Finite Group Databasebeta

← #29603545

Subgroups — #29603545

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic
2C2×#16839627C211yesmaximal, characteristic
3C2×C4⋊C4×Dic61C211yesmaximal, characteristic
4#21444079C212yesmaximal
5#21444074C212yesmaximal
6#21444050C212yesmaximal
7#21444048C211yesmaximal, characteristic
8#21444048C211yesmaximal, characteristic
9#21444044C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic
11C61×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×C4×Dic61C2212yes—
16C22×C4×Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839660—24no—
19#16839627C418yescomplemented
20C4⋊C4×Dic61—24no—
21C2×#14519684C2212yes—
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61C2×C414yes—
49C2×C4⋊Dic61D414yes—
50C2×#11758196—24no—
51C2×#11758196—24no—
52C2×#11758196—42no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—22no—
55C2×C4×Dic61—22no—
56C2×C4×Dic61—22no—
57C2×C4×Dic61—24no—
58C2×C4×Dic61—24no—
59C2×C4×Dic61—42no—
60C2×C4×Dic61C2×C414yes—
61C2×C4×Dic61Q814yes—
62#14519684—22no—
63#14519684—22no—
64#14519684—24no—
65#14519684—24no—
66#14519684—22no—
67#14519684—24no—
68#14519684—22no—
69#14519684—42no—
70#14519684—42no—
71#14519684—42no—
72#14519684C2×C418yes—
73#14519684C2×C418yes—
74C23×C4×C61C2312yes—
75C23×C4×C61C2312yes—
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61C2×C414yes—
85C2×C42×C61—22no—
86C2×C42×C61—22no—
87C2×C42×C61—22no—
88#95×C61—24no—
89#95×C61—42no—
90C24×C61C2411yescharacteristic
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61C22×C414yes—
117C22×C4×C61C22×C412yes—
118C22×C4×C61C2×D412yes—
119C22×C4×C61C2×Q812yes—
120C22×C4×C61#4112yes—
121C22×C4×C61#4112yes—
122C22×C4×C61#4112yes—
123C22×C4×C61#4112yes—
124C22×C4×C61#4112yes—
125C22×C4×C61#4112yes—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C22×C412yes—
161C22×Dic61C22×C412yes—
162C22×Dic61C22×C414yes—
163C22×Dic61C2×D414yes—
164C22×Dic61C2×Q812yes—
165C22×Dic61C2×Q812yes—
166C22×Dic61#4112yes—
167C22×Dic61#4112yes—
168C4⋊C4×C61—28no—
169C4⋊C4×C61—44no—
170C42×C61—44no—
171C4⋊Dic61—28no—
172C4⋊Dic61—28no—
173#11758196—48no—
174C4×Dic61—28no—
175C4×Dic61—28no—
176C4×Dic61—48no—
177C23×C61C23×C411yescharacteristic
178C23×C61C22×D411yescharacteristic
179C23×C61C22×Q811yescharacteristic
180C23×C61C2×#4111yescharacteristic
181C23×C61C2×#4111yescharacteristic
182C23×C61C2×#4111yescharacteristic
183C23×C61C2×#4111yescharacteristic
184C23×C61C2×#4111yescharacteristic
185C23×C61C2×#4111yescharacteristic
186C23×C61C2×#4111yescharacteristic
187C23×C61C2×#4111yescharacteristic
188C23×C61H(5,𝔽2)11yescharacteristic
189C23×C61H(5,𝔽2)11yescharacteristic
190C23×C612−1+411yescharacteristic
191C23×C612−1+411yescharacteristic
192C2×C4×C61—24no—
193C2×C4×C61—24no—
194C2×C4×C61—24no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—42no—
206C2×C4×C61—41no—
207C2×C4×C61—42no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—42no—
211C2×C4×C61—41no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61#11714yes—
221C2×C4×C61C4×D414yes—
222C2×C4×C61C4×Q814yes—
223C2×C4×C61C22⋊Q814yes—
224C2×C4×C61#12314yes—
225C2×C4×C61#12514yes—
226C2×C4×C61#12614yes—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—24no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—24no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—24no—
242C2×Dic61—22no—
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—24no—
247C2×Dic61—24no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—41no—
252C2×Dic61—42no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—42no—
266C2×Dic61—41no—
267C2×Dic61—42no—
268C2×Dic61#12514yes—
269#14030—611nomaximal, Sylow
270C22×C61C2×#11711yescharacteristic
271C22×C61C2×C4×D411yescharacteristic
272C22×C61C2×C4×Q811yescharacteristic
273C22×C61C4×#4111yescharacteristic
274C22×C61C4×#4111yescharacteristic
275C22×C61#52011yescharacteristic
276C22×C61#52011yescharacteristic
277C22×C61C2×C22⋊Q811yescharacteristic
278C22×C61C2×#12311yescharacteristic
279C22×C61C2×#12511yescharacteristic
280C22×C61C2×#12511yescharacteristic
281C22×C61C2×#12611yescharacteristic
282C22×C61#52911yescharacteristic
283C22×C61#52911yescharacteristic
284C22×C61#53311yescharacteristic
285C22×C61#54011yescharacteristic
286C22×C61#54111yescharacteristic
287C22×C61#54411yescharacteristic
288C22×C61#54411yescharacteristic
289C22×C61#54611yescharacteristic
290C22×C61#54611yescharacteristic
291C22×C61#54811yescharacteristic
292C22×C61#54811yescharacteristic
293C22×C61#55211yescharacteristic
294C22×C61#55211yescharacteristic
295C22×C61#55311yescharacteristic
296C22×C61#55311yescharacteristic
297C22×C61#55511yescharacteristic
298C22×C61#55511yescharacteristic
299C22×C61#55611yescharacteristic
300C22×C61#55611yescharacteristic
301C22×C61#55611yescharacteristic
302C22×C61#55611yescharacteristic
303C22×C61#55911yescharacteristic
304C22×C61#55911yescharacteristic
305C4×C61—44no—
306C4×C61—42no—
307C4×C61—42no—
308C4×C61—82no—
309C4×C61#38718yes—
310Dic61—24no—
311Dic61—42no—
312Dic61—42no—
313Dic61—44no—
314Dic61—44no—
315Dic61—42no—
316C2×#389—611no—
317C2×#382—611no—
318C2×C4×C4⋊C4—611no—
319#1443—612no—
320#1442—612no—
321#1436—612no—
322C4⋊#95—611no—
323C4⋊#95—611no—
324C4⋊#95D6111yescharacteristic
325#1434—612no—
326C4×#95—611no—
327C2×C61C2×#38711yescharacteristic
328C2×C61C4×#12511yescharacteristic
329C2×C61#233011yescharacteristic
330C2×C61#234611yescharacteristic
331C2×C61#234711yescharacteristic
332C2×C61#236711yescharacteristic
333C2×C61#236711yescharacteristic
334C2×C61#242011yescharacteristic
335C2×C61#242111yescharacteristic
336C2×C61#243911yescharacteristic
337C2×C61#244211yescharacteristic
338C2×C61#251311yescharacteristic
339C2×C61#251411yescharacteristic
340C2×C61#257011yescharacteristic
341C2×C61#257111yescharacteristic
342C22×C4⋊C4—611no—
343C22×C4⋊C4—611no—
344C22×C4⋊C4—612no—
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C4⋊C4C2×D6111yescharacteristic
347C22×C42—611no—
348C22×C42—611no—
349C22×C42—612no—
350C22×C42C2×D6111yescharacteristic
351#389—1224no—
352#382—618no—
353C4×C4⋊C4—1224no—
354C2×#95—612no—
355C2×#95—612no—
356C2×#95—611no—
357C2×#95—611no—
358C2×#95—611no—
359C2×#95—611no—
360C2×#95—612no—
361C2×#95—612no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—612no—
365C2×#95—612no—
366C2×#95C2×D6112yes—
367C2×#95C2×D6112yes—
368C61#1403011yescharacteristic, complemented, Sylow
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4C22×D6112yes—
376C23×C4C22×D6112yes—
377C23×C4C22×D6111yescharacteristic
378C23×C4C22×D6111yescharacteristic
379C23×C4C22×D6111yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—614no—
386C2×C4⋊C4—614no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1224no—
392C2×C4⋊C4—1224no—
393C2×C4⋊C4—2442no—
394C2×C4⋊C4C4×D6114yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—614no—
399C2×C42—614no—
400C2×C42—1222no—
401C2×C42—1222no—
402C2×C42—1222no—
403C2×C42—1222no—
404C2×C42—1224no—
405C2×C42—1224no—
406C2×C42—2442no—
407#95—24no—
408#95—42no—
409#95—618no—
410#95—618no—
411#95—1224no—
412#95—1222no—
413#95—1222no—
414#95—1224no—
415#95—1224no—
416#95—1222no—
417#95—1222no—
418#95—2442no—
419#95—2442no—
420#95—2442no—
421C24C23×D6111yescharacteristic
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—614no—
453C22×C4—614no—
454C22×C4—612no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1222no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1222no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1222no—
489C22×C4C2×C4×D6114yes—
490C22×C4C2×C4×D6112yes—
491C22×C4#1175822212yes—
492C22×C4#1175822212yes—
493C22×C4D4×D6112yes—
494C22×C4#1175822412yes—
495C22×C4#1175822412yes—
496C22×C4#1175822412yes—
497C22×C4Q8×D6112yes—
498C22×C4#1175822612yes—
499C4⋊C4—28no—
500C4⋊C4—44no—
501C4⋊C4—1228no—
502C4⋊C4—1228no—
503C4⋊C4—2448no—
504C42—44no—
505C42—1228no—
506C42—1228no—
507C42—2448no—
508C23C22×C4×D6111yescharacteristic
509C23C2×D4×D6111yescharacteristic
510C23C2×Q8×D6111yescharacteristic
511C23#41×D6111yescharacteristic
512C23#41×D6111yescharacteristic
513C23C2×#1175822411yescharacteristic
514C23C2×#1175822411yescharacteristic
515C23C2×#1175822411yescharacteristic
516C23C2×#1175822211yescharacteristic
517C23C2×#1175822211yescharacteristic
518C23C2×#1175822611yescharacteristic
519C23#1451982211yescharacteristic
520C23#1451982311yescharacteristic
521C23#1451982411yescharacteristic
522C23#1451982511yescharacteristic
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—614no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1224no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1224no—
564C2×C4—1222no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2442no—
576C2×C4—2441no—
577C2×C4—2442no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2442no—
592C2×C4—2441no—
593C2×C4#1451973414yes—
594C2×C4#1451973714yes—
595C2×C4#1451974214yes—
596C2×C4#1451975514yes—
597C2×C4#1451975914yes—
598C2×C4#1451976714yes—
599C2×C4#1451977014yes—
600C22C2×#1451973411yescharacteristic
601C22C2×#1451973711yescharacteristic
602C22C2×#1451974211yescharacteristic
603C22C4×#1175822411yescharacteristic
604C22C4×#1175822611yescharacteristic
605C22#1684024111yescharacteristic
606C22#1684024411yescharacteristic
607C22C2×#1451975511yescharacteristic
608C22C2×#1451975911yescharacteristic
609C22#125×D6111yescharacteristic
610C22C2×#1451976711yescharacteristic
611C22C2×#1451977011yescharacteristic
612C22#1684029311yescharacteristic
613C22#1684029811yescharacteristic
614C22#1684031711yescharacteristic
615C22#1684036511yescharacteristic
616C22#1684037211yescharacteristic
617C22#1684038911yescharacteristic
618C22#1684039211yescharacteristic
619C22#1684040311yescharacteristic
620C22#1684040911yescharacteristic
621C22#1684041811yescharacteristic
622C22#1684042211yescharacteristic
623C22#1684044711yescharacteristic
624C22#1684045311yescharacteristic
625C22#1684046011yescharacteristic
626C22#1684046211yescharacteristic
627C22#1684047511yescharacteristic
628C22#1684047711yescharacteristic
629C22#1684048011yescharacteristic
630C22#1684048111yescharacteristic
631C22#1684048511yescharacteristic
632C22#1684048611yescharacteristic
633C22#1684049411yescharacteristic
634C22#1684049811yescharacteristic
635C4—42no—
636C4—42no—
637C4—44no—
638C4—82no—
639C4—1224no—
640C4—2442no—
641C4—2442no—
642C4—2444no—
643C4—2444no—
644C4—2442no—
645C4#1683964418yes—
646C2C2×#1683964411yescharacteristic
647C2#2144837811yescharacteristic
648C2#2144855911yescharacteristic
649C2#2144870011yescharacteristic
650C2#2144870811yescharacteristic
651C2#2144888911yescharacteristic
652C2#2144889511yescharacteristic
653C2#2144931311yescharacteristic
654C2#2144932411yescharacteristic
655C2#2144951211yescharacteristic
656C2#2144954511yescharacteristic
657C2#2145041411yescharacteristic
658C2#2145042511yescharacteristic
659C2#2145104911yescharacteristic
660C2#2145105911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, prime radical, cosocleC24×C61C24
hypercenterC4⋊#95D61
hypocenterC61#14030
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
19. #16839627C4semidirect
368. C61#14030semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
C2×#168396272
C2×C4⋊C4×Dic612
#214440792
#214440742
#214440502
#214440482
#214440442
C4×#145196842
C61×C4⋊#952
#1403061