Finite Group Databasebeta

← C3×#14173 #10632780

Subgroups — C3×#14173 #10632780

Order 768.

2322 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×C3×#387C211yesmaximal, characteristic, complemented
5C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#1440C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8C3×#1438C211yesmaximal, characteristic
9C3×#1437C211yesmaximal, characteristic, complemented
10C3×#1436C211yesmaximal, characteristic, complemented
11C3×#1436C211yesmaximal, characteristic, complemented
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×C22⋊#95C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14173C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C2×C3×C4×D4—24no—
21C2×C3×C4×D4—24no—
22C2×C3×C4×D4—24no—
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C42C2211yescharacteristic
37C22×C3×C42C2211yescharacteristic
38C22×C3×C42C2211yescharacteristic
39C3×#394C418yescomplemented
40C3×#388—24no—
41C3×#387—24no—
42C3×C4×C22⋊C4—24no—
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×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C22×C4×D4C2×C311yescharacteristic
60C2×#394C2×C311yescharacteristic
61C2×#388C2×C311yescharacteristic, complemented
62C2×#387C2×C311yescharacteristic, complemented
63C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
64#1440C2×C311yescharacteristic, complemented
65#1439C2×C311yescharacteristic, complemented
66#1438C2×C311yescharacteristic
67#1437C2×C311yescharacteristic, complemented
68#1436C2×C311yescharacteristic, complemented
69#1436C2×C311yescharacteristic, complemented
70#1436C2×C311yescharacteristic, complemented
71C22⋊#95C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic, complemented
73C22⋊#95C2×C311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4C2×C414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—41no—
93C23×C3×C4—41no—
94C23×C3×C4—41no—
95C23×C3×C4—41no—
96C23×C3×C4D414yes—
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
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C3×C4×D4—232no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4C2×C414yescomplemented
119C2×C3×C4⋊C4D414yes—
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⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—41no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4—41no—
144C2×C3×C22⋊C4—41no—
145C2×C3×C22⋊C4C2×C414yescomplemented
146C2×C3×C22⋊C4C2×C414yescomplemented
147C2×C3×C22⋊C4C2×C414yescomplemented
148C2×C3×C22⋊C4C2×C414yescomplemented
149C2×C3×C22⋊C4D414yes—
150C2×C3×C42—22no—
151C2×C3×C42—22no—
152C2×C3×C42—22no—
153C2×C3×C42—22no—
154C2×C3×C42—22no—
155C2×C3×C42—22no—
156C2×C3×C42—22no—
157C2×C3×C42—41no—
158C2×C3×C42—41no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—41no—
172C3×#95—41no—
173C3×#95—41no—
174C3×#95C2×C414yescomplemented
175C23×D4C22×C311yescharacteristic
176C24×C4C22×C311yescharacteristic
177C24×C4C22×C311yescharacteristic
178C2×C4×D4—24no—
179C2×C4×D4—24no—
180C2×C4×D4—24no—
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C42C22×C311yescharacteristic
195C22×C42C22×C311yescharacteristic
196C22×C42C22×C311yescharacteristic
197#394C3×C418yescomplemented
198#388—24no—
199#387—24no—
200C4×C22⋊C4—24no—
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3C22×C412yes—
242C24×C3C22×C412yes—
243C24×C3C2×D412yes—
244C24×C3C2×D412yes—
245C24×C3#4112yes—
246C24×C3#4112yes—
247C24×C3C2411yescharacteristic
248C2×C3×D4—28no—
249C2×C3×D4—28no—
250C2×C3×D4—28no—
251C2×C3×D4—28no—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
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—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—28no—
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—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—28no—
317C22×C3×C4—28no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—44no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4—44no—
343C22×C3×C4C22×C412yes—
344C22×C3×C4C22×C412yes—
345C22×C3×C4C22×C412yes—
346C22×C3×C4C22×C412yes—
347C22×C3×C4C22×C412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4C2×D412yes—
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D412yes—
353C22×C3×C4C2×D412yes—
354C22×C3×C4C2×D412yes—
355C22×C3×C4#4112yes—
356C22×C3×C4#4112yes—
357C22×C3×C4#4112yes—
358C22×C3×C4#4112yes—
359C22×C3×C4#4112yes—
360C3×C4⋊C4—28no—
361C3×C4⋊C4—28no—
362C3×C4⋊C4—44no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—28no—
365C3×C22⋊C4—28no—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368C3×C22⋊C4—44no—
369C3×C22⋊C4—44no—
370C3×C22⋊C4—44no—
371C3×C22⋊C4—44no—
372C3×C22⋊C4—44no—
373C3×C42—28no—
374C3×C42—44no—
375C3×C42—44no—
376C25C23×C311yescharacteristic
377C25C23×C311yescharacteristic
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4C2×C3×C414yes—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—41no—
398C23×C4C3×D414yes—
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403C23×C4C23×C311yescharacteristic
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C23×C4C23×C311yescharacteristic
407C23×C4C23×C311yescharacteristic
408C23×C4C23×C311yescharacteristic
409C23×C4C23×C311yescharacteristic
410C23×C4C23×C311yescharacteristic
411C23×C4C23×C311yescharacteristic
412C4×D4—232no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4C2×C3×C414yescomplemented
421C2×C4⋊C4C3×D414yes—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4C2×C3×C414yescomplemented
448C2×C22⋊C4C2×C3×C414yescomplemented
449C2×C22⋊C4C2×C3×C414yescomplemented
450C2×C22⋊C4C2×C3×C414yescomplemented
451C2×C22⋊C4C3×D414yes—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—41no—
460C2×C42—41no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—41no—
474#95—41no—
475#95—41no—
476#95C2×C3×C414yescomplemented
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3C4×D414yes—
546C23×C3C4×D414yes—
547C23×C3C23×C411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3C22×D411yescharacteristic
550C23×C3C22×D411yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3C2×#4111yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3H(5,𝔽2)11yescharacteristic
559C23×C3H(5,𝔽2)11yescharacteristic
560C23×C3H(5,𝔽2)11yescharacteristic
561C23×C32−1+411yescharacteristic
562C3×D4—232no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—416no—
606C2×C3×C4—416no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4C4×D414yes—
654C2×C3×C4#12014yes—
655C2×C3×C4#12314yes—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C22×C3×C412yes—
681C24C22×C3×C412yes—
682C24C2×C3×D412yes—
683C24C2×C3×D412yes—
684C24C3×#4112yes—
685C24C3×#4112yes—
686C24C24×C311yescharacteristic
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—28no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—28no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4C22×C3×C412yes—
783C22×C4C22×C3×C412yes—
784C22×C4C22×C3×C412yes—
785C22×C4C22×C3×C412yes—
786C22×C4C22×C3×C412yes—
787C22×C4C2×C3×D412yes—
788C22×C4C2×C3×D412yes—
789C22×C4C2×C3×D412yes—
790C22×C4C2×C3×D412yes—
791C22×C4C2×C3×D412yes—
792C22×C4C2×C3×D412yes—
793C22×C4C2×C3×D412yes—
794C22×C4C3×#4112yes—
795C22×C4C3×#4112yes—
796C22×C4C3×#4112yes—
797C22×C4C3×#4112yes—
798C22×C4C3×#4112yes—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—44no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C42—28no—
813C42—44no—
814C42—44no—
815C22×C3—24no—
816C22×C3—24no—
817C22×C3—24no—
818C22×C3—24no—
819C22×C3—24no—
820C22×C3—24no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3C2×C4×D411yescharacteristic
846C22×C3C2×C4×D411yescharacteristic
847C22×C3C2×C4×D411yescharacteristic
848C22×C3C4×#4111yescharacteristic
849C22×C3C4×#4111yescharacteristic
850C22×C3#51811yescharacteristic
851C22×C3#52011yescharacteristic
852C22×C3C2×#12011yescharacteristic
853C22×C3C2×#12311yescharacteristic
854C22×C3#52511yescharacteristic
855C22×C3#52511yescharacteristic
856C22×C3#52511yescharacteristic
857C22×C3#52511yescharacteristic
858C22×C3#52911yescharacteristic
859C22×C3#52911yescharacteristic
860C22×C3#53411yescharacteristic
861C22×C3#53711yescharacteristic
862C22×C3#53811yescharacteristic
863C22×C3#53911yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54611yescharacteristic
867C22×C3#54611yescharacteristic
868C22×C3#54611yescharacteristic
869C22×C3#54711yescharacteristic
870C22×C3#54811yescharacteristic
871C22×C3#55011yescharacteristic
872C22×C3#55111yescharacteristic
873C22×C3#55211yescharacteristic
874C22×C3#55311yescharacteristic
875C22×C3#55311yescharacteristic
876C22×C3#55311yescharacteristic
877C22×C3#55511yescharacteristic
878C22×C3#55611yescharacteristic
879C22×C3#55911yescharacteristic
880C3×C4—24no—
881C3×C4—24no—
882C3×C4—24no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—42no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—81no—
892C3×C4—81no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23C3×C4×D414yes—
962C23C3×C4×D414yes—
963C23C23×C3×C411yescharacteristic
964C23C22×C3×D411yescharacteristic
965C23C22×C3×D411yescharacteristic
966C23C22×C3×D411yescharacteristic
967C23C2×C3×#4111yescharacteristic
968C23C2×C3×#4111yescharacteristic
969C23C2×C3×#4111yescharacteristic
970C23C2×C3×#4111yescharacteristic
971C23C2×C3×#4111yescharacteristic
972C23C2×C3×#4111yescharacteristic
973C23C2×C3×#4111yescharacteristic
974C23C3×H(5,𝔽2)11yescharacteristic
975C23C3×H(5,𝔽2)11yescharacteristic
976C23C3×H(5,𝔽2)11yescharacteristic
977C23C3×2−1+411yescharacteristic
978D4—232no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4C3×C4×D414yes—
1070C2×C4C3×#12014yes—
1071C2×C4C3×#12314yes—
1072C2×C3—44no—
1073C2×C3—44no—
1074C2×C3C4×#12011yescharacteristic
1075C2×C3C4×#12311yescharacteristic
1076C2×C3#232511yescharacteristic
1077C2×C3#235911yescharacteristic
1078C2×C3#236311yescharacteristic
1079C2×C3#236411yescharacteristic
1080C2×C3#236711yescharacteristic
1081C2×C3#240511yescharacteristic
1082C2×C3#240711yescharacteristic
1083C2×C3#245911yescharacteristic
1084C2×C3#246011yescharacteristic
1085C2×C3#246611yescharacteristic
1086C2×C3#246711yescharacteristic
1087C2×C3#248511yescharacteristic
1088C2×C3#260011yescharacteristic
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22C2×C3×C4×D411yescharacteristic
1120C22C2×C3×C4×D411yescharacteristic
1121C22C2×C3×C4×D411yescharacteristic
1122C22C3×C4×#4111yescharacteristic
1123C22C3×C4×#4111yescharacteristic
1124C22C3×#51811yescharacteristic
1125C22C3×#52011yescharacteristic
1126C22C2×C3×#12011yescharacteristic
1127C22C2×C3×#12311yescharacteristic
1128C22C3×#52511yescharacteristic
1129C22C3×#52511yescharacteristic
1130C22C3×#52511yescharacteristic
1131C22C3×#52511yescharacteristic
1132C22C3×#52911yescharacteristic
1133C22C3×#52911yescharacteristic
1134C22C3×#53411yescharacteristic
1135C22C3×#53711yescharacteristic
1136C22C3×#53811yescharacteristic
1137C22C3×#53911yescharacteristic
1138C22C3×#54611yescharacteristic
1139C22C3×#54611yescharacteristic
1140C22C3×#54611yescharacteristic
1141C22C3×#54611yescharacteristic
1142C22C3×#54611yescharacteristic
1143C22C3×#54711yescharacteristic
1144C22C3×#54811yescharacteristic
1145C22C3×#55011yescharacteristic
1146C22C3×#55111yescharacteristic
1147C22C3×#55211yescharacteristic
1148C22C3×#55311yescharacteristic
1149C22C3×#55311yescharacteristic
1150C22C3×#55311yescharacteristic
1151C22C3×#55511yescharacteristic
1152C22C3×#55611yescharacteristic
1153C22C3×#55911yescharacteristic
1154C4—24no—
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—81no—
1166C4—81no—
1167C3#1417311yescharacteristic, direct product factor, Sylow
1168C2—44no—
1169C2—44no—
1170C2C3×C4×#12011yescharacteristic
1171C2C3×C4×#12311yescharacteristic
1172C2C3×#232511yescharacteristic
1173C2C3×#235911yescharacteristic
1174C2C3×#236311yescharacteristic
1175C2C3×#236411yescharacteristic
1176C2C3×#236711yescharacteristic
1177C2C3×#240511yescharacteristic
1178C2C3×#240711yescharacteristic
1179C2C3×#245911yescharacteristic
1180C2C3×#246011yescharacteristic
1181C2C3×#246611yescharacteristic
1182C2C3×#246711yescharacteristic
1183C2C3×#248511yescharacteristic
1184C2C3×#260011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×#388C2semidirect
4. C2×C3×#387C2semidirect
5. C2×C3×C4×C22⋊C4C2semidirect
6. C3×#1440C2semidirect
7. C3×#1439C2semidirect
9. C3×#1437C2semidirect
10. C3×#1436C2semidirect
11. C3×#1436C2semidirect
12. C3×#1436C2semidirect
13. C3×C22⋊#95C2semidirect
14. C3×C22⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14173C3direct (N × H)
39. C3×#394C4semidirect
61. C2×#388C2×C3semidirect
62. C2×#387C2×C3semidirect
63. C2×C4×C22⋊C4C2×C3semidirect
64. #1440C2×C3semidirect
65. #1439C2×C3semidirect
67. #1437C2×C3semidirect
68. #1436C2×C3semidirect
69. #1436C2×C3semidirect
70. #1436C2×C3semidirect
71. C22⋊#95C2×C3semidirect
72. C22⋊#95C2×C3semidirect
73. C22⋊#95C2×C3semidirect
118. C2×C3×C4⋊C4C2×C4semidirect
145. C2×C3×C22⋊C4C2×C4semidirect
146. C2×C3×C22⋊C4C2×C4semidirect
147. C2×C3×C22⋊C4C2×C4semidirect
148. C2×C3×C22⋊C4C2×C4semidirect
174. C3×#95C2×C4semidirect
197. #394C3×C4semidirect
420. C2×C4⋊C4C2×C3×C4semidirect
447. C2×C22⋊C4C2×C3×C4semidirect
448. C2×C22⋊C4C2×C3×C4semidirect
449. C2×C22⋊C4C2×C3×C4semidirect
450. C2×C22⋊C4C2×C3×C4semidirect
476. #95C2×C3×C4semidirect
1167. C3#14173direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#3942
C2×C3×#3882
C2×C3×#3872
C2×C3×C4×C22⋊C42
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14362
C3×C22⋊#952
#141733