Finite Group Databasebeta

← #29729490

Subgroups — #29729490

Order 15616.

760 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840066C211yesmaximal, characteristic
2#21450808C211yesmaximal, characteristic
3#21448919C211yesmaximal, characteristic
4#21447210C211yesmaximal, characteristic
5#21447196C211yesmaximal, characteristic
6#21447064C211yesmaximal, characteristic
7#21447064C211yesmaximal, characteristic
8#21446743C211yesmaximal, characteristic
9#21446740C211yesmaximal, characteristic
10#21446740C211yesmaximal, characteristic
11#21446542C211yesmaximal, characteristic
12#21446463C211yesmaximal, characteristic
13#21446456C211yesmaximal, characteristic
14#21445650C211yesmaximal, characteristic
15C2×C61×#491C211yesmaximal, characteristic
16C2×#14519775C2211yescharacteristic
17C2×#14519775C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19#16840066—24no—
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33#16839693—21no—
34#16839693—21no—
35#16839669C2211yescharacteristic
36#16839669C2211yescharacteristic
37#16839661—21no—
38#16839661C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839658—21no—
41#16839658—21no—
42#16839648—21no—
43#16839648—21no—
44C4⋊C4×Dic61—21no—
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×#125×C61C2211yescharacteristic
55C61×#491—24no—
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519775—22no—
65#14519775—22no—
66#14519775—41no—
67#14519775—41no—
68C4×Dic122—22no—
69C4×Dic122—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519710—22no—
89#14519708—22no—
90C4⋊#92418—22no—
91#14519706—41no—
92#14519706—41no—
93#14519702—22no—
94#14519702—22no—
95#14519701—22no—
96#14519701—22no—
97#14519701—41no—
98#14519701—41no—
99#14519700—22no—
100#14519700—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112C22×Q8×C61C2311yescharacteristic
113C22×Q8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C4⋊Q8×C61—22no—
117C4⋊Q8×C61—22no—
118#125×C61—22no—
119#125×C61D414yes—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C42×C61C2311yescharacteristic
127#103×C61—22no—
128#103×C61—22no—
129#103×C61—22no—
130#103×C61—22no—
131#97×C61—22no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122#4112yes—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—24no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—42no—
176C4⋊C4×C61—42no—
177C4⋊C4×C61C2×D412yes—
178C4⋊C4×C61C2×D412yes—
179C42×C61C2×D412yes—
180C42×C61#4112yes—
181C4⋊Dic61—21no—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—42no—
189C4⋊Dic61—81no—
190C4⋊Dic61#4112yes—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195#11758196—42no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—42no—
201C4×Dic61—42no—
202C4×Dic61—81no—
203C4×Dic61—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C23×C61C22×D411yescharacteristic
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61#12112yes—
236C2×C4×C61#12112yes—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61H(5,𝔽2)11yescharacteristic
242C2×C4×C612−1+411yescharacteristic
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
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—41no—
265C2×Dic61#13712yes—
266C2×Dic61#13712yes—
267Dic122—22no—
268Dic122—22no—
269Dic122—41no—
270Dic122—41no—
271C8×C61—41no—
272C8×C61—41no—
273#92418—41no—
274#92418—41no—
275#25290—611nomaximal, Sylow
276C22×C61C2×#12111yescharacteristic
277C22×C61#54611yescharacteristic
278C22×C61#54811yescharacteristic
279C22×C61C2×#13711yescharacteristic
280C22×C61C2×#13711yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57811yescharacteristic
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—81no—
288C4×C61—81no—
289C4×C61#52911yescharacteristic
290C4×C61#54211yescharacteristic
291C4×C61#54811yescharacteristic
292C4×C61#55011yescharacteristic
293Dic61—22no—
294Dic61—22no—
295Dic61—42no—
296Dic61—42no—
297Dic61—41no—
298Dic61—41no—
299Dic61—81no—
300Dic61—81no—
301C2×#491D6111yescharacteristic
302C2×#479—611no—
303#2546—611no—
304#2370—611no—
305#2068—611no—
306#2066—611no—
307#2043—611no—
308#2043—611no—
309#1981—611no—
310#1981—611no—
311#1981—611no—
312#1940—611no—
313#1928—611no—
314#1927—611no—
315#1763—611no—
316C2×C61#242611yescharacteristic
317C2×C61#303911yescharacteristic
318C2×C61#304611yescharacteristic
319C2×C61#331211yescharacteristic
320C2×C61#332011yescharacteristic
321C2×C61#337211yescharacteristic
322C2×C61#337411yescharacteristic
323C2×C4⋊Q8—611no—
324C2×C4⋊Q8—611no—
325C2×C4⋊Q8C2×D6111yescharacteristic
326C2×#125C2×D6111yescharacteristic
327C2×C4×Q8—611no—
328#491—24no—
329#479—1224no—
330C2×#107—611no—
331C2×#106—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×#103—611no—
340C2×#103—611no—
341C2×#103—611no—
342C2×#103—611no—
343C2×#103C2×D6111yescharacteristic
344C2×#103C2×D6111yescharacteristic
345C2×#103C2×D6111yescharacteristic
346C2×#103C2×D6111yescharacteristic
347C2×#97C2×D6111yescharacteristic
348#398—1221no—
349#398—1221no—
350#391—611no—
351#391—611no—
352#389—611no—
353#389—611no—
354#389—1221no—
355#389—1221no—
356#389—1221no—
357#387—1221no—
358#387—1221no—
359C4×C4⋊C4—611no—
360C4×C4⋊C4—611no—
361C4×C4⋊C4—611no—
362C4×C4⋊C4—611no—
363C4×C4⋊C4—1221no—
364#340—611no—
365#340—611no—
366#336—611no—
367#336—611no—
368C61#2529011yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×Q8C22×D6111yescharacteristic
371C22×Q8C22×D6111yescharacteristic
372C22×C8—611no—
373C22×C8—611no—
374C22×C8C22×D6111yescharacteristic
375C22×C8C22×D6111yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—1222no—
379C4⋊Q8—1222no—
380C4⋊Q8—2441no—
381C4⋊Q8—2441no—
382#125—22no—
383#125C22⋊D6114yes—
384C4×Q8—1222no—
385C4×Q8—1222no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411#107—1222no—
412#106—1222no—
413C4⋊C8—1222no—
414C4⋊C8—2441no—
415C4⋊C8—2441no—
416#103—22no—
417#103—22no—
418#103—22no—
419#103—22no—
420#103—1222no—
421#103—1222no—
422#103—1222no—
423#103—1222no—
424#103—1222no—
425#103—1222no—
426#103—2441no—
427#103—2441no—
428#97—22no—
429#95—611no—
430#95—611no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—612no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×Q8—1221no—
456C2×Q8—1221no—
457C2×Q8—1221no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—612no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—4881no—
500C4⋊C4—2442no—
501C4⋊C4—2442no—
502C4⋊C4—2442no—
503C4⋊C4—2442no—
504C4⋊C4—2442no—
505C4⋊C4—2442no—
506C4⋊C4C2×C22⋊D6112yes—
507C4⋊C4C2×C22⋊D6112yes—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42—4881no—
513C42—4881no—
514C42—2442no—
515C42—2442no—
516C42#1175822412yes—
517C42C2×C22⋊D6112yes—
518C23C2×D4×D6111yescharacteristic
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—1222no—
528Q8—1222no—
529Q8—2441no—
530Q8—2441no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4#1451974912yes—
572C2×C4#1451974912yes—
573C2×C4C22×C22⋊D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C2×C4C2×#1175822411yescharacteristic
577C2×C4#1451982311yescharacteristic
578C2×C4#1451982411yescharacteristic
579C8—41no—
580C8—41no—
581C8—2441no—
582C8—2441no—
583C22C2×#1451974911yescharacteristic
584C22#1684040511yescharacteristic
585C22#1684042011yescharacteristic
586C22#137×D6111yescharacteristic
587C22#137×D6111yescharacteristic
588C22#1684057111yescharacteristic
589C22#1684057811yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—1222no—
597C4—1222no—
598C4—4881no—
599C4—4881no—
600C4—2441no—
601C4—2442no—
602C4—2442no—
603C4—2441no—
604C4#1684029111yescharacteristic
605C4#1684038111yescharacteristic
606C4#1684041911yescharacteristic
607C4#1684043111yescharacteristic
608C2#2144938811yescharacteristic
609C2#2145530411yescharacteristic
610C2#2145537311yescharacteristic
611C2#2145786911yescharacteristic
612C2#2145798911yescharacteristic
613C2#2145859711yescharacteristic
614C2#2145861911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#491C2
socle, prime radicalC23×C61C22×D4
hypercenterC2×#491D61
hypocenterC61#25290
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
368. C61#25290semidirect

Maximal subgroups

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

subgroupindex
C2×#168400662
#214508082
#214489192
#214472102
#214471962
#214470642
#214467432
#214467402
#214465422
#214464632
#214464562
#214456502
C2×C61×#4912
#2529061