Finite Group Databasebeta

← #29646104

Subgroups — #29646104

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519756C211yesmaximal, characteristic
2C2×#16839726C211yesmaximal, characteristic
3#21444184C214yesmaximal, complemented
4#21444182C214yesmaximal, complemented
5#21444148C214yesmaximal, complemented
6C2×C61×#407C211yesmaximal, characteristic
7C23×Dic122C411yescharacteristic
8C22×#11758194—21no—
9C2×#14519756—21no—
10C2×#14519756—21no—
11C2×#14519756—21no—
12C2×#14519756—21no—
13C2×#14519756—21no—
14C2×#14519756—21no—
15C2×#14519756—21no—
16C2×#14519756—21no—
17C2×#14519756C412yes—
18C2×#14519756C412yes—
19C2×#14519756C2212yes—
20C2×#14519756C2212yes—
21C22×C4⋊Dic61C411yescharacteristic
22C22×#11758196C2212yes—
23C22×C22⋊Dic61C412yes—
24#16839726—21no—
25#16839726—21no—
26#16839726C2212yes—
27#16839726C2212yes—
28C2×C22⋊#92418—21no—
29C2×C22⋊#92418C2212yes—
30#16839487C22116yescomplemented
31C24×C4×C61C2211yescharacteristic
32C22×M16×C61—21no—
33C61×#407—21no—
34C61×#407—21no—
35C61×#407C2212yes—
36C61×#407C2212yes—
37C2×C22⋊C8×C61—21no—
38C2×C22⋊C8×C61C2212yes—
39C22×Dic122—21no—
40C22×Dic122—21no—
41C22×Dic122—21no—
42C22×Dic122—21no—
43C22×Dic122—44no—
44C22×Dic122C2×C412yes—
45C22×Dic122C2×C412yes—
46C23×Dic61C2×C412yes—
47C23×Dic61C2×C412yes—
48C2×#11758194—22no—
49C2×#11758194—22no—
50C2×#11758194—44no—
51C22×#92418—22no—
52#14519756—22no—
53#14519756—22no—
54#14519756—22no—
55#14519756—22no—
56#14519756—22no—
57#14519756—22no—
58#14519756—22no—
59#14519756—22no—
60#14519756—22no—
61#14519756—22no—
62#14519756—22no—
63#14519756—22no—
64#14519756—22no—
65#14519756—22no—
66#14519756—22no—
67#14519756—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2×C412yes—
73C2×C4⋊Dic61C2×C412yes—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196C2×C414yes—
79C2×#11758196C2314yes—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61C2×C414yes—
85C2×C22⋊Dic61C2×C414yes—
86C22⋊#92418—22no—
87C22⋊#92418—22no—
88C22⋊#92418—22no—
89C22⋊#92418C2314yes—
90C25×C61C2×C411yescharacteristic
91C23×C4×C61—44no—
92C23×C4×C61C2×C411yescharacteristic
93C23×C4×C61C2×C411yescharacteristic
94C23×C4×C61C2×C411yescharacteristic
95C23×C4×C61D411yescharacteristic
96C23×C4×C61D411yescharacteristic
97C23×C4×C61D411yescharacteristic
98C23×C4×C61D411yescharacteristic
99C23×C4×C61D411yescharacteristic
100C23×C4×C61D411yescharacteristic
101C23×C4×C61D411yescharacteristic
102C23×C4×C61D411yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C2×M16×C61—22no—
107C2×M16×C61—22no—
108C2×M16×C61—44no—
109C22×C8×C61—22no—
110C22⋊C8×C61—22no—
111C22⋊C8×C61—22no—
112C22⋊C8×C61—22no—
113C22⋊C8×C61C2314yes—
114C24×C61—24no—
115C24×C61—42no—
116C24×C61—42no—
117C24×C61C22⋊C411yescharacteristic
118C24×C61C22⋊C411yescharacteristic
119C24×C61C22⋊C411yescharacteristic
120C24×C61C22⋊C411yescharacteristic
121C24×C61C22×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C24×C61C22×C411yescharacteristic
124C22×C4×C61—24no—
125C22×C4×C61—24no—
126C22×C4×C61—24no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—42no—
137C22×C4×C61—42no—
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C22⋊C411yescharacteristic
145C22×C4×C61C22⋊C411yescharacteristic
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22⋊C411yescharacteristic
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—44no—
171C22×Dic61—44no—
172C22×Dic61C22×C414yes—
173C22×Dic61C22×C414yes—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—44no—
179C2×Dic122—44no—
180C2×Dic122—44no—
181C2×Dic122—44no—
182C2×Dic122—44no—
183C2×Dic122—44no—
184M16×C61—44no—
185M16×C61—44no—
186C2×C8×C61—24no—
187C2×C8×C61—44no—
188C22⋊Dic61—24no—
189C22⋊Dic61—24no—
190C22⋊Dic61—24no—
191C22⋊Dic61—24no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196#11758196—24no—
197#11758196—24no—
198#11758196—24no—
199#11758196—24no—
200#11758194—44no—
201#11758194—44no—
202C2×#92418—24no—
203C2×#92418—44no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—416no—
225C23×C61#10114yes—
226C23×C61C2×C22⋊C411yescharacteristic
227C23×C61C2×C22⋊C411yescharacteristic
228C23×C61C2×C22⋊C411yescharacteristic
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C23×C411yescharacteristic
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61#9914yes—
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—28no—
272C2×Dic61—44no—
273C2×Dic61—44no—
274C2×Dic61—44no—
275C2×Dic61—44no—
276C2×Dic61—44no—
277Dic122—44no—
278Dic122—44no—
279Dic122—44no—
280Dic122—44no—
281C8×C61—44no—
282#92418—44no—
283#17397—611nomaximal, Sylow
284C22×C61—28no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—44no—
302C22×C61—44no—
303C22×C61—44no—
304C22×C61—44no—
305C22×C61—44no—
306C22×C61—44no—
307C22×C61C2×#9912yes—
308C22×C61C2×#10112yes—
309C22×C61C2×#10112yes—
310C22×C61C2×#10112yes—
311C22×C61C22×C22⋊C411yescharacteristic
312C22×C61#56812yes—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61C2×#9912yes—
320C4×C61C2×#9912yes—
321Dic61—44no—
322Dic61—44no—
323C22×C22⋊Q8—611no—
324C2×#407—611no—
325C2×#407D6111yescharacteristic
326#1472—614no—
327#1472—614no—
328#1463—614no—
329C2×C61—22no—
330C2×C61—22no—
331C2×C61—22no—
332C2×C61—22no—
333C2×C61—22no—
334C2×C61—41no—
335C2×C61—41no—
336C2×C61#287911yescharacteristic
337C2×C61C22×#9911yescharacteristic
338C2×C61C22×#10111yescharacteristic
339C23×Q8—611no—
340C24×C4C2×D6111yescharacteristic
341C22×M16—21no—
342C22×M16—1221no—
343C2×C22⋊Q8—612no—
344C2×C22⋊Q8—612no—
345C2×C22⋊Q8—612no—
346C2×C22⋊Q8—612no—
347C2×C22⋊Q8—1221no—
348C2×C22⋊Q8—1221no—
349C2×C22⋊Q8—1221no—
350C2×C22⋊Q8—1221no—
351C2×C22⋊Q8—1221no—
352C2×C22⋊Q8—1221no—
353C2×C22⋊Q8—1221no—
354C2×C22⋊Q8—1221no—
355C22×C4⋊C4—611no—
356C22×C4⋊C4—612no—
357C22×C22⋊C4—612no—
358#407—21no—
359#407—21no—
360#407—612no—
361#407—612no—
362#407—1221no—
363#407—1221no—
364#407C2×D6112yes—
365#407C2×D6112yes—
366C2×C22⋊C8—21no—
367C2×C22⋊C8—612no—
368C2×C22⋊C8—1221no—
369C2×C22⋊C8C2×D6112yes—
370#324—6116no—
371C61#1739711yescharacteristic, complemented, Sylow
372C25C4×D6111yescharacteristic
373C22×Q8—612no—
374C22×Q8—612no—
375C22×Q8—1221no—
376C22×Q8—1221no—
377C22×Q8—1221no—
378C22×Q8—1221no—
379C22×Q8—2444no—
380C23×C4—44no—
381C23×C4—612no—
382C23×C4—612no—
383C23×C4C4×D6111yescharacteristic
384C23×C4C4×D6111yescharacteristic
385C23×C4C4×D6111yescharacteristic
386C23×C4D24411yescharacteristic
387C23×C4D24411yescharacteristic
388C23×C4D24411yescharacteristic
389C23×C4D24411yescharacteristic
390C23×C4C22⋊D6111yescharacteristic
391C23×C4C22⋊D6111yescharacteristic
392C23×C4C22⋊D6111yescharacteristic
393C23×C4C22⋊D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C23×C4C22×D6111yescharacteristic
396C23×C4C22×D6111yescharacteristic
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—44no—
400C2×M16—1222no—
401C2×M16—1222no—
402C2×M16—2444no—
403C22×C8—22no—
404C22×C8—1222no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—1222no—
408C22⋊Q8—1222no—
409C22⋊Q8—1222no—
410C22⋊Q8—1222no—
411C22⋊Q8—1222no—
412C22⋊Q8—1222no—
413C22⋊Q8—1222no—
414C22⋊Q8—1222no—
415C22⋊Q8—1222no—
416C22⋊Q8—1222no—
417C22⋊Q8—1222no—
418C22⋊Q8—1222no—
419C22⋊Q8—1222no—
420C22⋊Q8—1222no—
421C2×C4⋊C4—614no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4—614no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1222no—
430C2×C4⋊C4—1222no—
431C2×C4⋊C4—1222no—
432C2×C4⋊C4—1222no—
433C2×C22⋊C4—614no—
434C2×C22⋊C4—614no—
435C2×C22⋊C4—1222no—
436C2×C22⋊C4—1222no—
437C2×C22⋊C4—1222no—
438C2×C22⋊C4—1222no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441C22⋊C8—22no—
442C22⋊C8—614no—
443C22⋊C8—1222no—
444C22⋊C8—1222no—
445C22⋊C8—1222no—
446C22⋊C8C22×D6114yes—
447C24—24no—
448C24—42no—
449C24—42no—
450C24#1175819811yescharacteristic
451C24#1175819811yescharacteristic
452C24#1175819811yescharacteristic
453C24#1175819811yescharacteristic
454C24C2×C4×D6111yescharacteristic
455C24C2×C4×D6111yescharacteristic
456C24C2×C4×D6111yescharacteristic
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×Q8—1222no—
461C2×Q8—2444no—
462C2×Q8—2444no—
463C2×Q8—2444no—
464C2×Q8—2444no—
465C2×Q8—2444no—
466C2×Q8—2444no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—614no—
482C22×C4—614no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—2444no—
488C22×C4—2444no—
489C22×C4#1175819811yescharacteristic
490C22×C4#1175819811yescharacteristic
491C22×C4#1175819811yescharacteristic
492C22×C4#1175819811yescharacteristic
493C22×C4#1175819811yescharacteristic
494C22×C4#1175819811yescharacteristic
495C22×C4#1175819811yescharacteristic
496C22×C4#1175819811yescharacteristic
497C22×C4#1175819811yescharacteristic
498C22×C4#1175819811yescharacteristic
499C22×C4#1175819811yescharacteristic
500C22×C4#1175819811yescharacteristic
501C22×C4C2×C4×D6111yescharacteristic
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×D24411yescharacteristic
505C22×C4C2×D24411yescharacteristic
506C22×C4C2×D24411yescharacteristic
507C22×C4C2×D24411yescharacteristic
508C22×C4C2×D24411yescharacteristic
509C22×C4C2×D24411yescharacteristic
510C22×C4C2×C22⋊D6111yescharacteristic
511C22×C4C2×C22⋊D6111yescharacteristic
512C22×C4C2×C22⋊D6111yescharacteristic
513C22×C4C2×C22⋊D6111yescharacteristic
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C23×D6111yescharacteristic
517M16—44no—
518M16—44no—
519M16—2444no—
520M16—2444no—
521C2×C8—24no—
522C2×C8—44no—
523C2×C8—1224no—
524C2×C8—2444no—
525C4⋊C4—1224no—
526C4⋊C4—1224no—
527C4⋊C4—1224no—
528C4⋊C4—1224no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C22⋊C4—1224no—
534C22⋊C4—1224no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—416no—
558C23#1451969514yes—
559C23C2×#1175819811yescharacteristic
560C23C2×#1175819811yescharacteristic
561C23C2×#1175819811yescharacteristic
562C23C2×#1175819811yescharacteristic
563C23C2×#1175819811yescharacteristic
564C23C2×#1175819811yescharacteristic
565C23C22×C4×D6111yescharacteristic
566Q8—2444no—
567Q8—2444no—
568Q8—2444no—
569Q8—2444no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1228no—
600C2×C4—2444no—
601C2×C4—2444no—
602C2×C4—2444no—
603C2×C4—2444no—
604C2×C4—2444no—
605C2×C4#1451969114yes—
606C2×C4C2×#1175819811yescharacteristic
607C2×C4C2×#1175819811yescharacteristic
608C2×C4C2×#1175819811yescharacteristic
609C2×C4C2×#1175819811yescharacteristic
610C2×C4C2×#1175819811yescharacteristic
611C2×C4C2×#1175819811yescharacteristic
612C2×C4C22×C22⋊D6111yescharacteristic
613C2×C4C22×D24411yescharacteristic
614C8—44no—
615C8—2444no—
616C22—28no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—44no—
634C22—44no—
635C22—44no—
636C22—44no—
637C22—44no—
638C22—44no—
639C22C2×#1451969112yes—
640C22C2×#1451969512yes—
641C22C2×#1451969512yes—
642C22C2×#1451969512yes—
643C22C22×#1175819811yescharacteristic
644C22#1684052812yes—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—2444no—
652C4—2444no—
653C4C2×#1451969112yes—
654C4C2×#1451969112yes—
655C2—22no—
656C2—22no—
657C2—22no—
658C2—22no—
659C2—22no—
660C2—41no—
661C2—41no—
662C2#2145426311yescharacteristic
663C2C22×#1451969111yescharacteristic
664C2C22×#1451969511yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC22×C61C22×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#407D61
hypocenterC61#17397
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #21444184C2semidirect
4. #21444182C2semidirect
5. #21444148C2semidirect
30. #16839487C22semidirect
371. C61#17397semidirect

Maximal subgroups

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

subgroupindex
C22×#145197562
C2×#168397262
#214441842
#214441822
#214441482
C2×C61×#4072
#1739761