Finite Group Databasebeta

← C3×#60376 #10678983

Subgroups — C3×#60376 #10678983

Order 768.

4824 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#585C211yesmaximal, characteristic, complemented
2C2×C3×#577C211yesmaximal, characteristic, complemented
3C2×C3×#576C211yesmaximal, characteristic, complemented
4C3×#3488C211yesmaximal, characteristic, complemented
5C3×#3013C213yesmaximal, complemented
6C3×#3012C213yesmaximal, complemented
7C3×#3010C213yesmaximal, complemented
8C3×#3008C213yesmaximal, complemented
9C3×#3006C213yesmaximal, complemented
10C3×#3005C213yesmaximal, complemented
11C3×#3002C213yesmaximal, complemented
12C2×C3×#449C213yesmaximal, complemented
13C3×#2898C211yesmaximal, characteristic, complemented
14C3×#2897C211yesmaximal, characteristic, complemented
15C3×#2880C211yesmaximal, characteristic, complemented
16#60376C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#585—28no—
18C3×#585—28no—
19C2×C3×2−1+4—21no—
20C2×C3×2−1+4C2211yescharacteristic
21C2×C3×2−1+4C2213yescomplemented
22C2×C3×H(5,𝔽2)—23no—
23C2×C3×H(5,𝔽2)C2211yescharacteristic
24C2×C3×H(5,𝔽2)C2213yescomplemented
25C2×C3×H(5,𝔽2)C2211yescharacteristic, complemented
26C22×C3×#41—23no—
27C22×C3×#41—21no—
28C22×C3×#41C2211yescharacteristic
29C22×C3×#41C2213yescomplemented
30C22×C3×#41C2213yescomplemented
31C3×#577—28no—
32C3×#576—28no—
33C2×C3×#137C2213yescomplemented
34C2×C3×AGL(1,ℤ/8)C2213yescomplemented
35C2×C3×AGL(1,ℤ/8)C2213yescomplemented
36C2×C3×AGL(1,ℤ/8)C2213yescomplemented
37C2×C3×#135C2213yescomplemented
38C2×C3×#135C2213yescomplemented
39C22×C3×SD16C2213yescomplemented
40C22×C3×D8C2213yescomplemented
41C2×C3×#131C2211yescharacteristic, complemented
42C2×C3×#131C2211yescharacteristic, complemented
43C3×#550—21no—
44C3×#548—21no—
45C3×#546—23no—
46C3×D42—23no—
47C3×#537C2213yescomplemented
48C3×#535C2213yescomplemented
49C3×#525C2213yescomplemented
50C2×C3×#121C2213yescomplemented
51C3×#520C2211yescharacteristic, complemented
52C3×#452C2211yescharacteristic, complemented
53C3×#452C2213yescomplemented
54C3×#452C2216yescomplemented
55C3×#451C2213yescomplemented
56C3×#450C2213yescomplemented
57C3×#449C2213yescomplemented
58C3×#449C2216yescomplemented
59C3×#449C2216yescomplemented
60C3×#449C2216yescomplemented
61C3×#449C2213yescomplemented
62C3×#449C2216yescomplemented
63C3×#448C2213yescomplemented
64C3×#448C2216yescomplemented
65C3×#447C2213yescomplemented
66C3×#447C2216yescomplemented
67C3×#419C2213yescomplemented
68C3×#418C2213yescomplemented
69C3×#417C2213yescomplemented
70C3×#417C2213yescomplemented
71C3×#416C2213yescomplemented
72C3×#416C2213yescomplemented
73C2×C3×#103C2213yescomplemented
74C2×C3×#102C2213yescomplemented
75C3×#408C2213yescomplemented
76C3×#408C2213yescomplemented
77C3×#407C2213yescomplemented
78C2×C3×C22⋊C8C2213yescomplemented
79C2×#585C2×C311yescharacteristic, complemented
80C2×#577C2×C311yescharacteristic, complemented
81C2×#576C2×C311yescharacteristic, complemented
82#3488C2×C311yescharacteristic, complemented
83#3013C2×C313yescomplemented
84#3012C2×C313yescomplemented
85#3010C2×C313yescomplemented
86#3008C2×C313yescomplemented
87#3006C2×C313yescomplemented
88#3005C2×C313yescomplemented
89#3002C2×C313yescomplemented
90C2×#449C2×C313yescomplemented
91#2898C2×C311yescharacteristic, complemented
92#2897C2×C311yescharacteristic, complemented
93#2880C2×C311yescharacteristic, complemented
94C3×2−1+4—216no—
95C3×2−1+4—24no—
96C3×2−1+4—212no—
97C3×2−1+4—212no—
98C3×2−1+4D418yescomplemented
99C3×H(5,𝔽2)—248no—
100C3×H(5,𝔽2)—24no—
101C3×H(5,𝔽2)—212no—
102C3×H(5,𝔽2)—212no—
103C3×H(5,𝔽2)—24no—
104C3×H(5,𝔽2)—24no—
105C3×H(5,𝔽2)D418yescomplemented
106C2×C3×#41—216no—
107C2×C3×#41—248no—
108C2×C3×#41—24no—
109C2×C3×#41—24no—
110C2×C3×#41—212no—
111C2×C3×#41—212no—
112C2×C3×#41—21no—
113C2×C3×#41—23no—
114C2×C3×#41—21no—
115C2×C3×#41—212no—
116C2×C3×#41—23no—
117C2×C3×#41—26no—
118C2×C3×#41—23no—
119C2×C3×#41—212no—
120C2×C3×#41—23no—
121C2×C3×#41—23no—
122C2×C3×#41—23no—
123C2×C3×#41—23no—
124C2×C3×#41D413yes—
125C2×C3×#41D411yescharacteristic
126C2×C3×#41C2313yes—
127C2×C3×#41C2313yes—
128C2×C3×#41C2311yescharacteristic
129C2×C3×#41C2316yes—
130C2×C3×#41C2313yes—
131C2×C3×#41C2313yes—
132C2×C3×#41C2313yes—
133C2×C3×#41C2311yescharacteristic
134C22×C3×Q8—21no—
135C22×C3×Q8—23no—
136C22×C3×Q8D411yescharacteristic
137C22×C3×Q8C2313yes—
138C22×C3×Q8C2313yes—
139C22×C3×D4—23no—
140C22×C3×D4—23no—
141C22×C3×D4—23no—
142C22×C3×D4—26no—
143C22×C3×D4—23no—
144C22×C3×D4—23no—
145C22×C3×D4—23no—
146C22×C3×D4D413yes—
147C22×C3×D4C2313yes—
148C22×C3×D4C2313yes—
149C22×C3×D4C2313yes—
150C23×C3×C4—23no—
151C23×C3×C4—23no—
152C23×C3×C4C2313yes—
153C3×#137—212no—
154C3×AGL(1,ℤ/8)—212no—
155C3×AGL(1,ℤ/8)—212no—
156C3×AGL(1,ℤ/8)—212no—
157C3×#135—212no—
158C3×#135—212no—
159C2×C3×Q16C2311yescharacteristic
160C2×C3×Q16C2313yes—
161C2×C3×SD16—212no—
162C2×C3×SD16C2313yes—
163C2×C3×SD16C2316yes—
164C2×C3×SD16C2311yescharacteristic
165C2×C3×SD16C2313yes—
166C2×C3×SD16C2313yes—
167C2×C3×D8—212no—
168C2×C3×D8C2313yes—
169C2×C3×D8C2316yes—
170C2×C3×D8C2313yes—
171C3×#131—24no—
172C3×#131—24no—
173C2×C3×M16C2313yes—
174C2×C3×M16C2313yes—
175C22×C3×C8C2313yes—
176C22×C3×C8C2313yes—
177C3×#127—23no—
178C3×#124—23no—
179C3×#123—23no—
180C3×C22⋊Q8—23no—
181C3×C22⋊Q8C2313yes—
182C3×C22⋊Q8C2311yescharacteristic
183C3×#121—26no—
184C3×#121—23no—
185C3×#121—23no—
186C3×#121—23no—
187C3×#121C2316yes—
188C3×#121C2313yes—
189C3×#121C2313yes—
190C3×#120—23no—
191C3×#120—26no—
192C3×C4×Q8—21no—
193C3×C4×D4—23no—
194C3×C4×D4—23no—
195C3×C4×D4—23no—
196C3×#117C2313yes—
197C2×C3×C4⋊C4C2313yes—
198C2×C3×C22⋊C4—23no—
199C3×#103C2313yes—
200C3×#103C2316yes—
201C3×#103C2311yescharacteristic
202C3×#103C2313yes—
203C3×#103C2313yes—
204C3×#102C2313yes—
205C3×#102C2316yes—
206C3×#102C2311yescharacteristic
207C3×#102C2313yes—
208C3×#102C2313yes—
209C3×C22⋊C8C2311yescharacteristic
210C3×C22⋊C8C2313yes—
211C3×C22⋊C8C2313yes—
212C3×C22⋊C8C2313yes—
213C3×C22⋊C8C2316yes—
214#585—28no—
215#585—28no—
216C2×2−1+4—21no—
217C2×2−1+4C22×C311yescharacteristic
218C2×2−1+4C22×C313yescomplemented
219C2×H(5,𝔽2)—23no—
220C2×H(5,𝔽2)C22×C311yescharacteristic
221C2×H(5,𝔽2)C22×C313yescomplemented
222C2×H(5,𝔽2)C22×C311yescharacteristic, complemented
223C22×#41—23no—
224C22×#41—21no—
225C22×#41C22×C311yescharacteristic
226C22×#41C22×C313yescomplemented
227C22×#41C22×C313yescomplemented
228#577—28no—
229#576—28no—
230C2×#137C22×C313yescomplemented
231C2×AGL(1,ℤ/8)C22×C313yescomplemented
232C2×AGL(1,ℤ/8)C22×C313yescomplemented
233C2×AGL(1,ℤ/8)C22×C313yescomplemented
234C2×#135C22×C313yescomplemented
235C2×#135C22×C313yescomplemented
236C22×SD16C22×C313yescomplemented
237C22×D8C22×C313yescomplemented
238C2×#131C22×C311yescharacteristic, complemented
239C2×#131C22×C311yescharacteristic, complemented
240#550—21no—
241#548—21no—
242#546—23no—
243D42—23no—
244#537C22×C313yescomplemented
245#535C22×C313yescomplemented
246#525C22×C313yescomplemented
247C2×#121C22×C313yescomplemented
248#520C22×C311yescharacteristic, complemented
249#452C22×C311yescharacteristic, complemented
250#452C22×C313yescomplemented
251#452C22×C316yescomplemented
252#451C22×C313yescomplemented
253#450C22×C313yescomplemented
254#449C22×C313yescomplemented
255#449C22×C316yescomplemented
256#449C22×C316yescomplemented
257#449C22×C316yescomplemented
258#449C22×C313yescomplemented
259#449C22×C316yescomplemented
260#448C22×C313yescomplemented
261#448C22×C316yescomplemented
262#447C22×C313yescomplemented
263#447C22×C316yescomplemented
264#419C22×C313yescomplemented
265#418C22×C313yescomplemented
266#417C22×C313yescomplemented
267#417C22×C313yescomplemented
268#416C22×C313yescomplemented
269#416C22×C313yescomplemented
270C2×#103C22×C313yescomplemented
271C2×#102C22×C313yescomplemented
272#408C22×C313yescomplemented
273#408C22×C313yescomplemented
274#407C22×C313yescomplemented
275C2×C22⋊C8C22×C313yescomplemented
276C24×C3—23no—
277C24×C3—23no—
278C24×C3—23no—
279C24×C3C2×D413yes—
280C3×#41—224no—
281C3×#41—224no—
282C3×#41—248no—
283C3×#41—224no—
284C3×#41—224no—
285C3×#41—224no—
286C3×#41—224no—
287C3×#41—24no—
288C3×#41—28no—
289C3×#41—22no—
290C3×#41—26no—
291C3×#41—212no—
292C3×#41—212no—
293C3×#41—224no—
294C3×#41—22no—
295C3×#41—26no—
296C3×#41—212no—
297C3×#41—26no—
298C3×#41—26no—
299C3×#41—26no—
300C3×#41—26no—
301C3×#41—26no—
302C3×#41—26no—
303C3×#41—44no—
304C3×#41C2×D414yes—
305C3×#41C2×D414yes—
306C3×#41C2×D4112yescomplemented
307C3×#41C2×D4112yescomplemented
308C2×C3×Q8—224no—
309C2×C3×Q8—28no—
310C2×C3×Q8—24no—
311C2×C3×Q8—26no—
312C2×C3×Q8—26no—
313C2×C3×Q8—23no—
314C2×C3×Q8—23no—
315C2×C3×Q8—26no—
316C2×C3×Q8C2×D413yes—
317C2×C3×Q8C2×D411yescharacteristic
318C2×C3×Q8C2×D4112yescomplemented
319C2×C3×Q8C2411yescharacteristic
320C2×C3×Q8C2411yescharacteristic
321C2×C3×Q8C2413yes—
322C2×C3×D4—224no—
323C2×C3×D4—248no—
324C2×C3×D4—224no—
325C2×C3×D4—224no—
326C2×C3×D4—26no—
327C2×C3×D4—23no—
328C2×C3×D4—21no—
329C2×C3×D4—23no—
330C2×C3×D4—23no—
331C2×C3×D4—224no—
332C2×C3×D4—212no—
333C2×C3×D4—26no—
334C2×C3×D4—26no—
335C2×C3×D4—23no—
336C2×C3×D4—23no—
337C2×C3×D4—23no—
338C2×C3×D4—26no—
339C2×C3×D4—23no—
340C2×C3×D4—23no—
341C2×C3×D4—26no—
342C2×C3×D4—26no—
343C2×C3×D4—26no—
344C2×C3×D4—23no—
345C2×C3×D4—412no—
346C2×C3×D4—86no—
347C2×C3×D4C2×D416yes—
348C2×C3×D4C2×D413yes—
349C2×C3×D4C2×D413yes—
350C2×C3×D4C2×D4112yescomplemented
351C2×C3×D4C2413yes—
352C2×C3×D4C2411yescharacteristic
353C2×C3×D4C2413yes—
354C22×C3×C4—224no—
355C22×C3×C4—224no—
356C22×C3×C4—23no—
357C22×C3×C4—23no—
358C22×C3×C4—23no—
359C22×C3×C4—21no—
360C22×C3×C4—26no—
361C22×C3×C4—23no—
362C22×C3×C4—23no—
363C22×C3×C4—26no—
364C22×C3×C4—26no—
365C22×C3×C4—23no—
366C22×C3×C4—23no—
367C22×C3×C4C2×D413yes—
368C22×C3×C4C2×D413yes—
369C22×C3×C4C2×D413yes—
370C22×C3×C4C2411yescharacteristic
371C22×C3×C4C2413yes—
372C22×C3×C4C2413yes—
373C3×Q16—22no—
374C3×Q16—26no—
375C3×SD16—26no—
376C3×SD16—212no—
377C3×SD16—26no—
378C3×SD16—22no—
379C3×SD16—26no—
380C3×D8—26no—
381C3×D8—212no—
382C3×D8—26no—
383C3×M16—26no—
384C3×M16—26no—
385C2×C3×C8—26no—
386C2×C3×C8—26no—
387C2×C3×C8C2411yescharacteristic
388C2×C3×C8C2413yes—
389C2×C3×C8C2411yescharacteristic
390C2×C3×C8C2413yes—
391C3×C4⋊C4—23no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—23no—
394C3×C4⋊C4C2413yes—
395C3×C4⋊C4C2411yescharacteristic
396C3×C22⋊C4—23no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—23no—
399C3×C22⋊C4—23no—
400C3×C22⋊C4—26no—
401C3×C22⋊C4—23no—
402C3×C42—23no—
4032−1+4—216no—
4042−1+4—24no—
4052−1+4—212no—
4062−1+4—212no—
4072−1+4C3×D418yescomplemented
408H(5,𝔽2)—248no—
409H(5,𝔽2)—24no—
410H(5,𝔽2)—212no—
411H(5,𝔽2)—212no—
412H(5,𝔽2)—24no—
413H(5,𝔽2)—24no—
414H(5,𝔽2)C3×D418yescomplemented
415C2×#41—216no—
416C2×#41—248no—
417C2×#41—24no—
418C2×#41—24no—
419C2×#41—212no—
420C2×#41—212no—
421C2×#41—21no—
422C2×#41—23no—
423C2×#41—21no—
424C2×#41—212no—
425C2×#41—23no—
426C2×#41—26no—
427C2×#41—23no—
428C2×#41—212no—
429C2×#41—23no—
430C2×#41—23no—
431C2×#41—23no—
432C2×#41—23no—
433C2×#41C3×D413yes—
434C2×#41C3×D411yescharacteristic
435C2×#41C23×C313yes—
436C2×#41C23×C313yes—
437C2×#41C23×C311yescharacteristic
438C2×#41C23×C316yes—
439C2×#41C23×C313yes—
440C2×#41C23×C313yes—
441C2×#41C23×C313yes—
442C2×#41C23×C311yescharacteristic
443C22×Q8—21no—
444C22×Q8—23no—
445C22×Q8C3×D411yescharacteristic
446C22×Q8C23×C313yes—
447C22×Q8C23×C313yes—
448C22×D4—23no—
449C22×D4—23no—
450C22×D4—23no—
451C22×D4—26no—
452C22×D4—23no—
453C22×D4—23no—
454C22×D4—23no—
455C22×D4C3×D413yes—
456C22×D4C23×C313yes—
457C22×D4C23×C313yes—
458C22×D4C23×C313yes—
459C23×C4—23no—
460C23×C4—23no—
461C23×C4C23×C313yes—
462#137—212no—
463AGL(1,ℤ/8)—212no—
464AGL(1,ℤ/8)—212no—
465AGL(1,ℤ/8)—212no—
466#135—212no—
467#135—212no—
468C2×Q16C23×C311yescharacteristic
469C2×Q16C23×C313yes—
470C2×SD16—212no—
471C2×SD16C23×C313yes—
472C2×SD16C23×C316yes—
473C2×SD16C23×C311yescharacteristic
474C2×SD16C23×C313yes—
475C2×SD16C23×C313yes—
476C2×D8—212no—
477C2×D8C23×C313yes—
478C2×D8C23×C316yes—
479C2×D8C23×C313yes—
480#131—24no—
481#131—24no—
482C2×M16C23×C313yes—
483C2×M16C23×C313yes—
484C22×C8C23×C313yes—
485C22×C8C23×C313yes—
486#127—23no—
487#124—23no—
488#123—23no—
489C22⋊Q8—23no—
490C22⋊Q8C23×C311yescharacteristic
491C22⋊Q8C23×C313yes—
492#121—26no—
493#121—23no—
494#121—23no—
495#121—23no—
496#121C23×C313yes—
497#121C23×C316yes—
498#121C23×C313yes—
499#120—23no—
500#120—26no—
501C4×Q8—21no—
502C4×D4—23no—
503C4×D4—23no—
504C4×D4—23no—
505#117C23×C313yes—
506C2×C4⋊C4C23×C313yes—
507C2×C22⋊C4—23no—
508#103C23×C313yes—
509#103C23×C316yes—
510#103C23×C311yescharacteristic
511#103C23×C313yes—
512#103C23×C313yes—
513#102C23×C313yes—
514#102C23×C316yes—
515#102C23×C311yescharacteristic
516#102C23×C313yes—
517#102C23×C313yes—
518C22⋊C8C23×C311yescharacteristic
519C22⋊C8C23×C313yes—
520C22⋊C8C23×C313yes—
521C22⋊C8C23×C313yes—
522C22⋊C8C23×C316yes—
523C23×C3—212no—
524C23×C3—23no—
525C23×C3—21no—
526C23×C3—26no—
527C23×C3—212no—
528C23×C3—23no—
529C23×C3—43no—
530C23×C3—43no—
531C23×C3—46no—
532C23×C3—83no—
533C23×C3—83no—
534C23×C3—83no—
535C23×C3—83no—
536C23×C3—83no—
537C23×C3—83no—
538C23×C3C22×D413yes—
539C23×C3C22×D411yescharacteristic
540C23×C3C22×D413yes—
541C3×Q8—212no—
542C3×Q8—26no—
543C3×Q8—212no—
544C3×Q8—21no—
545C3×Q8—23no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8#12014yes—
549C3×Q8C22×D412yes—
550C3×Q8C22×D416yes—
551C3×D4—224no—
552C3×D4—212no—
553C3×D4—24no—
554C3×D4—212no—
555C3×D4—212no—
556C3×D4—212no—
557C3×D4—212no—
558C3×D4—26no—
559C3×D4—212no—
560C3×D4—23no—
561C3×D4—21no—
562C3×D4—23no—
563C3×D4—23no—
564C3×D4—46no—
565C3×D4—46no—
566C3×D4—46no—
567C3×D4—83no—
568C3×D4—86no—
569C3×D4#120112yes—
570C3×D4C22×D412yes—
571C3×D4C22×D416yes—
572C2×C3×C4—212no—
573C2×C3×C4—24no—
574C2×C3×C4—212no—
575C2×C3×C4—224no—
576C2×C3×C4—26no—
577C2×C3×C4—212no—
578C2×C3×C4—23no—
579C2×C3×C4—21no—
580C2×C3×C4—26no—
581C2×C3×C4—212no—
582C2×C3×C4—212no—
583C2×C3×C4—26no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—23no—
587C2×C3×C4—23no—
588C2×C3×C4—21no—
589C2×C3×C4—23no—
590C2×C3×C4—21no—
591C2×C3×C4—46no—
592C2×C3×C4—83no—
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D413yes—
595C2×C3×C4C22×D413yes—
596C2×C3×C4C22×D416yes—
597C2×C3×C4C22×D416yes—
598C2×C3×C4C2511yescharacteristic
599C3×C8—21no—
600C3×C8—21no—
601C3×C8—23no—
602C3×C8—23no—
603C24—23no—
604C24—23no—
605C24—23no—
606C24C2×C3×D413yes—
607#41—224no—
608#41—224no—
609#41—248no—
610#41—224no—
611#41—224no—
612#41—224no—
613#41—224no—
614#41—24no—
615#41—28no—
616#41—22no—
617#41—26no—
618#41—212no—
619#41—212no—
620#41—224no—
621#41—22no—
622#41—26no—
623#41—212no—
624#41—26no—
625#41—26no—
626#41—26no—
627#41—26no—
628#41—26no—
629#41—26no—
630#41—44no—
631#41C2×C3×D414yes—
632#41C2×C3×D414yes—
633#41C2×C3×D4112yescomplemented
634#41C2×C3×D4112yescomplemented
635C2×Q8—224no—
636C2×Q8—28no—
637C2×Q8—24no—
638C2×Q8—26no—
639C2×Q8—26no—
640C2×Q8—23no—
641C2×Q8—23no—
642C2×Q8—26no—
643C2×Q8C2×C3×D413yes—
644C2×Q8C2×C3×D411yescharacteristic
645C2×Q8C2×C3×D4112yescomplemented
646C2×Q8C24×C311yescharacteristic
647C2×Q8C24×C311yescharacteristic
648C2×Q8C24×C313yes—
649C2×D4—224no—
650C2×D4—248no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—26no—
654C2×D4—23no—
655C2×D4—21no—
656C2×D4—23no—
657C2×D4—23no—
658C2×D4—224no—
659C2×D4—212no—
660C2×D4—26no—
661C2×D4—26no—
662C2×D4—23no—
663C2×D4—23no—
664C2×D4—23no—
665C2×D4—26no—
666C2×D4—23no—
667C2×D4—23no—
668C2×D4—26no—
669C2×D4—26no—
670C2×D4—26no—
671C2×D4—23no—
672C2×D4—412no—
673C2×D4—86no—
674C2×D4C2×C3×D416yes—
675C2×D4C2×C3×D413yes—
676C2×D4C2×C3×D413yes—
677C2×D4C2×C3×D4112yescomplemented
678C2×D4C24×C313yes—
679C2×D4C24×C311yescharacteristic
680C2×D4C24×C313yes—
681C22×C4—224no—
682C22×C4—224no—
683C22×C4—23no—
684C22×C4—23no—
685C22×C4—23no—
686C22×C4—21no—
687C22×C4—26no—
688C22×C4—23no—
689C22×C4—23no—
690C22×C4—26no—
691C22×C4—26no—
692C22×C4—23no—
693C22×C4—23no—
694C22×C4C2×C3×D413yes—
695C22×C4C2×C3×D413yes—
696C22×C4C2×C3×D413yes—
697C22×C4C24×C311yescharacteristic
698C22×C4C24×C313yes—
699C22×C4C24×C313yes—
700Q16—22no—
701Q16—26no—
702SD16—26no—
703SD16—212no—
704SD16—26no—
705SD16—22no—
706SD16—26no—
707D8—26no—
708D8—212no—
709D8—26no—
710M16—26no—
711M16—26no—
712C2×C8—26no—
713C2×C8—26no—
714C2×C8C24×C311yescharacteristic
715C2×C8C24×C313yes—
716C2×C8C24×C311yescharacteristic
717C2×C8C24×C313yes—
718C4⋊C4—23no—
719C4⋊C4—21no—
720C4⋊C4—23no—
721C4⋊C4C24×C313yes—
722C4⋊C4C24×C311yescharacteristic
723C22⋊C4—23no—
724C22⋊C4—21no—
725C22⋊C4—23no—
726C22⋊C4—23no—
727C22⋊C4—26no—
728C22⋊C4—23no—
729C42—23no—
730C22×C3—23no—
731C22×C3—23no—
732C22×C3—23no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—23no—
736C22×C3—23no—
737C22×C3—21no—
738C22×C3—26no—
739C22×C3—22no—
740C22×C3—43no—
741C22×C3—41no—
742C22×C3—43no—
743C22×C3—41no—
744C22×C3—43no—
745C22×C3—43no—
746C22×C3—43no—
747C22×C3—86no—
748C22×C3—812no—
749C22×C3—812no—
750C22×C3—166no—
751C22×C3C2×#12016yes—
752C22×C3C23×D411yescharacteristic
753C3×C4—21no—
754C3×C4—26no—
755C3×C4—22no—
756C3×C4—23no—
757C3×C4—41no—
758C3×C4—43no—
759C3×C4—41no—
760C3×C4C2×#12016yes—
761C3×C4C23×D411yescharacteristic
762C3×C4C23×D411yescharacteristic
763C23—212no—
764C23—23no—
765C23—21no—
766C23—26no—
767C23—212no—
768C23—23no—
769C23—43no—
770C23—43no—
771C23—46no—
772C23—83no—
773C23—83no—
774C23—83no—
775C23—83no—
776C23—83no—
777C23—83no—
778C23C22×C3×D413yes—
779C23C22×C3×D411yescharacteristic
780C23C22×C3×D413yes—
781Q8—212no—
782Q8—21no—
783Q8—23no—
784Q8—26no—
785Q8—212no—
786Q8—21no—
787Q8—21no—
788Q8C3×#12014yes—
789Q8C22×C3×D412yes—
790Q8C22×C3×D416yes—
791D4—224no—
792D4—212no—
793D4—24no—
794D4—212no—
795D4—212no—
796D4—212no—
797D4—212no—
798D4—23no—
799D4—21no—
800D4—23no—
801D4—23no—
802D4—26no—
803D4—212no—
804D4—46no—
805D4—46no—
806D4—46no—
807D4—86no—
808D4—83no—
809D4C3×#120112yes—
810D4C22×C3×D412yes—
811D4C22×C3×D416yes—
812C2×C4—212no—
813C2×C4—24no—
814C2×C4—212no—
815C2×C4—224no—
816C2×C4—23no—
817C2×C4—21no—
818C2×C4—26no—
819C2×C4—212no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—23no—
823C2×C4—23no—
824C2×C4—26no—
825C2×C4—212no—
826C2×C4—212no—
827C2×C4—26no—
828C2×C4—21no—
829C2×C4—23no—
830C2×C4—21no—
831C2×C4—46no—
832C2×C4—83no—
833C2×C4C22×C3×D411yescharacteristic
834C2×C4C22×C3×D413yes—
835C2×C4C22×C3×D416yes—
836C2×C4C22×C3×D416yes—
837C2×C4C22×C3×D413yes—
838C2×C4C25×C311yescharacteristic
839C8—21no—
840C8—21no—
841C8—23no—
842C8—23no—
843C2×C3—26no—
844C2×C3—43no—
845C2×C3—41no—
846C2×C3—46no—
847C2×C3—42no—
848C2×C3—83no—
849C2×C3C22×#12011yescharacteristic
850C2×C3#358411yescharacteristic
851C2×C3#358511yescharacteristic
852C22—23no—
853C22—23no—
854C22—23no—
855C22—21no—
856C22—26no—
857C22—22no—
858C22—23no—
859C22—21no—
860C22—21no—
861C22—23no—
862C22—43no—
863C22—41no—
864C22—43no—
865C22—41no—
866C22—43no—
867C22—43no—
868C22—43no—
869C22—86no—
870C22—812no—
871C22—812no—
872C22—166no—
873C22C2×C3×#12016yes—
874C22C23×C3×D411yescharacteristic
875C4—21no—
876C4—26no—
877C4—22no—
878C4—23no—
879C4—41no—
880C4—41no—
881C4—43no—
882C4C2×C3×#12016yes—
883C4C23×C3×D411yescharacteristic
884C4C23×C3×D411yescharacteristic
885C3#6037611yescharacteristic, direct product factor, Sylow
886C2—26no—
887C2—43no—
888C2—41no—
889C2—46no—
890C2—42no—
891C2—83no—
892C2C22×C3×#12011yescharacteristic
893C2C3×#358411yescharacteristic
894C2C3×#358511yescharacteristic
subgroupG/H
center, socleC22×C3C23×D4
commutator, Frattini, cosocleC2×C4C25×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#585C2semidirect
2. C2×C3×#577C2semidirect
3. C2×C3×#576C2semidirect
4. C3×#3488C2semidirect
5. C3×#3013C2semidirect
6. C3×#3012C2semidirect
7. C3×#3010C2semidirect
8. C3×#3008C2semidirect
9. C3×#3006C2semidirect
10. C3×#3005C2semidirect
11. C3×#3002C2semidirect
12. C2×C3×#449C2semidirect
13. C3×#2898C2semidirect
14. C3×#2897C2semidirect
15. C3×#2880C2semidirect
16. #60376C3direct (N × H)
21. C2×C3×2−1+4C22semidirect
24. C2×C3×H(5,𝔽2)C22semidirect
25. C2×C3×H(5,𝔽2)C22semidirect
29. C22×C3×#41C22semidirect
30. C22×C3×#41C22semidirect
33. C2×C3×#137C22semidirect
34. C2×C3×AGL(1,ℤ/8)C22semidirect
35. C2×C3×AGL(1,ℤ/8)C22semidirect
36. C2×C3×AGL(1,ℤ/8)C22semidirect
37. C2×C3×#135C22semidirect
38. C2×C3×#135C22semidirect
39. C22×C3×SD16C22semidirect
40. C22×C3×D8C22semidirect
41. C2×C3×#131C22semidirect
42. C2×C3×#131C22semidirect
47. C3×#537C22semidirect
48. C3×#535C22semidirect
49. C3×#525C22semidirect
50. C2×C3×#121C22semidirect
51. C3×#520C22semidirect
52. C3×#452C22semidirect
53. C3×#452C22semidirect
54. C3×#452C22semidirect
55. C3×#451C22semidirect
56. C3×#450C22semidirect
57. C3×#449C22semidirect
58. C3×#449C22semidirect
59. C3×#449C22semidirect
60. C3×#449C22semidirect
61. C3×#449C22semidirect
62. C3×#449C22semidirect
63. C3×#448C22semidirect
64. C3×#448C22semidirect
65. C3×#447C22semidirect
66. C3×#447C22semidirect
67. C3×#419C22semidirect
68. C3×#418C22semidirect
69. C3×#417C22semidirect
70. C3×#417C22semidirect
71. C3×#416C22semidirect
72. C3×#416C22semidirect
73. C2×C3×#103C22semidirect
74. C2×C3×#102C22semidirect
75. C3×#408C22semidirect
76. C3×#408C22semidirect
77. C3×#407C22semidirect
78. C2×C3×C22⋊C8C22semidirect
79. C2×#585C2×C3semidirect
80. C2×#577C2×C3semidirect
81. C2×#576C2×C3semidirect
82. #3488C2×C3semidirect
83. #3013C2×C3semidirect
84. #3012C2×C3semidirect
85. #3010C2×C3semidirect
86. #3008C2×C3semidirect
87. #3006C2×C3semidirect
88. #3005C2×C3semidirect
89. #3002C2×C3semidirect
90. C2×#449C2×C3semidirect
91. #2898C2×C3semidirect
92. #2897C2×C3semidirect
93. #2880C2×C3semidirect
98. C3×2−1+4D4semidirect
105. C3×H(5,𝔽2)D4semidirect
218. C2×2−1+4C22×C3semidirect
221. C2×H(5,𝔽2)C22×C3semidirect
222. C2×H(5,𝔽2)C22×C3semidirect
226. C22×#41C22×C3semidirect
227. C22×#41C22×C3semidirect
230. C2×#137C22×C3semidirect
231. C2×AGL(1,ℤ/8)C22×C3semidirect
232. C2×AGL(1,ℤ/8)C22×C3semidirect
233. C2×AGL(1,ℤ/8)C22×C3semidirect
234. C2×#135C22×C3semidirect
235. C2×#135C22×C3semidirect
236. C22×SD16C22×C3semidirect
237. C22×D8C22×C3semidirect
238. C2×#131C22×C3semidirect
239. C2×#131C22×C3semidirect
244. #537C22×C3semidirect
245. #535C22×C3semidirect
246. #525C22×C3semidirect
247. C2×#121C22×C3semidirect
248. #520C22×C3semidirect
249. #452C22×C3semidirect
250. #452C22×C3semidirect
251. #452C22×C3semidirect
252. #451C22×C3semidirect
253. #450C22×C3semidirect
254. #449C22×C3semidirect
255. #449C22×C3semidirect
256. #449C22×C3semidirect
257. #449C22×C3semidirect
258. #449C22×C3semidirect
259. #449C22×C3semidirect
260. #448C22×C3semidirect
261. #448C22×C3semidirect
262. #447C22×C3semidirect
263. #447C22×C3semidirect
264. #419C22×C3semidirect
265. #418C22×C3semidirect
266. #417C22×C3semidirect
267. #417C22×C3semidirect
268. #416C22×C3semidirect
269. #416C22×C3semidirect
270. C2×#103C22×C3semidirect
271. C2×#102C22×C3semidirect
272. #408C22×C3semidirect
273. #408C22×C3semidirect
274. #407C22×C3semidirect
275. C2×C22⋊C8C22×C3semidirect
306. C3×#41C2×D4semidirect
307. C3×#41C2×D4semidirect
318. C2×C3×Q8C2×D4semidirect
350. C2×C3×D4C2×D4semidirect
407. 2−1+4C3×D4semidirect
414. H(5,𝔽2)C3×D4semidirect
633. #41C2×C3×D4semidirect
634. #41C2×C3×D4semidirect
645. C2×Q8C2×C3×D4semidirect
677. C2×D4C2×C3×D4semidirect
885. C3#60376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5852
C2×C3×#5772
C2×C3×#5762
C3×#34882
C3×#30132
C3×#30122
C3×#30102
C3×#30082
C3×#30062
C3×#30052
C3×#30022
C2×C3×#4492
C3×#28982
C3×#28972
C3×#28802
#603763