Finite Group Databasebeta

← #29685369

Subgroups — #29685369

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840352C211yesmaximal, characteristic
2#21448416C211yesmaximal, characteristic, complemented
3#21448171C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446655C211yesmaximal, characteristic, complemented
6#21446654C211yesmaximal, characteristic, complemented
7#21446271C214yesmaximal, complemented
8#21445606C214yesmaximal, complemented
9C61×#1996C211yesmaximal, characteristic, complemented
10#16840352—22no—
11#16840352—22no—
12#16840352—22no—
13#16840352—22no—
14C2×#14519772C412yescomplemented
15C2×#14519766C412yescomplemented
16C2×#14519762C412yescomplemented
17C2×#14519752C412yescomplemented
18C2×#14519751C2211yescharacteristic
19C2×#14519747C2212yes—
20C2×#14519737C2212yes—
21C22×#11758198C2211yescharacteristic
22C2×C22⋊C4×D61C2212yes—
23C2×#14519691C2214yes—
24C2×#14519691C2214yes—
25#16839654—22no—
26#16839652—22no—
27#16839622C2211yescharacteristic
28#16839617C2212yes—
29C22⋊C4×Dic61C2212yes—
30C22⋊C4×Dic61C2212yes—
31C4×#11758198—22no—
32C4×C22⋊Dic61C2211yescharacteristic
33#16839609—22no—
34#16839529C2214yes—
35C2×C22⋊Q8×C61C2211yescharacteristic
36C61×#380C2211yescharacteristic
37C4×C22⋊C4×C61C2211yescharacteristic
38C61×#342C2214yes—
39C24×D61C2311yescharacteristic
40C22×D244C2×C412yes—
41C22×D244C2×C412yes—
42C22×D244C2×C411yescharacteristic, complemented
43C22×C22⋊D61C2312yes—
44C23×Dic61C2311yescharacteristic
45C22×C4×D61—22no—
46C22×C4×D61C2×C412yescomplemented
47#14519772—24no—
48#14519772—24no—
49#14519766—24no—
50#14519766—24no—
51#14519762—24no—
52#14519762—24no—
53#14519752—24no—
54#14519752—24no—
55#14519751—21no—
56#14519751—21no—
57#14519751—21no—
58#14519751—21no—
59#14519747—24no—
60#14519747—24no—
61#14519737—24no—
62#14519737—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61C2×C411yescharacteristic, complemented
65C2×#11758196C2×C412yescomplemented
66C2×C22⋊Dic61C2312yes—
67C2×C22⋊Dic61C2312yes—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198C2×C412yes—
72C2×#11758198C2×C412yes—
73C2×#11758198C2×C412yes—
74C2×#11758198C2×C412yes—
75C2×#11758198C2×C412yescomplemented
76C2×#11758198C2×C412yescomplemented
77C2×#11758198D412yes—
78C2×#11758198D412yes—
79C2×#11758198D412yes—
80C2×#11758198D412yes—
81C22⋊C4×D61—24no—
82C22⋊C4×D61—24no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61C2×C412yescomplemented
87#14519691—28no—
88#14519691—28no—
89#14519684—21no—
90#14519684—21no—
91#14519684—22no—
92#14519684—22no—
93C22×Q8×C61C2×C411yescharacteristic, complemented
94C23×C4×C61C2311yescharacteristic
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97C22⋊Q8×C61—21no—
98C22⋊Q8×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2×C412yescomplemented
101C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
102C2×C22⋊C4×C61C2312yes—
103C2×C22⋊C4×C61C2312yes—
104C2×C22⋊C4×C61C2312yes—
105C2×C42×C61—21no—
106#95×C61—21no—
107#95×C61—21no—
108C24×C61C2411yescharacteristic
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—81no—
112C23×D61—81no—
113C23×D61C22×C412yes—
114C23×D61C22×C412yes—
115C23×D61C2×D412yes—
116C23×D61C2×D412yes—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—81no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—81no—
123C22×C4×C61C22×C412yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—24no—
134C2×C22⋊D61—24no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—81no—
138C22×Dic61C22×C412yes—
139C22×Dic61C22×C412yes—
140C22×Dic61C2×D412yes—
141C22×Dic61C2×D412yes—
142C2×D244—24no—
143C2×D244—24no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—82no—
147C2×D244—82no—
148C2×D244—81no—
149C2×C4×D61—28no—
150C2×C4×D61—24no—
151C2×C4×D61—82no—
152C2×C4×D61—82no—
153C2×C4×D61—82no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—81no—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—24no—
163C22⋊C4×C61#4114yes—
164C42×C61—81no—
165C22⋊Dic61—22no—
166C22⋊Dic61—24no—
167C22⋊Dic61#4114yes—
168#11758198—28no—
169#11758198—24no—
170#11758198—24no—
171#11758198—22no—
172#11758198—22no—
173#11758198—24no—
174#11758198—82no—
175#11758198—82no—
176#11758198C22⋊C414yes—
177#11758198C22⋊C414yes—
178#11758198C22⋊C414yes—
179#11758198C22⋊C414yes—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—81no—
183#11758196—24no—
184C4×Dic61—24no—
185C4×Dic61—82no—
186C4×Dic61—82no—
187C4×Dic61—81no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61C23×C411yescharacteristic
191C23×C61C22×D411yescharacteristic
192C23×C61C22×D411yescharacteristic
193C23×C61C2×#4112yes—
194C23×C61C2×#4112yes—
195C22×D61—22no—
196C22×D61—22no—
197C22×D61—24no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—24no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—84no—
211C22×D61—84no—
212C22×D61C2×C22⋊C414yes—
213Q8×C61—81no—
214Q8×C61—81no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C22⋊D61—44no—
236C22⋊D61—42no—
237C22⋊D61—42no—
238C2×Dic61—22no—
239C2×Dic61—24no—
240C2×Dic61—24no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61C2×C22⋊C414yes—
250D244—81no—
251D244—81no—
252D244—84no—
253D244—84no—
254C4×D61—84no—
255C4×D61—88no—
256#21422—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—42no—
264C22×C61—42no—
265C22×C61C22×C22⋊C411yescharacteristic
266C22×C61C4×#4112yes—
267C22×C61#52512yes—
268C22×C61#53211yescharacteristic
269C22×C61#53211yescharacteristic
270C2×D61—24no—
271C2×D61—24no—
272C2×D61—24no—
273C2×D61—44no—
274C2×D61—44no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—82no—
279C2×D61—82no—
280C2×D61—84no—
281C2×D61—84no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—44no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61—82no—
290Dic61—24no—
291Dic61—44no—
292Dic61—42no—
293Dic61—82no—
294C2×#538—611no—
295#2312—611no—
296#2273—611no—
297#1996—611no—
298#1996D6111yescharacteristic, complemented
299#1964—611no—
300#1964—611no—
301#1898—614no—
302C4×#99—614no—
303C2×C61—22no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—22no—
307C2×C61#229711yescharacteristic
308C2×C61#288311yescharacteristic
309C2×C61#288311yescharacteristic
310D61—44no—
311D61—82no—
312#538—1222no—
313#538—1222no—
314#538—1222no—
315#538—1222no—
316C2×#126—612no—
317C2×#124—612no—
318C2×#123—612no—
319C2×C22⋊Q8C2×D6111yescharacteristic
320C2×#121—611no—
321C2×#121—612no—
322C2×#120—612no—
323C2×C4×D4—612no—
324C22×C22⋊C4—611no—
325C22×C22⋊C4—612no—
326C2×#99—614no—
327C2×#99—614no—
328#388—1222no—
329#388—1222no—
330#380—611no—
331#380C2×D6111yescharacteristic
332#379—612no—
333C4×C22⋊C4—611no—
334C4×C22⋊C4—612no—
335C4×C22⋊C4—612no—
336C4×C22⋊C4—1222no—
337C4×C22⋊C4—1222no—
338C4×C22⋊C4C2×D6111yescharacteristic
339#342—614no—
340#342C2×D6114yes—
341C61#2142211yescharacteristic, complemented, Sylow
342C25—611no—
343C22×Q8C4×D6111yescharacteristic, complemented
344C22×D4—612no—
345C22×D4—612no—
346C22×D4—612no—
347C22×D4—611no—
348C23×C4—611no—
349C23×C4—612no—
350C23×C4—1222no—
351C23×C4C22×D6111yescharacteristic
352#126—1224no—
353#126—1224no—
354#124—1224no—
355#124—1224no—
356#123—1224no—
357#123—1224no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362#121—1224no—
363#121—1224no—
364#121—1221no—
365#121—1221no—
366#121—1221no—
367#121—1221no—
368#120—1224no—
369#120—1224no—
370C4×D4—1224no—
371C4×D4—1224no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4C4×D6112yescomplemented
377C2×C4⋊C4C4×D6111yescharacteristic, complemented
378C2×C22⋊C4—612no—
379C2×C22⋊C4—612no—
380C2×C22⋊C4—612no—
381C2×C22⋊C4—612no—
382C2×C22⋊C4—612no—
383C2×C22⋊C4—612no—
384C2×C22⋊C4—612no—
385C2×C22⋊C4—612no—
386C2×C22⋊C4—612no—
387C2×C22⋊C4—612no—
388C2×C22⋊C4—612no—
389C2×C22⋊C4—612no—
390C2×C22⋊C4—1224no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1224no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4—1222no—
395C2×C22⋊C4C22×D6112yes—
396C2×C22⋊C4C22×D6112yes—
397C2×C22⋊C4C22×D6112yes—
398C2×C42—21no—
399C2×C42—612no—
400C2×C42—1222no—
401C2×C42—1222no—
402C2×C42—1221no—
403#99—1228no—
404#99—1228no—
405#95—21no—
406#95—21no—
407#95—1222no—
408#95—1222no—
409#95—1221no—
410#95—1221no—
411C24—612no—
412C24—612no—
413C24—612no—
414C24—612no—
415C24—1222no—
416C24—1222no—
417C24—4881no—
418C24—4881no—
419C24C23×D6111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—81no—
423C2×D4—1224no—
424C2×D4—1224no—
425C2×D4—1222no—
426C2×D4—1222no—
427C2×D4—1224no—
428C2×D4—1224no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—4881no—
432C2×D4—4882no—
433C2×D4—4882no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—81no—
437C22×C4—612no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—1224no—
442C22×C4—1228no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—4882no—
446C22×C4—4882no—
447C22×C4—4882no—
448C22×C4—4881no—
449C22×C4C2×C4×D6112yes—
450C22×C4C2×C4×D6112yes—
451C22×C4C2×C4×D6111yescharacteristic
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—1224no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—4881no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—614no—
471C22⋊C4—614no—
472C22⋊C4—614no—
473C22⋊C4—614no—
474C22⋊C4—614no—
475C22⋊C4—1224no—
476C22⋊C4—1224no—
477C22⋊C4—1224no—
478C22⋊C4—1228no—
479C22⋊C4—1222no—
480C22⋊C4—1222no—
481C22⋊C4—1222no—
482C22⋊C4—1224no—
483C22⋊C4—4882no—
484C22⋊C4—4882no—
485C22⋊C4#1175822614yes—
486C42—81no—
487C42—1224no—
488C42—4881no—
489C42—4882no—
490C42—4882no—
491C23—41no—
492C23—41no—
493C23—614no—
494C23—1224no—
495C23—1222no—
496C23—1222no—
497C23—1222no—
498C23—1222no—
499C23—1224no—
500C23—1222no—
501C23—4884no—
502C23—4884no—
503C23—2442no—
504C23—2442no—
505C23—2442no—
506C23—2442no—
507C23—2442no—
508C23—2442no—
509C23—2442no—
510C23—2442no—
511C23C22×C4×D6111yescharacteristic
512C23C2×D4×D6111yescharacteristic
513C23C2×D4×D6111yescharacteristic
514C23#41×D6112yes—
515C23C2×#1175822612yes—
516Q8—81no—
517Q8—81no—
518D4—4881no—
519D4—4881no—
520D4—4884no—
521D4—4884no—
522D4—2444no—
523D4—2442no—
524D4—2442no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—614no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—4884no—
546C2×C4—4888no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C22⋊C4×D6111yescharacteristic
557C2×C4C22⋊C4×D6111yescharacteristic
558C2×C4C22⋊C4×D6111yescharacteristic
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—1224no—
568C22—1224no—
569C22—1224no—
570C22—4884no—
571C22—4882no—
572C22—4882no—
573C22—4884no—
574C22—2444no—
575C22—2444no—
576C22—2442no—
577C22—2442no—
578C22—2442no—
579C22C2×C22⋊C4×D6111yescharacteristic
580C22C4×#1175822612yes—
581C22#1684027512yes—
582C22#1684031111yescharacteristic
583C22#1684031311yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—82no—
592C4—1224no—
593C4—4882no—
594C4—2444no—
595C4—2442no—
596C2—22no—
597C2—21no—
598C2—21no—
599C2—22no—
600C2—4882no—
601C2—2444no—
602C2#2144830811yescharacteristic
603C2#2145427711yescharacteristic
604C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840352C2
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448416C2semidirect
3. #21448171C2semidirect
4. #21446805C2semidirect
5. #21446655C2semidirect
6. #21446654C2semidirect
7. #21446271C2semidirect
8. #21445606C2semidirect
9. C61×#1996C2semidirect
14. C2×#14519772C4semidirect
15. C2×#14519766C4semidirect
16. C2×#14519762C4semidirect
17. C2×#14519752C4semidirect
42. C22×D244C2×C4semidirect
46. C22×C4×D61C2×C4semidirect
64. C2×C4⋊Dic61C2×C4semidirect
65. C2×#11758196C2×C4semidirect
75. C2×#11758198C2×C4semidirect
76. C2×#11758198C2×C4semidirect
86. C2×C4×Dic61C2×C4semidirect
93. C22×Q8×C61C2×C4semidirect
100. C2×C4⋊C4×C61C2×C4semidirect
101. C2×C4⋊C4×C61C2×C4semidirect
298. #1996D61semidirect
341. C61#21422semidirect
343. C22×Q8C4×D61semidirect
376. C2×C4⋊C4C4×D61semidirect
377. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403522
#214484162
#214481712
#214468052
#214466552
#214466542
#214462712
#214456062
C61×#19962
#2142261