristic, complemented
4C3×#2433C211yesmaximal, characteristic, complemented
5C3×#2027C212yesmaximal, complemented
6C3×#2002C212yesmaximal, complemented
7C3×#1900C211yesmaximal, characteristic, complemented
8C3×#1887C212yesmaximal, complemented
9C3×#1883C212yesmaximal, complemented
10C3×#1871C211yesmaximal, characteristic, complemented
11C3×#1826C211yesmaximal, characteristic, complemented
12#23954C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)C2212yes—
15C22×C3×M16C2211yescharacteristic
16C3×#555—21no—
17C3×#553—21no—
18C3×#553—21no—
19C3×#551—22no—
20C3×#547—21no—
21C3×#546—22no—
22C3×#544C2211yescharacteristic, complemented
23C3×#542—21no—
24C3×#540—21no—
25C3×#535C2211yescharacteristic, complemented
26C3×#532—21no—
27C2×C3×#127C2212yes—
28C3×#529—21no—
29C3×#525C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#120—22no—
32C3×#520C2211yescharacteristic, complemented
33C3×#518C2211yescharacteristic, complemented
34C2×C3×#117C2211yescharacteristic
35C3×#450—21no—
36C3×#450—21no—
37C3×#447—21no—
38C3×#447—21no—
39C2×C3×#104C2212yescomplemented
40C3×#418—21no—
41C3×#418—21no—
42C3×#418C2212yes—
43C3×#418C2212yes—
44C3×#418C2212yes—
45C2×C3×#102—21no—
46C2×C3×#102—21no—
47C2×C3×#100C2212yescomplemented
48C3×#407C2211yescharacteristic
49C3×#392—22no—
50C3×#390C2212yes—
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×#343C2212yescomplemented
53C3×#339C2212yescomplemented
54C3×#339C2212yescomplemented
55C3×#339C2212yescomplemented
56#3494C2×C311yescharacteristic, complemented
57#3003C2×C311yescharacteristic, complemented
58C2×#418C2×C311yescharacteristic, complemented
59#2433C2×C311yescharacteristic, complemented
60#2027C2×C312yescomplemented
61#2002C2×C312yescomplemented
62#1900C2×C311yescharacteristic, complemented
63#1887C2×C312yescomplemented
64#1883C2×C312yescomplemented
65#1871C2×C311yescharacteristic, complemented
66#1826C2×C311yescharacteristic, complemented
67C25×C3—21no—
68C2×C3×#41—22no—
69C2×C3×#41C2311yescharacteristic
70C22×C3×D4—24no—
71C22×C3×D4—24no—
72C22×C3×D4—21no—
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4—21no—
77C22×C3×D4—42no—
78C22×C3×D4D412yes—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2312yes—
81C23×C3×C4C2311yescharacteristic
82C3×AGL(1,ℤ/8)—24no—
83C3×AGL(1,ℤ/8)—42no—
84C2×C3×SD16—22no—
85C2×C3×D8—22no—
86C2×C3×M16—21no—
87C2×C3×M16—42no—
88C2×C3×M16C2312yes—
89C2×C3×M16C2312yes—
90C22×C3×C8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—21no—
93C3×#127—21no—
94C3×#127—24no—
95C3×#127—42no—
96C3×#126—22no—
97C3×#126—22no—
98C3×#125—21no—
99C3×#125—21no—
100C3×#124—22no—
101C3×#124—22no—
102C3×#124—21no—
103C3×#123—22no—
104C3×#123—22no—
105C3×#123—22no—
106C3×#123—22no—
107C3×#123—21no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8D411yescharacteristic, complemented
111C3×C22⋊Q8D411yescharacteristic, complemented
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—21no—
116C3×#121—21no—
117C3×#121—21no—
118C3×#121—21no—
119C3×#121—21no—
120C3×#121—21no—
121C3×#121D411yescharacteristic, complemented
122C3×#121D411yescharacteristic, complemented
123C3×#120—21no—
124C3×#120—22no—
125C3×#120—48no—
126C3×C4×Q8—21no—
127C3×C4×D4—22no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—22no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×#117—22no—
138C3×#117—21no—
139C3×#117—21no—
140C3×#117—21no—
141C3×#117D411yescharacteristic, complemented
142C3×#117D411yescharacteristic, complemented
143C3×#117C2311yescharacteristic
144C3×#117C2311yescharacteristic
145C3×#117C2311yescharacteristic
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4D411yescharacteristic, complemented
148C2×C3×C4⋊C4D411yescharacteristic, complemented
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—22no—
153C2×C3×C22⋊C4—24no—
154C2×C3×C22⋊C4D412yes—
155C2×C3×C42—21no—
156C2×C3×C42C2312yes—
157C3×#104—42no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#100—42no—
165C3×C22⋊C8—21no—
166C3×C22⋊C8—21no—
167C3×#95—21no—
168C23×D4C22×C311yescharacteristic
169C2×AGL(1,ℤ/8)C22×C312yes—
170C22×M16C22×C311yescharacteristic
171#555—21no—
172#553—21no—
173#553—21no—
174#551—22no—
175#547—21no—
176#546—22no—
177#544C22×C311yescharacteristic, complemented
178#542—21no—
179#540—21no—
180#535C22×C311yescharacteristic, complemented
181#532—21no—
182C2×#127C22×C312yes—
183#529—21no—
184#525C22×C311yescharacteristic
185C2×#121C22×C311yescharacteristic
186C2×#120—22no—
187#520C22×C311yescharacteristic, complemented
188#518C22×C311yescharacteristic, complemented
189C2×#117C22×C311yescharacteristic
190#450—21no—
191#450—21no—
192#447—21no—
193#447—21no—
194C2×#104C22×C312yescomplemented
195#418—21no—
196#418—21no—
197#418C22×C312yes—
198#418C22×C312yes—
199#418C22×C312yes—
200C2×#102—21no—
201C2×#102—21no—
202C2×#100C22×C312yescomplemented
203#407C22×C311yescharacteristic
204#392—22no—
205#390C22×C312yes—
206C4×C22⋊C4C22×C311yescharacteristic
207#343C22×C312yescomplemented
208#339C22×C312yescomplemented
209#339C22×C312yescomplemented
210#339C22×C312yescomplemented
211C24×C3—22no—
212C24×C3—44no—
213C24×C3—44no—
214C24×C3—41no—
215C24×C3—41no—
216C24×C3—82no—
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D412yes—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—84no—
222C2×C3×Q8—22no—
223C2×C3×Q8C2×D411yescharacteristic
224C2×C3×D4—24no—
225C2×C3×D4—24no—
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—22no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—48no—
248C2×C3×D4—44no—
249C2×C3×D4—48no—
250C2×C3×D4—41no—
251C2×C3×D4—41no—
252C2×C3×D4—84no—
253C2×C3×D4C2×D411yescharacteristic
254C2×C3×D4#4114yescomplemented
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—21no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2411yescharacteristic
271C3×SD16—44no—
272C3×D8—44no—
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—22no—
276C3×M16—22no—
277C3×M16—42no—
278C2×C3×C8—22no—
279C2×C3×C8—22no—
280C2×C3×C8—42no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—22no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D411yescharacteristic
292C3×C4⋊C4C2×D411yescharacteristic
293C3×C4⋊C4C2×D411yescharacteristic
294C3×C4⋊C4C2×D411yescharacteristic
295C3×C4⋊C4C2×D411yescharacteristic
296C3×C4⋊C4C2×D411yescharacteristic
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—21no—
313C3×C22⋊C4—21no—
314C3×C22⋊C4—48no—
315C3×C42—22no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—21no—
321C3×C42—22no—
322C3×C42—22no—
323C25—21no—
324C2×#41—22no—
325C2×#41C23×C311yescharacteristic
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—42no—
334C22×D4C3×D412yes—
335C22×D4C23×C311yescharacteristic
336C22×D4C23×C312yes—
337C23×C4C23×C311yescharacteristic
338AGL(1,ℤ/8)—24no—
339AGL(1,ℤ/8)—42no—
340C2×SD16—22no—
341C2×D8—22no—
342C2×M16—21no—
343C2×M16—42no—
344C2×M16C23×C312yes—
345C2×M16C23×C312yes—
346C22×C8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349#127—21no—
350#127—24no—
351#127—42no—
352#126—22no—
353#126—22no—
354#125—21no—
355#125—21no—
356#124—22no—
357#124—22no—
358#124—21no—
359#123—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—21no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8C3×D411yescharacteristic, complemented
367C22⋊Q8C3×D411yescharacteristic, complemented
368#121—22no—
369#121—22no—
370#121—22no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121C3×D411yescharacteristic, complemented
378#121C3×D411yescharacteristic, complemented
379#120—21no—
380#120—22no—
381#120—48no—
382C4×Q8—21no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—22no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117C3×D411yescharacteristic, complemented
398#117C3×D411yescharacteristic, complemented
399#117C23×C311yescharacteristic
400#117C23×C311yescharacteristic
401#117C23×C311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4C3×D411yescharacteristic, complemented
404C2×C4⋊C4C3×D411yescharacteristic, complemented
405C2×C4⋊C4C23×C311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4C3×D412yes—
411C2×C42—21no—
412C2×C42C23×C312yes—
413#104—42no—
414#102—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418#102—22no—
419#102—22no—
420#100—42no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423#95—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—21no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—41no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—82no—
440C23×C3—82no—
441C23×C3—82no—
442C23×C3—816no—
443C23×C3—82no—
444C23×C3#12011yescharacteristic
445C23×C3#12011yescharacteristic
446C23×C3C22×D411yescharacteristic
447C3×Q8—22no—
448C3×Q8—82no—
449C3×D4—24no—
450C3×D4—22no—
451C3×D4—24no—
452C3×D4—44no—
453C3×D4—44no—
454C3×D4—42no—
455C3×D4—44no—
456C3×D4—42no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—42no—
460C3×D4—42no—
461C3×D4—42no—
462C3×D4—81no—
463C3×D4—82no—
464C3×D4—82no—
465C3×D4—82no—
466C3×D4—816no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—24no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—42no—
489C2×C3×C4—81no—
490C2×C3×C4—82no—
491C2×C3×C4—82no—
492C2×C3×C4—82no—
493C2×C3×C4#12011yescharacteristic
494C2×C3×C4#12011yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4112yes—
498C2×C3×C4H(5,𝔽2)12yes—
499C3×C8—42no—
500C3×C8—42no—
501C24—22no—
502C24—44no—
503C24—44no—
504C24—41no—
505C24—41no—
506C24—82no—
507C24C2×C3×D411yescharacteristic
508C24C2×C3×D412yes—
509#41—22no—
510#41—22no—
511#41—84no—
512C2×Q8—22no—
513C2×Q8C2×C3×D411yescharacteristic
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—48no—
538C2×D4—44no—
539C2×D4—48no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—84no—
543C2×D4C2×C3×D411yescharacteristic
544C2×D4C3×#4114yescomplemented
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C2×C3×D412yes—
560C22×C4C24×C311yescharacteristic
561SD16—44no—
562D8—44no—
563M16—22no—
564M16—22no—
565M16—22no—
566M16—22no—
567M16—42no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—42no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×C3×D411yescharacteristic
582C4⋊C4C2×C3×D411yescharacteristic
583C4⋊C4C2×C3×D411yescharacteristic
584C4⋊C4C2×C3×D411yescharacteristic
585C4⋊C4C2×C3×D411yescharacteristic
586C4⋊C4C2×C3×D411yescharacteristic
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—24no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—48no—
605C42—22no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—22no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—44no—
621C22×C3—48no—
622C22×C3—41no—
623C22×C3—44no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—84no—
630C22×C3—84no—
631C22×C3—88no—
632C22×C3—88no—
633C22×C3—82no—
634C22×C3—82no—
635C22×C3#45312yes—
636C22×C3C2×#12011yescharacteristic
637C22×C3#54612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—44no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—42no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4#52511yescharacteristic
650C3×C4#53511yescharacteristic
651C3×C4#54612yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—21no—
656C23—24no—
657C23—24no—
658C23—41no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23—816no—
671C23—82no—
672C23C3×#12011yescharacteristic
673C23C3×#12011yescharacteristic
674C23C22×C3×D411yescharacteristic
675Q8—22no—
676Q8—82no—
677D4—24no—
678D4—22no—
679D4—24no—
680D4—44no—
681D4—44no—
682D4—44no—
683D4—42no—
684D4—42no—
685D4—41no—
686D4—42no—
687D4—41no—
688D4—42no—
689D4—42no—
690D4—82no—
691D4—81no—
692D4—82no—
693D4—82no—
694D4—816no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4C3×#12011yescharacteristic
722C2×C4C3×#12011yescharacteristic
723C2×C4C22×C3×D411yescharacteristic
724C2×C4C22×C3×D411yescharacteristic
725C2×C4C2×C3×#4112yes—
726C2×C4C3×H(5,𝔽2)12yes—
727C8—42no—
728C8—42no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—41no—
732C2×C3—81no—
733C2×C3—82no—
734C2×C3—84no—
735C2×C3#240411yescharacteristic
736C2×C3C2×#45311yescharacteristic
737C2×C3#302111yescharacteristic
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—44no—
746C22—48no—
747C22—41no—
748C22—44no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—84no—
755C22—84no—
756C22—88no—
757C22—88no—
758C22—82no—
759C22—82no—
760C22C3×#45312yes—
761C22C2×C3×#12011yescharacteristic
762C22C3×#54612yes—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4C3×#52511yescharacteristic
775C4C3×#53511yescharacteristic
776C4C3×#54612yes—
777C3#2395411yescharacteristic, direct product factor, Sylow
778C2—22no—
779C2—22no—
780C2—41no—
781C2—84no—
782C2—82no—
783C2—81no—
784C2C3×#240411yescharacteristic
785C2C2×C3×#45311yescharacteristic
786C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ 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×#3494C2semidirect
2. C3×#3003C2semidirect
3. C2×C3×#418C2semidirect
4. C3×#2433C2semidirect
5. C3×#2027C2semidirect
6. C3×#2002C2semidirect
7. C3×#1900C2semidirect
8. C3×#1887C2semidirect
9. C3×#1883C2semidirect
10. C3×#1871C2semidirect
11. C3×#1826C2semidirect
12. #23954C3direct (N × H)
22. C3×#544C22semidirect
25. C3×#535C22semidirect
32. C3×#520C22semidirect
33. C3×#518C22semidirect
39. C2×C3×#104C22semidirect
47. C2×C3×#100C22semidirect
52. C3×#343C22semidirect
53. C3×#339C22semidirect
54. C3×#339C22semidirect
55. C3×#339C22semidirect
56. #3494C2×C3semidirect
57. #3003C2×C3semidirect
58. C2×#418C2×C3semidirect
59. #2433C2×C3semidirect
60. #2027C2×C3semidirect
61. #2002C2×C3semidirect
62. #1900C2×C3semidirect
63. #1887C2×C3semidirect
64. #1883C2×C3semidirect
65. #1871C2×C3semidirect
66. #1826C2×C3semidirect
110. C3×C22⋊Q8D4semidirect
111. C3×C22⋊Q8D4semidirect
121. C3×#121D4semidirect
122. C3×#121D4semidirect
141. C3×#117D4semidirect
142. C3×#117D4semidirect
147. C2×C3×C4⋊C4D4semidirect
148. C2×C3×C4⋊C4D4semidirect
177. #544C22×C3semidirect
180. #535C22×C3semidirect
187. #520C22×C3semidirect
188. #518C22×C3semidirect
194. C2×#104C22×C3semidirect
202. C2×#100C22×C3semidirect
207. #343C22×C3semidirect
208. #339C22×C3semidirect
209. #339C22×C3semidirect
210. #339C22×C3semidirect
254. C2×C3×D4#41semidirect
366. C22⋊Q8C3×D4semidirect
367. C22⋊Q8C3×D4semidirect
377. #121C3×D4semidirect
378. #121C3×D4semidirect
397. #117C3×D4semidirect
398. #117C3×D4semidirect
403. C2×C4⋊C4C3×D4semidirect
404. C2×C4⋊C4C3×D4semidirect
544. C2×D4C3×#41semidirect
777. C3#23954direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30032
C2×C3×#4182
C3×#24332
C3×#20272
C3×#20022
C3×#19002
C3×#18872
C3×#18832
C3×#18712
C3×#18262
#239543