Finite Group Databasebeta

← C3×#29600 #10648207

Subgroups — C3×#29600 #10648207

Order 768.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C2×C3×#482C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C3×#2847C211yesmaximal, characteristic, complemented
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1999C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1825C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1779C211yesmaximal, characteristic, complemented
16#29600C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic, complemented
21C3×#525—24no—
22C3×#525—24no—
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#120—21no—
32C2×C3×#120—21no—
33C2×C3×C4×D4—21no—
34C2×C3×C4×D4—21no—
35C2×C3×#117C2211yescharacteristic
36C3×#482—24no—
37C3×#449—24no—
38C2×C3×#107C2211yescharacteristic, complemented
39C2×C3×#106C2211yescharacteristic, complemented
40C2×C3×#103C2211yescharacteristic, complemented
41C2×C3×#103C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#102C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C3×#386—21no—
55C3×#386—21no—
56C3×#386—21no—
57C3×#380C2211yescharacteristic
58C3×#380C2211yescharacteristic
59C3×#380C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C2×#525C2×C311yescharacteristic, complemented
65C2×#482C2×C311yescharacteristic, complemented
66C2×#449C2×C311yescharacteristic, complemented
67#2847C2×C311yescharacteristic, complemented
68#2036C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2034C2×C311yescharacteristic, complemented
71#2033C2×C311yescharacteristic, complemented
72#2000C2×C311yescharacteristic, complemented
73#2000C2×C311yescharacteristic, complemented
74#1999C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1825C2×C311yescharacteristic, complemented
77#1788C2×C311yescharacteristic, complemented
78#1779C2×C311yescharacteristic, complemented
79C25×C3D411yescharacteristic
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C2×C3×#41D414yescomplemented
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—22no—
96C23×C3×C4—22no—
97C23×C3×C4—21no—
98C23×C3×C4—41no—
99C23×C3×C4—41no—
100C23×C3×C4—41no—
101C23×C3×C4—41no—
102C23×C3×C4D411yescharacteristic
103C23×C3×C4D411yescharacteristic
104C23×C3×C4D411yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C2×C3×SD16—22no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×D8—22no—
112C2×C3×D8—41no—
113C2×C3×D8—41no—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C3×#123—28no—
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8—22no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×#121—22no—
124C3×#121—22no—
125C3×#121—22no—
126C3×#121—22no—
127C3×#121—22no—
128C3×#121—22no—
129C3×#121—41no—
130C3×#121—41no—
131C3×#121—41no—
132C3×#121—41no—
133C3×#120—28no—
134C3×#120—44no—
135C3×C4×D4—28no—
136C3×C4×D4—28no—
137C3×#117—22no—
138C3×#117D414yescomplemented
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
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×C42—21no—
158C3×#107—22no—
159C3×#106—22no—
160C3×#103—22no—
161C3×#103—41no—
162C3×#103—41no—
163C3×#102—22no—
164C3×#102—22no—
165C3×#102—22no—
166C3×#102—41no—
167C3×#102—41no—
168C3×C22⋊C8—22no—
169C3×C22⋊C8—22no—
170C3×C22⋊C8—41no—
171C3×C22⋊C8—41no—
172C3×C22⋊C8—41no—
173C3×C22⋊C8—41no—
174C3×#95—21no—
175C3×#95—21no—
176C3×#95—21no—
177C22×#41C22×C311yescharacteristic
178C24×C4C22×C311yescharacteristic
179C22×SD16C22×C311yescharacteristic, complemented
180C22×D8C22×C311yescharacteristic, complemented
181#525—24no—
182#525—24no—
183C2×#123—21no—
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×C22⋊Q8C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×#121C22×C311yescharacteristic
188C2×#121C22×C311yescharacteristic
189C2×#121C22×C311yescharacteristic
190C2×#121C22×C311yescharacteristic
191C2×#120—21no—
192C2×#120—21no—
193C2×C4×D4—21no—
194C2×C4×D4—21no—
195C2×#117C22×C311yescharacteristic
196#482—24no—
197#449—24no—
198C2×#107C22×C311yescharacteristic, complemented
199C2×#106C22×C311yescharacteristic, complemented
200C2×#103C22×C311yescharacteristic, complemented
201C2×#103C22×C311yescharacteristic, complemented
202C2×#103C22×C311yescharacteristic, complemented
203C2×#102C22×C311yescharacteristic, complemented
204C2×#102C22×C311yescharacteristic, complemented
205C2×#102C22×C311yescharacteristic, complemented
206C2×#102C22×C311yescharacteristic, complemented
207C2×#102C22×C311yescharacteristic, complemented
208C2×C22⋊C8C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×C22⋊C8C22×C311yescharacteristic
212C2×C22⋊C8C22×C311yescharacteristic
213C2×C22⋊C8C22×C311yescharacteristic
214#386—21no—
215#386—21no—
216#386—21no—
217#380C22×C311yescharacteristic
218#380C22×C311yescharacteristic
219#380C22×C311yescharacteristic
220#340C22×C311yescharacteristic, complemented
221#340C22×C311yescharacteristic, complemented
222#340C22×C311yescharacteristic, complemented
223#340C22×C311yescharacteristic, complemented
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—41no—
230C24×C3—41no—
231C24×C3—41no—
232C24×C3—41no—
233C24×C3C2×D411yescharacteristic
234C24×C3C2×D411yescharacteristic
235C24×C3C2×D411yescharacteristic
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C3×#41—44no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8C2×D412yes—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—24no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
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×D4C2×D412yes—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—22no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—24no—
287C22×C3×C4—21no—
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—41no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—41no—
306C22×C3×C4—41no—
307C22×C3×C4—41no—
308C22×C3×C4—44no—
309C22×C3×C4—44no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—42no—
313C22×C3×C4—42no—
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2411yescharacteristic
320C3×SD16—44no—
321C3×D8—44no—
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×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—24no—
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⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4C2×D412yes—
345C3×C4⋊C4C2×D412yes—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—42no—
353C3×C22⋊C4—42no—
354C3×C22⋊C4—42no—
355C3×C22⋊C4—42no—
356C3×C22⋊C4—42no—
357C3×C42—24no—
358C25C3×D411yescharacteristic
359C2×#41—22no—
360C2×#41—41no—
361C2×#41—41no—
362C2×#41—41no—
363C2×#41—41no—
364C2×#41C3×D414yescomplemented
365C22×Q8C23×C311yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4C23×C311yescharacteristic
373C22×D4C23×C311yescharacteristic
374C23×C4—21no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4C3×D411yescharacteristic
382C23×C4C3×D411yescharacteristic
383C23×C4C3×D411yescharacteristic
384C23×C4C23×C311yescharacteristic
385C23×C4C23×C311yescharacteristic
386C23×C4C23×C311yescharacteristic
387C2×SD16—22no—
388C2×SD16—41no—
389C2×SD16—41no—
390C2×D8—22no—
391C2×D8—41no—
392C2×D8—41no—
393C22×C8C23×C311yescharacteristic
394C22×C8C23×C311yescharacteristic
395C22×C8C23×C311yescharacteristic
396C22×C8C23×C311yescharacteristic
397#123—28no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—41no—
409#121—41no—
410#121—41no—
411#121—41no—
412#120—28no—
413#120—44no—
414C4×D4—28no—
415C4×D4—28no—
416#117—22no—
417#117C3×D414yescomplemented
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4C23×C311yescharacteristic
421C2×C4⋊C4C23×C311yescharacteristic
422C2×C4⋊C4C23×C311yescharacteristic
423C2×C4⋊C4C23×C311yescharacteristic
424C2×C4⋊C4C23×C311yescharacteristic
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⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C42—21no—
437#107—22no—
438#106—22no—
439#103—22no—
440#103—41no—
441#103—41no—
442#102—22no—
443#102—22no—
444#102—22no—
445#102—41no—
446#102—41no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—41no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453#95—21no—
454#95—21no—
455#95—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—41no—
483C23×C3—41no—
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#12012yes—
496C23×C3#13512yes—
497C23×C3AGL(1,ℤ/8)12yes—
498C23×C3C22×D411yescharacteristic
499C3×Q8—22no—
500C3×Q8—22no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—48no—
506C3×D4—48no—
507C3×D4—48no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—84no—
515C3×D4—84no—
516C3×D4—84no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—44no—
533C2×C3×C4—44no—
534C2×C3×C4—48no—
535C2×C3×C4—44no—
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—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#12012yes—
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4H(5,𝔽2)11yescharacteristic
563C2×C3×C4H(5,𝔽2)11yescharacteristic
564C2×C3×C4H(5,𝔽2)11yescharacteristic
565C2×C3×C4H(5,𝔽2)11yescharacteristic
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—41no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—21no—
574C24—21no—
575C24—41no—
576C24—41no—
577C24—41no—
578C24—41no—
579C24C2×C3×D411yescharacteristic
580C24C2×C3×D411yescharacteristic
581C24C2×C3×D411yescharacteristic
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C2×C3×D412yes—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×C3×D412yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
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—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4C2×C3×D411yescharacteristic
661C22×C4C2×C3×D411yescharacteristic
662C22×C4C2×C3×D411yescharacteristic
663C22×C4C2×C3×D412yes—
664C22×C4C2×C3×D412yes—
665C22×C4C24×C311yescharacteristic
666SD16—44no—
667D8—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4C2×C3×D412yes—
691C4⋊C4C2×C3×D412yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C42—24no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—416no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3C2×#12011yescharacteristic
741C22×C3#53411yescharacteristic
742C22×C3#53411yescharacteristic
743C22×C3C2×#13511yescharacteristic
744C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
745C22×C3#57511yescharacteristic
746C22×C3#57511yescharacteristic
747C3×C4—22no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—81no—
754C3×C4—81no—
755C3×C4—81no—
756C3×C4#53411yescharacteristic
757C3×C4#53411yescharacteristic
758C3×C4#53511yescharacteristic
759C3×C4#53511yescharacteristic
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
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—
799C23C3×#12012yes—
800C23C3×#13512yes—
801C23C3×AGL(1,ℤ/8)12yes—
802C23C22×C3×D411yescharacteristic
803Q8—22no—
804Q8—22no—
805Q8—41no—
806Q8—41no—
807D4—22no—
808D4—22no—
809D4—48no—
810D4—48no—
811D4—48no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—41no—
816D4—41no—
817D4—41no—
818D4—84no—
819D4—84no—
820D4—84no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—48no—
839C2×C4—44no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
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×C4C3×#12012yes—
864C2×C4C22×C3×D411yescharacteristic
865C2×C4C22×C3×D411yescharacteristic
866C2×C4C3×H(5,𝔽2)11yescharacteristic
867C2×C4C3×H(5,𝔽2)11yescharacteristic
868C2×C4C3×H(5,𝔽2)11yescharacteristic
869C2×C4C3×H(5,𝔽2)11yescharacteristic
870C8—41no—
871C8—41no—
872C8—41no—
873C8—41no—
874C2×C3—42no—
875C2×C3—42no—
876C2×C3—42no—
877C2×C3—82no—
878C2×C3—161no—
879C2×C3#261311yescharacteristic
880C2×C3#300211yescharacteristic
881C2×C3#300611yescharacteristic
882C2×C3#318811yescharacteristic
883C2×C3#319111yescharacteristic
884C2×C3#319411yescharacteristic
885C2×C3#319711yescharacteristic
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—416no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22C2×C3×#12011yescharacteristic
923C22C3×#53411yescharacteristic
924C22C3×#53411yescharacteristic
925C22C2×C3×#13511yescharacteristic
926C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
927C22C3×#57511yescharacteristic
928C22C3×#57511yescharacteristic
929C4—22no—
930C4—42no—
931C4—42no—
932C4—41no—
933C4—41no—
934C4—42no—
935C4—81no—
936C4—81no—
937C4—81no—
938C4C3×#53411yescharacteristic
939C4C3×#53411yescharacteristic
940C4C3×#53511yescharacteristic
941C4C3×#53511yescharacteristic
942C3#2960011yescharacteristic, direct product factor, Sylow
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2C3×#261311yescharacteristic
949C2C3×#300211yescharacteristic
950C2C3×#300611yescharacteristic
951C2C3×#318811yescharacteristic
952C2C3×#319111yescharacteristic
953C2C3×#319411yescharacteristic
954C2C3×#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×#482C2semidirect
3. C2×C3×#449C2semidirect
4. C3×#2847C2semidirect
5. C3×#2036C2semidirect
6. C3×#2035C2semidirect
7. C3×#2034C2semidirect
8. C3×#2033C2semidirect
9. C3×#2000C2semidirect
10. C3×#2000C2semidirect
11. C3×#1999C2semidirect
12. C3×#1999C2semidirect
13. C3×#1825C2semidirect
14. C3×#1788C2semidirect
15. C3×#1779C2semidirect
16. #29600C3direct (N × H)
19. C22×C3×SD16C22semidirect
20. C22×C3×D8C22semidirect
38. C2×C3×#107C22semidirect
39. C2×C3×#106C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#103C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C2×#525C2×C3semidirect
65. C2×#482C2×C3semidirect
66. C2×#449C2×C3semidirect
67. #2847C2×C3semidirect
68. #2036C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #2033C2×C3semidirect
72. #2000C2×C3semidirect
73. #2000C2×C3semidirect
74. #1999C2×C3semidirect
75. #1999C2×C3semidirect
76. #1825C2×C3semidirect
77. #1788C2×C3semidirect
78. #1779C2×C3semidirect
85. C2×C3×#41D4semidirect
138. C3×#117D4semidirect
179. C22×SD16C22×C3semidirect
180. C22×D8C22×C3semidirect
198. C2×#107C22×C3semidirect
199. C2×#106C22×C3semidirect
200. C2×#103C22×C3semidirect
201. C2×#103C22×C3semidirect
202. C2×#103C22×C3semidirect
203. C2×#102C22×C3semidirect
204. C2×#102C22×C3semidirect
205. C2×#102C22×C3semidirect
206. C2×#102C22×C3semidirect
207. C2×#102C22×C3semidirect
220. #340C22×C3semidirect
221. #340C22×C3semidirect
222. #340C22×C3semidirect
223. #340C22×C3semidirect
364. C2×#41C3×D4semidirect
417. #117C3×D4semidirect
942. C3#29600direct (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×#4822
C2×C3×#4492
C3×#28472
C3×#20362
C3×#20352
C3×#20342
C3×#20332
C3×#20002
C3×#19992
C3×#18252
C3×#17882
C3×#17792
#296003