Finite Group Databasebeta

← #29603698

Subgroups — #29603698

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839658C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic
3C2×C4×#11758196C211yesmaximal, characteristic
4#21444085C212yesmaximal
5#21444074C212yesmaximal
6#21444054C212yesmaximal
7#21444050C212yesmaximal
8#21444049C211yesmaximal, characteristic
9#21444048C211yesmaximal, characteristic
10#21444048C211yesmaximal, characteristic
11C61×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2211yescharacteristic
15C22×#11758196C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20#16839658C418yescomplemented
21C4⋊C4×Dic61—24no—
22C4×#11758196—24no—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
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×Dic61C2312yes—
40C23×Dic61C2311yescharacteristic
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⋊Dic61Q814yes—
50C2×#11758196—22no—
51C2×#11758196—22no—
52C2×#11758196—22no—
53C2×#11758196—22no—
54C2×#11758196—22no—
55C2×#11758196—42no—
56C2×#11758196—42no—
57C2×#11758196C2×C418yes—
58C2×#11758196Q814yes—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61—24no—
64C2×C4×Dic61—42no—
65C2×C4×Dic61—42no—
66C2×C4×Dic61C2×C414yes—
67C2×C4×Dic61D414yes—
68#14519684—24no—
69#14519684—22no—
70#14519684—22no—
71#14519684—24no—
72#14519684—24no—
73#14519684—24no—
74#14519684—42no—
75#14519684—42no—
76#14519684—42no—
77#14519684C2×C418yes—
78C23×C4×C61C2312yes—
79C23×C4×C61C2312yes—
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61C2×C414yes—
89C2×C42×C61—22no—
90C2×C42×C61—22no—
91C2×C42×C61—22no—
92#95×C61—42no—
93#95×C61—42no—
94C24×C61C2411yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61C22×C414yes—
121C22×C4×C61C22×C412yes—
122C22×C4×C61C2×D412yes—
123C22×C4×C61C2×Q812yes—
124C22×C4×C61C2×Q812yes—
125C22×C4×C61#4112yes—
126C22×C4×C61#4112yes—
127C22×C4×C61#4112yes—
128C22×C4×C61#4112yes—
129C22×C4×C61#4112yes—
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—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61C22×C414yes—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C412yes—
165C22×Dic61C2×D412yes—
166C22×Dic61C2×D412yes—
167C22×Dic61C2×Q814yes—
168C22×Dic61C2×Q812yes—
169C22×Dic61C2×Q812yes—
170C22×Dic61#4112yes—
171C22×Dic61#4112yes—
172C4⋊C4×C61—28no—
173C4⋊C4×C61—44no—
174C42×C61—44no—
175C4⋊Dic61—28no—
176C4⋊Dic61—28no—
177#11758196—28no—
178#11758196—28no—
179#11758196—48no—
180C4×Dic61—28no—
181C4×Dic61—28no—
182C4×Dic61—48no—
183C23×C61C23×C411yescharacteristic
184C23×C61C22×D411yescharacteristic
185C23×C61C22×Q811yescharacteristic
186C23×C61C22×Q811yescharacteristic
187C23×C61C2×#4111yescharacteristic
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4111yescharacteristic
190C23×C61C2×#4111yescharacteristic
191C23×C61C2×#4111yescharacteristic
192C23×C61C2×#4111yescharacteristic
193C23×C61C2×#4111yescharacteristic
194C23×C61H(5,𝔽2)11yescharacteristic
195C23×C61H(5,𝔽2)11yescharacteristic
196C23×C61H(5,𝔽2)11yescharacteristic
197C23×C612−1+411yescharacteristic
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—42no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—41no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61#11714yes—
227C2×C4×C61C4×D414yes—
228C2×C4×C61C4×Q814yes—
229C2×C4×C61C22⋊Q814yes—
230C2×C4×C61#12314yes—
231C2×C4×C61#12514yes—
232C2×C4×C61#12614yes—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—22no—
249C2×Dic61—24no—
250C2×Dic61—22no—
251C2×Dic61—24no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61C4×Q814yes—
274C2×Dic61C22⋊Q814yes—
275#14041—611nomaximal, Sylow
276C22×C61C2×#11711yescharacteristic
277C22×C61C2×C4×D411yescharacteristic
278C22×C61C2×C4×Q811yescharacteristic
279C22×C61C2×C4×Q811yescharacteristic
280C22×C61C4×#4111yescharacteristic
281C22×C61#51811yescharacteristic
282C22×C61#52011yescharacteristic
283C22×C61C2×C22⋊Q811yescharacteristic
284C22×C61C2×C22⋊Q811yescharacteristic
285C22×C61C2×#12311yescharacteristic
286C22×C61#52511yescharacteristic
287C22×C61C2×#12511yescharacteristic
288C22×C61C2×#12611yescharacteristic
289C22×C61#52911yescharacteristic
290C22×C61#53311yescharacteristic
291C22×C61#53511yescharacteristic
292C22×C61#53711yescharacteristic
293C22×C61#54011yescharacteristic
294C22×C61#54211yescharacteristic
295C22×C61#55211yescharacteristic
296C22×C61#55311yescharacteristic
297C22×C61#55311yescharacteristic
298C22×C61#55311yescharacteristic
299C22×C61#55411yescharacteristic
300C22×C61#55411yescharacteristic
301C22×C61#55411yescharacteristic
302C22×C61#55411yescharacteristic
303C22×C61#55511yescharacteristic
304C22×C61#55611yescharacteristic
305C22×C61#55711yescharacteristic
306C22×C61#55711yescharacteristic
307C22×C61Q8211yescharacteristic
308C22×C61#55911yescharacteristic
309C22×C61#55911yescharacteristic
310C22×C61#55911yescharacteristic
311C4×C61—44no—
312C4×C61—42no—
313C4×C61—42no—
314C4×C61—82no—
315C4×C61#38718yes—
316Dic61—24no—
317Dic61—24no—
318Dic61—42no—
319Dic61—44no—
320Dic61—44no—
321Dic61—42no—
322C2×#389—611no—
323C2×C4×C4⋊C4—611no—
324C2×C4×C4⋊C4—611no—
325#1445—612no—
326#1442—612no—
327#1436—612no—
328#1436—612no—
329C4⋊#95—611no—
330C4⋊#95—611no—
331C4⋊#95—611no—
332C4⋊#95D6111yescharacteristic
333C2×C61C2×#38711yescharacteristic
334C2×C61C4×C22⋊Q811yescharacteristic
335C2×C61#232411yescharacteristic
336C2×C61#235511yescharacteristic
337C2×C61#235711yescharacteristic
338C2×C61#236911yescharacteristic
339C2×C61#237011yescharacteristic
340C2×C61#248511yescharacteristic
341C2×C61#248711yescharacteristic
342C2×C61#250711yescharacteristic
343C2×C61#250911yescharacteristic
344C2×C61#251111yescharacteristic
345C2×C61#251311yescharacteristic
346C2×C61#258011yescharacteristic
347C2×C61#258211yescharacteristic
348C22×C4⋊C4—611no—
349C22×C4⋊C4—611no—
350C22×C4⋊C4—611no—
351C22×C4⋊C4—612no—
352C22×C4⋊C4—611no—
353C22×C4⋊C4C2×D6111yescharacteristic
354C22×C4⋊C4C2×D6111yescharacteristic
355C22×C42—611no—
356C22×C42—611no—
357C22×C42—612no—
358C22×C42C2×D6111yescharacteristic
359#389—618no—
360C4×C4⋊C4—1224no—
361C4×C4⋊C4—1224no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—612no—
365C2×#95—612no—
366C2×#95—611no—
367C2×#95—612no—
368C2×#95—611no—
369C2×#95—612no—
370C2×#95—612no—
371C2×#95—612no—
372C2×#95C2×D6112yes—
373C2×#95C2×D6112yes—
374C61#1404111yescharacteristic, complemented, Sylow
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—612no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—612no—
381C23×C4C22×D6112yes—
382C23×C4C22×D6112yes—
383C23×C4C22×D6111yescharacteristic
384C23×C4C22×D6111yescharacteristic
385C23×C4C22×D6111yescharacteristic
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—614no—
392C2×C4⋊C4—614no—
393C2×C4⋊C4—614no—
394C2×C4⋊C4—618no—
395C2×C4⋊C4—1222no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—2442no—
405C2×C4⋊C4—2442no—
406C2×C4⋊C4C4×D6114yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—614no—
411C2×C42—614no—
412C2×C42—1222no—
413C2×C42—1222no—
414C2×C42—1222no—
415C2×C42—1222no—
416C2×C42—1224no—
417C2×C42—2442no—
418C2×C42—2442no—
419#95—42no—
420#95—42no—
421#95—618no—
422#95—1222no—
423#95—1222no—
424#95—1224no—
425#95—1224no—
426#95—1224no—
427#95—1224no—
428#95—2442no—
429#95—2442no—
430#95—2442no—
431C24C23×D6111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—614no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—614no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1221no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4C2×C4×D6114yes—
500C22×C4C2×C4×D6112yes—
501C22×C4#1175822212yes—
502C22×C4#1175822212yes—
503C22×C4D4×D6112yes—
504C22×C4#1175822412yes—
505C22×C4#1175822412yes—
506C22×C4Q8×D6112yes—
507C22×C4Q8×D6112yes—
508C22×C4#1175822612yes—
509C4⋊C4—28no—
510C4⋊C4—44no—
511C4⋊C4—1228no—
512C4⋊C4—1228no—
513C4⋊C4—1228no—
514C4⋊C4—1228no—
515C4⋊C4—2448no—
516C42—44no—
517C42—1228no—
518C42—1228no—
519C42—2448no—
520C23C22×C4×D6111yescharacteristic
521C23C2×D4×D6111yescharacteristic
522C23C2×Q8×D6111yescharacteristic
523C23C2×Q8×D6111yescharacteristic
524C23#41×D6111yescharacteristic
525C23#41×D6111yescharacteristic
526C23C2×#1175822411yescharacteristic
527C23C2×#1175822411yescharacteristic
528C23C2×#1175822211yescharacteristic
529C23C2×#1175822211yescharacteristic
530C23C2×#1175822611yescharacteristic
531C23#1451982211yescharacteristic
532C23#1451982211yescharacteristic
533C23#1451982311yescharacteristic
534C23#1451982411yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—614no—
564C2×C4—614no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1222no—
581C2×C4—1224no—
582C2×C4—1222no—
583C2×C4—1224no—
584C2×C4—1222no—
585C2×C4—1224no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—2441no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4#1451973414yes—
606C2×C4#1451973714yes—
607C2×C4#1451974214yes—
608C2×C4#1451975514yes—
609C2×C4#1451975914yes—
610C2×C4#1451976714yes—
611C2×C4#1451977014yes—
612C22C2×#1451973411yescharacteristic
613C22C2×#1451973711yescharacteristic
614C22C4×Q8×D6111yescharacteristic
615C22C2×#1451974211yescharacteristic
616C22C4×#1175822611yescharacteristic
617C22#1684023411yescharacteristic
618C22#1684024111yescharacteristic
619C22C22⋊Q8×D6111yescharacteristic
620C22C2×#1451975511yescharacteristic
621C22C2×#1451975911yescharacteristic
622C22#1684027511yescharacteristic
623C22C2×#1451976711yescharacteristic
624C22C2×#1451977011yescharacteristic
625C22#1684029111yescharacteristic
626C22#1684031711yescharacteristic
627C22#1684032811yescharacteristic
628C22#1684034111yescharacteristic
629C22#1684036611yescharacteristic
630C22#1684038111yescharacteristic
631C22#1684045411yescharacteristic
632C22#1684045611yescharacteristic
633C22#1684045911yescharacteristic
634C22#1684046011yescharacteristic
635C22#1684046711yescharacteristic
636C22#1684046811yescharacteristic
637C22#1684047011yescharacteristic
638C22#1684047311yescharacteristic
639C22#1684047611yescharacteristic
640C22#1684048011yescharacteristic
641C22#1684048911yescharacteristic
642C22#1684049011yescharacteristic
643C22#1684049211yescharacteristic
644C22#1684049511yescharacteristic
645C22#1684049511yescharacteristic
646C22#1684049711yescharacteristic
647C4—44no—
648C4—42no—
649C4—42no—
650C4—82no—
651C4—1224no—
652C4—1224no—
653C4—2442no—
654C4—2444no—
655C4—2442no—
656C4—2444no—
657C4#1683964418yes—
658C2C2×#1683964411yescharacteristic
659C2#2144835711yescharacteristic
660C2#2144851511yescharacteristic
661C2#2144877211yescharacteristic
662C2#2144878811yescharacteristic
663C2#2144890511yescharacteristic
664C2#2144892011yescharacteristic
665C2#2145011811yescharacteristic
666C2#2145013211yescharacteristic
667C2#2145034211yescharacteristic
668C2#2145036411yescharacteristic
669C2#2145039611yescharacteristic
670C2#2145041811yescharacteristic
671C2#2145117911yescharacteristic
672C2#2145119111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, prime radical, cosocleC24×C61C24
hypercenterC4⋊#95D61
hypocenterC61#14041
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
20. #16839658C4semidirect
374. C61#14041semidirect

Maximal subgroups

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

subgroupindex
C2×#168396582
C2×C4⋊C4×Dic612
C2×C4×#117581962
#214440852
#214440742
#214440542
#214440502
#214440492
#214440482
C61×C4⋊#952
#1404161