Finite Group Databasebeta

← C3×#60430 #10679037

Subgroups — C3×#60430 #10679037

Order 768.

2762 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#577C211yesmaximal, characteristic, complemented
2C2×C3×#576C211yesmaximal, characteristic, complemented
3C3×#3500C211yesmaximal, characteristic, complemented
4C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
5C3×#3046C213yesmaximal, complemented
6C3×#3045C213yesmaximal, complemented
7C3×#3042C213yesmaximal, complemented
8C3×#3041C213yesmaximal, complemented
9C3×#3040C213yesmaximal, complemented
10C3×#3036C213yesmaximal, complemented
11C3×#3035C213yesmaximal, complemented
12C2×C3×#463C213yesmaximal, complemented
13C3×#2906C211yesmaximal, characteristic, complemented
14C3×#2898C211yesmaximal, characteristic, complemented
15C3×#2897C211yesmaximal, characteristic, complemented
16#60430C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C3×#577—28no—
21C3×#576—28no—
22C2×C3×#137C2213yescomplemented
23C2×C3×AGL(1,ℤ/8)C2213yes—
24C2×C3×AGL(1,ℤ/8)C2213yes—
25C2×C3×AGL(1,ℤ/8)C2213yescomplemented
26C2×C3×#135C2213yes—
27C2×C3×#135C2213yescomplemented
28C22×C3×SD16C2213yescomplemented
29C22×C3×D8C2213yes—
30C2×C3×#131C2211yescharacteristic
31C2×C3×#131C2211yescharacteristic
32C3×#548—21no—
33C3×#548—21no—
34C3×#546—23no—
35C3×#546—23no—
36C3×#536C2213yescomplemented
37C3×#535C2213yescomplemented
38C3×#532C2213yescomplemented
39C2×C3×#124C2213yescomplemented
40C3×#520—21no—
41C3×#520C2211yescharacteristic
42C3×#520C2213yescomplemented
43C3×#518—23no—
44C3×#518C2213yescomplemented
45C3×C4×#41—21no—
46C3×C4×#41C2211yescharacteristic
47C3×C4×#41C2213yescomplemented
48C2×C3×C4×D4—23no—
49C2×C3×C4×D4C2213yescomplemented
50C3×#464C2211yescharacteristic, complemented
51C3×#464C2213yescomplemented
52C3×#464C2216yescomplemented
53C3×#463C2213yescomplemented
54C3×#463C2216yescomplemented
55C3×#463C2216yescomplemented
56C3×#463C2216yescomplemented
57C3×#463C2213yescomplemented
58C3×#463C2216yescomplemented
59C3×#462C2213yescomplemented
60C3×#461C2213yescomplemented
61C3×#461C2216yescomplemented
62C3×#460C2213yescomplemented
63C3×#459C2213yescomplemented
64C3×#459C2216yescomplemented
65C3×#424C2213yescomplemented
66C3×#424C2213yescomplemented
67C3×#423C2213yescomplemented
68C2×C3×C4⋊C8C2213yescomplemented
69C3×#419C2213yescomplemented
70C3×#418C2213yescomplemented
71C3×#417C2213yescomplemented
72C3×#417C2213yescomplemented
73C3×#416C2213yescomplemented
74C3×#416C2213yescomplemented
75C2×C3×#103C2213yescomplemented
76C2×C3×#102C2213yescomplemented
77C2×#577C2×C311yescharacteristic, complemented
78C2×#576C2×C311yescharacteristic, complemented
79#3500C2×C311yescharacteristic, complemented
80C4×H(5,𝔽2)C2×C311yescharacteristic, complemented
81#3046C2×C313yescomplemented
82#3045C2×C313yescomplemented
83#3042C2×C313yescomplemented
84#3041C2×C313yescomplemented
85#3040C2×C313yescomplemented
86#3036C2×C313yescomplemented
87#3035C2×C313yescomplemented
88C2×#463C2×C313yescomplemented
89#2906C2×C311yescharacteristic, complemented
90#2898C2×C311yescharacteristic, complemented
91#2897C2×C311yescharacteristic, complemented
92C3×2−1+4—24no—
93C3×2−1+4—24no—
94C3×H(5,𝔽2)—24no—
95C3×H(5,𝔽2)—24no—
96C3×H(5,𝔽2)—24no—
97C3×H(5,𝔽2)D418yescomplemented
98C2×C3×#41—21no—
99C2×C3×#41—21no—
100C2×C3×#41—23no—
101C2×C3×#41C2313yes—
102C2×C3×#41C2313yes—
103C2×C3×#41C2313yes—
104C2×C3×#41C2311yescharacteristic
105C22×C3×Q8—21no—
106C22×C3×Q8C2313yes—
107C22×C3×D4—23no—
108C22×C3×D4—23no—
109C22×C3×D4C2313yes—
110C22×C3×D4C2313yes—
111C23×C3×C4—23no—
112C3×#137—212no—
113C3×AGL(1,ℤ/8)—212no—
114C3×AGL(1,ℤ/8)—212no—
115C3×AGL(1,ℤ/8)—212no—
116C3×#135—212no—
117C3×#135—212no—
118C2×C3×Q16C2311yescharacteristic
119C2×C3×Q16C2313yes—
120C2×C3×SD16—212no—
121C2×C3×SD16C2313yes—
122C2×C3×SD16C2316yes—
123C2×C3×SD16C2313yes—
124C2×C3×SD16C2313yes—
125C2×C3×SD16C2311yescharacteristic
126C2×C3×D8—212no—
127C2×C3×D8C2313yes—
128C2×C3×D8C2316yes—
129C2×C3×D8C2313yes—
130C3×#131—24no—
131C3×#131—24no—
132C2×C3×M16C2313yes—
133C2×C3×M16C2313yes—
134C22×C3×C8C2313yes—
135C22×C3×C8C2313yes—
136C3×C4⋊Q8C2313yes—
137C3×#127C2313yes—
138C3×#124—23no—
139C3×#124—23no—
140C3×#124C2313yes—
141C3×#124C2316yes—
142C3×#124C2311yescharacteristic
143C3×#123—26no—
144C3×C22⋊Q8—23no—
145C3×C22⋊Q8—23no—
146C3×#121—23no—
147C3×#121—23no—
148C3×#121—23no—
149C3×#121—23no—
150C3×#120—26no—
151C3×C4×Q8—21no—
152C3×C4×Q8D411yescharacteristic
153C3×C4×Q8D411yescharacteristic
154C3×C4×Q8C2313yes—
155C3×C4×Q8C2311yescharacteristic
156C3×C4×D4—23no—
157C3×C4×D4—23no—
158C3×C4×D4—23no—
159C3×C4×D4—23no—
160C3×C4×D4—23no—
161C3×C4×D4—26no—
162C3×C4×D4—23no—
163C3×C4×D4—23no—
164C3×C4×D4—23no—
165C3×C4×D4—23no—
166C3×C4×D4D413yes—
167C3×C4×D4D413yes—
168C3×C4×D4C2316yes—
169C3×C4×D4C2313yes—
170C3×C4×D4C2313yes—
171C3×#117—23no—
172C3×#117—23no—
173C3×#117C2313yes—
174C3×#117C2313yes—
175C2×C3×C4⋊C4—23no—
176C2×C3×C4⋊C4C2313yes—
177C2×C3×C22⋊C4—23no—
178C2×C3×C22⋊C4—23no—
179C2×C3×C22⋊C4—23no—
180C2×C3×C22⋊C4—26no—
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×#102C2311yescharacteristic
196C3×#102C2313yes—
197C3×#102C2313yes—
198C2×2−1+4C22×C311yescharacteristic
199C2×H(5,𝔽2)C22×C311yescharacteristic
200C2×H(5,𝔽2)C22×C311yescharacteristic
201#577—28no—
202#576—28no—
203C2×#137C22×C313yescomplemented
204C2×AGL(1,ℤ/8)C22×C313yes—
205C2×AGL(1,ℤ/8)C22×C313yes—
206C2×AGL(1,ℤ/8)C22×C313yescomplemented
207C2×#135C22×C313yes—
208C2×#135C22×C313yescomplemented
209C22×SD16C22×C313yescomplemented
210C22×D8C22×C313yes—
211C2×#131C22×C311yescharacteristic
212C2×#131C22×C311yescharacteristic
213#548—21no—
214#548—21no—
215#546—23no—
216#546—23no—
217#536C22×C313yescomplemented
218#535C22×C313yescomplemented
219#532C22×C313yescomplemented
220C2×#124C22×C313yescomplemented
221#520—21no—
222#520C22×C311yescharacteristic
223#520C22×C313yescomplemented
224#518—23no—
225#518C22×C313yescomplemented
226C4×#41—21no—
227C4×#41C22×C311yescharacteristic
228C4×#41C22×C313yescomplemented
229C2×C4×D4—23no—
230C2×C4×D4C22×C313yescomplemented
231#464C22×C311yescharacteristic, complemented
232#464C22×C313yescomplemented
233#464C22×C316yescomplemented
234#463C22×C313yescomplemented
235#463C22×C316yescomplemented
236#463C22×C316yescomplemented
237#463C22×C316yescomplemented
238#463C22×C313yescomplemented
239#463C22×C316yescomplemented
240#462C22×C313yescomplemented
241#461C22×C313yescomplemented
242#461C22×C316yescomplemented
243#460C22×C313yescomplemented
244#459C22×C313yescomplemented
245#459C22×C316yescomplemented
246#424C22×C313yescomplemented
247#424C22×C313yescomplemented
248#423C22×C313yescomplemented
249C2×C4⋊C8C22×C313yescomplemented
250#419C22×C313yescomplemented
251#418C22×C313yescomplemented
252#417C22×C313yescomplemented
253#417C22×C313yescomplemented
254#416C22×C313yescomplemented
255#416C22×C313yescomplemented
256C2×#103C22×C313yescomplemented
257C2×#102C22×C313yescomplemented
258C24×C3—23no—
259C24×C3—23no—
260C3×#41—28no—
261C3×#41—26no—
262C3×#41—26no—
263C3×#41—26no—
264C3×#41—26no—
265C3×#41—26no—
266C3×#41—44no—
267C3×#41—412no—
268C3×#41C2×D4112yes—
269C3×#41C2×D414yes—
270C3×#41#4114yes—
271C2×C3×Q8—23no—
272C2×C3×Q8—26no—
273C2×C3×Q8—26no—
274C2×C3×Q8—44no—
275C2×C3×Q8C2×D411yescharacteristic
276C2×C3×Q8C2413yes—
277C2×C3×Q8C2411yescharacteristic
278C2×C3×Q8C2411yescharacteristic
279C2×C3×D4—23no—
280C2×C3×D4—224no—
281C2×C3×D4—23no—
282C2×C3×D4—23no—
283C2×C3×D4—23no—
284C2×C3×D4—26no—
285C2×C3×D4—23no—
286C2×C3×D4—23no—
287C2×C3×D4—23no—
288C2×C3×D4—26no—
289C2×C3×D4—26no—
290C2×C3×D4—412no—
291C2×C3×D4C2×D4112yes—
292C2×C3×D4C2×D413yes—
293C2×C3×D4C2413yes—
294C2×C3×D4C2411yescharacteristic
295C2×C3×D4C2413yes—
296C22×C3×C4—23no—
297C22×C3×C4—23no—
298C22×C3×C4—23no—
299C22×C3×C4—23no—
300C22×C3×C4—23no—
301C22×C3×C4—23no—
302C22×C3×C4—23no—
303C22×C3×C4—26no—
304C22×C3×C4—86no—
305C22×C3×C4C2×D413yes—
306C22×C3×C4C2×D413yes—
307C22×C3×C4C2413yes—
308C3×Q16—22no—
309C3×Q16—26no—
310C3×SD16—22no—
311C3×SD16—26no—
312C3×SD16—26no—
313C3×SD16—212no—
314C3×SD16—26no—
315C3×D8—26no—
316C3×D8—212no—
317C3×D8—26no—
318C3×M16—26no—
319C3×M16—26no—
320C2×C3×C8—26no—
321C2×C3×C8—26no—
322C2×C3×C8C2411yescharacteristic
323C2×C3×C8C2413yes—
324C2×C3×C8C2411yescharacteristic
325C2×C3×C8C2413yes—
326C3×C4⋊C4—23no—
327C3×C4⋊C4—23no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—23no—
330C3×C4⋊C4—23no—
331C3×C4⋊C4C2×D413yes—
332C3×C4⋊C4C2×D413yes—
333C3×C4⋊C4C2413yes—
334C3×C4⋊C4C2411yescharacteristic
335C3×C22⋊C4—23no—
336C3×C22⋊C4—23no—
337C3×C22⋊C4—26no—
338C3×C22⋊C4—23no—
339C3×C22⋊C4—23no—
340C3×C22⋊C4—23no—
341C3×C22⋊C4—26no—
342C3×C22⋊C4—26no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4C2×D416yes—
346C3×C42—21no—
347C3×C42—23no—
348C3×C42—23no—
349C3×C42C2×D413yes—
350C3×C42C2×D413yes—
351C3×C42C2411yescharacteristic
352C3×C42C2413yes—
3532−1+4—24no—
3542−1+4—24no—
355H(5,𝔽2)—24no—
356H(5,𝔽2)—24no—
357H(5,𝔽2)—24no—
358H(5,𝔽2)C3×D418yescomplemented
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—23no—
362C2×#41C23×C313yes—
363C2×#41C23×C313yes—
364C2×#41C23×C313yes—
365C2×#41C23×C311yescharacteristic
366C22×Q8—21no—
367C22×Q8C23×C313yes—
368C22×D4—23no—
369C22×D4—23no—
370C22×D4C23×C313yes—
371C22×D4C23×C313yes—
372C23×C4—23no—
373#137—212no—
374AGL(1,ℤ/8)—212no—
375AGL(1,ℤ/8)—212no—
376AGL(1,ℤ/8)—212no—
377#135—212no—
378#135—212no—
379C2×Q16C23×C311yescharacteristic
380C2×Q16C23×C313yes—
381C2×SD16—212no—
382C2×SD16C23×C313yes—
383C2×SD16C23×C316yes—
384C2×SD16C23×C313yes—
385C2×SD16C23×C313yes—
386C2×SD16C23×C311yescharacteristic
387C2×D8—212no—
388C2×D8C23×C313yes—
389C2×D8C23×C316yes—
390C2×D8C23×C313yes—
391#131—24no—
392#131—24no—
393C2×M16C23×C313yes—
394C2×M16C23×C313yes—
395C22×C8C23×C313yes—
396C22×C8C23×C313yes—
397C4⋊Q8C23×C313yes—
398#127C23×C313yes—
399#124—23no—
400#124—23no—
401#124C23×C313yes—
402#124C23×C316yes—
403#124C23×C311yescharacteristic
404#123—26no—
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407#121—23no—
408#121—23no—
409#121—23no—
410#121—23no—
411#120—26no—
412C4×Q8—21no—
413C4×Q8C3×D411yescharacteristic
414C4×Q8C3×D411yescharacteristic
415C4×Q8C23×C311yescharacteristic
416C4×Q8C23×C313yes—
417C4×D4—23no—
418C4×D4—23no—
419C4×D4—23no—
420C4×D4—23no—
421C4×D4—23no—
422C4×D4—26no—
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4C3×D413yes—
428C4×D4C3×D413yes—
429C4×D4C23×C313yes—
430C4×D4C23×C316yes—
431C4×D4C23×C313yes—
432#117—23no—
433#117—23no—
434#117C23×C313yes—
435#117C23×C313yes—
436C2×C4⋊C4—23no—
437C2×C4⋊C4C23×C313yes—
438C2×C22⋊C4—23no—
439C2×C22⋊C4—23no—
440C2×C22⋊C4—23no—
441C2×C22⋊C4—26no—
442C2×C42—23no—
443C2×C42C23×C313yes—
444C4⋊C8C23×C311yescharacteristic
445C4⋊C8C23×C313yes—
446C4⋊C8C23×C313yes—
447C4⋊C8C23×C313yes—
448C4⋊C8C23×C316yes—
449#103C23×C313yes—
450#103C23×C316yes—
451#103C23×C311yescharacteristic
452#103C23×C313yes—
453#103C23×C313yes—
454#102C23×C313yes—
455#102C23×C316yes—
456#102C23×C311yescharacteristic
457#102C23×C313yes—
458#102C23×C313yes—
459C23×C3—23no—
460C23×C3—212no—
461C23×C3—23no—
462C23×C3—21no—
463C23×C3—46no—
464C23×C3—83no—
465C23×C3—83no—
466C23×C3—83no—
467C23×C3—83no—
468C23×C3C22×D413yes—
469C3×Q8—21no—
470C3×Q8—23no—
471C3×Q8—21no—
472C3×Q8—23no—
473C3×Q8—21no—
474C3×Q8—46no—
475C3×Q8#12114yes—
476C3×Q8C22×D412yes—
477C3×D4—212no—
478C3×D4—212no—
479C3×D4—23no—
480C3×D4—21no—
481C3×D4—23no—
482C3×D4—23no—
483C3×D4—21no—
484C3×D4—46no—
485C3×D4—46no—
486C3×D4—46no—
487C3×D4—83no—
488C3×D4—83no—
489C3×D4#121112yes—
490C3×D4C22×D416yes—
491C2×C3×C4—21no—
492C2×C3×C4—212no—
493C2×C3×C4—21no—
494C2×C3×C4—23no—
495C2×C3×C4—23no—
496C2×C3×C4—21no—
497C2×C3×C4—43no—
498C2×C3×C4—43no—
499C2×C3×C4—46no—
500C2×C3×C4—46no—
501C2×C3×C4—46no—
502C2×C3×C4—46no—
503C2×C3×C4—83no—
504C2×C3×C4—86no—
505C2×C3×C4—83no—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D413yes—
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D413yes—
510C2×C3×C4C22×D413yes—
511C2×C3×C4C22×D416yes—
512C2×C3×C4C2×#4116yes—
513C2×C3×C4C2511yescharacteristic
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—23no—
517C3×C8—23no—
518C24—23no—
519C24—23no—
520#41—28no—
521#41—26no—
522#41—26no—
523#41—26no—
524#41—26no—
525#41—26no—
526#41—44no—
527#41—412no—
528#41C2×C3×D4112yes—
529#41C2×C3×D414yes—
530#41C3×#4114yes—
531C2×Q8—23no—
532C2×Q8—26no—
533C2×Q8—26no—
534C2×Q8—44no—
535C2×Q8C2×C3×D411yescharacteristic
536C2×Q8C24×C313yes—
537C2×Q8C24×C311yescharacteristic
538C2×Q8C24×C311yescharacteristic
539C2×D4—23no—
540C2×D4—224no—
541C2×D4—23no—
542C2×D4—23no—
543C2×D4—23no—
544C2×D4—26no—
545C2×D4—23no—
546C2×D4—23no—
547C2×D4—23no—
548C2×D4—26no—
549C2×D4—26no—
550C2×D4—412no—
551C2×D4C2×C3×D4112yes—
552C2×D4C2×C3×D413yes—
553C2×D4C24×C313yes—
554C2×D4C24×C311yescharacteristic
555C2×D4C24×C313yes—
556C22×C4—23no—
557C22×C4—23no—
558C22×C4—23no—
559C22×C4—23no—
560C22×C4—23no—
561C22×C4—23no—
562C22×C4—23no—
563C22×C4—26no—
564C22×C4—86no—
565C22×C4C2×C3×D413yes—
566C22×C4C2×C3×D413yes—
567C22×C4C24×C313yes—
568Q16—22no—
569Q16—26no—
570SD16—22no—
571SD16—26no—
572SD16—26no—
573SD16—212no—
574SD16—26no—
575D8—26no—
576D8—212no—
577D8—26no—
578M16—26no—
579M16—26no—
580C2×C8—26no—
581C2×C8—26no—
582C2×C8C24×C311yescharacteristic
583C2×C8C24×C313yes—
584C2×C8C24×C311yescharacteristic
585C2×C8C24×C313yes—
586C4⋊C4—23no—
587C4⋊C4—23no—
588C4⋊C4—21no—
589C4⋊C4—23no—
590C4⋊C4—23no—
591C4⋊C4C2×C3×D413yes—
592C4⋊C4C2×C3×D413yes—
593C4⋊C4C24×C313yes—
594C4⋊C4C24×C311yescharacteristic
595C22⋊C4—23no—
596C22⋊C4—23no—
597C22⋊C4—26no—
598C22⋊C4—23no—
599C22⋊C4—23no—
600C22⋊C4—23no—
601C22⋊C4—26no—
602C22⋊C4—26no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4C2×C3×D416yes—
606C42—21no—
607C42—23no—
608C42—23no—
609C42C2×C3×D413yes—
610C42C2×C3×D413yes—
611C42C24×C311yescharacteristic
612C42C24×C313yes—
613C22×C3—23no—
614C22×C3—23no—
615C22×C3—26no—
616C22×C3—43no—
617C22×C3—43no—
618C22×C3—41no—
619C22×C3—43no—
620C22×C3—41no—
621C22×C3—43no—
622C22×C3—41no—
623C22×C3—43no—
624C22×C3—812no—
625C22×C3—166no—
626C22×C3C2×#12116yes—
627C22×C3C23×D411yescharacteristic
628C3×C4—21no—
629C3×C4—23no—
630C3×C4—21no—
631C3×C4—23no—
632C3×C4—22no—
633C3×C4—41no—
634C3×C4—43no—
635C3×C4—41no—
636C3×C4—43no—
637C3×C4C2×#12116yes—
638C3×C4C23×D411yescharacteristic
639C3×C4C22×#4111yescharacteristic
640C23—23no—
641C23—212no—
642C23—23no—
643C23—21no—
644C23—46no—
645C23—83no—
646C23—83no—
647C23—83no—
648C23—83no—
649C23C22×C3×D413yes—
650Q8—21no—
651Q8—23no—
652Q8—21no—
653Q8—23no—
654Q8—21no—
655Q8—46no—
656Q8C3×#12114yes—
657Q8C22×C3×D412yes—
658D4—212no—
659D4—23no—
660D4—21no—
661D4—23no—
662D4—23no—
663D4—21no—
664D4—212no—
665D4—46no—
666D4—46no—
667D4—46no—
668D4—83no—
669D4—83no—
670D4C3×#121112yes—
671D4C22×C3×D416yes—
672C2×C4—21no—
673C2×C4—212no—
674C2×C4—21no—
675C2×C4—23no—
676C2×C4—23no—
677C2×C4—21no—
678C2×C4—43no—
679C2×C4—43no—
680C2×C4—46no—
681C2×C4—46no—
682C2×C4—46no—
683C2×C4—46no—
684C2×C4—86no—
685C2×C4—83no—
686C2×C4—83no—
687C2×C4C22×C3×D411yescharacteristic
688C2×C4C22×C3×D413yes—
689C2×C4C22×C3×D411yescharacteristic
690C2×C4C22×C3×D413yes—
691C2×C4C22×C3×D416yes—
692C2×C4C22×C3×D413yes—
693C2×C4C2×C3×#4116yes—
694C2×C4C25×C311yescharacteristic
695C8—21no—
696C8—21no—
697C8—23no—
698C8—23no—
699C2×C3—26no—
700C2×C3—46no—
701C2×C3—81no—
702C2×C3—83no—
703C2×C3C22×#12111yescharacteristic
704C2×C3#358411yescharacteristic
705C2×C3#358511yescharacteristic
706C22—23no—
707C22—23no—
708C22—26no—
709C22—43no—
710C22—43no—
711C22—41no—
712C22—43no—
713C22—41no—
714C22—43no—
715C22—41no—
716C22—43no—
717C22—812no—
718C22—166no—
719C22C2×C3×#12116yes—
720C22C23×C3×D411yescharacteristic
721C4—22no—
722C4—21no—
723C4—23no—
724C4—21no—
725C4—23no—
726C4—41no—
727C4—43no—
728C4—41no—
729C4—43no—
730C4C2×C3×#12116yes—
731C4C23×C3×D411yescharacteristic
732C4C22×C3×#4111yescharacteristic
733C3#6043011yescharacteristic, direct product factor, Sylow
734C2—26no—
735C2—46no—
736C2—83no—
737C2—81no—
738C2C22×C3×#12111yescharacteristic
739C2C3×#358411yescharacteristic
740C2C3×#358511yescharacteristic
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×#577C2semidirect
2. C2×C3×#576C2semidirect
3. C3×#3500C2semidirect
4. C3×C4×H(5,𝔽2)C2semidirect
5. C3×#3046C2semidirect
6. C3×#3045C2semidirect
7. C3×#3042C2semidirect
8. C3×#3041C2semidirect
9. C3×#3040C2semidirect
10. C3×#3036C2semidirect
11. C3×#3035C2semidirect
12. C2×C3×#463C2semidirect
13. C3×#2906C2semidirect
14. C3×#2898C2semidirect
15. C3×#2897C2semidirect
16. #60430C3direct (N × H)
22. C2×C3×#137C22semidirect
25. C2×C3×AGL(1,ℤ/8)C22semidirect
27. C2×C3×#135C22semidirect
28. C22×C3×SD16C22semidirect
36. C3×#536C22semidirect
37. C3×#535C22semidirect
38. C3×#532C22semidirect
39. C2×C3×#124C22semidirect
42. C3×#520C22semidirect
44. C3×#518C22semidirect
47. C3×C4×#41C22semidirect
49. C2×C3×C4×D4C22semidirect
50. C3×#464C22semidirect
51. C3×#464C22semidirect
52. C3×#464C22semidirect
53. C3×#463C22semidirect
54. C3×#463C22semidirect
55. C3×#463C22semidirect
56. C3×#463C22semidirect
57. C3×#463C22semidirect
58. C3×#463C22semidirect
59. C3×#462C22semidirect
60. C3×#461C22semidirect
61. C3×#461C22semidirect
62. C3×#460C22semidirect
63. C3×#459C22semidirect
64. C3×#459C22semidirect
65. C3×#424C22semidirect
66. C3×#424C22semidirect
67. C3×#423C22semidirect
68. C2×C3×C4⋊C8C22semidirect
69. C3×#419C22semidirect
70. C3×#418C22semidirect
71. C3×#417C22semidirect
72. C3×#417C22semidirect
73. C3×#416C22semidirect
74. C3×#416C22semidirect
75. C2×C3×#103C22semidirect
76. C2×C3×#102C22semidirect
77. C2×#577C2×C3semidirect
78. C2×#576C2×C3semidirect
79. #3500C2×C3semidirect
80. C4×H(5,𝔽2)C2×C3semidirect
81. #3046C2×C3semidirect
82. #3045C2×C3semidirect
83. #3042C2×C3semidirect
84. #3041C2×C3semidirect
85. #3040C2×C3semidirect
86. #3036C2×C3semidirect
87. #3035C2×C3semidirect
88. C2×#463C2×C3semidirect
89. #2906C2×C3semidirect
90. #2898C2×C3semidirect
91. #2897C2×C3semidirect
97. C3×H(5,𝔽2)D4semidirect
203. C2×#137C22×C3semidirect
206. C2×AGL(1,ℤ/8)C22×C3semidirect
208. C2×#135C22×C3semidirect
209. C22×SD16C22×C3semidirect
217. #536C22×C3semidirect
218. #535C22×C3semidirect
219. #532C22×C3semidirect
220. C2×#124C22×C3semidirect
223. #520C22×C3semidirect
225. #518C22×C3semidirect
228. C4×#41C22×C3semidirect
230. C2×C4×D4C22×C3semidirect
231. #464C22×C3semidirect
232. #464C22×C3semidirect
233. #464C22×C3semidirect
234. #463C22×C3semidirect
235. #463C22×C3semidirect
236. #463C22×C3semidirect
237. #463C22×C3semidirect
238. #463C22×C3semidirect
239. #463C22×C3semidirect
240. #462C22×C3semidirect
241. #461C22×C3semidirect
242. #461C22×C3semidirect
243. #460C22×C3semidirect
244. #459C22×C3semidirect
245. #459C22×C3semidirect
246. #424C22×C3semidirect
247. #424C22×C3semidirect
248. #423C22×C3semidirect
249. C2×C4⋊C8C22×C3semidirect
250. #419C22×C3semidirect
251. #418C22×C3semidirect
252. #417C22×C3semidirect
253. #417C22×C3semidirect
254. #416C22×C3semidirect
255. #416C22×C3semidirect
256. C2×#103C22×C3semidirect
257. C2×#102C22×C3semidirect
358. H(5,𝔽2)C3×D4semidirect
733. C3#60430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5772
C2×C3×#5762
C3×#35002
C3×C4×H(5,𝔽2)2
C3×#30462
C3×#30452
C3×#30422
C3×#30412
C3×#30402
C3×#30362
C3×#30352
C2×C3×#4632
C3×#29062
C3×#28982
C3×#28972
#604303