Finite Group Databasebeta

← #29649972

Subgroups — #29649972

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454795C211yesmaximal, characteristic, complemented
2#41×#92418C211yesmaximal, characteristic, complemented
3#21444698C211yesmaximal, characteristic, complemented
4#21444691C211yesmaximal, characteristic, complemented
5#21444684C211yesmaximal, characteristic, complemented
6#21444677C211yesmaximal, characteristic, complemented
7#21444643C211yesmaximal, characteristic, complemented
8#21444638C211yesmaximal, characteristic, complemented
9SD16⋊#92418C211yesmaximal, characteristic, complemented
10SD16⋊#92418C211yesmaximal, characteristic, complemented
11#21444599C211yesmaximal, characteristic, complemented
12#21444253C211yesmaximal, characteristic, complemented
13#21444227C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#3102C211yesmaximal, characteristic
16#16839893C2211yescharacteristic
17Q8×#92418C2211yescharacteristic
18Q8×#92418C2211yescharacteristic
19Q8×#92418C2211yescharacteristic
20#16839840C2211yescharacteristic
21#16839834—21no—
22D4×#92418—21no—
23D4×#92418—21no—
24D4×#92418—21no—
25D4×#92418C2211yescharacteristic
26D4×#92418C2211yescharacteristic
27D4×#92418C2211yescharacteristic
28#16839823—21no—
29#16839819C2211yescharacteristic
30#16839815—21no—
31#16839815C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839718—21no—
34C2×C4×#92418—21no—
35C2×C4×#92418C2211yescharacteristic
36#16839515C2211yescharacteristic
37#16839515C2211yescharacteristic
38#16839513C2211yescharacteristic
39#16839513C2211yescharacteristic
40Q8⋊#92418C2211yescharacteristic
41Q8⋊#92418C2211yescharacteristic
42Q8⋊#92418C2211yescharacteristic
43Q8⋊#92418C2211yescharacteristic
44D4⋊#92418C2211yescharacteristic
45D4⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48#16839484C2211yescharacteristic
49#16839484C2211yescharacteristic
50#16839483C2211yescharacteristic
51#16839483C2211yescharacteristic
52C61×#529C2211yescharacteristic
53C4×#41×C61C2211yescharacteristic
54C61×#485C411yescharacteristic
55C61×#482C411yescharacteristic
56C61×#479C411yescharacteristic
57C61×#478C411yescharacteristic
58C61×#464C411yescharacteristic
59C61×#463C411yescharacteristic
60C61×#452C411yescharacteristic
61C61×#449C411yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C4×SD16×C61C2211yescharacteristic
64C4×SD16×C61C2211yescharacteristic
65C4×D8×C61C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C2×#11758194—21no—
68C22×#92418—21no—
69C22×#92418—21no—
70C22×#92418—21no—
71C22×#92418D411yescharacteristic
72C22×#92418D411yescharacteristic
73C4⋊#92418—21no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418C2311yescharacteristic
79C4⋊#92418C2311yescharacteristic
80C4⋊#92418C2311yescharacteristic
81C4⋊#92418C2311yescharacteristic
82C22⋊#92418—21no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C22⋊#92418—21no—
86C22⋊#92418—21no—
87C22⋊#92418—21no—
88C22⋊#92418—21no—
89#14519688—21no—
90#14519688—21no—
91C4×#92418—21no—
92C4×#92418—21no—
93C4×#92418—21no—
94C4×#92418—21no—
95C4×#92418D411yescharacteristic
96C4×#92418D411yescharacteristic
97C4×#92418C2311yescharacteristic
98C4×#92418C2311yescharacteristic
99C4×#92418C2311yescharacteristic
100C4×#92418C2311yescharacteristic
101C2×#41×C61C2×C411yescharacteristic
102C2×Q16×C61C2×C411yescharacteristic
103C2×SD16×C61C2×C411yescharacteristic
104C2×SD16×C61C2×C411yescharacteristic
105C2×D8×C61C2×C411yescharacteristic
106#126×C61—21no—
107#125×C61C2×C411yescharacteristic
108#124×C61C2×C411yescharacteristic
109#123×C61—21no—
110C22⋊Q8×C61C2×C411yescharacteristic
111#121×C61C2×C411yescharacteristic
112C4×Q8×C61C2×C411yescharacteristic
113C4×Q8×C61C2311yescharacteristic
114C4×Q8×C61C2311yescharacteristic
115C4×D4×C61—21no—
116C4×D4×C61—21no—
117C4×D4×C61—21no—
118C4×D4×C61C2×C411yescharacteristic
119C4×D4×C61C2311yescharacteristic
120C4×D4×C61C2311yescharacteristic
121#117×C61—21no—
122#117×C61—21no—
123#117×C61C2×C411yescharacteristic
124C2×C42×C61—21no—
125C2×C42×C61C2311yescharacteristic
126#107×C61C2×C411yescharacteristic
127#107×C61C2×C411yescharacteristic
128#106×C61C2×C411yescharacteristic
129#106×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132#103×C61C2×C411yescharacteristic
133#103×C61C2×C411yescharacteristic
134#103×C61C2×C411yescharacteristic
135#103×C61C2×C411yescharacteristic
136#102×C61C2×C411yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141C22⋊C8×C61C2×C411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61C22×C411yescharacteristic
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159Q16×C61—22no—
160SD16×C61—22no—
161SD16×C61—22no—
162D8×C61—22no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61C22×C411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61#4111yescharacteristic
192C42×C61C2411yescharacteristic
193#11758194—42no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—41no—
201C2×#92418—41no—
202C2×#92418—42no—
203C2×#92418—42no—
204C2×#92418—42no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61#13112yes—
216D4×C61—24no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—42no—
221D4×C61#13112yes—
222C2×C4×C61—24no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#17909—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—22no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61C2×C4×D411yescharacteristic
270C4×C61—21no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61C2×#13111yescharacteristic
281C4×C61C2×#13111yescharacteristic
282C4×C61#57511yescharacteristic
283C4×C61#57511yescharacteristic
284#3102D6111yescharacteristic
285#2966—611no—
286C8×#41—611no—
287#1588—611no—
288#1587—611no—
289#1586—611no—
290#1585—611no—
291#1580—611no—
292#1579—611no—
293SD16⋊C8—611no—
294SD16⋊C8—611no—
295#1572—611no—
296#1488—611no—
297#1482—611no—
298#1452—611no—
299C2×C61—41no—
300C2×C61—42no—
301C2×C61—81no—
302C2×C61#292911yescharacteristic
303C2×C61#294311yescharacteristic
304C2×C61#295511yescharacteristic
305#529C2×D6111yescharacteristic
306C4×#41C2×D6111yescharacteristic
307#485Dic6111yescharacteristic
308#482Dic6111yescharacteristic
309#479Dic6111yescharacteristic
310#478Dic6111yescharacteristic
311#464Dic6111yescharacteristic
312#463Dic6111yescharacteristic
313#452Dic6111yescharacteristic
314#449Dic6111yescharacteristic
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16C2×D6111yescharacteristic
320C4×SD16C2×D6111yescharacteristic
321C4×SD16C2×D6111yescharacteristic
322C4×D8C2×D6111yescharacteristic
323#436—611no—
324#435—1221no—
325C8×D4—611no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330C8×D4—1221no—
331#433—1221no—
332#432—611no—
333#431—611no—
334#431—611no—
335#431—1221no—
336#431C2×D6111yescharacteristic
337#405—1221no—
338C2×C4×C8—611no—
339C2×C4×C8—1221no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354#322—611no—
355#322—611no—
356C61#1790911yescharacteristic, complemented, Sylow
357C2×#41C2×Dic6111yescharacteristic
358C2×Q16C2×Dic6111yescharacteristic
359C2×SD16C2×Dic6111yescharacteristic
360C2×SD16C2×Dic6111yescharacteristic
361C2×D8C2×Dic6111yescharacteristic
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—21no—
369#125C2×Dic6111yescharacteristic
370#124C2×Dic6111yescharacteristic
371#123—21no—
372C22⋊Q8C2×Dic6111yescharacteristic
373#121C2×Dic6111yescharacteristic
374C4×Q8C2×Dic6111yescharacteristic
375C4×Q8C22×D6111yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic6111yescharacteristic
381C4×D4C22×D6111yescharacteristic
382C4×D4C22×D6111yescharacteristic
383#117—21no—
384#117—21no—
385#117C2×Dic6111yescharacteristic
386C2×C42—21no—
387C2×C42C22×D6111yescharacteristic
388#107C2×Dic6111yescharacteristic
389#107C2×Dic6111yescharacteristic
390#106C2×Dic6111yescharacteristic
391#106C2×Dic6111yescharacteristic
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C2×Dic6111yescharacteristic
402C4⋊C8C2×Dic6111yescharacteristic
403#103C2×Dic6111yescharacteristic
404#103C2×Dic6111yescharacteristic
405#103C2×Dic6111yescharacteristic
406#103C2×Dic6111yescharacteristic
407#102C2×Dic6111yescharacteristic
408#102C2×Dic6111yescharacteristic
409#102C2×Dic6111yescharacteristic
410#102C2×Dic6111yescharacteristic
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8C2×Dic6111yescharacteristic
419C22⋊C8C2×Dic6111yescharacteristic
420#97—1221no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8C22×Dic6111yescharacteristic
437C2×Q8C22×Dic6111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×Dic6111yescharacteristic
441C2×D4C22×Dic6111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4D4×D6111yescharacteristic
447C22×C4#1175822411yescharacteristic
448C22×C4C22×Dic6111yescharacteristic
449Q16—22no—
450SD16—22no—
451SD16—22no—
452D8—22no—
453M16—2442no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2441no—
465C2×C8—2441no—
466C2×C8—2442no—
467C2×C8—2442no—
468C2×C8—2442no—
469C2×C8C22×Dic6111yescharacteristic
470C2×C8C22×Dic6111yescharacteristic
471C2×C8C22×Dic6111yescharacteristic
472C2×C8C22×Dic6111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C22×Dic6111yescharacteristic
480C4⋊C4C22×Dic6111yescharacteristic
481C4⋊C4C22×Dic6111yescharacteristic
482C4⋊C4C22×Dic6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42D4×D6111yescharacteristic
496C42#1175822411yescharacteristic
497C42C22×Dic6111yescharacteristic
498C42C23×D6111yescharacteristic
499C23—21no—
500C23—21no—
501C23D4×Dic6111yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#1451978412yes—
506D4—24no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4#1451978412yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4D4×Dic6111yescharacteristic
530C2×C4D4×Dic6111yescharacteristic
531C2×C4D4×Dic6111yescharacteristic
532C2×C4C23×Dic6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C2×#1175822411yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×D4×Dic6111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4C2×#1451978411yescharacteristic
570C4C2×#1451978411yescharacteristic
571C4#1684055911yescharacteristic
572C4#1684055911yescharacteristic
573C2—41no—
574C2—42no—
575C2—81no—
576C2#2145451411yescharacteristic
577C2#2145462011yescharacteristic
578C2#2145472211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#3102C2
socleC22×C61C2×C4×D4
prime radicalC61×#449C4
cosocleC42×C61C24
hypercenter#3102D61
hypocenterC61#17909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #21454795C2semidirect
2. #41×#92418C2semidirect
3. #21444698C2semidirect
4. #21444691C2semidirect
5. #21444684C2semidirect
6. #21444677C2semidirect
7. #21444643C2semidirect
8. #21444638C2semidirect
9. SD16⋊#92418C2semidirect
10. SD16⋊#92418C2semidirect
11. #21444599C2semidirect
12. #21444253C2semidirect
13. #21444227C2semidirect
14. #21444112C2semidirect
356. C61#17909semidirect

Maximal subgroups

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

subgroupindex
#214547952
#41×#924182
#214446982
#214446912
#214446842
#214446772
#214446432
#214446382
SD16⋊#924182
#214445992
#214442532
#214442272
#214441122
C61×#31022
#1790961