Finite Group Databasebeta

← C3×#25761 #10644368

Subgroups — C3×#25761 #10644368

Order 768.

1582 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3C2×C3×#464C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#451C211yesmaximal, characteristic, complemented
7C2×C3×#448C211yesmaximal, characteristic, complemented
8C3×#2540C211yesmaximal, characteristic, complemented
9C3×#2001C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1983C211yesmaximal, characteristic, complemented
14C3×#1954C211yesmaximal, characteristic, complemented
15C3×C4×#103C211yesmaximal, characteristic, complemented
16#25761C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×D8C2211yescharacteristic
25C3×#548—24no—
26C3×#548—24no—
27C2×C3×#124—21no—
28C2×C3×#124C2211yescharacteristic
29C2×C3×#124C2211yescharacteristic
30C2×C3×C22⋊Q8—21no—
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C22⋊Q8C2211yescharacteristic
33C2×C3×C22⋊Q8C2211yescharacteristic
34C2×C3×#121—21no—
35C2×C3×#121C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C2×C3×C4×Q8C2211yescharacteristic
39C2×C3×C4×D4—21no—
40C2×C3×C4×D4C2211yescharacteristic
41C3×#495—24no—
42C3×#464—24no—
43C3×#452—24no—
44C3×#451—24no—
45C3×#449—24no—
46C3×#448—24no—
47C2×C3×C4⋊C8C2211yescharacteristic
48C2×C3×#103C2211yescharacteristic
49C2×C3×#103C2211yescharacteristic
50C2×C3×#103C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#103C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×#102C2211yescharacteristic
55C2×C3×#102C2211yescharacteristic
56C2×C3×C22⋊C8C2211yescharacteristic
57C2×C3×C22⋊C8C2211yescharacteristic
58C2×C3×C22⋊C8C2211yescharacteristic
59C2×C3×C22⋊C8C2211yescharacteristic
60C2×C3×C4×C8C2211yescharacteristic
61C3×#399—21no—
62C3×#392—21no—
63C3×#390—21no—
64C3×#390—21no—
65C3×C4×C4⋊C4C2211yescharacteristic
66C3×#340C2211yescharacteristic
67C3×#340C2211yescharacteristic
68C2×#548C2×C311yescharacteristic, complemented
69C2×#495C2×C311yescharacteristic, complemented
70C2×#464C2×C311yescharacteristic, complemented
71C2×#452C2×C311yescharacteristic, complemented
72C2×#449C2×C311yescharacteristic, complemented
73C2×#451C2×C311yescharacteristic, complemented
74C2×#448C2×C311yescharacteristic, complemented
75#2540C2×C311yescharacteristic, complemented
76#2001C2×C311yescharacteristic, complemented
77#2000C2×C311yescharacteristic, complemented
78#2000C2×C311yescharacteristic, complemented
79#1999C2×C311yescharacteristic, complemented
80#1983C2×C311yescharacteristic, complemented
81#1954C2×C311yescharacteristic, complemented
82C4×#103C2×C311yescharacteristic, complemented
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—41no—
88C2×C3×#41—41no—
89C22×C3×Q8—22no—
90C22×C3×Q8—22no—
91C22×C3×Q8—21no—
92C22×C3×Q8—22no—
93C22×C3×Q8—22no—
94C22×C3×Q8—41no—
95C22×C3×Q8—41no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4D411yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C2×C3×Q16—22no—
111C2×C3×Q16—22no—
112C2×C3×Q16—22no—
113C2×C3×Q16—22no—
114C2×C3×Q16—22no—
115C2×C3×Q16—41no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—22no—
122C2×C3×SD16—22no—
123C2×C3×SD16—41no—
124C2×C3×SD16—41no—
125C2×C3×D8—22no—
126C2×C3×D8—22no—
127C2×C3×D8—41no—
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C3×#124—28no—
133C3×#124—22no—
134C3×#124—22no—
135C3×#124—22no—
136C3×#124D414yescomplemented
137C3×C22⋊Q8—28no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8—22no—
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8—41no—
143C3×C22⋊Q8—41no—
144C3×#121—28no—
145C3×#121—22no—
146C3×#121—22no—
147C3×#121—22no—
148C3×#121—22no—
149C3×#121—41no—
150C3×#121—41no—
151C3×C4×Q8—22no—
152C3×C4×Q8D414yescomplemented
153C3×C4×D4—28no—
154C3×C4×D4—22no—
155C3×C4×D4—22no—
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4D411yescharacteristic
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C4⋊C4C2311yescharacteristic
164C2×C3×C22⋊C4—21no—
165C2×C3×C22⋊C4—21no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—21no—
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—21no—
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4D411yescharacteristic
175C2×C3×C22⋊C4D411yescharacteristic
176C2×C3×C42—21no—
177C2×C3×C42—21no—
178C2×C3×C42C2311yescharacteristic
179C3×C4⋊C8—22no—
180C3×#103—22no—
181C3×#103—22no—
182C3×#103—22no—
183C3×#103D414yescomplemented
184C3×#103D414yescomplemented
185C3×#102—22no—
186C3×#102—22no—
187C3×#102—22no—
188C3×C22⋊C8—22no—
189C3×C22⋊C8—22no—
190C3×C22⋊C8—22no—
191C3×C22⋊C8—22no—
192C3×C4×C8—22no—
193C3×#95—21no—
194C22×#41C22×C311yescharacteristic
195C23×Q8C22×C311yescharacteristic
196C22×Q16C22×C311yescharacteristic
197C22×Q16C22×C311yescharacteristic
198C22×SD16C22×C311yescharacteristic
199C22×SD16C22×C311yescharacteristic
200C22×SD16C22×C311yescharacteristic
201C22×D8C22×C311yescharacteristic
202#548—24no—
203#548—24no—
204C2×#124—21no—
205C2×#124C22×C311yescharacteristic
206C2×#124C22×C311yescharacteristic
207C2×C22⋊Q8—21no—
208C2×C22⋊Q8C22×C311yescharacteristic
209C2×C22⋊Q8C22×C311yescharacteristic
210C2×C22⋊Q8C22×C311yescharacteristic
211C2×#121—21no—
212C2×#121C22×C311yescharacteristic
213C2×#121C22×C311yescharacteristic
214C2×#121C22×C311yescharacteristic
215C2×C4×Q8C22×C311yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4C22×C311yescharacteristic
218#495—24no—
219#464—24no—
220#452—24no—
221#451—24no—
222#449—24no—
223#448—24no—
224C2×C4⋊C8C22×C311yescharacteristic
225C2×#103C22×C311yescharacteristic
226C2×#103C22×C311yescharacteristic
227C2×#103C22×C311yescharacteristic
228C2×#103C22×C311yescharacteristic
229C2×#103C22×C311yescharacteristic
230C2×#102C22×C311yescharacteristic
231C2×#102C22×C311yescharacteristic
232C2×#102C22×C311yescharacteristic
233C2×C22⋊C8C22×C311yescharacteristic
234C2×C22⋊C8C22×C311yescharacteristic
235C2×C22⋊C8C22×C311yescharacteristic
236C2×C22⋊C8C22×C311yescharacteristic
237C2×C4×C8C22×C311yescharacteristic
238#399—21no—
239#392—21no—
240#390—21no—
241#390—21no—
242C4×C4⋊C4C22×C311yescharacteristic
243#340C22×C311yescharacteristic
244#340C22×C311yescharacteristic
245C24×C3—21no—
246C24×C3—21no—
247C24×C3C2×D411yescharacteristic
248C24×C3C2×D411yescharacteristic
249C3×#41—44no—
250C3×#41—44no—
251C3×#41—44no—
252C3×#41—44no—
253C2×C3×Q8—24no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—42no—
269C2×C3×Q8—42no—
270C2×C3×Q8—44no—
271C2×C3×Q8—44no—
272C2×C3×Q8—44no—
273C2×C3×Q8—44no—
274C2×C3×Q8C2×D412yes—
275C2×C3×Q8C2×D412yes—
276C2×C3×Q8C2×D412yes—
277C2×C3×Q8C2×D412yes—
278C2×C3×D4—24no—
279C2×C3×D4—24no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—41no—
294C2×C3×D4—42no—
295C2×C3×D4—42no—
296C2×C3×D4—42no—
297C2×C3×D4—42no—
298C2×C3×D4—42no—
299C2×C3×D4—42no—
300C2×C3×D4—42no—
301C2×C3×D4—42no—
302C2×C3×D4—81no—
303C2×C3×D4—81no—
304C2×C3×D4C2×D412yes—
305C22×C3×C4—21no—
306C22×C3×C4—24no—
307C22×C3×C4—24no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—42no—
326C22×C3×C4—42no—
327C22×C3×C4—42no—
328C22×C3×C4—42no—
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C3×Q16—44no—
335C3×Q16—44no—
336C3×SD16—44no—
337C3×SD16—44no—
338C3×SD16—44no—
339C3×D8—44no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8C2×D412yes—
351C2×C3×C8C2×D412yes—
352C3×C4⋊C4—24no—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—22no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—42no—
359C3×C4⋊C4—42no—
360C3×C4⋊C4C2×D412yes—
361C3×C4⋊C4C2×D412yes—
362C3×C4⋊C4C2×D412yes—
363C3×C22⋊C4—24no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—22no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4—42no—
370C3×C22⋊C4—42no—
371C3×C22⋊C4—42no—
372C3×C22⋊C4—42no—
373C3×C22⋊C4—42no—
374C3×C22⋊C4—42no—
375C3×C42—24no—
376C3×C42—81no—
377C3×C42C2×D412yes—
378C3×C42C2×D412yes—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—41no—
384C2×#41—41no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—21no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—41no—
391C22×Q8—41no—
392C22×Q8C23×C311yescharacteristic
393C22×Q8C23×C311yescharacteristic
394C22×Q8C23×C311yescharacteristic
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4C3×D411yescharacteristic
400C22×D4C23×C311yescharacteristic
401C22×D4C23×C311yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C2×Q16—22no—
407C2×Q16—22no—
408C2×Q16—22no—
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—41no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—41no—
420C2×SD16—41no—
421C2×D8—22no—
422C2×D8—22no—
423C2×D8—41no—
424C22×C8C23×C311yescharacteristic
425C22×C8C23×C311yescharacteristic
426C22×C8C23×C311yescharacteristic
427C22×C8C23×C311yescharacteristic
428#124—28no—
429#124—22no—
430#124—22no—
431#124—22no—
432#124C3×D414yescomplemented
433C22⋊Q8—28no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—41no—
439C22⋊Q8—41no—
440#121—28no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—41no—
446#121—41no—
447C4×Q8—22no—
448C4×Q8C3×D414yescomplemented
449C4×D4—28no—
450C4×D4—22no—
451C4×D4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4C3×D411yescharacteristic
457C2×C4⋊C4C23×C311yescharacteristic
458C2×C4⋊C4C23×C311yescharacteristic
459C2×C4⋊C4C23×C311yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4C3×D411yescharacteristic
471C2×C22⋊C4C3×D411yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C311yescharacteristic
475C4⋊C8—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103C3×D414yescomplemented
480#103C3×D414yescomplemented
481#102—22no—
482#102—22no—
483#102—22no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C4×C8—22no—
489#95—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3#13512yes—
518C23×C3C22×D411yescharacteristic
519C3×Q8—22no—
520C3×Q8—22no—
521C3×Q8—22no—
522C3×Q8—22no—
523C3×Q8—22no—
524C3×Q8—48no—
525C3×Q8—41no—
526C3×Q8—41no—
527C3×Q8—41no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8#12714yes—
532C3×D4—22no—
533C3×D4—22no—
534C3×D4—44no—
535C3×D4—48no—
536C3×D4—48no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—41no—
542C3×D4—41no—
543C3×D4—84no—
544C3×D4—84no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—48no—
563C2×C3×C4—48no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4#12012yes—
584C2×C3×C4#12012yes—
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4H(5,𝔽2)11yescharacteristic
590C2×C3×C4H(5,𝔽2)11yescharacteristic
591C3×C8—22no—
592C3×C8—22no—
593C3×C8—41no—
594C3×C8—41no—
595C24—21no—
596C24—21no—
597C24C2×C3×D411yescharacteristic
598C24C2×C3×D411yescharacteristic
599#41—44no—
600#41—44no—
601#41—44no—
602#41—44no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8C2×C3×D412yes—
625C2×Q8C2×C3×D412yes—
626C2×Q8C2×C3×D412yes—
627C2×Q8C2×C3×D412yes—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×C3×D412yes—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4C2×C3×D411yescharacteristic
680C22×C4C2×C3×D411yescharacteristic
681C22×C4C2×C3×D411yescharacteristic
682C22×C4C2×C3×D411yescharacteristic
683C22×C4C24×C311yescharacteristic
684Q16—44no—
685Q16—44no—
686SD16—44no—
687SD16—44no—
688SD16—44no—
689D8—44no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8C2×C3×D412yes—
701C2×C8C2×C3×D412yes—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—22no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4C2×C3×D412yes—
711C4⋊C4C2×C3×D412yes—
712C4⋊C4C2×C3×D412yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C42—24no—
726C42—81no—
727C42C2×C3×D412yes—
728C42C2×C3×D412yes—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—42no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—42no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3C2×#12011yescharacteristic
758C22×C3D4211yescharacteristic
759C22×C3D4211yescharacteristic
760C22×C3C2×#13511yescharacteristic
761C22×C3#57511yescharacteristic
762C22×C3#57711yescharacteristic
763C22×C3#57811yescharacteristic
764C3×C4—24no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—81no—
774C3×C4C2×#12711yescharacteristic
775C3×C4#53511yescharacteristic
776C3×C4D4211yescharacteristic
777C3×C4D4211yescharacteristic
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23C3×#13512yes—
806C23C22×C3×D411yescharacteristic
807Q8—22no—
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—48no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—41no—
817Q8—41no—
818Q8—41no—
819Q8C3×#12714yes—
820D4—22no—
821D4—22no—
822D4—44no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4C3×#12012yes—
872C2×C4C3×#12012yes—
873C2×C4C22×C3×D411yescharacteristic
874C2×C4C22×C3×D411yescharacteristic
875C2×C4C22×C3×D411yescharacteristic
876C2×C4C22×C3×D411yescharacteristic
877C2×C4C3×H(5,𝔽2)11yescharacteristic
878C2×C4C3×H(5,𝔽2)11yescharacteristic
879C8—22no—
880C8—22no—
881C8—41no—
882C8—41no—
883C2×C3—42no—
884C2×C3—81no—
885C2×C3—82no—
886C2×C3—161no—
887C2×C3#243311yescharacteristic
888C2×C3#300211yescharacteristic
889C2×C3#301311yescharacteristic
890C2×C3#327511yescharacteristic
891C2×C3#327711yescharacteristic
892C2×C3#328211yescharacteristic
893C2×C3#328511yescharacteristic
894C22—22no—
895C22—22no—
896C22—22no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22C2×C3×#12011yescharacteristic
923C22C3×D4211yescharacteristic
924C22C3×D4211yescharacteristic
925C22C2×C3×#13511yescharacteristic
926C22C3×#57511yescharacteristic
927C22C3×#57711yescharacteristic
928C22C3×#57811yescharacteristic
929C4—24no—
930C4—22no—
931C4—22no—
932C4—41no—
933C4—41no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—81no—
939C4C2×C3×#12711yescharacteristic
940C4C3×#53511yescharacteristic
941C4C3×D4211yescharacteristic
942C4C3×D4211yescharacteristic
943C3#2576111yescharacteristic, direct product factor, Sylow
944C2—42no—
945C2—81no—
946C2—82no—
947C2—161no—
948C2C3×#243311yescharacteristic
949C2C3×#300211yescharacteristic
950C2C3×#301311yescharacteristic
951C2C3×#327511yescharacteristic
952C2C3×#327711yescharacteristic
953C2C3×#328211yescharacteristic
954C2C3×#328511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C2×C3×#495C2semidirect
3. C2×C3×#464C2semidirect
4. C2×C3×#452C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#451C2semidirect
7. C2×C3×#448C2semidirect
8. C3×#2540C2semidirect
9. C3×#2001C2semidirect
10. C3×#2000C2semidirect
11. C3×#2000C2semidirect
12. C3×#1999C2semidirect
13. C3×#1983C2semidirect
14. C3×#1954C2semidirect
15. C3×C4×#103C2semidirect
16. #25761C3direct (N × H)
68. C2×#548C2×C3semidirect
69. C2×#495C2×C3semidirect
70. C2×#464C2×C3semidirect
71. C2×#452C2×C3semidirect
72. C2×#449C2×C3semidirect
73. C2×#451C2×C3semidirect
74. C2×#448C2×C3semidirect
75. #2540C2×C3semidirect
76. #2001C2×C3semidirect
77. #2000C2×C3semidirect
78. #2000C2×C3semidirect
79. #1999C2×C3semidirect
80. #1983C2×C3semidirect
81. #1954C2×C3semidirect
82. C4×#103C2×C3semidirect
136. C3×#124D4semidirect
152. C3×C4×Q8D4semidirect
183. C3×#103D4semidirect
184. C3×#103D4semidirect
432. #124C3×D4semidirect
448. C4×Q8C3×D4semidirect
479. #103C3×D4semidirect
480. #103C3×D4semidirect
943. C3#25761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×C3×#4952
C2×C3×#4642
C2×C3×#4522
C2×C3×#4492
C2×C3×#4512
C2×C3×#4482
C3×#25402
C3×#20012
C3×#20002
C3×#19992
C3×#19832
C3×#19542
C3×C4×#1032
#257613