Finite Group Databasebeta

← C3×#29744 #10648351

Subgroups — C3×#29744 #10648351

Order 768.

1168 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#407C211yesmaximal, characteristic, complemented
3C3×#2848C211yesmaximal, characteristic, complemented
4C3×#2847C211yesmaximal, characteristic
5C3×#2076C211yesmaximal, characteristic, complemented
6C3×#2075C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2034C211yesmaximal, characteristic, complemented
10C3×#2033C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1895C211yesmaximal, characteristic, complemented
14C3×#1894C211yesmaximal, characteristic, complemented
15C3×#1809C211yesmaximal, characteristic, complemented
16#29744C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic, complemented
19C22×C3×M16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#120—21no—
28C3×#468—24no—
29C2×C3×#107C2211yescharacteristic, complemented
30C2×C3×#107C2211yescharacteristic, complemented
31C2×C3×#106C2211yescharacteristic, complemented
32C2×C3×#103C2211yescharacteristic, complemented
33C2×C3×#103C2211yescharacteristic, complemented
34C2×C3×#103C2211yescharacteristic, complemented
35C2×C3×#102C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic, complemented
38C3×#407—24no—
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic
43C3×#386—21no—
44C3×#386—21no—
45C3×#386—21no—
46C3×#385—21no—
47C3×#385—21no—
48C3×#385—21no—
49C3×#380C2211yescharacteristic
50C3×#380C2211yescharacteristic
51C3×#380C2211yescharacteristic
52C3×#380C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#379—21no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58C3×#340C2211yescharacteristic, complemented
59C3×#340C2211yescharacteristic, complemented
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C2×#468C2×C311yescharacteristic, complemented
63C2×#407C2×C311yescharacteristic, complemented
64#2848C2×C311yescharacteristic, complemented
65#2847C2×C311yescharacteristic
66#2076C2×C311yescharacteristic, complemented
67#2075C2×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#1895C2×C311yescharacteristic, complemented
75#1894C2×C311yescharacteristic, complemented
76#1809C2×C311yescharacteristic, complemented
77C25×C3D411yescharacteristic
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4D411yescharacteristic
90C23×C3×C4D411yescharacteristic
91C23×C3×C4D411yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×M16—22no—
99C2×C3×M16—41no—
100C2×C3×M16—41no—
101C2×C3×M16—41no—
102C2×C3×M16—41no—
103C2×C3×M16D414yescomplemented
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—41no—
111C3×C22⋊Q8—41no—
112C3×C22⋊Q8—41no—
113C3×C22⋊Q8—41no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—41no—
117C3×#121—41no—
118C3×#121—41no—
119C3×#121—41no—
120C3×#120—44no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C3×#107—22no—
143C3×#107—41no—
144C3×#106—41no—
145C3×#103—22no—
146C3×#103—41no—
147C3×#103—41no—
148C3×#102—22no—
149C3×#102—41no—
150C3×#102—41no—
151C3×C22⋊C8—22no—
152C3×C22⋊C8—22no—
153C3×C22⋊C8—22no—
154C3×C22⋊C8—22no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C24×C4C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic, complemented
163C22×M16C22×C311yescharacteristic
164C22×M16C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×C22⋊Q8C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×#121C22×C311yescharacteristic
170C2×#121C22×C311yescharacteristic
171C2×#120—21no—
172#468—24no—
173C2×#107C22×C311yescharacteristic, complemented
174C2×#107C22×C311yescharacteristic, complemented
175C2×#106C22×C311yescharacteristic, complemented
176C2×#103C22×C311yescharacteristic, complemented
177C2×#103C22×C311yescharacteristic, complemented
178C2×#103C22×C311yescharacteristic, complemented
179C2×#102C22×C311yescharacteristic, complemented
180C2×#102C22×C311yescharacteristic, complemented
181C2×#102C22×C311yescharacteristic, complemented
182#407—24no—
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic
187#386—21no—
188#386—21no—
189#386—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#380C22×C311yescharacteristic
194#380C22×C311yescharacteristic
195#380C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#379—21no—
200#340C22×C311yescharacteristic, complemented
201#340C22×C311yescharacteristic, complemented
202#340C22×C311yescharacteristic, complemented
203#340C22×C311yescharacteristic, complemented
204#340C22×C311yescharacteristic, complemented
205#340C22×C311yescharacteristic, complemented
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—22no—
209C24×C3—21no—
210C24×C3—41no—
211C24×C3—41no—
212C24×C3—41no—
213C24×C3—41no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—41no—
265C22×C3×C4—41no—
266C22×C3×C4—41no—
267C22×C3×C4—41no—
268C22×C3×C4—41no—
269C22×C3×C4—41no—
270C22×C3×C4—44no—
271C22×C3×C4—44no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D412yes—
278C22×C3×C4#4112yes—
279C22×C3×C4C2411yescharacteristic
280C3×SD16—44no—
281C3×M16—44no—
282C3×M16—44no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8C2×D412yes—
294C2×C3×C8C2×D412yes—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C25C3×D411yescharacteristic
323C22×Q8C23×C311yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C23×C311yescharacteristic
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—41no—
331C23×C4—41no—
332C23×C4—41no—
333C23×C4—41no—
334C23×C4C3×D411yescharacteristic
335C23×C4C3×D411yescharacteristic
336C23×C4C3×D411yescharacteristic
337C23×C4C23×C311yescharacteristic
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C311yescharacteristic
340C2×SD16—22no—
341C2×SD16—41no—
342C2×SD16—41no—
343C2×M16—22no—
344C2×M16—41no—
345C2×M16—41no—
346C2×M16—41no—
347C2×M16—41no—
348C2×M16C3×D414yescomplemented
349C22×C8C23×C311yescharacteristic
350C22×C8C23×C311yescharacteristic
351C22×C8C23×C311yescharacteristic
352C22×C8C23×C311yescharacteristic
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—41no—
356C22⋊Q8—41no—
357C22⋊Q8—41no—
358C22⋊Q8—41no—
359#121—22no—
360#121—22no—
361#121—41no—
362#121—41no—
363#121—41no—
364#121—41no—
365#120—44no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387#107—22no—
388#107—41no—
389#106—41no—
390#103—22no—
391#103—41no—
392#103—41no—
393#102—22no—
394#102—41no—
395#102—41no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3#12112yes—
439C23×C3AGL(1,ℤ/8)12yes—
440C23×C3#13712yes—
441C23×C3C22×D411yescharacteristic
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—84no—
451C3×D4—84no—
452C3×D4—84no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4#12112yes—
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502C2×C3×C4H(5,𝔽2)11yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504C3×C8—22no—
505C3×C8—22no—
506C3×C8—41no—
507C3×C8—41no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—41no—
513C24—41no—
514C24—41no—
515C24—41no—
516C24C2×C3×D411yescharacteristic
517C24C2×C3×D411yescharacteristic
518C24C2×C3×D411yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4C2×C3×D411yescharacteristic
577C22×C4C2×C3×D411yescharacteristic
578C22×C4C2×C3×D411yescharacteristic
579C22×C4C2×C3×D412yes—
580C22×C4C3×#4112yes—
581C22×C4C24×C311yescharacteristic
582SD16—44no—
583M16—44no—
584M16—44no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C2×C3×D412yes—
596C2×C8C2×C3×D412yes—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—416no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3C2×#12111yescharacteristic
654C22×C3#53411yescharacteristic
655C22×C3#53411yescharacteristic
656C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
657C22×C3C2×#13711yescharacteristic
658C22×C3#57511yescharacteristic
659C22×C3#57511yescharacteristic
660C3×C4—22no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4#53411yescharacteristic
671C3×C4#53511yescharacteristic
672C3×C4#53811yescharacteristic
673C3×C4#53811yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23C3×#12112yes—
707C23C3×AGL(1,ℤ/8)12yes—
708C23C3×#13712yes—
709C23C22×C3×D411yescharacteristic
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—84no—
719D4—84no—
720D4—84no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4C3×#12112yes—
766C2×C4C22×C3×D411yescharacteristic
767C2×C4C2×C3×#4111yescharacteristic
768C2×C4C3×H(5,𝔽2)11yescharacteristic
769C2×C4C3×H(5,𝔽2)11yescharacteristic
770C2×C4C3×H(5,𝔽2)11yescharacteristic
771C2×C4C3×H(5,𝔽2)11yescharacteristic
772C8—22no—
773C8—22no—
774C8—41no—
775C8—41no—
776C2×C3—42no—
777C2×C3—42no—
778C2×C3—42no—
779C2×C3—161no—
780C2×C3#261711yescharacteristic
781C2×C3#305511yescharacteristic
782C2×C3#305611yescharacteristic
783C2×C3#319311yescharacteristic
784C2×C3#319411yescharacteristic
785C2×C3#319611yescharacteristic
786C2×C3#319711yescharacteristic
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—416no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22C2×C3×#12111yescharacteristic
817C22C3×#53411yescharacteristic
818C22C3×#53411yescharacteristic
819C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
820C22C2×C3×#13711yescharacteristic
821C22C3×#57511yescharacteristic
822C22C3×#57511yescharacteristic
823C4—22no—
824C4—41no—
825C4—41no—
826C4—81no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4C3×#53411yescharacteristic
834C4C3×#53511yescharacteristic
835C4C3×#53811yescharacteristic
836C4C3×#53811yescharacteristic
837C3#2974411yescharacteristic, direct product factor, Sylow
838C2—42no—
839C2—42no—
840C2—42no—
841C2—161no—
842C2C3×#261711yescharacteristic
843C2C3×#305511yescharacteristic
844C2C3×#305611yescharacteristic
845C2C3×#319311yescharacteristic
846C2C3×#319411yescharacteristic
847C2C3×#319611yescharacteristic
848C2C3×#319711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2847C2
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×#468C2semidirect
2. C2×C3×#407C2semidirect
3. C3×#2848C2semidirect
5. C3×#2076C2semidirect
6. C3×#2075C2semidirect
7. C3×#2036C2semidirect
8. C3×#2035C2semidirect
9. C3×#2034C2semidirect
10. C3×#2033C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1895C2semidirect
14. C3×#1894C2semidirect
15. C3×#1809C2semidirect
16. #29744C3direct (N × H)
18. C22×C3×SD16C22semidirect
29. C2×C3×#107C22semidirect
30. C2×C3×#107C22semidirect
31. C2×C3×#106C22semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#103C22semidirect
34. C2×C3×#103C22semidirect
35. C2×C3×#102C22semidirect
36. C2×C3×#102C22semidirect
37. C2×C3×#102C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. C3×#340C22semidirect
59. C3×#340C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C2×#468C2×C3semidirect
63. C2×#407C2×C3semidirect
64. #2848C2×C3semidirect
66. #2076C2×C3semidirect
67. #2075C2×C3semidirect
68. #2036C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #2033C2×C3semidirect
72. #2000C2×C3semidirect
73. #2000C2×C3semidirect
74. #1895C2×C3semidirect
75. #1894C2×C3semidirect
76. #1809C2×C3semidirect
103. C2×C3×M16D4semidirect
162. C22×SD16C22×C3semidirect
173. C2×#107C22×C3semidirect
174. C2×#107C22×C3semidirect
175. C2×#106C22×C3semidirect
176. C2×#103C22×C3semidirect
177. C2×#103C22×C3semidirect
178. C2×#103C22×C3semidirect
179. C2×#102C22×C3semidirect
180. C2×#102C22×C3semidirect
181. C2×#102C22×C3semidirect
200. #340C22×C3semidirect
201. #340C22×C3semidirect
202. #340C22×C3semidirect
203. #340C22×C3semidirect
204. #340C22×C3semidirect
205. #340C22×C3semidirect
348. C2×M16C3×D4semidirect
837. C3#29744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4072
C3×#28482
C3×#28472
C3×#20762
C3×#20752
C3×#20362
C3×#20352
C3×#20342
C3×#20332
C3×#20002
C3×#18952
C3×#18942
C3×#18092
#297443