Finite Group Databasebeta

← #29679727

Subgroups — #29679727

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2C2×#16839727C212yesmaximal
3#21445889C212yesmaximal, complemented
4#21445888C212yesmaximal, complemented
5#21445887C211yesmaximal, characteristic, complemented
6#21445886C211yesmaximal, characteristic, complemented
7#21445886C211yesmaximal, characteristic, complemented
8#21445514C212yesmaximal, complemented
9#21445511C211yesmaximal, characteristic, complemented
10#336×D61C211yesmaximal, characteristic, complemented
11C61×#1817C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C22×#11758189C2212yes—
14C22×C8×D61C2212yes—
15C4×#11758222—28no—
16C2×C4×Dic122C411yescharacteristic
17C2×C4×Dic122C411yescharacteristic
18C2×C4×D244C411yescharacteristic
19C2×C4×D244C411yescharacteristic
20C2×C4×C22⋊D61C411yescharacteristic
21C2×C4×C22⋊D61C411yescharacteristic
22C2×C4×C22⋊D61C411yescharacteristic
23C2×C4×C22⋊D61C411yescharacteristic
24C2×#14519736C2211yescharacteristic
25C2×#14519734C2211yescharacteristic
26C2×#14519734C2211yescharacteristic
27C2×C42×D61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839727—28no—
30C2×C22⋊#92418C2212yes—
31C2×#14519689C2212yes—
32C2×#14519689C2212yes—
33#16839517C2212yes—
34#16839517C2211yescharacteristic
35#16839517C2211yescharacteristic
36#16839516C2212yes—
37#16839516C2212yes—
38#16839516C2212yes—
39#16839516C2212yes—
40C22×C42×C61C2211yescharacteristic
41C2×C22⋊C8×C61C2212yes—
42C61×#336C2212yes—
43C61×#336C2211yescharacteristic
44C61×#336C2211yescharacteristic
45C2×#11758222—22no—
46C2×#11758222—24no—
47C2×#11758222—22no—
48C2×#11758222D418yes—
49C22×Dic122C2×C411yescharacteristic
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2311yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758189—24no—
60C2×#11758189—24no—
61C2×#11758189—24no—
62C22×#92418C2312yes—
63C22×#92418C2312yes—
64C2×C8×D61—24no—
65C2×C8×D61—24no—
66C2×C8×D61—24no—
67C4×Dic122—24no—
68C4×Dic122—24no—
69C4×D244—24no—
70C4×D244—24no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—24no—
73C4×C22⋊D61—24no—
74C4×C22⋊D61—24no—
75#14519736—24no—
76#14519734—24no—
77#14519734—24no—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C42×D61—24no—
97C42×D61—24no—
98C22⋊#92418—24no—
99#14519689—24no—
100#14519689—24no—
101C23×C4×C61C2×C411yescharacteristic
102C23×C4×C61C2×C411yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C22×C8×C61C2312yes—
105C22×C8×C61C2312yes—
106C2×C42×C61—24no—
107C2×C42×C61C2×C411yescharacteristic
108C2×C42×C61C2×C411yescharacteristic
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C22⋊C8×C61—24no—
112C24×C61C22×C411yescharacteristic
113C23×D61C22×C411yescharacteristic
114C23×D61C22×C411yescharacteristic
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C2×D414yes—
130C22×C4×C61C2411yescharacteristic
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61C22⋊C414yes—
136C2×C22⋊D61C22⋊C414yes—
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143#11758222—216no—
144#11758222—216no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244C22⋊C414yes—
148C2×C4×D61—22no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×C4×D61—41no—
163C2×C4×D61C2×D414yes—
164C2×C4×D61C2×D414yes—
165C2×C4×D61#4112yes—
166C2×C4×D61#4114yes—
167C2×C4×D61#4112yes—
168C2×Dic122—22no—
169C2×Dic122—22no—
170C2×Dic122C22⋊C414yes—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61—22no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198—22no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193C4×Dic61—22no—
194C4×Dic61—22no—
195C4×Dic61—22no—
196C4×Dic61—22no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205#11758189—48no—
206C8×D61—48no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61C2×C22⋊C412yes—
214C23×C61C23×C411yescharacteristic
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61C2×C22⋊C412yes—
226C22×D61C2×C22⋊C412yes—
227C22×D61#11712yes—
228C22×D61#11712yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—44no—
244C2×C4×C61—44no—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61#13112yes—
247C2×C4×C61#13112yes—
248C2×C4×C61C22×D412yes—
249C2×C4×C61C2×#4112yes—
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C22⋊D61—28no—
253C22⋊D61—28no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61C2×C22⋊C412yes—
269C2×Dic61C2×C22⋊C412yes—
270C2×Dic61#11712yes—
271C2×Dic61#11712yes—
272D244—28no—
273C4×D61—24no—
274C4×D61—24no—
275C4×D61—44no—
276C4×D61—44no—
277C4×D61—44no—
278C4×D61—44no—
279C4×D61#12318yes—
280C4×D61#12318yes—
281Dic122—28no—
282C8×C61—42no—
283C8×C61—42no—
284#92418—42no—
285#92418—42no—
286#20684—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61C22×C22⋊C411yescharacteristic
295C22×C61C2×#11711yescharacteristic
296C22×C61C2×#11711yescharacteristic
297C22×C61C2×#13111yescharacteristic
298C22×C61C2×#13111yescharacteristic
299C22×C61#56811yescharacteristic
300C22×C61#56811yescharacteristic
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—22no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61#38114yes—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61C2×#12312yes—
321C4×C61C2×#12312yes—
322Dic61—22no—
323Dic61—41no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61#38114yes—
328C2×C4×#41—611no—
329C2×#408—612no—
330#1818—612no—
331#1818—612no—
332#1817—611no—
333#1817—611no—
334#1817—611no—
335#1817D6111yescharacteristic, complemented
336#1729—612no—
337#1728—611no—
338C2×#336—611no—
339C2×C61—42no—
340C2×C61C2×#38111yescharacteristic
341C2×C61#288011yescharacteristic
342C2×C61#288011yescharacteristic
343C2×C61#292211yescharacteristic
344C2×C61#292311yescharacteristic
345C2×C61#292511yescharacteristic
346C2×C61#292511yescharacteristic
347D61—24no—
348D61—42no—
349C22×#41—611no—
350C22×M16—612no—
351C23×C8—612no—
352C4×#41—1228no—
353C2×C4×Q8—611no—
354C2×C4×Q8—611no—
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×C4×D4—611no—
359C2×C4×D4—611no—
360C2×C4×D4—611no—
361C2×#117—611no—
362C2×#117—611no—
363C2×#117—611no—
364C22×C42—611no—
365C22×C42—611no—
366C22×C42C2×D6111yescharacteristic
367#408—1228no—
368C2×C22⋊C8—612no—
369C2×C22⋊C8—612no—
370C2×C22⋊C8—612no—
371C2×C22⋊C8C2×D6112yes—
372#336—612no—
373#336—612no—
374#336—612no—
375#336—612no—
376#336—611no—
377#336—611no—
378#336—612no—
379#336C2×D6111yescharacteristic
380#336C2×D6111yescharacteristic
381#336C2×D6112yes—
382C61#2068411yescharacteristic, complemented, Sylow
383C2×#41—618no—
384C2×#41—1222no—
385C2×#41—1224no—
386C2×#41—1222no—
387C22×Q8—611no—
388C22×D4—611no—
389C22×D4—611no—
390C22×D4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4C4×D6111yescharacteristic
398C23×C4C4×D6111yescharacteristic
399C23×C4C22×D6111yescharacteristic
400C2×M16—1224no—
401C2×M16—1224no—
402C2×M16—1224no—
403C22×C8—612no—
404C22×C8—612no—
405C22×C8—1224no—
406C22×C8—1224no—
407C22×C8—1224no—
408C22×C8C22×D6112yes—
409C22×C8C22×D6112yes—
410C4×Q8—1224no—
411C4×Q8—1224no—
412C4×D4—1224no—
413C4×D4—1224no—
414C4×D4—1224no—
415C4×D4—1224no—
416C4×D4—1224no—
417C4×D4—1224no—
418#117—1224no—
419#117—1224no—
420#117—1224no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C42—24no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—1224no—
441C2×C42—1224no—
442C2×C42C4×D6111yescharacteristic
443C2×C42C4×D6111yescharacteristic
444C2×C42C22×D6111yescharacteristic
445C2×C42C22×D6111yescharacteristic
446C22⋊C8—24no—
447C22⋊C8—1224no—
448C22⋊C8—1224no—
449C22⋊C8—1224no—
450C24—611no—
451C24—611no—
452C24C2×C4×D6111yescharacteristic
453#41—12216no—
454#41—12216no—
455C2×Q8—614no—
456C2×Q8—1222no—
457C2×Q8—1222no—
458C2×D4—614no—
459C2×D4—614no—
460C2×D4—614no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—611no—
477C22×C4—614no—
478C22×C4—612no—
479C22×C4—614no—
480C22×C4—612no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—2441no—
499C22×C4—2441no—
500C22×C4—2441no—
501C22×C4—2441no—
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4C2×C4×D6111yescharacteristic
507C22×C4D4×D6114yes—
508C22×C4C23×D6111yescharacteristic
509M16—2448no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—1222no—
517C2×C8—1222no—
518C2×C8—1222no—
519C2×C8—1222no—
520C2×C8—1222no—
521C2×C8—1222no—
522C2×C8—2448no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—1222no—
540C42—1222no—
541C42—1222no—
542C42—1222no—
543C42—1222no—
544C42—1222no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—612no—
552C23—612no—
553C23—612no—
554C23—612no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23C22⋊C4×D6112yes—
566C23C22×C4×D6111yescharacteristic
567Q8—1228no—
568D4—1228no—
569D4—1228no—
570D4—1228no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—618no—
591C2×C4—618no—
592C2×C4—612no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—2444no—
610C2×C4—2444no—
611C2×C4—2444no—
612C2×C4—2444no—
613C2×C4C22⋊C4×D6112yes—
614C2×C4#1451978312yes—
615C2×C4#1451978512yes—
616C2×C4C2×D4×D6112yes—
617C2×C4#41×D6112yes—
618C2×C4#41×D6111yescharacteristic
619C2×C4#41×D6111yescharacteristic
620C8—42no—
621C8—42no—
622C8—2442no—
623C8—2442no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—614no—
632C22—1222no—
633C22—1222no—
634C22—1222no—
635C22—1222no—
636C22—1222no—
637C22—1222no—
638C22—1222no—
639C22—1222no—
640C22—1222no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22C2×C22⋊C4×D6111yescharacteristic
646C22#117×D6111yescharacteristic
647C22#117×D6111yescharacteristic
648C22C2×#1451978311yescharacteristic
649C22C2×#1451978511yescharacteristic
650C22#1684052811yescharacteristic
651C22#1684052811yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—614no—
658C4—1222no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C4—2441no—
663C4#123×D6112yes—
664C4#123×D6112yes—
665C2—42no—
666C2—1224no—
667C2—2442no—
668C2#381×D6111yescharacteristic
669C2#2145426511yescharacteristic
670C2#2145426911yescharacteristic
671C2#2145445811yescharacteristic
672C2#2145446511yescharacteristic
673C2#2145448011yescharacteristic
674C2#2145448611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1817C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1817D61
hypocenterC61#20684
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #21445889C2semidirect
4. #21445888C2semidirect
5. #21445887C2semidirect
6. #21445886C2semidirect
7. #21445886C2semidirect
8. #21445514C2semidirect
9. #21445511C2semidirect
10. #336×D61C2semidirect
11. C61×#1817C2semidirect
335. #1817D61semidirect
382. C61#20684semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168397272
#214458892
#214458882
#214458872
#214458862
#214455142
#214455112
#336×D612
C61×#18172
#2068461