Finite Group Databasebeta

← C3×#24390 #10642997

Subgroups — C3×#24390 #10642997

Order 768.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic, complemented
3C2×C3×#466C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C2×C3×#408C211yesmaximal, characteristic, complemented
6C3×#2615C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#1999C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1893C211yesmaximal, characteristic, complemented
13C3×#1875C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#24390C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic, complemented
22C23×C3×C8C2211yescharacteristic, complemented
23C3×#535—24no—
24C3×#535—24no—
25C2×C3×#127—21no—
26C2×C3×#124—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic, complemented
33C2×C3×#121C2211yescharacteristic, complemented
34C2×C3×#120—21no—
35C2×C3×#120—21no—
36C2×C3×#117C2211yescharacteristic
37C3×#469—24no—
38C3×#466—24no—
39C3×#447—24no—
40C2×C3×#107C2211yescharacteristic, complemented
41C2×C3×#106C2211yescharacteristic, complemented
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×#102C2211yescharacteristic, complemented
50C3×#408—24no—
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic, complemented
54C2×C3×C22⋊C8C2211yescharacteristic, complemented
55C3×#393—21no—
56C3×#392—21no—
57C3×#392—21no—
58C3×#392—21no—
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic, complemented
61C3×#380C2211yescharacteristic, complemented
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#535C2×C311yescharacteristic, complemented
67C2×#469C2×C311yescharacteristic, complemented
68C2×#466C2×C311yescharacteristic, complemented
69C2×#447C2×C311yescharacteristic, complemented
70C2×#408C2×C311yescharacteristic, complemented
71#2615C2×C311yescharacteristic, complemented
72#2034C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#1999C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1895C2×C311yescharacteristic, complemented
77#1893C2×C311yescharacteristic, complemented
78#1875C2×C311yescharacteristic, complemented
79#1854C2×C311yescharacteristic, complemented
80#1786C2×C311yescharacteristic, complemented
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8D411yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—22no—
100C22×C3×D4—22no—
101C22×C3×D4—41no—
102C22×C3×D4—41no—
103C22×C3×D4D411yescharacteristic
104C22×C3×D4D411yescharacteristic
105C22×C3×D4D411yescharacteristic
106C22×C3×D4C2311yescharacteristic
107C22×C3×D4C2311yescharacteristic
108C22×C3×D4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C2×C3×D8—22no—
113C2×C3×D8—22no—
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—41no—
117C2×C3×D8—41no—
118C2×C3×M16—22no—
119C2×C3×M16—22no—
120C2×C3×M16—41no—
121C22×C3×C8—22no—
122C22×C3×C8—22no—
123C22×C3×C8—41no—
124C22×C3×C8C2311yescharacteristic
125C22×C3×C8C2311yescharacteristic
126C22×C3×C8C2311yescharacteristic
127C22×C3×C8C2311yescharacteristic
128C3×#127—28no—
129C3×#124—28no—
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—22no—
134C3×#121—22no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—22no—
139C3×#121—22no—
140C3×#121—41no—
141C3×#121—41no—
142C3×#121D414yescomplemented
143C3×#121D414yescomplemented
144C3×#120—28no—
145C3×#120—28no—
146C3×#117—22no—
147C3×#117—22no—
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C42—21no—
165C3×#107—22no—
166C3×#106—22no—
167C3×#102—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—41no—
174C3×#102—41no—
175C3×C22⋊C8—22no—
176C3×C22⋊C8—22no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8D414yescomplemented
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C22×D8C22×C311yescharacteristic
185C22×D8C22×C311yescharacteristic
186C22×M16C22×C311yescharacteristic, complemented
187C23×C8C22×C311yescharacteristic, complemented
188#535—24no—
189#535—24no—
190C2×#127—21no—
191C2×#124—21no—
192C2×#121C22×C311yescharacteristic
193C2×#121C22×C311yescharacteristic
194C2×#121C22×C311yescharacteristic
195C2×#121C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic, complemented
198C2×#121C22×C311yescharacteristic, complemented
199C2×#120—21no—
200C2×#120—21no—
201C2×#117C22×C311yescharacteristic
202#469—24no—
203#466—24no—
204#447—24no—
205C2×#107C22×C311yescharacteristic, complemented
206C2×#106C22×C311yescharacteristic, complemented
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic, complemented
214C2×#102C22×C311yescharacteristic, complemented
215#408—24no—
216C2×C22⋊C8C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic, complemented
219C2×C22⋊C8C22×C311yescharacteristic, complemented
220#393—21no—
221#392—21no—
222#392—21no—
223#392—21no—
224#380C22×C311yescharacteristic
225#380C22×C311yescharacteristic, complemented
226#380C22×C311yescharacteristic, complemented
227#340C22×C311yescharacteristic, complemented
228#340C22×C311yescharacteristic, complemented
229#340C22×C311yescharacteristic, complemented
230#340C22×C311yescharacteristic, complemented
231C24×C3—24no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—81no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3—81no—
241C24×C3C2×D411yescharacteristic
242C24×C3C2×D411yescharacteristic
243C24×C3C2×D411yescharacteristic
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C3×#41—44no—
248C2×C3×Q8—22no—
249C2×C3×Q8—22no—
250C2×C3×Q8—41no—
251C2×C3×D4—24no—
252C2×C3×D4—22no—
253C2×C3×D4—22no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—41no—
283C2×C3×D4—41no—
284C2×C3×D4—41no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—42no—
290C2×C3×D4—81no—
291C2×C3×D4—81no—
292C2×C3×D4—81no—
293C2×C3×D4—81no—
294C2×C3×D4—81no—
295C2×C3×D4—81no—
296C2×C3×D4—81no—
297C2×C3×D4—81no—
298C2×C3×D4—81no—
299C2×C3×D4—81no—
300C2×C3×D4—81no—
301C2×C3×D4—81no—
302C2×C3×D4—81no—
303C2×C3×D4—81no—
304C2×C3×D4C2×D412yes—
305C2×C3×D4C2×D412yes—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4C2×D412yes—
331C22×C3×C4#4112yes—
332C22×C3×C4C2411yescharacteristic
333C3×D8—44no—
334C3×D8—44no—
335C3×M16—44no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
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—44no—
347C2×C3×C8C2×D412yes—
348C2×C3×C8C2×D412yes—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4C2×D412yes—
358C3×C4⋊C4C2×D412yes—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—24no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4—24no—
364C3×C22⋊C4—42no—
365C3×C22⋊C4—42no—
366C3×C22⋊C4—42no—
367C3×C22⋊C4—81no—
368C3×C22⋊C4—81no—
369C3×C22⋊C4—81no—
370C3×C42—24no—
371C25—21no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—41no—
377C2×#41—41no—
378C22×Q8C3×D411yescharacteristic
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—41no—
392C22×D4—41no—
393C22×D4C3×D411yescharacteristic
394C22×D4C3×D411yescharacteristic
395C22×D4C3×D411yescharacteristic
396C22×D4C23×C311yescharacteristic
397C22×D4C23×C311yescharacteristic
398C22×D4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C2×D8—22no—
403C2×D8—22no—
404C2×D8—22no—
405C2×D8—22no—
406C2×D8—41no—
407C2×D8—41no—
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—41no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—41no—
414C22×C8C23×C311yescharacteristic
415C22×C8C23×C311yescharacteristic
416C22×C8C23×C311yescharacteristic
417C22×C8C23×C311yescharacteristic
418#127—28no—
419#124—28no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121—41no—
431#121—41no—
432#121C3×D414yescomplemented
433#121C3×D414yescomplemented
434#120—28no—
435#120—28no—
436#117—22no—
437#117—22no—
438C2×C4⋊C4C23×C311yescharacteristic
439C2×C4⋊C4C23×C311yescharacteristic
440C2×C4⋊C4C23×C311yescharacteristic
441C2×C4⋊C4C23×C311yescharacteristic
442C2×C4⋊C4C23×C311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455#107—22no—
456#106—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—22no—
461#102—22no—
462#102—22no—
463#102—41no—
464#102—41no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8C3×D414yescomplemented
469#95—21no—
470#95—21no—
471#95—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—48no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
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—84no—
514C23×C3—84no—
515C23×C3—84no—
516C23×C3—84no—
517C23×C3—84no—
518C23×C3—84no—
519C23×C3#12012yes—
520C23×C3#12112yes—
521C23×C3C22×D411yescharacteristic
522C3×Q8—44no—
523C3×D4—22no—
524C3×D4—22no—
525C3×D4—22no—
526C3×D4—22no—
527C3×D4—44no—
528C3×D4—44no—
529C3×D4—48no—
530C3×D4—44no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—84no—
540C3×D4—84no—
541C3×D4—84no—
542C3×D4—84no—
543C3×D4—84no—
544C3×D4—84no—
545C3×D4—84no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—41no—
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#12012yes—
581C2×C3×C4#12112yes—
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C2×#4111yescharacteristic
586C2×C3×C4H(5,𝔽2)11yescharacteristic
587C2×C3×C4H(5,𝔽2)11yescharacteristic
588C3×C8—22no—
589C3×C8—22no—
590C3×C8—41no—
591C3×C8—41no—
592C24—24no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24—81no—
601C24—81no—
602C24C2×C3×D411yescharacteristic
603C24C2×C3×D411yescharacteristic
604C24C2×C3×D411yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—41no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—41no—
644C2×D4—41no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4—81no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4C2×C3×D412yes—
666C2×D4C2×C3×D412yes—
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—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4C2×C3×D411yescharacteristic
687C22×C4C2×C3×D411yescharacteristic
688C22×C4C2×C3×D412yes—
689C22×C4C2×C3×D412yes—
690C22×C4C2×C3×D411yescharacteristic
691C22×C4C2×C3×D412yes—
692C22×C4C3×#4112yes—
693C22×C4C24×C311yescharacteristic
694D8—44no—
695D8—44no—
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—44no—
708C2×C8C2×C3×D412yes—
709C2×C8C2×C3×D412yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C2×C3×D412yes—
719C4⋊C4C2×C3×D412yes—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—24no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—41no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—816no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3C2×#12011yescharacteristic
776C22×C3C2×#12111yescharacteristic
777C22×C3#53411yescharacteristic
778C22×C3#57611yescharacteristic
779C22×C3#57611yescharacteristic
780C22×C3#57611yescharacteristic
781C22×C3#57711yescharacteristic
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—41no—
785C3×C4—42no—
786C3×C4—42no—
787C3×C4—81no—
788C3×C4—81no—
789C3×C4—81no—
790C3×C4D4211yescharacteristic
791C3×C4D4211yescharacteristic
792C3×C4#54611yescharacteristic
793C3×C4#54611yescharacteristic
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—48no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—84no—
836C23—84no—
837C23—84no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23C3×#12012yes—
842C23C3×#12112yes—
843C23C22×C3×D411yescharacteristic
844Q8—44no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—44no—
850D4—44no—
851D4—48no—
852D4—44no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—41no—
861D4—84no—
862D4—84no—
863D4—84no—
864D4—84no—
865D4—84no—
866D4—84no—
867D4—84no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
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×C4C3×#12012yes—
903C2×C4C3×#12112yes—
904C2×C4C22×C3×D411yescharacteristic
905C2×C4C22×C3×D411yescharacteristic
906C2×C4C22×C3×D411yescharacteristic
907C2×C4C2×C3×#4111yescharacteristic
908C2×C4C3×H(5,𝔽2)11yescharacteristic
909C2×C4C3×H(5,𝔽2)11yescharacteristic
910C8—22no—
911C8—22no—
912C8—41no—
913C8—41no—
914C2×C3—42no—
915C2×C3—42no—
916C2×C3—81no—
917C2×C3—82no—
918C2×C3—82no—
919C2×C3—161no—
920C2×C3#241011yescharacteristic
921C2×C3#300811yescharacteristic
922C2×C3#301211yescharacteristic
923C2×C3#305811yescharacteristic
924C2×C3#306211yescharacteristic
925C2×C3#319811yescharacteristic
926C2×C3#319911yescharacteristic
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—42no—
948C22—42no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—816no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22C2×C3×#12011yescharacteristic
971C22C2×C3×#12111yescharacteristic
972C22C3×#53411yescharacteristic
973C22C3×#57611yescharacteristic
974C22C3×#57611yescharacteristic
975C22C3×#57611yescharacteristic
976C22C3×#57711yescharacteristic
977C4—22no—
978C4—22no—
979C4—41no—
980C4—42no—
981C4—42no—
982C4—81no—
983C4—81no—
984C4—81no—
985C4C3×D4211yescharacteristic
986C4C3×D4211yescharacteristic
987C4C3×#54611yescharacteristic
988C4C3×#54611yescharacteristic
989C3#2439011yescharacteristic, direct product factor, Sylow
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C3×#241011yescharacteristic
997C2C3×#300811yescharacteristic
998C2C3×#301211yescharacteristic
999C2C3×#305811yescharacteristic
1000C2C3×#306211yescharacteristic
1001C2C3×#319811yescharacteristic
1002C2C3×#319911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#535C2semidirect
2. C2×C3×#469C2semidirect
3. C2×C3×#466C2semidirect
4. C2×C3×#447C2semidirect
5. C2×C3×#408C2semidirect
6. C3×#2615C2semidirect
7. C3×#2034C2semidirect
8. C3×#2033C2semidirect
9. C3×#1999C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1893C2semidirect
13. C3×#1875C2semidirect
14. C3×#1854C2semidirect
15. C3×#1786C2semidirect
16. #24390C3direct (N × H)
21. C22×C3×M16C22semidirect
22. C23×C3×C8C22semidirect
32. C2×C3×#121C22semidirect
33. C2×C3×#121C22semidirect
40. C2×C3×#107C22semidirect
41. C2×C3×#106C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×#102C22semidirect
53. C2×C3×C22⋊C8C22semidirect
54. C2×C3×C22⋊C8C22semidirect
60. C3×#380C22semidirect
61. C3×#380C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. C2×#535C2×C3semidirect
67. C2×#469C2×C3semidirect
68. C2×#466C2×C3semidirect
69. C2×#447C2×C3semidirect
70. C2×#408C2×C3semidirect
71. #2615C2×C3semidirect
72. #2034C2×C3semidirect
73. #2033C2×C3semidirect
74. #1999C2×C3semidirect
75. #1999C2×C3semidirect
76. #1895C2×C3semidirect
77. #1893C2×C3semidirect
78. #1875C2×C3semidirect
79. #1854C2×C3semidirect
80. #1786C2×C3semidirect
142. C3×#121D4semidirect
143. C3×#121D4semidirect
178. C3×C22⋊C8D4semidirect
186. C22×M16C22×C3semidirect
187. C23×C8C22×C3semidirect
197. C2×#121C22×C3semidirect
198. C2×#121C22×C3semidirect
205. C2×#107C22×C3semidirect
206. C2×#106C22×C3semidirect
213. C2×#102C22×C3semidirect
214. C2×#102C22×C3semidirect
218. C2×C22⋊C8C22×C3semidirect
219. C2×C22⋊C8C22×C3semidirect
225. #380C22×C3semidirect
226. #380C22×C3semidirect
227. #340C22×C3semidirect
228. #340C22×C3semidirect
229. #340C22×C3semidirect
230. #340C22×C3semidirect
432. #121C3×D4semidirect
433. #121C3×D4semidirect
468. C22⋊C8C3×D4semidirect
989. C3#24390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×C3×#4692
C2×C3×#4662
C2×C3×#4472
C2×C3×#4082
C3×#26152
C3×#20342
C3×#20332
C3×#19992
C3×#18952
C3×#18932
C3×#18752
C3×#18542
C3×#17862
#243903