Finite Group Databasebeta

← #29602497

Subgroups — #29602497

Order 15616.

1370 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839661C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic
3#21444078C212yesmaximal
4#21444075C212yesmaximal
5#21444049C211yesmaximal, characteristic
6#21444048C211yesmaximal, characteristic
7#21444048C211yesmaximal, characteristic
8#21444048C212yesmaximal
9#21444045C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic
11C2×C61×#389C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2212yes—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4×Dic61C2211yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17C22×C4×Dic61C2212yes—
18#16839661—24no—
19C4⋊C4×Dic61C418yescomplemented
20C2×#14519684C2212yes—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2212yes—
34C22×C4⋊C4×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C61×#389—24no—
37C2×#95×C61C2212yes—
38C23×Dic61C2312yes—
39C23×Dic61C2312yes—
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—24no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—24no—
51C2×C4⋊Dic61—42no—
52C2×C4⋊Dic61C2×C414yes—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—22no—
55C2×C4×Dic61—22no—
56C2×C4×Dic61—22no—
57C2×C4×Dic61—22no—
58C2×C4×Dic61—42no—
59C2×C4×Dic61—42no—
60C2×C4×Dic61C2×C414yes—
61C2×C4×Dic61C2×C418yes—
62#14519684—24no—
63#14519684—22no—
64#14519684—22no—
65#14519684—22no—
66#14519684—24no—
67#14519684—42no—
68#14519684—42no—
69#14519684—42no—
70#14519684—42no—
71#14519684—42no—
72#14519684C2×C418yes—
73#14519684Q814yes—
74C23×C4×C61C2312yes—
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2312yes—
78C23×C4×C61C2311yescharacteristic
79C2×C4⋊C4×C61—24no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—24no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—42no—
85C2×C4⋊C4×C61C2×C414yes—
86C2×C4⋊C4×C61D414yes—
87C2×C4⋊C4×C61Q814yes—
88C2×C42×C61—22no—
89C2×C42×C61—22no—
90C2×C42×C61—22no—
91#95×C61—24no—
92C24×C61C2411yescharacteristic
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
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×D414yes—
119C22×C4×C61C2×D412yes—
120C22×C4×C61C2×Q812yes—
121C22×C4×C61C2×Q814yes—
122C22×C4×C61C2×Q812yes—
123C22×C4×C61#4112yes—
124C22×C4×C61#4112yes—
125C22×C4×C61#4112yes—
126C22×C4×C61#4112yes—
127C22×C4×C61#4112yes—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
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—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C414yes—
165C22×Dic61C22×C412yes—
166C22×Dic61C2×Q812yes—
167C22×Dic61C2×Q812yes—
168C22×Dic61#4112yes—
169C22×Dic61#4112yes—
170C4⋊C4×C61—48no—
171C4⋊C4×C61—44no—
172C4⋊C4×C61C4⋊C4116yes—
173C42×C61—44no—
174C4⋊Dic61—28no—
175C4⋊Dic61—48no—
176C4⋊Dic61—44no—
177C4×Dic61—28no—
178C4×Dic61—48no—
179C4×Dic61—44no—
180C23×C61C23×C411yescharacteristic
181C23×C61C22×D411yescharacteristic
182C23×C61C22×Q811yescharacteristic
183C23×C61C22×Q811yescharacteristic
184C23×C61C2×#4111yescharacteristic
185C23×C61C2×#4111yescharacteristic
186C23×C61C2×#4111yescharacteristic
187C23×C61C2×#4111yescharacteristic
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4111yescharacteristic
190C23×C61C2×#4111yescharacteristic
191C23×C61H(5,𝔽2)11yescharacteristic
192C23×C61H(5,𝔽2)11yescharacteristic
193C23×C61H(5,𝔽2)11yescharacteristic
194C23×C612−1+411yescharacteristic
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61C2×C4⋊C418yes—
223C2×C4×C61C2×C4⋊C414yes—
224C2×C4×C61#11714yes—
225C2×C4×C61#11714yes—
226C2×C4×C61#12414yes—
227C2×C4×C61#12414yes—
228C2×C4×C61#12514yes—
229C2×C4×C61#12514yes—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—24no—
238C2×Dic61—22no—
239C2×Dic61—24no—
240C2×Dic61—24no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—41no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61C4×Q814yes—
272#13933—611nomaximal, Sylow
273C22×C61C22×C4⋊C411yescharacteristic
274C22×C61C2×#11711yescharacteristic
275C22×C61C2×#11711yescharacteristic
276C22×C61C2×C4×Q811yescharacteristic
277C22×C61C4×#4111yescharacteristic
278C22×C61#51811yescharacteristic
279C22×C61#52011yescharacteristic
280C22×C61C2×#12411yescharacteristic
281C22×C61C2×#12411yescharacteristic
282C22×C61C2×#12511yescharacteristic
283C22×C61C2×#12511yescharacteristic
284C22×C61#52911yescharacteristic
285C22×C61#52911yescharacteristic
286C22×C61#53311yescharacteristic
287C22×C61#53311yescharacteristic
288C22×C61#54011yescharacteristic
289C22×C61#54011yescharacteristic
290C22×C61#54211yescharacteristic
291C22×C61#54211yescharacteristic
292C22×C61#54611yescharacteristic
293C22×C61#54611yescharacteristic
294C22×C61D4×Q811yescharacteristic
295C22×C61#55011yescharacteristic
296C22×C61#55311yescharacteristic
297C22×C61#55311yescharacteristic
298C22×C61#55311yescharacteristic
299C22×C61#55311yescharacteristic
300C22×C61#55411yescharacteristic
301C22×C61#55411yescharacteristic
302C22×C61#55411yescharacteristic
303C22×C61#55411yescharacteristic
304C22×C61#55611yescharacteristic
305C22×C61#55611yescharacteristic
306C22×C61#55711yescharacteristic
307C22×C61Q8211yescharacteristic
308C4×C61—28no—
309C4×C61—42no—
310C4×C61—42no—
311C4×C61—82no—
312C4×C61#38218yes—
313Dic61—24no—
314Dic61—44no—
315Dic61—42no—
316Dic61—42no—
317Dic61—42no—
318Dic61—82no—
319C2×#389—611no—
320C2×#389D6111yescharacteristic
321C2×C4×C4⋊C4—611no—
322#1442—612no—
323#1442—612no—
324C4⋊#95—611no—
325C4⋊#95—611no—
326C4⋊#95—611no—
327C4⋊#95—612no—
328#1434—612no—
329C4×#95—611no—
330C2×C61C2×#38211yescharacteristic
331C2×C61#229511yescharacteristic
332C2×C61#231911yescharacteristic
333C2×C61#234511yescharacteristic
334C2×C61#234711yescharacteristic
335C2×C61#234911yescharacteristic
336C2×C61Q8×C4⋊C411yescharacteristic
337C2×C61#249011yescharacteristic
338C2×C61#249011yescharacteristic
339C2×C61#249211yescharacteristic
340C2×C61#249211yescharacteristic
341C2×C61#250711yescharacteristic
342C2×C61#250711yescharacteristic
343C2×C61#250911yescharacteristic
344C2×C61#250911yescharacteristic
345C22×C4⋊C4—611no—
346C22×C4⋊C4—611no—
347C22×C4⋊C4—612no—
348C22×C4⋊C4C2×D6111yescharacteristic
349C22×C4⋊C4C2×D6112yes—
350C22×C4⋊C4C2×D6111yescharacteristic
351C22×C42—611no—
352C22×C42—612no—
353C22×C42—611no—
354C22×C42C2×D6111yescharacteristic
355#389—24no—
356#389—1224no—
357C4×C4⋊C4—618no—
358C2×#95—611no—
359C2×#95—612no—
360C2×#95—611no—
361C2×#95—611no—
362C2×#95—611no—
363C2×#95—612no—
364C2×#95—612no—
365C2×#95—612no—
366C2×#95—612no—
367C2×#95—612no—
368C2×#95—612no—
369C2×#95—612no—
370C2×#95C2×D6112yes—
371C61#1393311yescharacteristic, complemented, Sylow
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—612no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—612no—
378C23×C4C22×D6112yes—
379C23×C4C22×D6111yescharacteristic
380C23×C4C22×D6111yescharacteristic
381C23×C4C22×D6112yes—
382C23×C4C22×D6111yescharacteristic
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—614no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1222no—
392C2×C4⋊C4—1224no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1222no—
395C2×C4⋊C4—1224no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—2442no—
398C2×C4⋊C4Dic12214yes—
399C2×C4⋊C4C4×D6114yes—
400C2×C4⋊C4C22⋊D6114yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—614no—
405C2×C42—618no—
406C2×C42—1222no—
407C2×C42—1222no—
408C2×C42—1222no—
409C2×C42—1222no—
410C2×C42—1222no—
411C2×C42—2442no—
412C2×C42—2442no—
413#95—24no—
414#95—618no—
415#95—614no—
416#95—1222no—
417#95—1222no—
418#95—1224no—
419#95—1222no—
420#95—1224no—
421#95—2442no—
422#95—2442no—
423#95—2442no—
424#95—2442no—
425#95—2442no—
426C24C23×D6111yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—614no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
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—1222no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4C2×Dic12214yes—
493C22×C4C2×Dic12212yes—
494C22×C4C2×C4×D6114yes—
495C22×C4C2×C4×D6112yes—
496C22×C4#1175822412yes—
497C22×C4#1175822412yes—
498C22×C4#1175822412yes—
499C22×C4Q8×D6112yes—
500C22×C4#1175822612yes—
501C22×C4#1175822612yes—
502C22×C4C2×C22⋊D6114yes—
503C22×C4C2×C22⋊D6112yes—
504C4⋊C4—48no—
505C4⋊C4—44no—
506C4⋊C4—1228no—
507C4⋊C4—2448no—
508C4⋊C4—2444no—
509C4⋊C4#11758196116yes—
510C42—44no—
511C42—1228no—
512C42—2448no—
513C42—2444no—
514C23C22×C4×D6111yescharacteristic
515C23C22×C22⋊D6111yescharacteristic
516C23C2×Q8×D6111yescharacteristic
517C23C22×Dic12211yescharacteristic
518C23#41×D6111yescharacteristic
519C23#41×D6111yescharacteristic
520C23C2×#1175822411yescharacteristic
521C23C2×#1175822411yescharacteristic
522C23C2×#1175822411yescharacteristic
523C23C2×#1175822611yescharacteristic
524C23C2×#1175822611yescharacteristic
525C23#1451982211yescharacteristic
526C23#1451982311yescharacteristic
527C23#1451982311yescharacteristic
528C23#1451982511yescharacteristic
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—614no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2441no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4C2×#1175819618yes—
599C2×C4C2×#1175819614yes—
600C2×C4#1451973514yes—
601C2×C4#1451973514yes—
602C2×C4#1451976414yes—
603C2×C4#1451976614yes—
604C2×C4#1451976814yes—
605C2×C4#1451976814yes—
606C22C22×#1175819611yescharacteristic
607C22C2×#1451973511yescharacteristic
608C22C2×#1451973511yescharacteristic
609C22C4×Q8×D6111yescharacteristic
610C22C4×#1175822411yescharacteristic
611C22#1684023411yescharacteristic
612C22#1684024411yescharacteristic
613C22C2×#1451976411yescharacteristic
614C22C2×#1451976611yescharacteristic
615C22C2×#1451976811yescharacteristic
616C22C2×#1451976811yescharacteristic
617C22#1684029311yescharacteristic
618C22#1684029711yescharacteristic
619C22#1684031411yescharacteristic
620C22#1684031711yescharacteristic
621C22#1684036511yescharacteristic
622C22#1684036811yescharacteristic
623C22#1684038511yescharacteristic
624C22#1684038611yescharacteristic
625C22#1684040011yescharacteristic
626C22#1684040611yescharacteristic
627C22Q8×C22⋊D6111yescharacteristic
628C22#1684043111yescharacteristic
629C22#1684045911yescharacteristic
630C22#1684046411yescharacteristic
631C22#1684046511yescharacteristic
632C22#1684046511yescharacteristic
633C22#1684046911yescharacteristic
634C22#1684047011yescharacteristic
635C22#1684047111yescharacteristic
636C22#1684047311yescharacteristic
637C22#1684048311yescharacteristic
638C22#1684048611yescharacteristic
639C22#1684048811yescharacteristic
640C22Q8×Dic12211yescharacteristic
641C4—28no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4—1224no—
646C4—4882no—
647C4—2442no—
648C4—2444no—
649C4—2442no—
650C4—2442no—
651C4#1683962718yes—
652C2C2×#1683962711yescharacteristic
653C2#2144829011yescharacteristic
654C2#2144845811yescharacteristic
655C2#2144869511yescharacteristic
656C2#2144871111yescharacteristic
657C2#2144872411yescharacteristic
658C2Q8×#1175819611yescharacteristic
659C2#2145017311yescharacteristic
660C2#2145017411yescharacteristic
661C2#2145019511yescharacteristic
662C2#2145019611yescharacteristic
663C2#2145034811yescharacteristic
664C2#2145034911yescharacteristic
665C2#2145037011yescharacteristic
666C2#2145037111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#389C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#389D61
hypocenterC61#13933
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
19. C4⋊C4×Dic61C4semidirect
371. C61#13933semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×C4⋊C4×Dic612
#214440782
#214440752
#214440492
#214440482
#214440452
C4×#145196842
C2×C61×#3892
#1393361