Finite Group Databasebeta

← C3×#25762 #10644369

Subgroups — C3×#25762 #10644369

Order 768.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3C2×C3×#463C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#450C211yesmaximal, characteristic, complemented
7C2×C3×#447C211yesmaximal, 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×#102C211yesmaximal, characteristic, complemented
16#25762C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic, complemented
23C22×C3×D8C2211yescharacteristic
24C22×C3×D8C2211yescharacteristic
25C3×#546—24no—
26C3×#546—24no—
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic, complemented
29C2×C3×#123—21no—
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C22⋊Q8C2211yescharacteristic, complemented
33C2×C3×#121—21no—
34C2×C3×#121C2211yescharacteristic
35C2×C3×#121C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic, complemented
37C2×C3×#120—21no—
38C2×C3×C4×D4C2211yescharacteristic
39C2×C3×C4×D4C2211yescharacteristic
40C22×C3×C22⋊C4—21no—
41C3×#495—24no—
42C3×#463—24no—
43C3×#452—24no—
44C3×#450—24no—
45C3×#449—24no—
46C3×#447—24no—
47C2×C3×C4⋊C8C2211yescharacteristic, complemented
48C2×C3×#103C2211yescharacteristic, complemented
49C2×C3×#103C2211yescharacteristic, complemented
50C2×C3×#103C2211yescharacteristic, complemented
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×#102C2211yescharacteristic
55C2×C3×#102C2211yescharacteristic, complemented
56C2×C3×C22⋊C8C2211yescharacteristic
57C2×C3×C22⋊C8C2211yescharacteristic
58C2×C3×C22⋊C8C2211yescharacteristic, complemented
59C2×C3×C22⋊C8C2211yescharacteristic, complemented
60C2×C3×C4×C8C2211yescharacteristic, complemented
61C3×#399—21no—
62C3×#392—21no—
63C3×#390—21no—
64C3×#390—21no—
65C3×C4×C4⋊C4C2211yescharacteristic, complemented
66C3×#340C2211yescharacteristic, complemented
67C3×#340C2211yescharacteristic, complemented
68C2×#546C2×C311yescharacteristic, complemented
69C2×#495C2×C311yescharacteristic, complemented
70C2×#463C2×C311yescharacteristic, complemented
71C2×#452C2×C311yescharacteristic, complemented
72C2×#449C2×C311yescharacteristic, complemented
73C2×#450C2×C311yescharacteristic, complemented
74C2×#447C2×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×#102C2×C311yescharacteristic, complemented
83C25×C3—21no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—22no—
95C22×C3×D4—22no—
96C22×C3×D4—22no—
97C22×C3×D4—22no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4—41no—
102C22×C3×D4—41no—
103C22×C3×D4D411yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C22×C3×D4C2311yescharacteristic
107C23×C3×C4—21no—
108C23×C3×C4—21no—
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C2×C3×Q16—22no—
112C2×C3×Q16—22no—
113C2×C3×Q16—41no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—41no—
122C2×C3×SD16—41no—
123C2×C3×D8—22no—
124C2×C3×D8—22no—
125C2×C3×D8—22no—
126C2×C3×D8—22no—
127C2×C3×D8—22no—
128C2×C3×D8—41no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2311yescharacteristic
133C3×#124—22no—
134C3×#124—22no—
135C3×#124—22no—
136C3×#124D414yescomplemented
137C3×#123—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×#120—28no—
152C3×C4×D4—22no—
153C3×C4×D4—22no—
154C3×C4×D4—22no—
155C3×C4×D4D414yescomplemented
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4D411yescharacteristic
160C2×C3×C4⋊C4C2311yescharacteristic
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4—28no—
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⋊C4—21no—
175C2×C3×C22⋊C4D411yescharacteristic
176C2×C3×C22⋊C4D411yescharacteristic
177C2×C3×C42—21no—
178C2×C3×C42C2311yescharacteristic
179C3×C4⋊C8—22no—
180C3×#103—22no—
181C3×#103—22no—
182C3×#103—22no—
183C3×#102—22no—
184C3×#102—22no—
185C3×#102—22no—
186C3×#102D414yescomplemented
187C3×#102D414yescomplemented
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×D4C22×C311yescharacteristic
196C22×Q16C22×C311yescharacteristic, complemented
197C22×SD16C22×C311yescharacteristic
198C22×SD16C22×C311yescharacteristic
199C22×SD16C22×C311yescharacteristic, complemented
200C22×D8C22×C311yescharacteristic
201C22×D8C22×C311yescharacteristic
202#546—24no—
203#546—24no—
204C2×#124C22×C311yescharacteristic
205C2×#124C22×C311yescharacteristic, complemented
206C2×#123—21no—
207C2×C22⋊Q8C22×C311yescharacteristic
208C2×C22⋊Q8C22×C311yescharacteristic
209C2×C22⋊Q8C22×C311yescharacteristic, complemented
210C2×#121—21no—
211C2×#121C22×C311yescharacteristic
212C2×#121C22×C311yescharacteristic
213C2×#121C22×C311yescharacteristic, complemented
214C2×#120—21no—
215C2×C4×D4C22×C311yescharacteristic
216C2×C4×D4C22×C311yescharacteristic
217C22×C22⋊C4—21no—
218#495—24no—
219#463—24no—
220#452—24no—
221#450—24no—
222#449—24no—
223#447—24no—
224C2×C4⋊C8C22×C311yescharacteristic, complemented
225C2×#103C22×C311yescharacteristic, complemented
226C2×#103C22×C311yescharacteristic, complemented
227C2×#103C22×C311yescharacteristic, complemented
228C2×#102C22×C311yescharacteristic
229C2×#102C22×C311yescharacteristic
230C2×#102C22×C311yescharacteristic
231C2×#102C22×C311yescharacteristic
232C2×#102C22×C311yescharacteristic, complemented
233C2×C22⋊C8C22×C311yescharacteristic
234C2×C22⋊C8C22×C311yescharacteristic
235C2×C22⋊C8C22×C311yescharacteristic, complemented
236C2×C22⋊C8C22×C311yescharacteristic, complemented
237C2×C4×C8C22×C311yescharacteristic, complemented
238#399—21no—
239#392—21no—
240#390—21no—
241#390—21no—
242C4×C4⋊C4C22×C311yescharacteristic, complemented
243#340C22×C311yescharacteristic, complemented
244#340C22×C311yescharacteristic, complemented
245C24×C3—21no—
246C24×C3—24no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—42no—
250C24×C3—42no—
251C24×C3—42no—
252C24×C3—42no—
253C24×C3—81no—
254C24×C3—81no—
255C24×C3C2×D411yescharacteristic
256C24×C3C2×D411yescharacteristic
257C3×#41—44no—
258C3×#41—44no—
259C3×#41—44no—
260C3×#41—44no—
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—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8C2×D412yes—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—24no—
277C2×C3×D4—22no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
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—41no—
293C2×C3×D4—42no—
294C2×C3×D4—42no—
295C2×C3×D4—42no—
296C2×C3×D4—42no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—42no—
301C2×C3×D4—42no—
302C2×C3×D4—44no—
303C2×C3×D4—42no—
304C2×C3×D4—42no—
305C2×C3×D4—81no—
306C2×C3×D4—81no—
307C2×C3×D4—81no—
308C2×C3×D4—81no—
309C2×C3×D4C2×D412yes—
310C2×C3×D4C2×D412yes—
311C2×C3×D4C2×D412yes—
312C2×C3×D4C2×D412yes—
313C22×C3×C4—24no—
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—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—24no—
331C22×C3×C4—21no—
332C22×C3×C4—42no—
333C22×C3×C4—42no—
334C22×C3×C4—81no—
335C22×C3×C4—81no—
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2411yescharacteristic
341C3×Q16—44no—
342C3×SD16—44no—
343C3×SD16—44no—
344C3×SD16—44no—
345C3×D8—44no—
346C3×D8—44no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8—21no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8C2×D412yes—
358C2×C3×C8C2×D412yes—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—22no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—42no—
365C3×C4⋊C4—42no—
366C3×C4⋊C4C2×D412yes—
367C3×C4⋊C4C2×D412yes—
368C3×C4⋊C4C2×D412yes—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C22⋊C4—22no—
376C3×C22⋊C4—42no—
377C3×C22⋊C4—42no—
378C3×C22⋊C4—42no—
379C3×C22⋊C4—42no—
380C3×C22⋊C4—42no—
381C3×C22⋊C4—42no—
382C3×C42—81no—
383C3×C42C2×D412yes—
384C3×C42C2×D412yes—
385C25—21no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—41no—
391C2×#41—41no—
392C22×Q8C23×C311yescharacteristic
393C22×Q8C23×C311yescharacteristic
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—41no—
404C22×D4—41no—
405C22×D4C3×D411yescharacteristic
406C22×D4C23×C311yescharacteristic
407C22×D4C23×C311yescharacteristic
408C22×D4C23×C311yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C23×C4C23×C311yescharacteristic
412C23×C4C23×C311yescharacteristic
413C2×Q16—22no—
414C2×Q16—22no—
415C2×Q16—41no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—41no—
424C2×SD16—41no—
425C2×D8—22no—
426C2×D8—22no—
427C2×D8—22no—
428C2×D8—22no—
429C2×D8—22no—
430C2×D8—41no—
431C22×C8C23×C311yescharacteristic
432C22×C8C23×C311yescharacteristic
433C22×C8C23×C311yescharacteristic
434C22×C8C23×C311yescharacteristic
435#124—22no—
436#124—22no—
437#124—22no—
438#124C3×D414yescomplemented
439#123—28no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—41no—
445C22⋊Q8—41no—
446#121—28no—
447#121—22no—
448#121—22no—
449#121—22no—
450#121—22no—
451#121—41no—
452#121—41no—
453#120—28no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4C3×D414yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4C3×D411yescharacteristic
462C2×C4⋊C4C23×C311yescharacteristic
463C2×C4⋊C4C23×C311yescharacteristic
464C2×C4⋊C4C23×C311yescharacteristic
465C2×C22⋊C4—28no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4C3×D411yescharacteristic
478C2×C22⋊C4C3×D411yescharacteristic
479C2×C42—21no—
480C2×C42C23×C311yescharacteristic
481C4⋊C8—22no—
482#103—22no—
483#103—22no—
484#103—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102C3×D414yescomplemented
489#102C3×D414yescomplemented
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C4×C8—22no—
495#95—21no—
496C23×C3—21no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—22no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—48no—
514C23×C3—48no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—84no—
533C23×C3—84no—
534C23×C3—84no—
535C23×C3—84no—
536C23×C3—84no—
537C23×C3#13512yes—
538C23×C3C22×D411yescharacteristic
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—41no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×D4—22no—
548C3×D4—22no—
549C3×D4—22no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—44no—
553C3×D4—48no—
554C3×D4—48no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—41no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—84no—
562C3×D4—84no—
563C3×D4—84no—
564C3×D4#12714yes—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—48no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—84no—
600C2×C3×C4#12012yes—
601C2×C3×C4#12012yes—
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4H(5,𝔽2)11yescharacteristic
607C2×C3×C4H(5,𝔽2)11yescharacteristic
608C3×C8—22no—
609C3×C8—22no—
610C3×C8—41no—
611C3×C8—41no—
612C24—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—42no—
620C24—81no—
621C24—81no—
622C24C2×C3×D411yescharacteristic
623C24C2×C3×D411yescharacteristic
624#41—44no—
625#41—44no—
626#41—44no—
627#41—44no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8C2×C3×D412yes—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—22no—
643C2×D4—24no—
644C2×D4—22no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—41no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4C2×C3×D412yes—
677C2×D4C2×C3×D412yes—
678C2×D4C2×C3×D412yes—
679C2×D4C2×C3×D412yes—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4C2×C3×D411yescharacteristic
704C22×C4C2×C3×D411yescharacteristic
705C22×C4C2×C3×D411yescharacteristic
706C22×C4C2×C3×D411yescharacteristic
707C22×C4C24×C311yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711SD16—44no—
712D8—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×C3×D412yes—
725C2×C8C2×C3×D412yes—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4C2×C3×D412yes—
734C4⋊C4C2×C3×D412yes—
735C4⋊C4C2×C3×D412yes—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—22no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—81no—
750C42C2×C3×D412yes—
751C42C2×C3×D412yes—
752C22×C3—24no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—41no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—42no—
762C22×C3—41no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—41no—
767C22×C3—42no—
768C22×C3—41no—
769C22×C3—42no—
770C22×C3—41no—
771C22×C3—42no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—816no—
777C22×C3—81no—
778C22×C3—81no—
779C22×C3—81no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3C2×#12011yescharacteristic
789C22×C3D4211yescharacteristic
790C22×C3D4211yescharacteristic
791C22×C3C2×#13511yescharacteristic
792C22×C3#57511yescharacteristic
793C22×C3#57611yescharacteristic
794C22×C3#57711yescharacteristic
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—81no—
804C3×C4C2×#12711yescharacteristic
805C3×C4#53511yescharacteristic
806C3×C4D4211yescharacteristic
807C3×C4D4211yescharacteristic
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—22no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—48no—
826C23—48no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23C3×#13512yes—
850C23C22×C3×D411yescharacteristic
851Q8—22no—
852Q8—22no—
853Q8—41no—
854Q8—41no—
855Q8—41no—
856Q8—41no—
857Q8—41no—
858Q8—41no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—44no—
865D4—48no—
866D4—48no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—84no—
874D4—84no—
875D4—84no—
876D4C3×#12714yes—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—48no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—84no—
912C2×C4C3×#12012yes—
913C2×C4C3×#12012yes—
914C2×C4C22×C3×D411yescharacteristic
915C2×C4C22×C3×D411yescharacteristic
916C2×C4C22×C3×D411yescharacteristic
917C2×C4C22×C3×D411yescharacteristic
918C2×C4C3×H(5,𝔽2)11yescharacteristic
919C2×C4C3×H(5,𝔽2)11yescharacteristic
920C8—22no—
921C8—22no—
922C8—41no—
923C8—41no—
924C2×C3—42no—
925C2×C3—44no—
926C2×C3—81no—
927C2×C3—82no—
928C2×C3—161no—
929C2×C3#243311yescharacteristic
930C2×C3#300211yescharacteristic
931C2×C3#301211yescharacteristic
932C2×C3#327311yescharacteristic
933C2×C3#327511yescharacteristic
934C2×C3#328011yescharacteristic
935C2×C3#328211yescharacteristic
936C22—24no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—41no—
945C22—42no—
946C22—41no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—41no—
955C22—42no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—816no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22C2×C3×#12011yescharacteristic
973C22C3×D4211yescharacteristic
974C22C3×D4211yescharacteristic
975C22C2×C3×#13511yescharacteristic
976C22C3×#57511yescharacteristic
977C22C3×#57611yescharacteristic
978C22C3×#57711yescharacteristic
979C4—22no—
980C4—22no—
981C4—41no—
982C4—41no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4C2×C3×#12711yescharacteristic
989C4C3×#53511yescharacteristic
990C4C3×D4211yescharacteristic
991C4C3×D4211yescharacteristic
992C3#2576211yescharacteristic, direct product factor, Sylow
993C2—42no—
994C2—44no—
995C2—81no—
996C2—82no—
997C2—161no—
998C2C3×#243311yescharacteristic
999C2C3×#300211yescharacteristic
1000C2C3×#301211yescharacteristic
1001C2C3×#327311yescharacteristic
1002C2C3×#327511yescharacteristic
1003C2C3×#328011yescharacteristic
1004C2C3×#328211yescharacteristic
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×#546C2semidirect
2. C2×C3×#495C2semidirect
3. C2×C3×#463C2semidirect
4. C2×C3×#452C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#450C2semidirect
7. C2×C3×#447C2semidirect
8. C3×#2540C2semidirect
9. C3×#2001C2semidirect
10. C3×#2000C2semidirect
11. C3×#2000C2semidirect
12. C3×#1999C2semidirect
13. C3×#1983C2semidirect
14. C3×#1954C2semidirect
15. C3×C4×#102C2semidirect
16. #25762C3direct (N × H)
19. C22×C3×Q16C22semidirect
22. C22×C3×SD16C22semidirect
28. C2×C3×#124C22semidirect
32. C2×C3×C22⋊Q8C22semidirect
36. C2×C3×#121C22semidirect
47. C2×C3×C4⋊C8C22semidirect
48. C2×C3×#103C22semidirect
49. C2×C3×#103C22semidirect
50. C2×C3×#103C22semidirect
55. C2×C3×#102C22semidirect
58. C2×C3×C22⋊C8C22semidirect
59. C2×C3×C22⋊C8C22semidirect
60. C2×C3×C4×C8C22semidirect
65. C3×C4×C4⋊C4C22semidirect
66. C3×#340C22semidirect
67. C3×#340C22semidirect
68. C2×#546C2×C3semidirect
69. C2×#495C2×C3semidirect
70. C2×#463C2×C3semidirect
71. C2×#452C2×C3semidirect
72. C2×#449C2×C3semidirect
73. C2×#450C2×C3semidirect
74. C2×#447C2×C3semidirect
75. #2540C2×C3semidirect
76. #2001C2×C3semidirect
77. #2000C2×C3semidirect
78. #2000C2×C3semidirect
79. #1999C2×C3semidirect
80. #1983C2×C3semidirect
81. #1954C2×C3semidirect
82. C4×#102C2×C3semidirect
136. C3×#124D4semidirect
155. C3×C4×D4D4semidirect
186. C3×#102D4semidirect
187. C3×#102D4semidirect
196. C22×Q16C22×C3semidirect
199. C22×SD16C22×C3semidirect
205. C2×#124C22×C3semidirect
209. C2×C22⋊Q8C22×C3semidirect
213. C2×#121C22×C3semidirect
224. C2×C4⋊C8C22×C3semidirect
225. C2×#103C22×C3semidirect
226. C2×#103C22×C3semidirect
227. C2×#103C22×C3semidirect
232. C2×#102C22×C3semidirect
235. C2×C22⋊C8C22×C3semidirect
236. C2×C22⋊C8C22×C3semidirect
237. C2×C4×C8C22×C3semidirect
242. C4×C4⋊C4C22×C3semidirect
243. #340C22×C3semidirect
244. #340C22×C3semidirect
438. #124C3×D4semidirect
457. C4×D4C3×D4semidirect
488. #102C3×D4semidirect
489. #102C3×D4semidirect
992. C3#25762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×C3×#4952
C2×C3×#4632
C2×C3×#4522
C2×C3×#4492
C2×C3×#4502
C2×C3×#4472
C3×#25402
C3×#20012
C3×#20002
C3×#19992
C3×#19832
C3×#19542
C3×C4×#1022
#257623