Finite Group Databasebeta

← C3×#24244 #10642851

Subgroups — C3×#24244 #10642851

Order 768.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
6C3×#2535C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2034C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1958C211yesmaximal, characteristic, complemented
12C3×#1954C211yesmaximal, characteristic, complemented
13C3×#1805C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#24244C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C3×#548—24no—
23C3×#548—24no—
24C2×C3×#124—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4—21no—
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×C4×D4C2211yescharacteristic
36C3×#463—24no—
37C3×#449—24no—
38C3×#448—24no—
39C3×C4×SD16—24no—
40C2×C3×#106C2211yescharacteristic
41C2×C3×C4⋊C8C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C2×C3×C4×C8C2211yescharacteristic
57C3×#397—21no—
58C3×#392—21no—
59C3×#386—21no—
60C3×#386—21no—
61C3×#382C2211yescharacteristic
62C3×#380C2211yescharacteristic
63C3×#380C2211yescharacteristic
64C3×#340C2211yescharacteristic
65C3×#340C2211yescharacteristic
66C2×#548C2×C311yescharacteristic, complemented
67C2×#463C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#448C2×C311yescharacteristic, complemented
70C2×C4×SD16C2×C311yescharacteristic, complemented
71#2535C2×C311yescharacteristic, complemented
72#2035C2×C311yescharacteristic, complemented
73#2034C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1958C2×C311yescharacteristic, complemented
77#1954C2×C311yescharacteristic, complemented
78#1805C2×C311yescharacteristic, complemented
79#1788C2×C311yescharacteristic, complemented
80#1787C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—21no—
90C22×C3×Q8—22no—
91C22×C3×Q8—22no—
92C22×C3×Q8—41no—
93C22×C3×Q8—41no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4D411yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4—21no—
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—41no—
113C2×C3×SD16D414yescomplemented
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—41no—
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C3×#124—28no—
122C3×#124—22no—
123C3×#124D414yescomplemented
124C3×C22⋊Q8—28no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—22no—
127C3×#121—28no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—41no—
133C3×#121—41no—
134C3×C4×Q8—22no—
135C3×C4×Q8D414yescomplemented
136C3×C4×D4—28no—
137C3×C4×D4—22no—
138C3×C4×D4—22no—
139C3×C4×D4—22no—
140C3×C4×D4—22no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4D411yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4D411yescharacteristic
158C2×C3×C22⋊C4D411yescharacteristic
159C2×C3×C42—21no—
160C2×C3×C42C2311yescharacteristic
161C3×#106—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—41no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—41no—
173C3×C22⋊C8—22no—
174C3×C22⋊C8—22no—
175C3×C22⋊C8—41no—
176C3×C22⋊C8—41no—
177C3×C4×C8—22no—
178C3×#95—21no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×Q8C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×D8C22×C311yescharacteristic
187#548—24no—
188#548—24no—
189C2×#124—21no—
190C2×#124C22×C311yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×#121—21no—
194C2×#121C22×C311yescharacteristic
195C2×#121C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×C4×Q8C22×C311yescharacteristic
198C2×C4×D4—21no—
199C2×C4×D4C22×C311yescharacteristic
200C2×C4×D4C22×C311yescharacteristic
201#463—24no—
202#449—24no—
203#448—24no—
204C4×SD16—24no—
205C2×#106C22×C311yescharacteristic
206C2×C4⋊C8C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×C311yescharacteristic
210C2×#103C22×C311yescharacteristic
211C2×#103C22×C311yescharacteristic
212C2×#103C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215C2×#102C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221C2×C4×C8C22×C311yescharacteristic
222#397—21no—
223#392—21no—
224#386—21no—
225#386—21no—
226#382C22×C311yescharacteristic
227#380C22×C311yescharacteristic
228#380C22×C311yescharacteristic
229#340C22×C311yescharacteristic
230#340C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3C2×D411yescharacteristic
234C24×C3C2×D411yescharacteristic
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C2×C3×Q8—24no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—42no—
249C2×C3×Q8—42no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8C2×D412yes—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8C2×D412yes—
257C2×C3×Q8#4112yes—
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—41no—
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—81no—
282C2×C3×D4—81no—
283C2×C3×D4C2×D412yes—
284C2×C3×D4C2×D412yes—
285C22×C3×C4—21no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—42no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4—81no—
311C22×C3×C4—81no—
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2411yescharacteristic
317C3×SD16—28no—
318C3×SD16—44no—
319C3×D8—44no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8C2×D412yes—
332C3×C4⋊C4—24no—
333C3×C4⋊C4—24no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4C2×D412yes—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—24no—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—22no—
348C3×C22⋊C4—22no—
349C3×C22⋊C4—42no—
350C3×C22⋊C4—42no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—81no—
353C3×C22⋊C4—81no—
354C3×C42—24no—
355C3×C42C2×D412yes—
356C3×C42C2×D412yes—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—41no—
362C2×#41—41no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—21no—
366C22×Q8—22no—
367C22×Q8—22no—
368C22×Q8—41no—
369C22×Q8—41no—
370C22×Q8C23×C311yescharacteristic
371C22×Q8C23×C311yescharacteristic
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4C3×D411yescharacteristic
377C22×D4C23×C311yescharacteristic
378C22×D4C23×C311yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C311yescharacteristic
383C23×C4C23×C311yescharacteristic
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—41no—
389C2×SD16C3×D414yescomplemented
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—41no—
393C22×C8C23×C311yescharacteristic
394C22×C8C23×C311yescharacteristic
395C22×C8C23×C311yescharacteristic
396C22×C8C23×C311yescharacteristic
397#124—28no—
398#124—22no—
399#124C3×D414yescomplemented
400C22⋊Q8—28no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403#121—28no—
404#121—22no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—41no—
409#121—41no—
410C4×Q8—22no—
411C4×Q8C3×D414yescomplemented
412C4×D4—28no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C3×D411yescharacteristic
420C2×C4⋊C4C23×C311yescharacteristic
421C2×C4⋊C4C23×C311yescharacteristic
422C2×C4⋊C4C23×C311yescharacteristic
423C2×C4⋊C4C23×C311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4C3×D411yescharacteristic
434C2×C22⋊C4C3×D411yescharacteristic
435C2×C42—21no—
436C2×C42C23×C311yescharacteristic
437#106—22no—
438C4⋊C8—22no—
439#103—22no—
440#103—22no—
441#103—22no—
442#103—22no—
443#103—22no—
444#103—41no—
445#102—22no—
446#102—22no—
447#102—22no—
448#102—41no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453C4×C8—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3#13512yes—
486C23×C3C22×D411yescharacteristic
487C3×Q8—22no—
488C3×Q8—22no—
489C3×Q8—22no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—48no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8#12114yes—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—44no—
501C3×D4—48no—
502C3×D4—48no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—84no—
508C3×D4—84no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—48no—
525C2×C3×C4—48no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—84no—
548C2×C3×C4#12012yes—
549C2×C3×C4#12012yes—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C2×#4111yescharacteristic
554C2×C3×C4H(5,𝔽2)11yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C3×C8—22no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—41no—
560C24—21no—
561C24—21no—
562C24C2×C3×D411yescharacteristic
563C24C2×C3×D411yescharacteristic
564#41—44no—
565#41—44no—
566#41—44no—
567#41—44no—
568C2×Q8—24no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—44no—
583C2×Q8C2×C3×D412yes—
584C2×Q8C2×C3×D412yes—
585C2×Q8C2×C3×D412yes—
586C2×Q8C3×#4112yes—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4C2×C3×D412yes—
613C2×D4C2×C3×D412yes—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×C3×D411yescharacteristic
642C22×C4C2×C3×D411yescharacteristic
643C22×C4C2×C3×D411yescharacteristic
644C22×C4C2×C3×D411yescharacteristic
645C22×C4C24×C311yescharacteristic
646SD16—28no—
647SD16—44no—
648D8—44no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8C2×C3×D412yes—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4C2×C3×D412yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—24no—
684C42C2×C3×D412yes—
685C42C2×C3×D412yes—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—42no—
698C22×C3—41no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3C2×#12011yescharacteristic
715C22×C3D4211yescharacteristic
716C22×C3#54611yescharacteristic
717C22×C3C2×#13511yescharacteristic
718C22×C3#57511yescharacteristic
719C22×C3#57711yescharacteristic
720C22×C3#57711yescharacteristic
721C3×C4—24no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—81no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—21no—
749C23—21no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23C3×#13512yes—
763C23C22×C3×D411yescharacteristic
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—48no—
770Q8—41no—
771Q8—41no—
772Q8C3×#12114yes—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—44no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—84no—
785D4—84no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—84no—
825C2×C4C3×#12012yes—
826C2×C4C3×#12012yes—
827C2×C4C22×C3×D411yescharacteristic
828C2×C4C22×C3×D411yescharacteristic
829C2×C4C22×C3×D411yescharacteristic
830C2×C4C2×C3×#4111yescharacteristic
831C2×C4C3×H(5,𝔽2)11yescharacteristic
832C2×C4C3×H(5,𝔽2)11yescharacteristic
833C8—22no—
834C8—41no—
835C8—41no—
836C8—41no—
837C2×C3—42no—
838C2×C3—81no—
839C2×C3—82no—
840C2×C3—82no—
841C2×C3#240811yescharacteristic
842C2×C3#300211yescharacteristic
843C2×C3#301011yescharacteristic
844C2×C3#327511yescharacteristic
845C2×C3#328211yescharacteristic
846C2×C3#330111yescharacteristic
847C2×C3#332611yescharacteristic
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22C2×C3×#12011yescharacteristic
877C22C3×D4211yescharacteristic
878C22C3×#54611yescharacteristic
879C22C2×C3×#13511yescharacteristic
880C22C3×#57511yescharacteristic
881C22C3×#57711yescharacteristic
882C22C3×#57711yescharacteristic
883C4—24no—
884C4—22no—
885C4—22no—
886C4—41no—
887C4—41no—
888C4—42no—
889C4—42no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4C2×C3×#12111yescharacteristic
894C4C3×#53511yescharacteristic
895C4C3×D4211yescharacteristic
896C4C3×#54611yescharacteristic
897C3#2424411yescharacteristic, direct product factor, Sylow
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2C3×#240811yescharacteristic
903C2C3×#300211yescharacteristic
904C2C3×#301011yescharacteristic
905C2C3×#327511yescharacteristic
906C2C3×#328211yescharacteristic
907C2C3×#330111yescharacteristic
908C2C3×#332611yescharacteristic
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×#463C2semidirect
3. C2×C3×#449C2semidirect
4. C2×C3×#448C2semidirect
5. C2×C3×C4×SD16C2semidirect
6. C3×#2535C2semidirect
7. C3×#2035C2semidirect
8. C3×#2034C2semidirect
9. C3×#2000C2semidirect
10. C3×#1999C2semidirect
11. C3×#1958C2semidirect
12. C3×#1954C2semidirect
13. C3×#1805C2semidirect
14. C3×#1788C2semidirect
15. C3×#1787C2semidirect
16. #24244C3direct (N × H)
66. C2×#548C2×C3semidirect
67. C2×#463C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#448C2×C3semidirect
70. C2×C4×SD16C2×C3semidirect
71. #2535C2×C3semidirect
72. #2035C2×C3semidirect
73. #2034C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1958C2×C3semidirect
77. #1954C2×C3semidirect
78. #1805C2×C3semidirect
79. #1788C2×C3semidirect
80. #1787C2×C3semidirect
113. C2×C3×SD16D4semidirect
123. C3×#124D4semidirect
135. C3×C4×Q8D4semidirect
389. C2×SD16C3×D4semidirect
399. #124C3×D4semidirect
411. C4×Q8C3×D4semidirect
897. C3#24244direct (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×#4632
C2×C3×#4492
C2×C3×#4482
C2×C3×C4×SD162
C3×#25352
C3×#20352
C3×#20342
C3×#20002
C3×#19992
C3×#19582
C3×#19542
C3×#18052
C3×#17882
C3×#17872
#242443