Finite Group Databasebeta

← C3×#15131 #10633738

Subgroups — C3×#15131 #10633738

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#396C212yesmaximal
2C2×C3×#389C211yesmaximal, characteristic, complemented
3C2×C3×#389C211yesmaximal, characteristic, complemented
4C2×C3×#384C211yesmaximal, characteristic, complemented
5C2×C3×#380C211yesmaximal, characteristic
6C2×C3×#380C211yesmaximal, characteristic
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
8C3×#1441C212yesmaximal, complemented
9C3×#1441C212yesmaximal, complemented
10C3×#1439C212yesmaximal
11C3×C4⋊#95C211yesmaximal, characteristic, complemented
12#15131C311yesmaximal, characteristic, direct product factor, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C3×#396—28no—
29C3×#389—24no—
30C3×#389—24no—
31C3×#384—24no—
32C3×#380—24no—
33C3×#380—24no—
34C3×C4×C22⋊C4—24no—
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×C3×#95C2212yes—
43C2×#396C2×C312yes—
44C2×#389C2×C311yescharacteristic, complemented
45C2×#389C2×C311yescharacteristic, complemented
46C2×#384C2×C311yescharacteristic, complemented
47C2×#380C2×C311yescharacteristic
48C2×#380C2×C311yescharacteristic
49C2×C4×C22⋊C4C2×C311yescharacteristic
50#1441C2×C312yescomplemented
51#1441C2×C312yescomplemented
52#1439C2×C312yes—
53C4⋊#95C2×C311yescharacteristic, complemented
54C25×C3C2311yescharacteristic
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4Q814yes—
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2312yes—
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—42no—
92C2×C3×C4⋊C4—42no—
93C2×C3×C4⋊C4—42no—
94C2×C3×C4⋊C4D414yes—
95C2×C3×C4⋊C4D414yes—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4D414yes—
107C2×C3×C22⋊C4Q814yes—
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—22no—
112C2×C3×C42—22no—
113C2×C3×C42D414yes—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95—24no—
117C3×#95—24no—
118C3×#95—24no—
119C3×#95—24no—
120C3×#95—24no—
121C3×#95—42no—
122C24×C4C22×C311yescharacteristic
123C22×C4⋊C4C22×C312yes—
124C22×C4⋊C4C22×C311yescharacteristic
125C22×C4⋊C4C22×C311yescharacteristic
126C22×C4⋊C4C22×C312yes—
127C22×C4⋊C4C22×C312yes—
128C22×C4⋊C4C22×C312yes—
129C22×C4⋊C4C22×C311yescharacteristic
130C22×C4⋊C4C22×C311yescharacteristic
131C22×C22⋊C4C22×C312yes—
132C22×C22⋊C4C22×C312yes—
133C22×C22⋊C4C22×C311yescharacteristic
134C22×C22⋊C4C22×C311yescharacteristic
135C22×C42C22×C311yescharacteristic
136C22×C42C22×C311yescharacteristic
137#396—28no—
138#389—24no—
139#389—24no—
140#384—24no—
141#380—24no—
142#380—24no—
143C4×C22⋊C4—24no—
144C2×#95C22×C312yes—
145C2×#95C22×C312yes—
146C2×#95C22×C312yes—
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C2×#95C22×C312yes—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3C2×D412yes—
165C24×C3C2×Q812yes—
166C24×C3C2×Q812yes—
167C24×C3C2411yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—28no—
207C22×C3×C4—28no—
208C22×C3×C4—28no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—44no—
224C22×C3×C4—44no—
225C22×C3×C4—44no—
226C22×C3×C4—44no—
227C22×C3×C4C2×D414yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×Q812yes—
237C22×C3×C4C2×Q812yes—
238C22×C3×C4C2×Q812yes—
239C22×C3×C4C2×Q812yes—
240C22×C3×C4#4112yes—
241C22×C3×C4#4112yes—
242C22×C3×C4#4112yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
245C3×C4⋊C4—28no—
246C3×C4⋊C4—28no—
247C3×C4⋊C4—48no—
248C3×C4⋊C4—48no—
249C3×C4⋊C4—48no—
250C3×C4⋊C4—48no—
251C3×C4⋊C4—44no—
252C3×C4⋊C4—44no—
253C3×C22⋊C4—28no—
254C3×C22⋊C4—28no—
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257C3×C42—28no—
258C3×C42—44no—
259C25C23×C311yescharacteristic
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4C3×Q814yes—
267C23×C4C23×C312yes—
268C23×C4C23×C312yes—
269C23×C4C23×C312yes—
270C23×C4C23×C312yes—
271C23×C4C23×C311yescharacteristic
272C23×C4C23×C311yescharacteristic
273C23×C4C23×C311yescharacteristic
274C23×C4C23×C311yescharacteristic
275C23×C4C23×C311yescharacteristic
276C23×C4C23×C311yescharacteristic
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4C3×D414yes—
300C2×C4⋊C4C3×D414yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4C3×D414yes—
312C2×C22⋊C4C3×Q814yes—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42C3×D414yes—
319#95—22no—
320#95—22no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—42no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3C4⋊Q814yes—
362C23×C3C22×D411yescharacteristic
363C23×C3C22×D411yescharacteristic
364C23×C3C22×D411yescharacteristic
365C23×C3C22×D411yescharacteristic
366C23×C3C22×Q811yescharacteristic
367C23×C3C22×Q811yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4111yescharacteristic
372C23×C3C2×#4111yescharacteristic
373C23×C3H(5,𝔽2)11yescharacteristic
374C23×C3H(5,𝔽2)11yescharacteristic
375C23×C32−1+411yescharacteristic
376C23×C32−1+411yescharacteristic
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—41no—
424C2×C3×C4—416no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4#12114yes—
440C2×C3×C4#12114yes—
441C2×C3×C4#12114yes—
442C2×C3×C4#12114yes—
443C2×C3×C4C22⋊Q814yes—
444C2×C3×C4C22⋊Q814yes—
445C2×C3×C4C22⋊Q814yes—
446C2×C3×C4C22⋊Q814yes—
447C2×C3×C4#12614yes—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24C2×C3×D412yes—
461C24C2×C3×Q812yes—
462C24C2×C3×Q812yes—
463C24C24×C311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4C2×C3×D414yes—
524C22×C4C2×C3×D412yes—
525C22×C4C2×C3×D414yes—
526C22×C4C2×C3×D412yes—
527C22×C4C2×C3×D412yes—
528C22×C4C2×C3×D412yes—
529C22×C4C2×C3×D412yes—
530C22×C4C2×C3×D412yes—
531C22×C4C2×C3×D412yes—
532C22×C4C2×C3×Q812yes—
533C22×C4C2×C3×Q812yes—
534C22×C4C2×C3×Q812yes—
535C22×C4C2×C3×Q812yes—
536C22×C4C3×#4112yes—
537C22×C4C3×#4112yes—
538C22×C4C3×#4112yes—
539C22×C4C3×#4112yes—
540C22×C4C3×#4112yes—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—48no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C42—28no—
554C42—44no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3C2×#12111yescharacteristic
571C22×C3C2×#12111yescharacteristic
572C22×C3C2×#12111yescharacteristic
573C22×C3C2×#12111yescharacteristic
574C22×C3C2×C22⋊Q811yescharacteristic
575C22×C3C2×C22⋊Q811yescharacteristic
576C22×C3C2×C22⋊Q811yescharacteristic
577C22×C3C2×C22⋊Q811yescharacteristic
578C22×C3C2×#12611yescharacteristic
579C22×C3C2×C4⋊Q811yescharacteristic
580C22×C3#53211yescharacteristic
581C22×C3#53311yescharacteristic
582C22×C3#53311yescharacteristic
583C22×C3#53711yescharacteristic
584C22×C3#53711yescharacteristic
585C22×C3#54011yescharacteristic
586C22×C3#54111yescharacteristic
587C22×C3#54411yescharacteristic
588C22×C3#54411yescharacteristic
589C22×C3D4211yescharacteristic
590C22×C3D4211yescharacteristic
591C22×C3#54611yescharacteristic
592C22×C3#54711yescharacteristic
593C22×C3#54711yescharacteristic
594C22×C3#54711yescharacteristic
595C22×C3#54811yescharacteristic
596C22×C3D4×Q811yescharacteristic
597C22×C3D4×Q811yescharacteristic
598C22×C3#55011yescharacteristic
599C22×C3#55211yescharacteristic
600C22×C3#55311yescharacteristic
601C22×C3#55411yescharacteristic
602C22×C3#55411yescharacteristic
603C22×C3#55511yescharacteristic
604C22×C3#55611yescharacteristic
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—42no—
608C3×C4—44no—
609C3×C4—42no—
610C3×C4—44no—
611C3×C4—42no—
612C3×C4—82no—
613C3×C4—82no—
614C3×C4#39618yescomplemented
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23C3×C4⋊Q814yes—
650C23C22×C3×D411yescharacteristic
651C23C22×C3×D411yescharacteristic
652C23C22×C3×D411yescharacteristic
653C23C22×C3×D411yescharacteristic
654C23C22×C3×Q811yescharacteristic
655C23C22×C3×Q811yescharacteristic
656C23C2×C3×#4111yescharacteristic
657C23C2×C3×#4111yescharacteristic
658C23C2×C3×#4111yescharacteristic
659C23C2×C3×#4111yescharacteristic
660C23C2×C3×#4111yescharacteristic
661C23C3×H(5,𝔽2)11yescharacteristic
662C23C3×H(5,𝔽2)11yescharacteristic
663C23C3×2−1+411yescharacteristic
664C23C3×2−1+411yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4C3×#12114yes—
728C2×C4C3×#12114yes—
729C2×C4C3×#12114yes—
730C2×C4C3×#12114yes—
731C2×C4C3×C22⋊Q814yes—
732C2×C4C3×C22⋊Q814yes—
733C2×C4C3×C22⋊Q814yes—
734C2×C4C3×C22⋊Q814yes—
735C2×C4C3×#12614yes—
736C2×C3—44no—
737C2×C3C2×#39611yescharacteristic
738C2×C3#241611yescharacteristic
739C2×C3#241711yescharacteristic
740C2×C3#242811yescharacteristic
741C2×C3#242911yescharacteristic
742C2×C3#243911yescharacteristic
743C2×C3#244011yescharacteristic
744C2×C3#244011yescharacteristic
745C2×C3#244111yescharacteristic
746C2×C3#249611yescharacteristic
747C2×C3#249711yescharacteristic
748C2×C3#253711yescharacteristic
749C2×C3#253811yescharacteristic
750C2×C3#262911yescharacteristic
751C2×C3#285711yescharacteristic
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22C2×C3×#12111yescharacteristic
768C22C2×C3×#12111yescharacteristic
769C22C2×C3×#12111yescharacteristic
770C22C2×C3×#12111yescharacteristic
771C22C2×C3×C22⋊Q811yescharacteristic
772C22C2×C3×C22⋊Q811yescharacteristic
773C22C2×C3×C22⋊Q811yescharacteristic
774C22C2×C3×C22⋊Q811yescharacteristic
775C22C2×C3×#12611yescharacteristic
776C22C2×C3×C4⋊Q811yescharacteristic
777C22C3×#53211yescharacteristic
778C22C3×#53311yescharacteristic
779C22C3×#53311yescharacteristic
780C22C3×#53711yescharacteristic
781C22C3×#53711yescharacteristic
782C22C3×#54011yescharacteristic
783C22C3×#54111yescharacteristic
784C22C3×#54411yescharacteristic
785C22C3×#54411yescharacteristic
786C22C3×D4211yescharacteristic
787C22C3×D4211yescharacteristic
788C22C3×#54611yescharacteristic
789C22C3×#54711yescharacteristic
790C22C3×#54711yescharacteristic
791C22C3×#54711yescharacteristic
792C22C3×#54811yescharacteristic
793C22C3×D4×Q811yescharacteristic
794C22C3×D4×Q811yescharacteristic
795C22C3×#55011yescharacteristic
796C22C3×#55211yescharacteristic
797C22C3×#55311yescharacteristic
798C22C3×#55411yescharacteristic
799C22C3×#55411yescharacteristic
800C22C3×#55511yescharacteristic
801C22C3×#55611yescharacteristic
802C4—24no—
803C4—24no—
804C4—42no—
805C4—44no—
806C4—42no—
807C4—44no—
808C4—42no—
809C4—82no—
810C4—82no—
811C4C3×#39618yescomplemented
812C3#1513111yescharacteristic, direct product factor, Sylow
813C2—44no—
814C2C2×C3×#39611yescharacteristic
815C2C3×#241611yescharacteristic
816C2C3×#241711yescharacteristic
817C2C3×#242811yescharacteristic
818C2C3×#242911yescharacteristic
819C2C3×#243911yescharacteristic
820C2C3×#244011yescharacteristic
821C2C3×#244011yescharacteristic
822C2C3×#244111yescharacteristic
823C2C3×#249611yescharacteristic
824C2C3×#249711yescharacteristic
825C2C3×#253711yescharacteristic
826C2C3×#253811yescharacteristic
827C2C3×#262911yescharacteristic
828C2C3×#285711yescharacteristic
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
2. C2×C3×#389C2semidirect
3. C2×C3×#389C2semidirect
4. C2×C3×#384C2semidirect
8. C3×#1441C2semidirect
9. C3×#1441C2semidirect
11. C3×C4⋊#95C2semidirect
12. #15131C3direct (N × H)
44. C2×#389C2×C3semidirect
45. C2×#389C2×C3semidirect
46. C2×#384C2×C3semidirect
50. #1441C2×C3semidirect
51. #1441C2×C3semidirect
53. C4⋊#95C2×C3semidirect
614. C3×C4#396semidirect
811. C4C3×#396semidirect
812. C3#15131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3962
C2×C3×#3892
C2×C3×#3842
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14412
C3×#14392
C3×C4⋊#952
#151313