Finite Group Databasebeta

← #29601816

Subgroups — #29601816

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519742C211yesmaximal, characteristic, complemented
2C2×#16839675C211yesmaximal, characteristic
3C2×#16839609C212yesmaximal
4C2×#16839609C211yesmaximal, characteristic
5#21444089C211yesmaximal, characteristic, complemented
6#21444077C212yesmaximal, complemented
7#21444063C212yesmaximal
8#21444061C211yesmaximal, characteristic
9#95×Dic61C212yesmaximal, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×#1442C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×#14519742—24no—
15C2×#14519742—28no—
16C22×#11758196C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2212yes—
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25#16839675C418yescomplemented
26#16839609—28no—
27#16839609—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—24no—
44C22×Dic122—24no—
45C22×Dic122C2×C414yescomplemented
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C22×C4×D61—24no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61Q814yescomplemented
56#14519742—232no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758198—24no—
61C2×#11758198—22no—
62C2×#11758198—24no—
63C2×#11758198—22no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198—22no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198C2×C414yes—
71C2×#11758198C2×C418yes—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61—24no—
80C2×C4×Dic61D414yes—
81C2×C4×Dic61D418yes—
82#14519684—22no—
83#14519684—22no—
84#14519684—24no—
85#14519684—24no—
86#14519684—24no—
87#14519684—24no—
88#14519684C2×C418yescomplemented
89C23×C4×C61C2312yes—
90C23×C4×C61C2312yes—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61—24no—
95C2×C4⋊C4×C61—22no—
96#95×C61—24no—
97#95×C61—22no—
98#95×C61—24no—
99#95×C61C2×C414yescomplemented
100C24×C61C2411yescharacteristic
101C23×D61—22no—
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—21no—
107C23×D61—22no—
108C23×D61—21no—
109C23×D61C22×C412yes—
110C23×D61C2×Q812yes—
111C23×D61#4112yes—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61C22×C414yes—
135C22×C4×C61C22×C412yes—
136C22×C4×C61C2×D414yes—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×Q812yes—
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—21no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C414yes—
161C22×Dic61C2×D412yes—
162C22×Dic61C2×D414yes—
163C22×Dic61C2×D414yes—
164C22×Dic61C2×D412yes—
165C22×Dic61C2×Q812yes—
166C22×Dic61#4114yes—
167C22×Dic61#4114yes—
168C22×Dic61#4112yes—
169C22×Dic61#4114yes—
170C2×C4×D61—28no—
171C2×C4×D61—216no—
172C2×C4×D61—44no—
173C2×C4×D61—44no—
174C2×C4×D61—48no—
175C2×Dic122—216no—
176C2×Dic122—28no—
177C2×Dic122—28no—
178C2×Dic122—28no—
179C2×Dic122—216no—
180C4⋊C4×C61—28no—
181#11758198—28no—
182#11758198—216no—
183#11758198—28no—
184#11758198—216no—
185#11758196—216no—
186C4×Dic61—216no—
187C4×Dic61—28no—
188C4×Dic61—48no—
189C4×Dic61—44no—
190C23×C61C23×C411yescharacteristic
191C23×C61C22×D412yes—
192C23×C61C22×D411yescharacteristic
193C23×C61C22×Q811yescharacteristic
194C23×C61C2×#4112yes—
195C23×C61C2×#4111yescharacteristic
196C23×C61C2×#4111yescharacteristic
197C23×C61C2×#4111yescharacteristic
198C23×C61C2×#4112yes—
199C23×C61C2×#4112yes—
200C23×C61C2×#4111yescharacteristic
201C22×D61—24no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—24no—
205C22×D61—22no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61—22no—
209C22×D61—24no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—24no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—42no—
216C22×D61—41no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—41no—
223C22×D61C4×Q814yescomplemented
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—42no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61C4×D414yes—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—22no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—41no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—41no—
276C2×Dic61C4×D418yes—
277C2×Dic61#12014yes—
278C2×Dic61C22⋊Q814yes—
279C2×Dic61C22⋊Q818yes—
280C2×Dic61#12414yes—
281C2×Dic61#12418yes—
282C4×D61—416no—
283Dic122—232no—
284C4×#393—611nomaximal, Sylow
285C22×C61C2×C4×D412yes—
286C22×C61C2×C4×D411yescharacteristic
287C22×C61C2×C4×Q811yescharacteristic
288C22×C61C4×#4111yescharacteristic
289C22×C61C4×#4112yes—
290C22×C61C2×#12011yescharacteristic
291C22×C61C2×C22⋊Q811yescharacteristic
292C22×C61C2×C22⋊Q812yes—
293C22×C61#52512yes—
294C22×C61#52511yescharacteristic
295C22×C61#52511yescharacteristic
296C22×C61#52512yes—
297C22×C61C2×#12411yescharacteristic
298C22×C61C2×#12412yes—
299C22×C61#52912yes—
300C22×C61#52912yes—
301C22×C61#52912yes—
302C22×C61#52912yes—
303C22×C61#52911yescharacteristic
304C22×C61#53212yes—
305C22×C61#53211yescharacteristic
306C22×C61#53311yescharacteristic
307C22×C61#53312yes—
308C2×D61—24no—
309C2×D61—28no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—44no—
314C2×D61—42no—
315C2×D61—44no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—44no—
319C4×C61—24no—
320C4×C61—42no—
321C4×C61—44no—
322C4×C61—42no—
323C4×C61—44no—
324Dic61—28no—
325Dic61—42no—
326Dic61—44no—
327Dic61—42no—
328Dic61#39318yescomplemented
329C22×C4×Q8—611no—
330C2×#393—611no—
331C2×C4×C22⋊C4—611no—
332C2×C4×C22⋊C4—612no—
333#1446—611no—
334#1442—612no—
335#1442D6111yescharacteristic, complemented
336#1439—612no—
337#1439—611no—
338C4×#95—612no—
339C4×#95—611no—
340C2×C61C4×#12011yescharacteristic
341C2×C61C4×C22⋊Q811yescharacteristic
342C2×C61C4×C22⋊Q812yes—
343C2×C61C4×#12411yescharacteristic
344C2×C61C4×#12412yes—
345C2×C61C2×#39311yescharacteristic
346C2×C61#238811yescharacteristic
347C2×C61#239611yescharacteristic
348C2×C61#239612yes—
349C2×C61#239811yescharacteristic
350C2×C61#239812yes—
351D61—44no—
352C23×Q8—611no—
353C24×C4—611no—
354C2×C4×Q8—1224no—
355C2×C4×Q8—1228no—
356C22×C4⋊C4—612no—
357C22×C4⋊C4C2×D6111yescharacteristic
358C22×C22⋊C4—612no—
359C22×C22⋊C4—611no—
360C22×C22⋊C4—611no—
361C22×C22⋊C4—612no—
362C22×C42—612no—
363C22×C42—611no—
364C22×C42—612no—
365C22×C42—611no—
366#393—618no—
367C4×C22⋊C4—1228no—
368C4×C22⋊C4—1224no—
369C2×#95—612no—
370C2×#95—612no—
371C2×#95—612no—
372C2×#95—612no—
373C2×#95—611no—
374C2×#95—611no—
375C2×#95—612no—
376C2×#95C2×D6112yes—
377C2×#95C2×D6112yes—
378C2×#95C2×D6111yescharacteristic
379C2×#95C2×D6111yescharacteristic
380C61C4×#39311yescharacteristic, complemented, Sylow
381C25—611no—
382C22×Q8—614no—
383C22×Q8—1224no—
384C22×Q8—1224no—
385C22×Q8—1222no—
386C22×Q8—1222no—
387C23×C4—611no—
388C23×C4—612no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—612no—
392C23×C4—614no—
393C23×C4—1222no—
394C23×C4—1224no—
395C23×C4—1224no—
396C23×C4—1222no—
397C23×C4C22×D6112yes—
398C23×C4C22×D6112yes—
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C23×C4C22×D6111yescharacteristic
402C4×Q8—12232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—1224no—
406C2×C4⋊C4—1224no—
407C2×C4⋊C4—1224no—
408C2×C22⋊C4—618no—
409C2×C22⋊C4—614no—
410C2×C22⋊C4—1224no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1224no—
414C2×C22⋊C4—1224no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4—1224no—
417C2×C22⋊C4—1222no—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1222no—
420C2×C42—618no—
421C2×C42—614no—
422C2×C42—1224no—
423C2×C42—1224no—
424C2×C42—1224no—
425C2×C42—1224no—
426C2×C42—1222no—
427C2×C42—1224no—
428C2×C42—1224no—
429C2×C42—1224no—
430#95—24no—
431#95—22no—
432#95—24no—
433#95—618no—
434#95—1224no—
435#95—1222no—
436#95—1224no—
437#95—1224no—
438#95—1224no—
439#95—1222no—
440#95C4×D6114yescomplemented
441C24—612no—
442C24—612no—
443C24—612no—
444C24—1222no—
445C24—1221no—
446C24—1222no—
447C24—1222no—
448C24—1221no—
449C24—1222no—
450C24—1221no—
451C24—1221no—
452C24C23×D6111yescharacteristic
453C2×Q8—12216no—
454C2×Q8—1228no—
455C2×Q8—1228no—
456C2×Q8—12216no—
457C2×Q8—1228no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—614no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—614no—
485C22×C4—614no—
486C22×C4—614no—
487C22×C4—614no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—614no—
491C22×C4—1228no—
492C22×C4—12216no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1221no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—2444no—
512C22×C4—2444no—
513C22×C4—2448no—
514C22×C4C2×C4×D6114yes—
515C22×C4C2×C4×D6112yes—
516C22×C4D4×D6114yes—
517C22×C4D4×D6112yes—
518C22×C4#1175822412yes—
519C22×C4Q8×D6112yes—
520C22×C4#1175822612yes—
521C4⋊C4—28no—
522C4⋊C4—12216no—
523C22⋊C4—12216no—
524C22⋊C4—12216no—
525C22⋊C4—1228no—
526C22⋊C4—1228no—
527C42—1228no—
528C42—12216no—
529C42—2444no—
530C42—2448no—
531C23—614no—
532C23—1224no—
533C23—1222no—
534C23—1222no—
535C23—1224no—
536C23—1222no—
537C23—1224no—
538C23—1224no—
539C23—1222no—
540C23—1224no—
541C23—1222no—
542C23—1222no—
543C23—1224no—
544C23—2441no—
545C23—2441no—
546C23—2442no—
547C23—2441no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23—2441no—
554C23C22×C4×D6111yescharacteristic
555C23C2×D4×D6112yes—
556C23C2×D4×D6111yescharacteristic
557C23C2×Q8×D6111yescharacteristic
558C23#41×D6112yes—
559C23#41×D6111yescharacteristic
560C23#41×D6111yescharacteristic
561C23#41×D6112yes—
562C23#41×D6112yes—
563C23C2×#1175822411yescharacteristic
564C23C2×#1175822611yescharacteristic
565Q8—12232no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—614no—
595C2×C4—614no—
596C2×C4—618no—
597C2×C4—614no—
598C2×C4—618no—
599C2×C4—618no—
600C2×C4—1224no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1222no—
607C2×C4—1224no—
608C2×C4—1222no—
609C2×C4—1224no—
610C2×C4—1222no—
611C2×C4—1224no—
612C2×C4—1224no—
613C2×C4—1222no—
614C2×C4—24416no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2441no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2441no—
624C2×C4#1451973914yes—
625C22—1224no—
626C22—1228no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22—2442no—
631C22—2444no—
632C22—2442no—
633C22—2444no—
634C22—2442no—
635C22—2444no—
636C22C4×D4×D6112yes—
637C22C2×#1451973911yescharacteristic
638C22C4×Q8×D6111yescharacteristic
639C22C4×#1175822411yescharacteristic
640C22#1684023012yes—
641C22#120×D6111yescharacteristic
642C22C22⋊Q8×D6111yescharacteristic
643C22C22⋊Q8×D6112yes—
644C22#1684027012yes—
645C22#1684027011yescharacteristic
646C22#1684027211yescharacteristic
647C22#1684027512yes—
648C22#124×D6111yescharacteristic
649C22#124×D6112yes—
650C22#1684028912yes—
651C22#1684029512yes—
652C22#1684029512yes—
653C22#1684029712yes—
654C22#1684029711yescharacteristic
655C22#1684030712yes—
656C22#1684031111yescharacteristic
657C22#1684031711yescharacteristic
658C22#1684031812yes—
659C4—24no—
660C4—42no—
661C4—44no—
662C4—42no—
663C4—44no—
664C4—618no—
665C4—1228no—
666C4—2442no—
667C4—2444no—
668C4—2442no—
669C2—2444no—
670C2#2144832011yescharacteristic
671C2#2144834911yescharacteristic
672C2#2144835312yes—
673C2#2144835811yescharacteristic
674C2#2144836012yes—
675C2#393×D6111yescharacteristic
676C2#2144903311yescharacteristic
677C2#2144909211yescharacteristic
678C2#2144909612yes—
679C2#2144910411yescharacteristic
680C2#2144910812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1442D61
hypocenterC61C4×#393
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C22×#14519742C2semidirect
5. #21444089C2semidirect
6. #21444077C2semidirect
9. #95×Dic61C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1442C2semidirect
25. #16839675C4semidirect
45. C22×Dic122C2×C4semidirect
55. C22×C4×D61Q8semidirect
88. #14519684C2×C4semidirect
99. #95×C61C2×C4semidirect
223. C22×D61C4×Q8semidirect
328. Dic61#393semidirect
335. #1442D61semidirect
380. C61C4×#393semidirect
440. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197422
C2×#168396752
C2×#168396092
#214440892
#214440772
#214440632
#214440612
#95×Dic612
C61×#14422
C4×#39361