Finite Group Databasebeta

← C3×#23957 #10642564

Subgroups — C3×#23957 #10642564

Order 768.

1318 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3495C211yesmaximal, characteristic, complemented
2C3×#3003C211yesmaximal, characteristic
3C2×C3×#418C211yesmaximal, characteristic, complemented
4C3×#2435C211yesmaximal, characteristic, complemented
5C3×#2027C212yesmaximal, complemented
6C3×#2003C212yesmaximal, complemented
7C3×#1901C211yesmaximal, characteristic, complemented
8C3×#1888C212yesmaximal, complemented
9C3×#1883C212yesmaximal, complemented
10C3×#1871C211yesmaximal, characteristic, complemented
11C3×#1826C211yesmaximal, characteristic, complemented
12#23957C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)C2212yes—
15C22×C3×M16C2211yescharacteristic
16C3×#556—21no—
17C3×#554—21no—
18C3×#552—21no—
19C3×#552—22no—
20C3×#552—21no—
21C3×#551—22no—
22C3×#544C2211yescharacteristic, complemented
23C3×#542—21no—
24C3×#541—21no—
25C3×#536C2211yescharacteristic, complemented
26C3×#533—21no—
27C3×#529—21no—
28C2×C3×#124C2212yes—
29C3×#525C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C3×#520C2211yescharacteristic, complemented
32C3×#519C2211yescharacteristic, complemented
33C2×C3×#117C2211yescharacteristic
34C3×#450—21no—
35C3×#450—21no—
36C3×#447—21no—
37C3×#447—21no—
38C2×C3×#104C2212yescomplemented
39C3×#418—21no—
40C3×#418—21no—
41C3×#418C2212yes—
42C3×#418C2212yes—
43C3×#418C2212yes—
44C2×C3×#102—21no—
45C2×C3×#102—21no—
46C2×C3×#101C2212yescomplemented
47C3×#407C2211yescharacteristic
48C3×#394—22no—
49C3×#390C2212yes—
50C3×#379—22no—
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×#343C2212yescomplemented
53C3×#339C2212yescomplemented
54C3×#339C2212yescomplemented
55C3×#339C2212yescomplemented
56#3495C2×C311yescharacteristic, complemented
57#3003C2×C311yescharacteristic
58C2×#418C2×C311yescharacteristic, complemented
59#2435C2×C311yescharacteristic, complemented
60#2027C2×C312yescomplemented
61#2003C2×C312yescomplemented
62#1901C2×C311yescharacteristic, complemented
63#1888C2×C312yescomplemented
64#1883C2×C312yescomplemented
65#1871C2×C311yescharacteristic, complemented
66#1826C2×C311yescharacteristic, complemented
67C25×C3—21no—
68C2×C3×#41C2311yescharacteristic
69C22×C3×Q8C2311yescharacteristic
70C22×C3×D4—24no—
71C22×C3×D4—21no—
72C22×C3×D4—21no—
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4—42no—
77C22×C3×D4C2312yes—
78C23×C3×C4C2311yescharacteristic
79C3×AGL(1,ℤ/8)—24no—
80C3×AGL(1,ℤ/8)—42no—
81C2×C3×SD16—22no—
82C2×C3×D8—22no—
83C2×C3×M16—21no—
84C2×C3×M16—42no—
85C2×C3×M16C2312yes—
86C2×C3×M16C2312yes—
87C22×C3×C8—21no—
88C3×C4⋊Q8—21no—
89C3×C4⋊Q8—21no—
90C3×C4⋊Q8—21no—
91C3×#126—22no—
92C3×#126—22no—
93C3×#126—22no—
94C3×#126—22no—
95C3×#125—22no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125—21no—
99C3×#125—21no—
100C3×#124—22no—
101C3×#124—21no—
102C3×#124—24no—
103C3×#124—42no—
104C3×#123—22no—
105C3×#123—22no—
106C3×#123—21no—
107C3×#123—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—21no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—21no—
113C3×C22⋊Q8—21no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—21no—
117C3×C22⋊Q8D411yescharacteristic
118C3×C22⋊Q8D411yescharacteristic
119C3×#121D411yescharacteristic
120C3×#121D411yescharacteristic
121C3×#120—21no—
122C3×C4×Q8—22no—
123C3×C4×Q8—21no—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—22no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×#117—22no—
134C3×#117—22no—
135C3×#117—21no—
136C3×#117—21no—
137C3×#117—22no—
138C3×#117—21no—
139C3×#117D411yescharacteristic
140C3×#117D411yescharacteristic
141C3×#117C2311yescharacteristic
142C3×#117C2311yescharacteristic
143C3×#117C2311yescharacteristic
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4D412yes—
146C2×C3×C4⋊C4D411yescharacteristic
147C2×C3×C4⋊C4D411yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—24no—
152C2×C3×C22⋊C4—24no—
153C2×C3×C22⋊C4D412yes—
154C2×C3×C42—21no—
155C2×C3×C42C2312yes—
156C3×#104—42no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#101—42no—
164C3×C22⋊C8—21no—
165C3×C22⋊C8—21no—
166C3×#95—21no—
167C23×D4C22×C311yescharacteristic
168C2×AGL(1,ℤ/8)C22×C312yes—
169C22×M16C22×C311yescharacteristic
170#556—21no—
171#554—21no—
172#552—21no—
173#552—22no—
174#552—21no—
175#551—22no—
176#544C22×C311yescharacteristic, complemented
177#542—21no—
178#541—21no—
179#536C22×C311yescharacteristic, complemented
180#533—21no—
181#529—21no—
182C2×#124C22×C312yes—
183#525C22×C311yescharacteristic
184C2×C22⋊Q8C22×C311yescharacteristic
185#520C22×C311yescharacteristic, complemented
186#519C22×C311yescharacteristic, complemented
187C2×#117C22×C311yescharacteristic
188#450—21no—
189#450—21no—
190#447—21no—
191#447—21no—
192C2×#104C22×C312yescomplemented
193#418—21no—
194#418—21no—
195#418C22×C312yes—
196#418C22×C312yes—
197#418C22×C312yes—
198C2×#102—21no—
199C2×#102—21no—
200C2×#101C22×C312yescomplemented
201#407C22×C311yescharacteristic
202#394—22no—
203#390C22×C312yes—
204#379—22no—
205C4×C22⋊C4C22×C311yescharacteristic
206#343C22×C312yescomplemented
207#339C22×C312yescomplemented
208#339C22×C312yescomplemented
209#339C22×C312yescomplemented
210C24×C3—22no—
211C24×C3—44no—
212C24×C3—44no—
213C24×C3—41no—
214C24×C3—41no—
215C24×C3—82no—
216C24×C3C2×D411yescharacteristic
217C3×#41—22no—
218C3×#41—22no—
219C2×C3×Q8—22no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—22no—
223C2×C3×Q8—22no—
224C2×C3×Q8C2×D411yescharacteristic
225C2×C3×D4—24no—
226C2×C3×D4—24no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—44no—
236C2×C3×D4—44no—
237C2×C3×D4—44no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—41no—
241C2×C3×D4—41no—
242C2×C3×D4C2×D411yescharacteristic
243C2×C3×D4#4114yes—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C3×SD16—44no—
260C3×D8—44no—
261C3×M16—22no—
262C3×M16—22no—
263C3×M16—22no—
264C3×M16—22no—
265C3×M16—42no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C2×C3×C8—42no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D411yescharacteristic
286C3×C4⋊C4C2×D411yescharacteristic
287C3×C4⋊C4C2×D411yescharacteristic
288C3×C4⋊C4C2×D411yescharacteristic
289C3×C4⋊C4C2×D411yescharacteristic
290C3×C4⋊C4C2×D411yescharacteristic
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—21no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—21no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—48no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—84no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—22no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—21no—
316C3×C42—22no—
317C3×C42—22no—
318C25—21no—
319C2×#41C23×C311yescharacteristic
320C22×Q8C23×C311yescharacteristic
321C22×D4—24no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—42no—
328C22×D4C23×C312yes—
329C23×C4C23×C311yescharacteristic
330AGL(1,ℤ/8)—24no—
331AGL(1,ℤ/8)—42no—
332C2×SD16—22no—
333C2×D8—22no—
334C2×M16—21no—
335C2×M16—42no—
336C2×M16C23×C312yes—
337C2×M16C23×C312yes—
338C22×C8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—22no—
346#125—22no—
347#125—22no—
348#125—22no—
349#125—21no—
350#125—21no—
351#124—22no—
352#124—21no—
353#124—24no—
354#124—42no—
355#123—22no—
356#123—22no—
357#123—21no—
358#123—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8C3×D411yescharacteristic
369C22⋊Q8C3×D411yescharacteristic
370#121C3×D411yescharacteristic
371#121C3×D411yescharacteristic
372#120—21no—
373C4×Q8—22no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384#117—22no—
385#117—22no—
386#117—21no—
387#117—21no—
388#117—22no—
389#117—21no—
390#117C3×D411yescharacteristic
391#117C3×D411yescharacteristic
392#117C23×C311yescharacteristic
393#117C23×C311yescharacteristic
394#117C23×C311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4C3×D412yes—
397C2×C4⋊C4C3×D411yescharacteristic
398C2×C4⋊C4C3×D411yescharacteristic
399C2×C4⋊C4C23×C311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4C3×D412yes—
405C2×C42—21no—
406C2×C42C23×C312yes—
407#104—42no—
408#102—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412#102—22no—
413#102—22no—
414#101—42no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417#95—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—24no—
422C23×C3—41no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—82no—
430C23×C3—82no—
431C23×C3—82no—
432C23×C3—816no—
433C23×C3—82no—
434C23×C3#12011yescharacteristic
435C23×C3#12011yescharacteristic
436C23×C3C22×D411yescharacteristic
437C3×Q8—22no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—42no—
441C3×Q8—82no—
442C3×D4—24no—
443C3×D4—22no—
444C3×D4—24no—
445C3×D4—44no—
446C3×D4—44no—
447C3×D4—42no—
448C3×D4—42no—
449C3×D4—42no—
450C3×D4—42no—
451C3×D4—81no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—42no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—81no—
477C2×C3×C4—82no—
478C2×C3×C4#12011yescharacteristic
479C2×C3×C4#12011yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C2×#4112yes—
483C2×C3×C4H(5,𝔽2)12yes—
484C3×C8—42no—
485C3×C8—42no—
486C24—22no—
487C24—44no—
488C24—44no—
489C24—41no—
490C24—41no—
491C24—82no—
492C24C2×C3×D411yescharacteristic
493#41—22no—
494#41—22no—
495C2×Q8—22no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8C2×C3×D411yescharacteristic
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4C2×C3×D411yescharacteristic
519C2×D4C3×#4114yes—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4C2×C3×D412yes—
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D411yescharacteristic
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C2×C3×D411yescharacteristic
532C22×C4C2×C3×D411yescharacteristic
533C22×C4C2×C3×D412yes—
534C22×C4C24×C311yescharacteristic
535SD16—44no—
536D8—44no—
537M16—22no—
538M16—22no—
539M16—22no—
540M16—22no—
541M16—42no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—42no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4C2×C3×D411yescharacteristic
562C4⋊C4C2×C3×D411yescharacteristic
563C4⋊C4C2×C3×D411yescharacteristic
564C4⋊C4C2×C3×D411yescharacteristic
565C4⋊C4C2×C3×D411yescharacteristic
566C4⋊C4C2×C3×D411yescharacteristic
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—48no—
582C22⋊C4—42no—
583C22⋊C4—84no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—22no—
593C42—22no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—44no—
602C22×C3—48no—
603C22×C3—41no—
604C22×C3—44no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—84no—
608C22×C3—88no—
609C22×C3—88no—
610C22×C3—82no—
611C22×C3—82no—
612C22×C3#45412yes—
613C22×C3C2×#12011yescharacteristic
614C22×C3#54612yes—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—82no—
627C3×C4#52511yescharacteristic
628C3×C4#53511yescharacteristic
629C3×C4#54612yes—
630C23—22no—
631C23—22no—
632C23—21no—
633C23—24no—
634C23—41no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—42no—
640C23—42no—
641C23—82no—
642C23—82no—
643C23—82no—
644C23—816no—
645C23—82no—
646C23C3×#12011yescharacteristic
647C23C3×#12011yescharacteristic
648C23C22×C3×D411yescharacteristic
649Q8—22no—
650Q8—41no—
651Q8—41no—
652Q8—42no—
653Q8—82no—
654D4—24no—
655D4—22no—
656D4—24no—
657D4—44no—
658D4—44no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—81no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—81no—
689C2×C4—82no—
690C2×C4C3×#12011yescharacteristic
691C2×C4C3×#12011yescharacteristic
692C2×C4C22×C3×D411yescharacteristic
693C2×C4C22×C3×D411yescharacteristic
694C2×C4C2×C3×#4112yes—
695C2×C4C3×H(5,𝔽2)12yes—
696C8—42no—
697C8—42no—
698C2×C3—22no—
699C2×C3—22no—
700C2×C3—41no—
701C2×C3—81no—
702C2×C3—84no—
703C2×C3#240411yescharacteristic
704C2×C3C2×#45411yescharacteristic
705C2×C3#302111yescharacteristic
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—44no—
714C22—48no—
715C22—41no—
716C22—44no—
717C22—41no—
718C22—41no—
719C22—84no—
720C22—88no—
721C22—88no—
722C22—82no—
723C22—82no—
724C22C3×#45412yes—
725C22C2×C3×#12011yescharacteristic
726C22C3×#54612yes—
727C4—21no—
728C4—21no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—82no—
739C4C3×#52511yescharacteristic
740C4C3×#53511yescharacteristic
741C4C3×#54612yes—
742C3#2395711yescharacteristic, direct product factor, Sylow
743C2—22no—
744C2—22no—
745C2—41no—
746C2—84no—
747C2—81no—
748C2C3×#240411yescharacteristic
749C2C2×C3×#45411yescharacteristic
750C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3003C2
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×#3495C2semidirect
3. C2×C3×#418C2semidirect
4. C3×#2435C2semidirect
5. C3×#2027C2semidirect
6. C3×#2003C2semidirect
7. C3×#1901C2semidirect
8. C3×#1888C2semidirect
9. C3×#1883C2semidirect
10. C3×#1871C2semidirect
11. C3×#1826C2semidirect
12. #23957C3direct (N × H)
22. C3×#544C22semidirect
25. C3×#536C22semidirect
31. C3×#520C22semidirect
32. C3×#519C22semidirect
38. C2×C3×#104C22semidirect
46. C2×C3×#101C22semidirect
52. C3×#343C22semidirect
53. C3×#339C22semidirect
54. C3×#339C22semidirect
55. C3×#339C22semidirect
56. #3495C2×C3semidirect
58. C2×#418C2×C3semidirect
59. #2435C2×C3semidirect
60. #2027C2×C3semidirect
61. #2003C2×C3semidirect
62. #1901C2×C3semidirect
63. #1888C2×C3semidirect
64. #1883C2×C3semidirect
65. #1871C2×C3semidirect
66. #1826C2×C3semidirect
176. #544C22×C3semidirect
179. #536C22×C3semidirect
185. #520C22×C3semidirect
186. #519C22×C3semidirect
192. C2×#104C22×C3semidirect
200. C2×#101C22×C3semidirect
206. #343C22×C3semidirect
207. #339C22×C3semidirect
208. #339C22×C3semidirect
209. #339C22×C3semidirect
742. C3#23957direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34952
C3×#30032
C2×C3×#4182
C3×#24352
C3×#20272
C3×#20032
C3×#19012
C3×#18882
C3×#18832
C3×#18712
C3×#18262
#239573