Finite Group Databasebeta

← #29679947

Subgroups — #29679947

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448202C212yesmaximal, complemented
2#21445893C212yesmaximal, complemented
3#21445807C214yesmaximal, complemented
4#21445734C212yesmaximal
5C4×#14519692C214yesmaximal, complemented
6C22×C4×D4×C61C211yesmaximal, characteristic
7C2×#14519736—22no—
8C2×#14519692C2218yes—
9#16839625—22no—
10#16839622—22no—
11#16839622C2214yescomplemented
12#16839618C2214yes—
13C4×C22⋊Dic61—22no—
14C4×C22⋊Dic61C2214yescomplemented
15#16839529C2218yescomplemented
16C23×D4×C61C2211yescharacteristic
17C24×C4×C61C411yescharacteristic, complemented
18C24×C4×C61C2211yescharacteristic
19C2×C4×D4×C61—22no—
20C2×C4×D4×C61—22no—
21C2×C4×D4×C61—22no—
22C2×C4×D4×C61—22no—
23C2×C4×D4×C61C412yescomplemented
24C2×C4×D4×C61C412yescomplemented
25C2×C4×D4×C61C2212yes—
26C2×C4×D4×C61C2212yes—
27C22×C4⋊C4×C61C411yescharacteristic, complemented
28C22×C22⋊C4×C61C411yescharacteristic, complemented
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C42×C61C411yescharacteristic, complemented
31#14519736—48no—
32C2×C4⋊Dic61—24no—
33C2×C22⋊Dic61—24no—
34C2×C22⋊Dic61—24no—
35C2×C22⋊Dic61C2318yes—
36C2×C4×Dic61—24no—
37#14519692—216no—
38#14519684—24no—
39#14519684—24no—
40C25×C61C2×C411yescharacteristic
41C25×C61C2311yescharacteristic
42C22×D4×C61—22no—
43C22×D4×C61—22no—
44C22×D4×C61—28no—
45C22×D4×C61C2×C412yes—
46C22×D4×C61C2312yes—
47C23×C4×C61—21no—
48C23×C4×C61—21no—
49C23×C4×C61—21no—
50C23×C4×C61—21no—
51C23×C4×C61—44no—
52C23×C4×C61—44no—
53C23×C4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C23×C4×C61C2×C412yes—
57C23×C4×C61C2×C412yes—
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C23×C4×C61C2×C411yescharacteristic
61C23×C4×C61C2×C411yescharacteristic
62C23×C4×C61D412yes—
63C23×C4×C61D412yes—
64C23×C4×C61D412yes—
65C23×C4×C61D412yes—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C4×D4×C61—24no—
69C4×D4×C61—24no—
70C4×D4×C61—24no—
71C4×D4×C61—24no—
72C4×D4×C61—24no—
73C4×D4×C61—24no—
74C4×D4×C61—24no—
75C4×D4×C61—24no—
76C2×C4⋊C4×C61—22no—
77C2×C4⋊C4×C61—22no—
78C2×C4⋊C4×C61C2×C412yes—
79C2×C4⋊C4×C61C2×C412yes—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—22no—
84C2×C22⋊C4×C61C2×C412yes—
85C2×C22⋊C4×C61C2×C412yes—
86C2×C22⋊C4×C61C2×C412yes—
87C2×C22⋊C4×C61C2312yes—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61C2×C412yes—
93C2×C42×C61C2×C412yes—
94C24×C61—21no—
95C24×C61—21no—
96C24×C61—24no—
97C24×C61—24no—
98C24×C61—42no—
99C24×C61—42no—
100C24×C61—42no—
101C24×C61—42no—
102C24×C61C22×C411yescharacteristic
103C24×C61C22×C411yescharacteristic
104C24×C61C22×C412yes—
105C24×C61C2×D412yes—
106C24×C61C2×D412yes—
107C24×C61C2411yescharacteristic
108C2×D4×C61—216no—
109C2×D4×C61—216no—
110C2×D4×C61—24no—
111C2×D4×C61—24no—
112C2×D4×C61—24no—
113C2×D4×C61—24no—
114C2×D4×C61—24no—
115C2×D4×C61#4118yes—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—24no—
119C22×C4×C61—28no—
120C22×C4×C61—24no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—44no—
132C22×C4×C61—44no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—44no—
137C22×C4×C61—44no—
138C22×C4×C61—44no—
139C22×C4×C61—44no—
140C22×C4×C61—44no—
141C22×C4×C61—44no—
142C22×C4×C61—44no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61C22⋊C411yescharacteristic
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22⋊C412yes—
149C22×C4×C61C22⋊C412yes—
150C22×C4×C61C22⋊C412yes—
151C22×C4×C61C22⋊C412yes—
152C22×C4×C61C22⋊C412yes—
153C22×C4×C61C22⋊C412yes—
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×Dic61—28no—
167C4⋊C4×C61—24no—
168C4⋊C4×C61—24no—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—24no—
171C22⋊C4×C61—24no—
172C22⋊C4×C61—24no—
173C42×C61—22no—
174C42×C61—22no—
175C42×C61—22no—
176C42×C61—22no—
177C22⋊Dic61—216no—
178C22⋊Dic61—48no—
179C22⋊Dic61—48no—
180C4⋊Dic61—48no—
181C4×Dic61—48no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—24no—
186C23×C61—24no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—24no—
191C23×C61—24no—
192C23×C61—24no—
193C23×C61—24no—
194C23×C61—41no—
195C23×C61—42no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—42no—
199C23×C61—41no—
200C23×C61—42no—
201C23×C61—416no—
202C23×C61—416no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61C2×C22⋊C412yes—
209C23×C61C2×C22⋊C411yescharacteristic
210C23×C61C2×C22⋊C411yescharacteristic
211C23×C61#11714yescomplemented
212C23×C61C23×C411yescharacteristic
213C23×C61C22×D412yes—
214C23×C61C2×#4114yes—
215D4×C61—216no—
216D4×C61—216no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—44no—
241C2×C4×C61—44no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—44no—
247C2×C4×C61—44no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61#9914yescomplemented
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C412yes—
254C2×C4×C61C2×C22⋊C412yes—
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61#11714yescomplemented
258C2×Dic61—48no—
259C2×Dic61—48no—
260C2×Dic61—48no—
261#20722—611nomaximal, Sylow
262C22×C61—28no—
263C22×C61—22no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—22no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—24no—
275C22×C61—44no—
276C22×C61—48no—
277C22×C61—48no—
278C22×C61—44no—
279C22×C61—44no—
280C22×C61—44no—
281C22×C61—48no—
282C22×C61—48no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61C2×#9912yes—
286C22×C61#41012yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C2×#11712yes—
289C22×C61#52514yes—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—22no—
293C4×C61—22no—
294C4×C61—24no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61C2×#9912yes—
298C4×C61C2×#9912yes—
299Dic61—88no—
300C22×C4×D4D6111yescharacteristic
301#2280—612no—
302#1819—612no—
303#1799—614no—
304#1781—612no—
305C4×#99—614no—
306C2×C61—24no—
307C2×C61—22no—
308C2×C61—22no—
309C2×C61—22no—
310C2×C61—42no—
311C2×C61—44no—
312C2×C61#228011yescharacteristic
313C2×C61C22×#9911yescharacteristic
314C2×C61C2×#41011yescharacteristic
315C23×D4C2×D6111yescharacteristic
316C24×C4Dic6111yescharacteristic, complemented
317C24×C4C2×D6111yescharacteristic
318C2×C4×D4—22no—
319C2×C4×D4—22no—
320C2×C4×D4—22no—
321C2×C4×D4—22no—
322C2×C4×D4Dic6112yescomplemented
323C2×C4×D4Dic6112yescomplemented
324C2×C4×D4C2×D6112yes—
325C2×C4×D4C2×D6112yes—
326C2×#117—1222no—
327C22×C4⋊C4Dic6111yescharacteristic, complemented
328C22×C22⋊C4Dic6111yescharacteristic, complemented
329C22×C22⋊C4C2×D6111yescharacteristic
330C22×C42Dic6111yescharacteristic, complemented
331C2×#99—618no—
332#381—1222no—
333#380—614no—
334#380—1222no—
335#379—614no—
336C4×C22⋊C4—614no—
337C4×C22⋊C4—1222no—
338#342—618no—
339C61#2072211yescharacteristic, complemented, Sylow
340C25C2×Dic6111yescharacteristic
341C25C22×D6111yescharacteristic
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—28no—
345C22×D4C2×Dic6112yes—
346C22×D4C22×D6112yes—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4C2×Dic6111yescharacteristic
354C23×C4C2×Dic6111yescharacteristic
355C23×C4C2×Dic6111yescharacteristic
356C23×C4C2×Dic6111yescharacteristic
357C23×C4C2×Dic6112yes—
358C23×C4C2×Dic6112yes—
359C23×C4C2×Dic6111yescharacteristic
360C23×C4C2×Dic6111yescharacteristic
361C23×C4C2×Dic6111yescharacteristic
362C23×C4C22⋊D6112yes—
363C23×C4C22⋊D6112yes—
364C23×C4C22⋊D6112yes—
365C23×C4C22⋊D6112yes—
366C23×C4C22×D6111yescharacteristic
367C23×C4C22×D6111yescharacteristic
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376#117—2448no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—1224no—
380C2×C4⋊C4C2×Dic6112yes—
381C2×C4⋊C4C2×Dic6112yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—618no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1224no—
389C2×C22⋊C4C2×Dic6112yes—
390C2×C22⋊C4C2×Dic6112yes—
391C2×C22⋊C4C2×Dic6112yes—
392C2×C22⋊C4C22×D6112yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—1224no—
398C2×C42C2×Dic6112yes—
399C2×C42C2×Dic6112yes—
400#99—12216no—
401#95—1224no—
402#95—1224no—
403C24—24no—
404C24—21no—
405C24—21no—
406C24—24no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24C22×Dic6111yescharacteristic
412C24C22×Dic6111yescharacteristic
413C24C22×Dic6112yes—
414C24C2×C22⋊D6112yes—
415C24C2×C22⋊D6112yes—
416C24C23×D6111yescharacteristic
417C2×D4—216no—
418C2×D4—216no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4#1175822218yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—1228no—
455C22×C4C22⋊Dic6111yescharacteristic
456C22×C4C22⋊Dic6111yescharacteristic
457C22×C4C22⋊Dic6112yes—
458C22×C4C22⋊Dic6112yes—
459C22×C4C22⋊Dic6111yescharacteristic
460C22×C4C22⋊Dic6112yes—
461C22×C4C22⋊Dic6112yes—
462C22×C4C22⋊Dic6112yes—
463C22×C4C22⋊Dic6112yes—
464C22×C4C22⋊Dic6111yescharacteristic
465C22×C4C22×Dic6111yescharacteristic
466C22×C4C22×Dic6111yescharacteristic
467C22×C4C22×Dic6112yes—
468C22×C4C22×Dic6112yes—
469C22×C4C22×Dic6112yes—
470C22×C4C22×Dic6111yescharacteristic
471C22×C4C22×Dic6111yescharacteristic
472C22×C4C2×C22⋊D6112yes—
473C22×C4C2×C22⋊D6112yes—
474C22×C4C2×C22⋊D6112yes—
475C22×C4C2×C22⋊D6112yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—2448no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—12216no—
484C22⋊C4—2448no—
485C22⋊C4—2448no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—2448no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—41no—
504C23—42no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—416no—
513C23—416no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23C2×C22⋊Dic6112yes—
518C23C2×C22⋊Dic6111yescharacteristic
519C23C2×C22⋊Dic6111yescharacteristic
520C23#1451973614yescomplemented
521C23C23×Dic6111yescharacteristic
522C23C22×C22⋊D6112yes—
523C23C2×#1175822214yes—
524D4—216no—
525D4—216no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—2448no—
560C2×C4—2448no—
561C2×C4—2448no—
562C2×C4#1451969214yescomplemented
563C2×C4C2×C22⋊Dic6111yescharacteristic
564C2×C4C2×C22⋊Dic6111yescharacteristic
565C2×C4C2×C22⋊Dic6112yes—
566C2×C4C2×C22⋊Dic6112yes—
567C2×C4C2×C22⋊Dic6111yescharacteristic
568C2×C4C2×C22⋊Dic6111yescharacteristic
569C2×C4#1451973614yescomplemented
570C22—28no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—21no—
577C22—21no—
578C22—22no—
579C22—22no—
580C22—24no—
581C22—22no—
582C22—22no—
583C22—44no—
584C22—48no—
585C22—48no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—48no—
590C22—48no—
591C22—42no—
592C22—42no—
593C22C2×#1451969212yes—
594C22#1683973612yes—
595C22C22×C22⋊Dic6111yescharacteristic
596C22C2×#1451973612yes—
597C22#1684027314yes—
598C4—24no—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—22no—
603C4—42no—
604C4—42no—
605C4—4888no—
606C4C2×#1451969212yes—
607C4C2×#1451969212yes—
608C2—24no—
609C2—22no—
610C2—22no—
611C2—22no—
612C2—42no—
613C2—44no—
614C2#2144820211yescharacteristic
615C2C22×#1451969211yescharacteristic
616C2C2×#1683973611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC22×C4×D4×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D4×C61C22
cosocleC24×C61C24
hypercenterC22×C4×D4D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21448202C2semidirect
2. #21445893C2semidirect
3. #21445807C2semidirect
5. C4×#14519692C2semidirect
11. #16839622C22semidirect
14. C4×C22⋊Dic61C22semidirect
15. #16839529C22semidirect
17. C24×C4×C61C4semidirect
23. C2×C4×D4×C61C4semidirect
24. C2×C4×D4×C61C4semidirect
27. C22×C4⋊C4×C61C4semidirect
28. C22×C22⋊C4×C61C4semidirect
30. C22×C42×C61C4semidirect
211. C23×C61#117semidirect
250. C2×C4×C61#99semidirect
257. C2×C4×C61#117semidirect
316. C24×C4Dic61semidirect
322. C2×C4×D4Dic61semidirect
323. C2×C4×D4Dic61semidirect
327. C22×C4⋊C4Dic61semidirect
328. C22×C22⋊C4Dic61semidirect
330. C22×C42Dic61semidirect
339. C61#20722semidirect
520. C23#14519736semidirect
562. C2×C4#14519692semidirect
569. C2×C4#14519736semidirect

Maximal subgroups

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

subgroupindex
#214482022
#214458932
#214458072
#214457342
C4×#145196922
C22×C4×D4×C612
#2072261