Finite Group Databasebeta

← C3×#24388 #10642995

Subgroups — C3×#24388 #10642995

Order 768.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic, complemented
3C2×C3×#468C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C2×C3×#407C211yesmaximal, characteristic, complemented
6C3×#2847C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1894C211yesmaximal, characteristic, complemented
13C3×#1875C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24388C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic, complemented
21C22×C3×M16C2211yescharacteristic
22C22×C3×M16C2211yescharacteristic
23C3×#525—24no—
24C3×#525—24no—
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic
33C2×C3×#120—21no—
34C2×C3×#120—21no—
35C2×C3×C4×D4—21no—
36C2×C3×C4×D4—21no—
37C2×C3×#117C2211yescharacteristic
38C3×#469—24no—
39C3×#468—24no—
40C3×#449—24no—
41C2×C3×#107C2211yescharacteristic, complemented
42C2×C3×#106C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×#102C2211yescharacteristic, complemented
51C3×#407—24no—
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C3×#386—21no—
57C3×#386—21no—
58C3×#386—21no—
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic
61C3×#380C2211yescharacteristic
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#525C2×C311yescharacteristic, complemented
67C2×#469C2×C311yescharacteristic, complemented
68C2×#468C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic, complemented
70C2×#407C2×C311yescharacteristic, complemented
71#2847C2×C311yescharacteristic, complemented
72#2035C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1895C2×C311yescharacteristic, complemented
77#1894C2×C311yescharacteristic, complemented
78#1875C2×C311yescharacteristic, complemented
79#1854C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C25×C3D411yescharacteristic
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×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—21no—
95C22×C3×D4C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4—22no—
98C23×C3×C4—22no—
99C23×C3×C4—22no—
100C23×C3×C4—21no—
101C23×C3×C4—22no—
102C23×C3×C4—41no—
103C23×C3×C4—41no—
104C23×C3×C4D411yescharacteristic
105C23×C3×C4D411yescharacteristic
106C23×C3×C4D411yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—41no—
113C2×C3×D8—22no—
114C2×C3×D8—22no—
115C2×C3×D8—41no—
116C2×C3×M16—22no—
117C2×C3×M16—22no—
118C2×C3×M16—22no—
119C2×C3×M16—22no—
120C2×C3×M16—41no—
121C2×C3×M16—41no—
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C22×C3×C8C2311yescharacteristic
126C3×#123—28no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8D414yescomplemented
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—22no—
134C3×#121—22no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—41no—
139C3×#121—41no—
140C3×#121D414yescomplemented
141C3×#120—28no—
142C3×#120—44no—
143C3×C4×D4—28no—
144C3×C4×D4—28no—
145C3×#117—22no—
146C3×#117—22no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
165C2×C3×C42—21no—
166C3×#107—22no—
167C3×#106—22no—
168C3×#103—22no—
169C3×#103—22no—
170C3×#103—41no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—22no—
174C3×#102—22no—
175C3×#102—41no—
176C3×C22⋊C8—22no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8—22no—
179C3×C22⋊C8D414yescomplemented
180C3×#95—21no—
181C3×#95—21no—
182C3×#95—21no—
183C22×#41C22×C311yescharacteristic
184C24×C4C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic, complemented
186C22×D8C22×C311yescharacteristic, complemented
187C22×M16C22×C311yescharacteristic
188C22×M16C22×C311yescharacteristic
189#525—24no—
190#525—24no—
191C2×#123—21no—
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic
194C2×#121C22×C311yescharacteristic
195C2×#121C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#120—21no—
200C2×#120—21no—
201C2×C4×D4—21no—
202C2×C4×D4—21no—
203C2×#117C22×C311yescharacteristic
204#469—24no—
205#468—24no—
206#449—24no—
207C2×#107C22×C311yescharacteristic, complemented
208C2×#106C22×C311yescharacteristic, complemented
209C2×#103C22×C311yescharacteristic, complemented
210C2×#103C22×C311yescharacteristic, complemented
211C2×#103C22×C311yescharacteristic, complemented
212C2×#102C22×C311yescharacteristic, complemented
213C2×#102C22×C311yescharacteristic, complemented
214C2×#102C22×C311yescharacteristic, complemented
215C2×#102C22×C311yescharacteristic, complemented
216C2×#102C22×C311yescharacteristic, complemented
217#407—24no—
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221C2×C22⋊C8C22×C311yescharacteristic
222#386—21no—
223#386—21no—
224#386—21no—
225#380C22×C311yescharacteristic
226#380C22×C311yescharacteristic
227#380C22×C311yescharacteristic
228#340C22×C311yescharacteristic, complemented
229#340C22×C311yescharacteristic, complemented
230#340C22×C311yescharacteristic, complemented
231#340C22×C311yescharacteristic, complemented
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—41no—
238C24×C3—41no—
239C24×C3—41no—
240C24×C3—41no—
241C24×C3C2×D411yescharacteristic
242C24×C3C2×D411yescharacteristic
243C24×C3C2×D411yescharacteristic
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C3×#41—44no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8C2×D412yes—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
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—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4C2×D412yes—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—24no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—41no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—42no—
319C22×C3×C4—42no—
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D412yes—
326C22×C3×C4#4112yes—
327C22×C3×C4C2411yescharacteristic
328C3×SD16—44no—
329C3×D8—44no—
330C3×M16—44no—
331C3×M16—44no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
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×C8C2×D412yes—
343C2×C3×C8C2×D412yes—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4C2×D412yes—
355C3×C4⋊C4C2×D412yes—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—42no—
362C3×C22⋊C4—42no—
363C3×C22⋊C4—42no—
364C3×C22⋊C4—42no—
365C3×C22⋊C4—42no—
366C3×C22⋊C4—42no—
367C3×C42—24no—
368C25C3×D411yescharacteristic
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—41no—
374C2×#41—41no—
375C22×Q8C23×C311yescharacteristic
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4C23×C311yescharacteristic
383C22×D4C23×C311yescharacteristic
384C23×C4—21no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—41no—
390C23×C4—41no—
391C23×C4C3×D411yescharacteristic
392C23×C4C3×D411yescharacteristic
393C23×C4C3×D411yescharacteristic
394C23×C4C23×C311yescharacteristic
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C2×SD16—22no—
398C2×SD16—22no—
399C2×SD16—41no—
400C2×D8—22no—
401C2×D8—22no—
402C2×D8—41no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—41no—
408C2×M16—41no—
409C22×C8C23×C311yescharacteristic
410C22×C8C23×C311yescharacteristic
411C22×C8C23×C311yescharacteristic
412C22×C8C23×C311yescharacteristic
413#123—28no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8C3×D414yescomplemented
418#121—22no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—41no—
426#121—41no—
427#121C3×D414yescomplemented
428#120—28no—
429#120—44no—
430C4×D4—28no—
431C4×D4—28no—
432#117—22no—
433#117—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C23×C311yescharacteristic
437C2×C4⋊C4C23×C311yescharacteristic
438C2×C4⋊C4C23×C311yescharacteristic
439C2×C4⋊C4C23×C311yescharacteristic
440C2×C4⋊C4C23×C311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
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×C42—21no—
453#107—22no—
454#106—22no—
455#103—22no—
456#103—22no—
457#103—41no—
458#102—22no—
459#102—22no—
460#102—22no—
461#102—22no—
462#102—41no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8C3×D414yescomplemented
467#95—21no—
468#95—21no—
469#95—21no—
470C23×C3—21no—
471C23×C3—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—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—22no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
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#12012yes—
510C23×C3#12112yes—
511C23×C3AGL(1,ℤ/8)12yes—
512C23×C3C22×D411yescharacteristic
513C3×Q8—22no—
514C3×Q8—22no—
515C3×Q8—41no—
516C3×Q8—41no—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—48no—
520C3×D4—48no—
521C3×D4—48no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—84no—
529C3×D4—84no—
530C3×D4—84no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—44no—
550C2×C3×C4—44no—
551C2×C3×C4—44no—
552C2×C3×C4—48no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
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#12012yes—
573C2×C3×C4#12112yes—
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D411yescharacteristic
577C2×C3×C4C2×#4111yescharacteristic
578C2×C3×C4H(5,𝔽2)11yescharacteristic
579C2×C3×C4H(5,𝔽2)11yescharacteristic
580C3×C8—22no—
581C3×C8—22no—
582C3×C8—41no—
583C3×C8—41no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—41no—
590C24—41no—
591C24—41no—
592C24—41no—
593C24C2×C3×D411yescharacteristic
594C24C2×C3×D411yescharacteristic
595C24C2×C3×D411yescharacteristic
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8C2×C3×D412yes—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4C2×C3×D412yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4C2×C3×D411yescharacteristic
673C22×C4C2×C3×D411yescharacteristic
674C22×C4C2×C3×D412yes—
675C22×C4C2×C3×D412yes—
676C22×C4C2×C3×D411yescharacteristic
677C22×C4C2×C3×D412yes—
678C22×C4C3×#4112yes—
679C22×C4C24×C311yescharacteristic
680SD16—44no—
681D8—44no—
682M16—44no—
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8C2×C3×D412yes—
695C2×C8C2×C3×D412yes—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4C2×C3×D412yes—
707C4⋊C4C2×C3×D412yes—
708C22⋊C4—24no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C42—24no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—416no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—81no—
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×C3C2×#12011yescharacteristic
757C22×C3C2×#12111yescharacteristic
758C22×C3#53411yescharacteristic
759C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
760C22×C3#57511yescharacteristic
761C22×C3#57511yescharacteristic
762C22×C3#57511yescharacteristic
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—41no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—81no—
770C3×C4—81no—
771C3×C4—81no—
772C3×C4D4211yescharacteristic
773C3×C4D4211yescharacteristic
774C3×C4#54611yescharacteristic
775C3×C4#54611yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23C3×#12012yes—
816C23C3×#12112yes—
817C23C3×AGL(1,ℤ/8)12yes—
818C23C22×C3×D411yescharacteristic
819Q8—22no—
820Q8—22no—
821Q8—41no—
822Q8—41no—
823D4—22no—
824D4—22no—
825D4—48no—
826D4—48no—
827D4—48no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—84no—
835D4—84no—
836D4—84no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—48no—
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×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4C3×#12012yes—
879C2×C4C3×#12112yes—
880C2×C4C22×C3×D411yescharacteristic
881C2×C4C22×C3×D411yescharacteristic
882C2×C4C22×C3×D411yescharacteristic
883C2×C4C2×C3×#4111yescharacteristic
884C2×C4C3×H(5,𝔽2)11yescharacteristic
885C2×C4C3×H(5,𝔽2)11yescharacteristic
886C8—22no—
887C8—22no—
888C8—41no—
889C8—41no—
890C2×C3—42no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—82no—
894C2×C3—161no—
895C2×C3#241011yescharacteristic
896C2×C3#300511yescharacteristic
897C2×C3#300611yescharacteristic
898C2×C3#305411yescharacteristic
899C2×C3#305511yescharacteristic
900C2×C3#319411yescharacteristic
901C2×C3#319711yescharacteristic
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—416no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22C2×C3×#12011yescharacteristic
939C22C2×C3×#12111yescharacteristic
940C22C3×#53411yescharacteristic
941C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
942C22C3×#57511yescharacteristic
943C22C3×#57511yescharacteristic
944C22C3×#57511yescharacteristic
945C4—22no—
946C4—22no—
947C4—41no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4C3×D4211yescharacteristic
955C4C3×D4211yescharacteristic
956C4C3×#54611yescharacteristic
957C4C3×#54611yescharacteristic
958C3#2438811yescharacteristic, direct product factor, Sylow
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C3×#241011yescharacteristic
965C2C3×#300511yescharacteristic
966C2C3×#300611yescharacteristic
967C2C3×#305411yescharacteristic
968C2C3×#305511yescharacteristic
969C2C3×#319411yescharacteristic
970C2C3×#319711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#525C2semidirect
2. C2×C3×#469C2semidirect
3. C2×C3×#468C2semidirect
4. C2×C3×#449C2semidirect
5. C2×C3×#407C2semidirect
6. C3×#2847C2semidirect
7. C3×#2035C2semidirect
8. C3×#2033C2semidirect
9. C3×#2000C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1894C2semidirect
13. C3×#1875C2semidirect
14. C3×#1854C2semidirect
15. C3×#1788C2semidirect
16. #24388C3direct (N × H)
19. C22×C3×SD16C22semidirect
20. C22×C3×D8C22semidirect
41. C2×C3×#107C22semidirect
42. C2×C3×#106C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×#102C22semidirect
50. C2×C3×#102C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. C2×#525C2×C3semidirect
67. C2×#469C2×C3semidirect
68. C2×#468C2×C3semidirect
69. C2×#449C2×C3semidirect
70. C2×#407C2×C3semidirect
71. #2847C2×C3semidirect
72. #2035C2×C3semidirect
73. #2033C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1895C2×C3semidirect
77. #1894C2×C3semidirect
78. #1875C2×C3semidirect
79. #1854C2×C3semidirect
80. #1788C2×C3semidirect
130. C3×C22⋊Q8D4semidirect
140. C3×#121D4semidirect
179. C3×C22⋊C8D4semidirect
185. C22×SD16C22×C3semidirect
186. C22×D8C22×C3semidirect
207. C2×#107C22×C3semidirect
208. C2×#106C22×C3semidirect
209. C2×#103C22×C3semidirect
210. C2×#103C22×C3semidirect
211. C2×#103C22×C3semidirect
212. C2×#102C22×C3semidirect
213. C2×#102C22×C3semidirect
214. C2×#102C22×C3semidirect
215. C2×#102C22×C3semidirect
216. C2×#102C22×C3semidirect
228. #340C22×C3semidirect
229. #340C22×C3semidirect
230. #340C22×C3semidirect
231. #340C22×C3semidirect
417. C22⋊Q8C3×D4semidirect
427. #121C3×D4semidirect
466. C22⋊C8C3×D4semidirect
958. C3#24388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×C3×#4692
C2×C3×#4682
C2×C3×#4492
C2×C3×#4072
C3×#28472
C3×#20352
C3×#20332
C3×#20002
C3×#19992
C3×#18952
C3×#18942
C3×#18752
C3×#18542
C3×#17882
#243883