Finite Group Databasebeta

← C3×#24245 #10642852

Subgroups — C3×#24245 #10642852

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C2×C3×C4×D8C211yesmaximal, characteristic, complemented
6C3×#2535C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1958C211yesmaximal, characteristic, complemented
12C3×#1954C211yesmaximal, characteristic, complemented
13C3×#1804C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#24245C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C3×#546—24no—
23C3×#546—24no—
24C2×C3×#124C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic, complemented
31C2×C3×#120—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×C4×D4C2211yescharacteristic, complemented
35C22×C3×C22⋊C4—21no—
36C3×#463—24no—
37C3×#449—24no—
38C3×#447—24no—
39C3×C4×D8—24no—
40C2×C3×#107C2211yescharacteristic, complemented
41C2×C3×C4⋊C8C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic, complemented
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic, complemented
55C2×C3×C22⋊C8C2211yescharacteristic, complemented
56C2×C3×C4×C8C2211yescharacteristic, complemented
57C3×#397—21no—
58C3×#392—21no—
59C3×#386—21no—
60C3×#386—21no—
61C3×#382C2211yescharacteristic, complemented
62C3×#380C2211yescharacteristic
63C3×#380C2211yescharacteristic, complemented
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#546C2×C311yescharacteristic, complemented
67C2×#463C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#447C2×C311yescharacteristic, complemented
70C2×C4×D8C2×C311yescharacteristic, complemented
71#2535C2×C311yescharacteristic, complemented
72#2036C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1958C2×C311yescharacteristic, complemented
77#1954C2×C311yescharacteristic, complemented
78#1804C2×C311yescharacteristic, complemented
79#1788C2×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×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—41no—
99C22×C3×D4—41no—
100C22×C3×D4D411yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4—21no—
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C2×C3×D8—22no—
113C2×C3×D8—22no—
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—41no—
117C2×C3×D8D414yescomplemented
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×#124—22no—
123C3×#124D414yescomplemented
124C3×#123—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×#120—28no—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C3×C4×D4—22no—
138C3×C4×D4—22no—
139C3×C4×D4—22no—
140C3×C4×D4D414yescomplemented
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4D411yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4—28no—
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⋊C4—21no—
158C2×C3×C22⋊C4D411yescharacteristic
159C2×C3×C22⋊C4D411yescharacteristic
160C2×C3×C42C2311yescharacteristic
161C3×#107—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#103—22no—
165C3×#103—41no—
166C3×#102—22no—
167C3×#102—22no—
168C3×#102—22no—
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×D4C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic, complemented
185C22×D8C22×C311yescharacteristic
186C22×D8C22×C311yescharacteristic
187#546—24no—
188#546—24no—
189C2×#124C22×C311yescharacteristic
190C2×#123—21no—
191C2×C22⋊Q8C22×C311yescharacteristic
192C2×#121—21no—
193C2×#121C22×C311yescharacteristic
194C2×#121C22×C311yescharacteristic
195C2×#121C22×C311yescharacteristic, complemented
196C2×#120—21no—
197C2×C4×D4C22×C311yescharacteristic
198C2×C4×D4C22×C311yescharacteristic
199C2×C4×D4C22×C311yescharacteristic, complemented
200C22×C22⋊C4—21no—
201#463—24no—
202#449—24no—
203#447—24no—
204C4×D8—24no—
205C2×#107C22×C311yescharacteristic, complemented
206C2×C4⋊C8C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#103C22×C311yescharacteristic, complemented
209C2×#103C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215C2×#102C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic, complemented
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic, complemented
220C2×C22⋊C8C22×C311yescharacteristic, complemented
221C2×C4×C8C22×C311yescharacteristic, complemented
222#397—21no—
223#392—21no—
224#386—21no—
225#386—21no—
226#382C22×C311yescharacteristic, complemented
227#380C22×C311yescharacteristic
228#380C22×C311yescharacteristic, complemented
229#340C22×C311yescharacteristic, complemented
230#340C22×C311yescharacteristic, complemented
231C24×C3—21no—
232C24×C3—24no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—42no—
239C24×C3—81no—
240C24×C3—81no—
241C24×C3C2×D411yescharacteristic
242C24×C3C2×D411yescharacteristic
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—24no—
255C2×C3×D4—22no—
256C2×C3×D4—24no—
257C2×C3×D4—22no—
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—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—41no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—44no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—44no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—81no—
285C2×C3×D4—81no—
286C2×C3×D4—81no—
287C2×C3×D4—81no—
288C2×C3×D4C2×D412yes—
289C2×C3×D4C2×D412yes—
290C2×C3×D4C2×D412yes—
291C2×C3×D4C2×D412yes—
292C2×C3×D4#4112yes—
293C22×C3×C4—24no—
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—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—24no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—42no—
313C22×C3×C4—42no—
314C22×C3×C4—42no—
315C22×C3×C4—81no—
316C22×C3×C4—81no—
317C22×C3×C4—81no—
318C22×C3×C4—81no—
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2411yescharacteristic
324C3×SD16—44no—
325C3×D8—28no—
326C3×D8—44no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
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×C8C2×D412yes—
339C3×C4⋊C4—24no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4C2×D412yes—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—42no—
357C3×C22⋊C4—42no—
358C3×C22⋊C4—42no—
359C3×C22⋊C4—81no—
360C3×C22⋊C4—81no—
361C3×C42C2×D412yes—
362C3×C42C2×D412yes—
363C25—21no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—41no—
369C2×#41—41no—
370C22×Q8C23×C311yescharacteristic
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—41no—
381C22×D4—41no—
382C22×D4C3×D411yescharacteristic
383C22×D4C23×C311yescharacteristic
384C22×D4C23×C311yescharacteristic
385C22×D4C23×C311yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—41no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8—41no—
399C2×D8C3×D414yescomplemented
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404#124—22no—
405#124C3×D414yescomplemented
406#123—28no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—28no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—22no—
414#121—41no—
415#121—41no—
416#120—28no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4C3×D414yescomplemented
423C2×C4⋊C4—21no—
424C2×C4⋊C4C3×D411yescharacteristic
425C2×C4⋊C4C23×C311yescharacteristic
426C2×C4⋊C4C23×C311yescharacteristic
427C2×C4⋊C4C23×C311yescharacteristic
428C2×C4⋊C4C23×C311yescharacteristic
429C2×C22⋊C4—28no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4C3×D411yescharacteristic
441C2×C22⋊C4C3×D411yescharacteristic
442C2×C42C23×C311yescharacteristic
443#107—22no—
444C4⋊C8—22no—
445#103—22no—
446#103—22no—
447#103—41no—
448#102—22no—
449#102—22no—
450#102—22no—
451#102—22no—
452#102—22no—
453#102—22no—
454#102—41no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—41no—
458C22⋊C8—41no—
459C4×C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—22no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—22no—
474C23×C3—21no—
475C23×C3—22no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—48no—
483C23×C3—48no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—84no—
501C23×C3—84no—
502C23×C3—84no—
503C23×C3—84no—
504C23×C3—84no—
505C23×C3#13512yes—
506C23×C3C22×D411yescharacteristic
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—22no—
518C3×D4—44no—
519C3×D4—48no—
520C3×D4—48no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—84no—
526C3×D4—84no—
527C3×D4—84no—
528C3×D4#12114yes—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—21no—
535C2×C3×C4—22no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—48no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
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—84no—
564C2×C3×C4—84no—
565C2×C3×C4#12012yes—
566C2×C3×C4#12012yes—
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4C22×D411yescharacteristic
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C2×#4111yescharacteristic
571C2×C3×C4H(5,𝔽2)11yescharacteristic
572C2×C3×C4H(5,𝔽2)11yescharacteristic
573C3×C8—22no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—41no—
577C24—21no—
578C24—24no—
579C24—21no—
580C24—21no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×C3×D411yescharacteristic
588C24C2×C3×D411yescharacteristic
589#41—44no—
590#41—44no—
591#41—44no—
592#41—44no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8C2×C3×D412yes—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—22no—
602C2×D4—24no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
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—41no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—44no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4C2×C3×D412yes—
635C2×D4C2×C3×D412yes—
636C2×D4C2×C3×D412yes—
637C2×D4C2×C3×D412yes—
638C2×D4C3×#4112yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4—81no—
665C22×C4C2×C3×D411yescharacteristic
666C22×C4C2×C3×D411yescharacteristic
667C22×C4C2×C3×D411yescharacteristic
668C22×C4C2×C3×D411yescharacteristic
669C22×C4C24×C311yescharacteristic
670SD16—44no—
671D8—28no—
672D8—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×C3×D412yes—
685C4⋊C4—24no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4C2×C3×D412yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—22no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42C2×C3×D412yes—
708C42C2×C3×D412yes—
709C22×C3—24no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—41no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—41no—
727C22×C3—42no—
728C22×C3—41no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—816no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3C2×#12011yescharacteristic
746C22×C3D4211yescharacteristic
747C22×C3#54611yescharacteristic
748C22×C3C2×#13511yescharacteristic
749C22×C3#57511yescharacteristic
750C22×C3#57611yescharacteristic
751C22×C3#57611yescharacteristic
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—42no—
757C3×C4—42no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4—81no—
761C3×C4C2×#12111yescharacteristic
762C3×C4#53511yescharacteristic
763C3×C4D4211yescharacteristic
764C3×C4#54611yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—48no—
784C23—48no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23—84no—
805C23—84no—
806C23C3×#13512yes—
807C23C22×C3×D411yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—22no—
819D4—44no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4—84no—
828D4—84no—
829D4C3×#12114yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—48no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
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—84no—
865C2×C4—84no—
866C2×C4C3×#12012yes—
867C2×C4C3×#12012yes—
868C2×C4C22×C3×D411yescharacteristic
869C2×C4C22×C3×D411yescharacteristic
870C2×C4C22×C3×D411yescharacteristic
871C2×C4C2×C3×#4111yescharacteristic
872C2×C4C3×H(5,𝔽2)11yescharacteristic
873C2×C4C3×H(5,𝔽2)11yescharacteristic
874C8—22no—
875C8—41no—
876C8—41no—
877C8—41no—
878C2×C3—42no—
879C2×C3—44no—
880C2×C3—81no—
881C2×C3—82no—
882C2×C3—82no—
883C2×C3#240811yescharacteristic
884C2×C3#300211yescharacteristic
885C2×C3#300811yescharacteristic
886C2×C3#327311yescharacteristic
887C2×C3#328011yescharacteristic
888C2×C3#329711yescharacteristic
889C2×C3#332211yescharacteristic
890C22—24no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22C2×C3×#12011yescharacteristic
927C22C3×D4211yescharacteristic
928C22C3×#54611yescharacteristic
929C22C2×C3×#13511yescharacteristic
930C22C3×#57511yescharacteristic
931C22C3×#57611yescharacteristic
932C22C3×#57611yescharacteristic
933C4—22no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4C2×C3×#12111yescharacteristic
943C4C3×#53511yescharacteristic
944C4C3×D4211yescharacteristic
945C4C3×#54611yescharacteristic
946C3#2424511yescharacteristic, direct product factor, Sylow
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C3×#240811yescharacteristic
953C2C3×#300211yescharacteristic
954C2C3×#300811yescharacteristic
955C2C3×#327311yescharacteristic
956C2C3×#328011yescharacteristic
957C2C3×#329711yescharacteristic
958C2C3×#332211yescharacteristic
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×#463C2semidirect
3. C2×C3×#449C2semidirect
4. C2×C3×#447C2semidirect
5. C2×C3×C4×D8C2semidirect
6. C3×#2535C2semidirect
7. C3×#2036C2semidirect
8. C3×#2033C2semidirect
9. C3×#2000C2semidirect
10. C3×#1999C2semidirect
11. C3×#1958C2semidirect
12. C3×#1954C2semidirect
13. C3×#1804C2semidirect
14. C3×#1788C2semidirect
15. C3×#1786C2semidirect
16. #24245C3direct (N × H)
19. C22×C3×SD16C22semidirect
30. C2×C3×#121C22semidirect
34. C2×C3×C4×D4C22semidirect
40. C2×C3×#107C22semidirect
41. C2×C3×C4⋊C8C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
51. C2×C3×#102C22semidirect
54. C2×C3×C22⋊C8C22semidirect
55. C2×C3×C22⋊C8C22semidirect
56. C2×C3×C4×C8C22semidirect
61. C3×#382C22semidirect
63. C3×#380C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. C2×#546C2×C3semidirect
67. C2×#463C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#447C2×C3semidirect
70. C2×C4×D8C2×C3semidirect
71. #2535C2×C3semidirect
72. #2036C2×C3semidirect
73. #2033C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1958C2×C3semidirect
77. #1954C2×C3semidirect
78. #1804C2×C3semidirect
79. #1788C2×C3semidirect
80. #1786C2×C3semidirect
117. C2×C3×D8D4semidirect
123. C3×#124D4semidirect
140. C3×C4×D4D4semidirect
184. C22×SD16C22×C3semidirect
195. C2×#121C22×C3semidirect
199. C2×C4×D4C22×C3semidirect
205. C2×#107C22×C3semidirect
206. C2×C4⋊C8C22×C3semidirect
207. C2×#103C22×C3semidirect
208. C2×#103C22×C3semidirect
209. C2×#103C22×C3semidirect
216. C2×#102C22×C3semidirect
219. C2×C22⋊C8C22×C3semidirect
220. C2×C22⋊C8C22×C3semidirect
221. C2×C4×C8C22×C3semidirect
226. #382C22×C3semidirect
228. #380C22×C3semidirect
229. #340C22×C3semidirect
230. #340C22×C3semidirect
399. C2×D8C3×D4semidirect
405. #124C3×D4semidirect
422. C4×D4C3×D4semidirect
946. C3#24245direct (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×#4632
C2×C3×#4492
C2×C3×#4472
C2×C3×C4×D82
C3×#25352
C3×#20362
C3×#20332
C3×#20002
C3×#19992
C3×#19582
C3×#19542
C3×#18042
C3×#17882
C3×#17862
#242453