Finite Group Databasebeta

← C3×#14767 #10633374

Subgroups — C3×#14767 #10633374

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic, complemented
2C2×C3×#385C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic
4C22×C3×#95C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic, complemented
6C3×#1443C211yesmaximal, characteristic, complemented
7C3×#1443C211yesmaximal, characteristic, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1442C211yesmaximal, characteristic, complemented
10C3×#1442C211yesmaximal, characteristic, complemented
11C3×#1441C211yesmaximal, characteristic, complemented
12C3×C22⋊#95C211yesmaximal, characteristic
13C3×C22⋊#95C211yesmaximal, characteristic
14C3×C22⋊#95C211yesmaximal, characteristic
15C3×C22⋊#95C211yesmaximal, characteristic
16#14767C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C3×#400—24no—
29C3×#385—24no—
30C3×#380—24no—
31C2×C3×#95—24no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×#400C2×C311yescharacteristic, complemented
57C2×#385C2×C311yescharacteristic
58C2×#380C2×C311yescharacteristic
59C22×#95C2×C311yescharacteristic
60#1445C2×C311yescharacteristic, complemented
61#1443C2×C311yescharacteristic, complemented
62#1443C2×C311yescharacteristic, complemented
63#1442C2×C311yescharacteristic, complemented
64#1442C2×C311yescharacteristic, complemented
65#1442C2×C311yescharacteristic, complemented
66#1441C2×C311yescharacteristic, complemented
67C22⋊#95C2×C311yescharacteristic
68C22⋊#95C2×C311yescharacteristic
69C22⋊#95C2×C311yescharacteristic
70C22⋊#95C2×C311yescharacteristic
71C25×C3C2311yescharacteristic
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4—41no—
92C23×C3×C4Q814yes—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4D414yes—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95—41no—
149C3×#95—41no—
150C3×#95—41no—
151C3×#95—41no—
152C3×#95—41no—
153C3×#95—41no—
154C3×#95D414yes—
155C24×C4C22×C311yescharacteristic
156C24×C4C22×C311yescharacteristic
157C24×C4C22×C311yescharacteristic
158C22×C4⋊C4C22×C311yescharacteristic
159C22×C4⋊C4C22×C311yescharacteristic
160C22×C4⋊C4C22×C311yescharacteristic
161C22×C4⋊C4C22×C311yescharacteristic
162C22×C22⋊C4C22×C311yescharacteristic
163C22×C22⋊C4C22×C311yescharacteristic
164C22×C22⋊C4C22×C311yescharacteristic
165C22×C22⋊C4C22×C311yescharacteristic
166#400—24no—
167#385—24no—
168#380—24no—
169C2×#95—24no—
170C2×#95C22×C311yescharacteristic
171C2×#95C22×C311yescharacteristic
172C2×#95C22×C311yescharacteristic
173C2×#95C22×C311yescharacteristic
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C2×#95C22×C311yescharacteristic
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3C2×D412yes—
203C24×C3C2×Q812yes—
204C24×C3#4112yes—
205C24×C3#4112yes—
206C24×C3#4112yes—
207C24×C3#4112yes—
208C24×C3#4112yes—
209C24×C3C2411yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—28no—
215C22×C3×C4—28no—
216C22×C3×C4—28no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
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—28no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
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—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—44no—
303C22×C3×C4—44no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4—44no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×Q812yes—
325C22×C3×C4C2×Q812yes—
326C22×C3×C4#4112yes—
327C22×C3×C4#4112yes—
328C22×C3×C4#4112yes—
329C3×C4⋊C4—44no—
330C3×C4⋊C4—44no—
331C3×C4⋊C4—44no—
332C3×C4⋊C4—44no—
333C3×C22⋊C4—28no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C25C23×C311yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—41no—
355C23×C4—41no—
356C23×C4—41no—
357C23×C4—41no—
358C23×C4C3×Q814yes—
359C23×C4C23×C311yescharacteristic
360C23×C4C23×C311yescharacteristic
361C23×C4C23×C311yescharacteristic
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C311yescharacteristic
371C23×C4C23×C311yescharacteristic
372C23×C4C23×C311yescharacteristic
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4C3×D414yes—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—41no—
413#95—41no—
414#95—41no—
415#95—41no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95—41no—
420#95C3×D414yes—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3C22⋊Q814yes—
450C23×C3#12314yes—
451C23×C3#12414yes—
452C23×C3#12514yes—
453C23×C3#12514yes—
454C23×C3#12614yes—
455C23×C3#12614yes—
456C23×C3C22×D411yescharacteristic
457C23×C3C22×D411yescharacteristic
458C23×C3C22×Q811yescharacteristic
459C23×C3C2×#4111yescharacteristic
460C23×C3C2×#4111yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3H(5,𝔽2)11yescharacteristic
468C23×C3H(5,𝔽2)11yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C32−1+411yescharacteristic
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—416no—
499C2×C3×C4—416no—
500C2×C3×C4—416no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
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—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—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×C4C22⋊Q814yes—
572C24—21no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24C2×C3×D412yes—
581C24C2×C3×Q812yes—
582C24C3×#4112yes—
583C24C3×#4112yes—
584C24C3×#4112yes—
585C24C3×#4112yes—
586C24C3×#4112yes—
587C24C24×C311yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
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—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—28no—
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—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4C2×C3×D412yes—
698C22×C4C2×C3×D412yes—
699C22×C4C2×C3×D412yes—
700C22×C4C2×C3×D412yes—
701C22×C4C2×C3×D412yes—
702C22×C4C2×C3×Q812yes—
703C22×C4C2×C3×Q812yes—
704C22×C4C3×#4112yes—
705C22×C4C3×#4112yes—
706C22×C4C3×#4112yes—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C22⋊C4—28no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—24no—
719C22×C3—24no—
720C22×C3—24no—
721C22×C3—24no—
722C22×C3—24no—
723C22×C3—24no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3#40018yescomplemented
730C22×C3C2×C22⋊Q811yescharacteristic
731C22×C3C2×C22⋊Q811yescharacteristic
732C22×C3C2×#12311yescharacteristic
733C22×C3#52511yescharacteristic
734C22×C3#52511yescharacteristic
735C22×C3C2×#12411yescharacteristic
736C22×C3C2×#12511yescharacteristic
737C22×C3C2×#12511yescharacteristic
738C22×C3C2×#12611yescharacteristic
739C22×C3C2×#12611yescharacteristic
740C22×C3#52911yescharacteristic
741C22×C3#52911yescharacteristic
742C22×C3#53311yescharacteristic
743C22×C3#53811yescharacteristic
744C22×C3#53811yescharacteristic
745C22×C3#53911yescharacteristic
746C22×C3#53911yescharacteristic
747C22×C3#54311yescharacteristic
748C22×C3#54411yescharacteristic
749C22×C3D4211yescharacteristic
750C22×C3#54611yescharacteristic
751C22×C3#54611yescharacteristic
752C22×C3#54611yescharacteristic
753C22×C3#54611yescharacteristic
754C22×C3#54711yescharacteristic
755C22×C3#54811yescharacteristic
756C22×C3#55111yescharacteristic
757C22×C3#55111yescharacteristic
758C22×C3#55111yescharacteristic
759C22×C3#55111yescharacteristic
760C22×C3#55211yescharacteristic
761C22×C3#55211yescharacteristic
762C22×C3#55311yescharacteristic
763C22×C3#55311yescharacteristic
764C22×C3#55311yescharacteristic
765C3×C4—24no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—81no—
774C3×C4—81no—
775C3×C4—81no—
776C3×C4—81no—
777C3×C4—81no—
778C3×C4—81no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23C3×C22⋊Q814yes—
808C23C3×#12314yes—
809C23C3×#12414yes—
810C23C3×#12514yes—
811C23C3×#12514yes—
812C23C3×#12614yes—
813C23C3×#12614yes—
814C23C22×C3×D411yescharacteristic
815C23C22×C3×D411yescharacteristic
816C23C22×C3×Q811yescharacteristic
817C23C2×C3×#4111yescharacteristic
818C23C2×C3×#4111yescharacteristic
819C23C2×C3×#4111yescharacteristic
820C23C2×C3×#4111yescharacteristic
821C23C2×C3×#4111yescharacteristic
822C23C2×C3×#4111yescharacteristic
823C23C2×C3×#4111yescharacteristic
824C23C2×C3×#4111yescharacteristic
825C23C3×H(5,𝔽2)11yescharacteristic
826C23C3×H(5,𝔽2)11yescharacteristic
827C23C3×H(5,𝔽2)11yescharacteristic
828C23C3×2−1+411yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
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—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—416no—
857C2×C4—416no—
858C2×C4—416no—
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×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4C3×C22⋊Q814yes—
930C2×C3—28no—
931C2×C3C2×#40011yescharacteristic
932C2×C3#243711yescharacteristic
933C2×C3#243811yescharacteristic
934C2×C3#244211yescharacteristic
935C2×C3#244311yescharacteristic
936C2×C3#244411yescharacteristic
937C2×C3#247211yescharacteristic
938C2×C3#248011yescharacteristic
939C2×C3#248111yescharacteristic
940C2×C3#248811yescharacteristic
941C2×C3#249311yescharacteristic
942C2×C3#251011yescharacteristic
943C2×C3#256911yescharacteristic
944C2×C3#264611yescharacteristic
945C2×C3#285111yescharacteristic
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22C3×#40018yescomplemented
961C22C2×C3×C22⋊Q811yescharacteristic
962C22C2×C3×C22⋊Q811yescharacteristic
963C22C2×C3×#12311yescharacteristic
964C22C3×#52511yescharacteristic
965C22C3×#52511yescharacteristic
966C22C2×C3×#12411yescharacteristic
967C22C2×C3×#12511yescharacteristic
968C22C2×C3×#12511yescharacteristic
969C22C2×C3×#12611yescharacteristic
970C22C2×C3×#12611yescharacteristic
971C22C3×#52911yescharacteristic
972C22C3×#52911yescharacteristic
973C22C3×#53311yescharacteristic
974C22C3×#53811yescharacteristic
975C22C3×#53811yescharacteristic
976C22C3×#53911yescharacteristic
977C22C3×#53911yescharacteristic
978C22C3×#54311yescharacteristic
979C22C3×#54411yescharacteristic
980C22C3×D4211yescharacteristic
981C22C3×#54611yescharacteristic
982C22C3×#54611yescharacteristic
983C22C3×#54611yescharacteristic
984C22C3×#54611yescharacteristic
985C22C3×#54711yescharacteristic
986C22C3×#54811yescharacteristic
987C22C3×#55111yescharacteristic
988C22C3×#55111yescharacteristic
989C22C3×#55111yescharacteristic
990C22C3×#55111yescharacteristic
991C22C3×#55211yescharacteristic
992C22C3×#55211yescharacteristic
993C22C3×#55311yescharacteristic
994C22C3×#55311yescharacteristic
995C22C3×#55311yescharacteristic
996C4—24no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—81no—
1005C4—81no—
1006C4—81no—
1007C4—81no—
1008C4—81no—
1009C4—81no—
1010C3#1476711yescharacteristic, direct product factor, Sylow
1011C2—28no—
1012C2C2×C3×#40011yescharacteristic
1013C2C3×#243711yescharacteristic
1014C2C3×#243811yescharacteristic
1015C2C3×#244211yescharacteristic
1016C2C3×#244311yescharacteristic
1017C2C3×#244411yescharacteristic
1018C2C3×#247211yescharacteristic
1019C2C3×#248011yescharacteristic
1020C2C3×#248111yescharacteristic
1021C2C3×#248811yescharacteristic
1022C2C3×#249311yescharacteristic
1023C2C3×#251011yescharacteristic
1024C2C3×#256911yescharacteristic
1025C2C3×#264611yescharacteristic
1026C2C3×#285111yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#400C2semidirect
5. C3×#1445C2semidirect
6. C3×#1443C2semidirect
7. C3×#1443C2semidirect
8. C3×#1442C2semidirect
9. C3×#1442C2semidirect
10. C3×#1442C2semidirect
11. C3×#1441C2semidirect
16. #14767C3direct (N × H)
56. C2×#400C2×C3semidirect
60. #1445C2×C3semidirect
61. #1443C2×C3semidirect
62. #1443C2×C3semidirect
63. #1442C2×C3semidirect
64. #1442C2×C3semidirect
65. #1442C2×C3semidirect
66. #1441C2×C3semidirect
729. C22×C3#400semidirect
960. C22C3×#400semidirect
1010. C3#14767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×C3×#3852
C2×C3×#3802
C22×C3×#952
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×C22⋊#952
#147673