Finite Group Databasebeta

← C3×#60433 #10679040

Subgroups — C3×#60433 #10679040

Order 768.

2678 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#578C211yesmaximal, characteristic, complemented
2C2×C3×#577C211yesmaximal, characteristic, complemented
3C3×#3500C211yesmaximal, characteristic, complemented
4C3×C4×2−1+4C211yesmaximal, characteristic, complemented
5C3×#3046C213yesmaximal, complemented
6C3×#3045C213yesmaximal, complemented
7C3×#3044C213yesmaximal, complemented
8C3×#3043C213yesmaximal, complemented
9C3×#3040C213yesmaximal, complemented
10C3×#3037C213yesmaximal, complemented
11C3×#3035C213yesmaximal, complemented
12C2×C3×#464C213yesmaximal, complemented
13C3×#2906C211yesmaximal, characteristic, complemented
14C3×#2898C211yesmaximal, characteristic, complemented
15C3×#2897C211yesmaximal, characteristic, complemented
16#60433C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×2−1+4C2211yescharacteristic
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C3×#578—28no—
21C3×#577—28no—
22C2×C3×#137C2213yes—
23C2×C3×#137C2213yescomplemented
24C2×C3×#137C2213yescomplemented
25C2×C3×AGL(1,ℤ/8)C2213yes—
26C2×C3×#135C2213yes—
27C2×C3×#135C2213yescomplemented
28C22×C3×Q16C2213yescomplemented
29C22×C3×SD16C2213yes—
30C2×C3×#131C2211yescharacteristic
31C2×C3×#131C2211yescharacteristic
32C3×#548—21no—
33C3×#548—21no—
34C3×#546—23no—
35C3×#546—23no—
36C3×#536C2213yes—
37C3×#535C2213yes—
38C3×#532C2213yes—
39C2×C3×#124C2213yes—
40C3×#520—23no—
41C3×#520C2211yescharacteristic
42C3×#520C2213yescomplemented
43C3×#519—21no—
44C3×#519C2213yescomplemented
45C3×C4×#41—23no—
46C3×C4×#41C2211yescharacteristic
47C3×C4×#41C2213yescomplemented
48C2×C3×C4×Q8—21no—
49C2×C3×C4×Q8C2213yescomplemented
50C3×#464C2213yescomplemented
51C3×#464C2216yescomplemented
52C3×#464C2216yescomplemented
53C3×#464C2216yescomplemented
54C3×#464C2213yescomplemented
55C3×#464C2216yescomplemented
56C3×#463C2211yescharacteristic, complemented
57C3×#463C2213yescomplemented
58C3×#463C2216yescomplemented
59C3×#462C2213yescomplemented
60C3×#462C2216yescomplemented
61C3×#461C2213yescomplemented
62C3×#460C2213yescomplemented
63C3×#460C2216yescomplemented
64C3×#459C2213yescomplemented
65C3×#424C2213yescomplemented
66C3×#424C2213yescomplemented
67C3×#423C2213yescomplemented
68C2×C3×C4⋊C8C2213yescomplemented
69C3×#419C2213yescomplemented
70C3×#418C2213yes—
71C3×#417C2213yes—
72C3×#417C2213yescomplemented
73C3×#416C2213yes—
74C3×#416C2213yescomplemented
75C2×C3×#103C2213yescomplemented
76C2×C3×#102C2213yes—
77C2×#578C2×C311yescharacteristic, complemented
78C2×#577C2×C311yescharacteristic, complemented
79#3500C2×C311yescharacteristic, complemented
80C4×2−1+4C2×C311yescharacteristic, complemented
81#3046C2×C313yescomplemented
82#3045C2×C313yescomplemented
83#3044C2×C313yescomplemented
84#3043C2×C313yescomplemented
85#3040C2×C313yescomplemented
86#3037C2×C313yescomplemented
87#3035C2×C313yescomplemented
88C2×#464C2×C313yescomplemented
89#2906C2×C311yescharacteristic, complemented
90#2898C2×C311yescharacteristic, complemented
91#2897C2×C311yescharacteristic, complemented
92C3×2−1+4—24no—
93C3×2−1+4—24no—
94C3×2−1+4—24no—
95C3×2−1+4D418yescomplemented
96C3×H(5,𝔽2)—24no—
97C3×H(5,𝔽2)—24no—
98C2×C3×#41—21no—
99C2×C3×#41—23no—
100C2×C3×#41—23no—
101C2×C3×#41C2313yes—
102C2×C3×#41C2313yes—
103C2×C3×#41C2313yes—
104C2×C3×#41C2311yescharacteristic
105C22×C3×Q8—21no—
106C22×C3×Q8—21no—
107C22×C3×Q8C2313yes—
108C22×C3×Q8C2313yes—
109C22×C3×D4—23no—
110C22×C3×D4C2313yes—
111C3×#137—212no—
112C3×#137—212no—
113C3×#137—212no—
114C3×AGL(1,ℤ/8)—212no—
115C3×#135—212no—
116C3×#135—212no—
117C2×C3×Q16—212no—
118C2×C3×Q16C2313yes—
119C2×C3×Q16C2316yes—
120C2×C3×Q16C2313yes—
121C2×C3×SD16—212no—
122C2×C3×SD16C2313yes—
123C2×C3×SD16C2316yes—
124C2×C3×SD16C2311yescharacteristic
125C2×C3×SD16C2313yes—
126C2×C3×SD16C2313yes—
127C2×C3×D8C2313yes—
128C2×C3×D8C2311yescharacteristic
129C3×#131—24no—
130C3×#131—24no—
131C2×C3×M16C2313yes—
132C2×C3×M16C2313yes—
133C22×C3×C8C2313yes—
134C22×C3×C8C2313yes—
135C3×C4⋊Q8C2313yes—
136C3×#127C2313yes—
137C3×#124—23no—
138C3×#124—23no—
139C3×#124C2313yes—
140C3×#124C2316yes—
141C3×#124C2311yescharacteristic
142C3×#123—26no—
143C3×C22⋊Q8—23no—
144C3×C22⋊Q8—23no—
145C3×#121—23no—
146C3×#121—23no—
147C3×#121—23no—
148C3×#121—23no—
149C3×#120—26no—
150C3×C4×Q8—21no—
151C3×C4×Q8—23no—
152C3×C4×Q8—23no—
153C3×C4×Q8—23no—
154C3×C4×Q8—23no—
155C3×C4×Q8D411yescharacteristic
156C3×C4×Q8D411yescharacteristic
157C3×C4×Q8C2316yes—
158C3×C4×Q8C2313yes—
159C3×C4×Q8C2313yes—
160C3×C4×D4—23no—
161C3×C4×D4—23no—
162C3×C4×D4—23no—
163C3×C4×D4—26no—
164C3×C4×D4—23no—
165C3×C4×D4—23no—
166C3×C4×D4D413yes—
167C3×C4×D4D413yes—
168C3×C4×D4C2313yes—
169C3×C4×D4C2311yescharacteristic
170C3×#117—23no—
171C3×#117—26no—
172C3×#117—23no—
173C3×#117C2313yes—
174C3×#117C2313yes—
175C2×C3×C4⋊C4—23no—
176C2×C3×C4⋊C4—23no—
177C2×C3×C4⋊C4C2313yes—
178C2×C3×C22⋊C4—23no—
179C2×C3×C22⋊C4—23no—
180C2×C3×C42—23no—
181C2×C3×C42—23no—
182C2×C3×C42C2313yes—
183C3×C4⋊C8C2311yescharacteristic
184C3×C4⋊C8C2313yes—
185C3×C4⋊C8C2313yes—
186C3×C4⋊C8C2313yes—
187C3×C4⋊C8C2316yes—
188C3×#103C2313yes—
189C3×#103C2316yes—
190C3×#103C2311yescharacteristic
191C3×#103C2313yes—
192C3×#103C2313yes—
193C3×#102C2313yes—
194C3×#102C2316yes—
195C3×#102C2313yes—
196C3×#102C2311yescharacteristic
197C3×#102C2313yes—
198C2×2−1+4C22×C311yescharacteristic
199C2×2−1+4C22×C311yescharacteristic
200C2×H(5,𝔽2)C22×C311yescharacteristic
201#578—28no—
202#577—28no—
203C2×#137C22×C313yes—
204C2×#137C22×C313yescomplemented
205C2×#137C22×C313yescomplemented
206C2×AGL(1,ℤ/8)C22×C313yes—
207C2×#135C22×C313yes—
208C2×#135C22×C313yescomplemented
209C22×Q16C22×C313yescomplemented
210C22×SD16C22×C313yes—
211C2×#131C22×C311yescharacteristic
212C2×#131C22×C311yescharacteristic
213#548—21no—
214#548—21no—
215#546—23no—
216#546—23no—
217#536C22×C313yes—
218#535C22×C313yes—
219#532C22×C313yes—
220C2×#124C22×C313yes—
221#520—23no—
222#520C22×C311yescharacteristic
223#520C22×C313yescomplemented
224#519—21no—
225#519C22×C313yescomplemented
226C4×#41—23no—
227C4×#41C22×C311yescharacteristic
228C4×#41C22×C313yescomplemented
229C2×C4×Q8—21no—
230C2×C4×Q8C22×C313yescomplemented
231#464C22×C313yescomplemented
232#464C22×C316yescomplemented
233#464C22×C316yescomplemented
234#464C22×C316yescomplemented
235#464C22×C313yescomplemented
236#464C22×C316yescomplemented
237#463C22×C311yescharacteristic, complemented
238#463C22×C313yescomplemented
239#463C22×C316yescomplemented
240#462C22×C313yescomplemented
241#462C22×C316yescomplemented
242#461C22×C313yescomplemented
243#460C22×C313yescomplemented
244#460C22×C316yescomplemented
245#459C22×C313yescomplemented
246#424C22×C313yescomplemented
247#424C22×C313yescomplemented
248#423C22×C313yescomplemented
249C2×C4⋊C8C22×C313yescomplemented
250#419C22×C313yescomplemented
251#418C22×C313yes—
252#417C22×C313yes—
253#417C22×C313yescomplemented
254#416C22×C313yes—
255#416C22×C313yescomplemented
256C2×#103C22×C313yescomplemented
257C2×#102C22×C313yes—
258C24×C3—23no—
259C3×#41—224no—
260C3×#41—26no—
261C3×#41—26no—
262C3×#41—26no—
263C3×#41—26no—
264C3×#41—26no—
265C3×#41—44no—
266C3×#41—412no—
267C3×#41C2×D4112yes—
268C3×#41C2×D414yes—
269C3×#41#4114yes—
270C2×C3×Q8—28no—
271C2×C3×Q8—23no—
272C2×C3×Q8—23no—
273C2×C3×Q8—26no—
274C2×C3×Q8—26no—
275C2×C3×Q8—26no—
276C2×C3×Q8—44no—
277C2×C3×Q8C2×D4112yes—
278C2×C3×Q8C2×D411yescharacteristic
279C2×C3×Q8C2413yes—
280C2×C3×Q8C2411yescharacteristic
281C2×C3×Q8C2413yes—
282C2×C3×D4—23no—
283C2×C3×D4—23no—
284C2×C3×D4—23no—
285C2×C3×D4—26no—
286C2×C3×D4—23no—
287C2×C3×D4—23no—
288C2×C3×D4—23no—
289C2×C3×D4—26no—
290C2×C3×D4—412no—
291C2×C3×D4C2×D413yes—
292C2×C3×D4C2413yes—
293C2×C3×D4C2411yescharacteristic
294C2×C3×D4C2411yescharacteristic
295C22×C3×C4—23no—
296C22×C3×C4—23no—
297C22×C3×C4—23no—
298C22×C3×C4—23no—
299C22×C3×C4—21no—
300C22×C3×C4—23no—
301C22×C3×C4—23no—
302C22×C3×C4—23no—
303C22×C3×C4C2×D413yes—
304C22×C3×C4C2×D413yes—
305C22×C3×C4C2413yes—
306C3×Q16—26no—
307C3×Q16—212no—
308C3×Q16—26no—
309C3×SD16—26no—
310C3×SD16—212no—
311C3×SD16—26no—
312C3×SD16—22no—
313C3×SD16—26no—
314C3×D8—22no—
315C3×D8—26no—
316C3×M16—26no—
317C3×M16—26no—
318C2×C3×C8—26no—
319C2×C3×C8—26no—
320C2×C3×C8C2411yescharacteristic
321C2×C3×C8C2413yes—
322C2×C3×C8C2411yescharacteristic
323C2×C3×C8C2413yes—
324C3×C4⋊C4—26no—
325C3×C4⋊C4—23no—
326C3×C4⋊C4—23no—
327C3×C4⋊C4—23no—
328C3×C4⋊C4—23no—
329C3×C4⋊C4—23no—
330C3×C4⋊C4C2×D413yes—
331C3×C4⋊C4C2×D413yes—
332C3×C4⋊C4C2413yes—
333C3×C4⋊C4C2411yescharacteristic
334C3×C22⋊C4—23no—
335C3×C22⋊C4—23no—
336C3×C22⋊C4—23no—
337C3×C22⋊C4—26no—
338C3×C22⋊C4—26no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—23no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4C2×D416yes—
344C3×C42—23no—
345C3×C42—23no—
346C3×C42—26no—
347C3×C42—23no—
348C3×C42C2×D413yes—
349C3×C42C2×D413yes—
350C3×C42C2411yescharacteristic
351C3×C42C2413yes—
3522−1+4—24no—
3532−1+4—24no—
3542−1+4—24no—
3552−1+4C3×D418yescomplemented
356H(5,𝔽2)—24no—
357H(5,𝔽2)—24no—
358C2×#41—21no—
359C2×#41—23no—
360C2×#41—23no—
361C2×#41C23×C313yes—
362C2×#41C23×C313yes—
363C2×#41C23×C313yes—
364C2×#41C23×C311yescharacteristic
365C22×Q8—21no—
366C22×Q8—21no—
367C22×Q8C23×C313yes—
368C22×Q8C23×C313yes—
369C22×D4—23no—
370C22×D4C23×C313yes—
371#137—212no—
372#137—212no—
373#137—212no—
374AGL(1,ℤ/8)—212no—
375#135—212no—
376#135—212no—
377C2×Q16—212no—
378C2×Q16C23×C313yes—
379C2×Q16C23×C316yes—
380C2×Q16C23×C313yes—
381C2×SD16—212no—
382C2×SD16C23×C313yes—
383C2×SD16C23×C316yes—
384C2×SD16C23×C311yescharacteristic
385C2×SD16C23×C313yes—
386C2×SD16C23×C313yes—
387C2×D8C23×C313yes—
388C2×D8C23×C311yescharacteristic
389#131—24no—
390#131—24no—
391C2×M16C23×C313yes—
392C2×M16C23×C313yes—
393C22×C8C23×C313yes—
394C22×C8C23×C313yes—
395C4⋊Q8C23×C313yes—
396#127C23×C313yes—
397#124—23no—
398#124—23no—
399#124C23×C313yes—
400#124C23×C316yes—
401#124C23×C311yescharacteristic
402#123—26no—
403C22⋊Q8—23no—
404C22⋊Q8—23no—
405#121—23no—
406#121—23no—
407#121—23no—
408#121—23no—
409#120—26no—
410C4×Q8—21no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8C3×D411yescharacteristic
416C4×Q8C3×D411yescharacteristic
417C4×Q8C23×C313yes—
418C4×Q8C23×C316yes—
419C4×Q8C23×C313yes—
420C4×D4—23no—
421C4×D4—23no—
422C4×D4—23no—
423C4×D4—26no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4C3×D413yes—
427C4×D4C3×D413yes—
428C4×D4C23×C311yescharacteristic
429C4×D4C23×C313yes—
430#117—23no—
431#117—26no—
432#117—23no—
433#117C23×C313yes—
434#117C23×C313yes—
435C2×C4⋊C4—23no—
436C2×C4⋊C4—23no—
437C2×C4⋊C4C23×C313yes—
438C2×C22⋊C4—23no—
439C2×C22⋊C4—23no—
440C2×C42—23no—
441C2×C42—23no—
442C2×C42C23×C313yes—
443C4⋊C8C23×C311yescharacteristic
444C4⋊C8C23×C313yes—
445C4⋊C8C23×C313yes—
446C4⋊C8C23×C313yes—
447C4⋊C8C23×C316yes—
448#103C23×C313yes—
449#103C23×C316yes—
450#103C23×C311yescharacteristic
451#103C23×C313yes—
452#103C23×C313yes—
453#102C23×C313yes—
454#102C23×C316yes—
455#102C23×C313yes—
456#102C23×C311yescharacteristic
457#102C23×C313yes—
458C23×C3—21no—
459C23×C3—23no—
460C23×C3—21no—
461C23×C3—46no—
462C23×C3—83no—
463C23×C3—83no—
464C23×C3C22×D413yes—
465C3×Q8—212no—
466C3×Q8—23no—
467C3×Q8—23no—
468C3×Q8—21no—
469C3×Q8—23no—
470C3×Q8—21no—
471C3×Q8—46no—
472C3×Q8#12114yes—
473C3×Q8C22×D416yes—
474C3×D4—212no—
475C3×D4—23no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—23no—
479C3×D4—21no—
480C3×D4—46no—
481C3×D4—46no—
482C3×D4—46no—
483C3×D4—83no—
484C3×D4—83no—
485C3×D4#121112yes—
486C3×D4C22×D412yes—
487C2×C3×C4—212no—
488C2×C3×C4—23no—
489C2×C3×C4—212no—
490C2×C3×C4—21no—
491C2×C3×C4—23no—
492C2×C3×C4—23no—
493C2×C3×C4—21no—
494C2×C3×C4—43no—
495C2×C3×C4—43no—
496C2×C3×C4—42no—
497C2×C3×C4—46no—
498C2×C3×C4—46no—
499C2×C3×C4—46no—
500C2×C3×C4—83no—
501C2×C3×C4—83no—
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D413yes—
504C2×C3×C4C22×D413yes—
505C2×C3×C4C22×D411yescharacteristic
506C2×C3×C4C22×D413yes—
507C2×C3×C4C22×D416yes—
508C2×C3×C4C2×#4116yes—
509C2×C3×C4C2511yescharacteristic
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—23no—
513C3×C8—23no—
514C24—23no—
515#41—224no—
516#41—26no—
517#41—26no—
518#41—26no—
519#41—26no—
520#41—26no—
521#41—44no—
522#41—412no—
523#41C2×C3×D4112yes—
524#41C2×C3×D414yes—
525#41C3×#4114yes—
526C2×Q8—28no—
527C2×Q8—23no—
528C2×Q8—23no—
529C2×Q8—26no—
530C2×Q8—26no—
531C2×Q8—26no—
532C2×Q8—44no—
533C2×Q8C2×C3×D4112yes—
534C2×Q8C2×C3×D411yescharacteristic
535C2×Q8C24×C313yes—
536C2×Q8C24×C311yescharacteristic
537C2×Q8C24×C313yes—
538C2×D4—23no—
539C2×D4—23no—
540C2×D4—23no—
541C2×D4—26no—
542C2×D4—23no—
543C2×D4—23no—
544C2×D4—23no—
545C2×D4—26no—
546C2×D4—412no—
547C2×D4C2×C3×D413yes—
548C2×D4C24×C313yes—
549C2×D4C24×C311yescharacteristic
550C2×D4C24×C311yescharacteristic
551C22×C4—23no—
552C22×C4—23no—
553C22×C4—23no—
554C22×C4—23no—
555C22×C4—21no—
556C22×C4—23no—
557C22×C4—23no—
558C22×C4—23no—
559C22×C4C2×C3×D413yes—
560C22×C4C2×C3×D413yes—
561C22×C4C24×C313yes—
562Q16—26no—
563Q16—212no—
564Q16—26no—
565SD16—26no—
566SD16—212no—
567SD16—26no—
568SD16—22no—
569SD16—26no—
570D8—22no—
571D8—26no—
572M16—26no—
573M16—26no—
574C2×C8—26no—
575C2×C8—26no—
576C2×C8C24×C311yescharacteristic
577C2×C8C24×C313yes—
578C2×C8C24×C311yescharacteristic
579C2×C8C24×C313yes—
580C4⋊C4—26no—
581C4⋊C4—23no—
582C4⋊C4—23no—
583C4⋊C4—23no—
584C4⋊C4—23no—
585C4⋊C4—23no—
586C4⋊C4C2×C3×D413yes—
587C4⋊C4C2×C3×D413yes—
588C4⋊C4C24×C313yes—
589C4⋊C4C24×C311yescharacteristic
590C22⋊C4—23no—
591C22⋊C4—23no—
592C22⋊C4—23no—
593C22⋊C4—26no—
594C22⋊C4—26no—
595C22⋊C4—21no—
596C22⋊C4—23no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4C2×C3×D416yes—
600C42—23no—
601C42—23no—
602C42—26no—
603C42—23no—
604C42C2×C3×D413yes—
605C42C2×C3×D413yes—
606C42C24×C311yescharacteristic
607C42C24×C313yes—
608C22×C3—23no—
609C22×C3—23no—
610C22×C3—22no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—43no—
615C22×C3—41no—
616C22×C3—43no—
617C22×C3—41no—
618C22×C3—43no—
619C22×C3—166no—
620C22×C3C2×#12116yes—
621C22×C3C23×D411yescharacteristic
622C3×C4—21no—
623C3×C4—23no—
624C3×C4—21no—
625C3×C4—23no—
626C3×C4—26no—
627C3×C4—43no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—43no—
631C3×C4C2×#12116yes—
632C3×C4C23×D411yescharacteristic
633C3×C4C22×#4111yescharacteristic
634C23—21no—
635C23—23no—
636C23—21no—
637C23—46no—
638C23—83no—
639C23—83no—
640C23C22×C3×D413yes—
641Q8—23no—
642Q8—212no—
643Q8—23no—
644Q8—21no—
645Q8—23no—
646Q8—21no—
647Q8—46no—
648Q8C3×#12114yes—
649Q8C22×C3×D416yes—
650D4—212no—
651D4—23no—
652D4—21no—
653D4—21no—
654D4—23no—
655D4—21no—
656D4—46no—
657D4—46no—
658D4—46no—
659D4—83no—
660D4—83no—
661D4C3×#121112yes—
662D4C22×C3×D412yes—
663C2×C4—23no—
664C2×C4—212no—
665C2×C4—212no—
666C2×C4—21no—
667C2×C4—23no—
668C2×C4—23no—
669C2×C4—21no—
670C2×C4—43no—
671C2×C4—43no—
672C2×C4—42no—
673C2×C4—46no—
674C2×C4—46no—
675C2×C4—46no—
676C2×C4—83no—
677C2×C4—83no—
678C2×C4C22×C3×D411yescharacteristic
679C2×C4C22×C3×D413yes—
680C2×C4C22×C3×D413yes—
681C2×C4C22×C3×D411yescharacteristic
682C2×C4C22×C3×D416yes—
683C2×C4C22×C3×D413yes—
684C2×C4C2×C3×#4116yes—
685C2×C4C25×C311yescharacteristic
686C8—21no—
687C8—21no—
688C8—23no—
689C8—23no—
690C2×C3—26no—
691C2×C3—42no—
692C2×C3—81no—
693C2×C3—83no—
694C2×C3C22×#12111yescharacteristic
695C2×C3#358411yescharacteristic
696C2×C3#358611yescharacteristic
697C22—23no—
698C22—23no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—43no—
704C22—41no—
705C22—43no—
706C22—41no—
707C22—43no—
708C22—166no—
709C22C2×C3×#12116yes—
710C22C23×C3×D411yescharacteristic
711C4—26no—
712C4—21no—
713C4—23no—
714C4—21no—
715C4—23no—
716C4—41no—
717C4—43no—
718C4—43no—
719C4—41no—
720C4C2×C3×#12116yes—
721C4C23×C3×D411yescharacteristic
722C4C22×C3×#4111yescharacteristic
723C3#6043311yescharacteristic, direct product factor, Sylow
724C2—26no—
725C2—42no—
726C2—83no—
727C2—81no—
728C2C22×C3×#12111yescharacteristic
729C2C3×#358411yescharacteristic
730C2C3×#358611yescharacteristic
subgroupG/H
center, socleC22×C3C23×D4
commutator, Frattini, cosocleC2×C4C25×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C4×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#578C2semidirect
2. C2×C3×#577C2semidirect
3. C3×#3500C2semidirect
4. C3×C4×2−1+4C2semidirect
5. C3×#3046C2semidirect
6. C3×#3045C2semidirect
7. C3×#3044C2semidirect
8. C3×#3043C2semidirect
9. C3×#3040C2semidirect
10. C3×#3037C2semidirect
11. C3×#3035C2semidirect
12. C2×C3×#464C2semidirect
13. C3×#2906C2semidirect
14. C3×#2898C2semidirect
15. C3×#2897C2semidirect
16. #60433C3direct (N × H)
23. C2×C3×#137C22semidirect
24. C2×C3×#137C22semidirect
27. C2×C3×#135C22semidirect
28. C22×C3×Q16C22semidirect
42. C3×#520C22semidirect
44. C3×#519C22semidirect
47. C3×C4×#41C22semidirect
49. C2×C3×C4×Q8C22semidirect
50. C3×#464C22semidirect
51. C3×#464C22semidirect
52. C3×#464C22semidirect
53. C3×#464C22semidirect
54. C3×#464C22semidirect
55. C3×#464C22semidirect
56. C3×#463C22semidirect
57. C3×#463C22semidirect
58. C3×#463C22semidirect
59. C3×#462C22semidirect
60. C3×#462C22semidirect
61. C3×#461C22semidirect
62. C3×#460C22semidirect
63. C3×#460C22semidirect
64. C3×#459C22semidirect
65. C3×#424C22semidirect
66. C3×#424C22semidirect
67. C3×#423C22semidirect
68. C2×C3×C4⋊C8C22semidirect
69. C3×#419C22semidirect
72. C3×#417C22semidirect
74. C3×#416C22semidirect
75. C2×C3×#103C22semidirect
77. C2×#578C2×C3semidirect
78. C2×#577C2×C3semidirect
79. #3500C2×C3semidirect
80. C4×2−1+4C2×C3semidirect
81. #3046C2×C3semidirect
82. #3045C2×C3semidirect
83. #3044C2×C3semidirect
84. #3043C2×C3semidirect
85. #3040C2×C3semidirect
86. #3037C2×C3semidirect
87. #3035C2×C3semidirect
88. C2×#464C2×C3semidirect
89. #2906C2×C3semidirect
90. #2898C2×C3semidirect
91. #2897C2×C3semidirect
95. C3×2−1+4D4semidirect
204. C2×#137C22×C3semidirect
205. C2×#137C22×C3semidirect
208. C2×#135C22×C3semidirect
209. C22×Q16C22×C3semidirect
223. #520C22×C3semidirect
225. #519C22×C3semidirect
228. C4×#41C22×C3semidirect
230. C2×C4×Q8C22×C3semidirect
231. #464C22×C3semidirect
232. #464C22×C3semidirect
233. #464C22×C3semidirect
234. #464C22×C3semidirect
235. #464C22×C3semidirect
236. #464C22×C3semidirect
237. #463C22×C3semidirect
238. #463C22×C3semidirect
239. #463C22×C3semidirect
240. #462C22×C3semidirect
241. #462C22×C3semidirect
242. #461C22×C3semidirect
243. #460C22×C3semidirect
244. #460C22×C3semidirect
245. #459C22×C3semidirect
246. #424C22×C3semidirect
247. #424C22×C3semidirect
248. #423C22×C3semidirect
249. C2×C4⋊C8C22×C3semidirect
250. #419C22×C3semidirect
253. #417C22×C3semidirect
255. #416C22×C3semidirect
256. C2×#103C22×C3semidirect
355. 2−1+4C3×D4semidirect
723. C3#60433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5782
C2×C3×#5772
C3×#35002
C3×C4×2−1+42
C3×#30462
C3×#30452
C3×#30442
C3×#30432
C3×#30402
C3×#30372
C3×#30352
C2×C3×#4642
C3×#29062
C3×#28982
C3×#28972
#604333