Finite Group Databasebeta

← #29575599

Subgroups — #29575599

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839726C211yesmaximal, characteristic, complemented
2C2×#16839496C212yesmaximal, complemented
3#21444042C211yesmaximal, characteristic, complemented
4#21443697C212yesmaximal, complemented
5C61×#2847C211yesmaximal, characteristic
6C22×#11758194—21no—
7C22×C22⋊Dic61—21no—
8#16839726—24no—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11C2×#14519684—21no—
12C2×#14519684C2212yes—
13#16839496—24no—
14C24×C4×C61C2211yescharacteristic
15C2×#121×C61C411yescharacteristic, complemented
16C2×#121×C61C411yescharacteristic, complemented
17C2×#121×C61C2211yescharacteristic
18C2×#120×C61—21no—
19C61×#386—21no—
20C61×#386—21no—
21C61×#386—21no—
22C61×#380C411yescharacteristic, complemented
23C61×#380C411yescharacteristic, complemented
24C61×#380C2211yescharacteristic
25C23×Dic61—22no—
26C2×#11758194—24no—
27C2×#11758194—42no—
28C2×#11758194—42no—
29C22×#92418—22no—
30C2×C22⋊Dic61—24no—
31C2×C22⋊Dic61—42no—
32C2×C22⋊Dic61—42no—
33C22⋊#92418—24no—
34C22⋊#92418—22no—
35C22⋊#92418D414yescomplemented
36#14519684—22no—
37#14519684—22no—
38#14519684—42no—
39C25×C61D411yescharacteristic
40C22×D4×C61—21no—
41C22×D4×C61—21no—
42C22×D4×C61—21no—
43C22×D4×C61C2×C411yescharacteristic
44C23×C4×C61—22no—
45C23×C4×C61—22no—
46C23×C4×C61—42no—
47C23×C4×C61—42no—
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54#121×C61—22no—
55#121×C61—22no—
56#121×C61—42no—
57#121×C61—42no—
58#120×C61—44no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68#95×C61—21no—
69#95×C61—21no—
70#95×C61—21no—
71C24×C61—22no—
72C24×C61—22no—
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—22no—
76C24×C61—22no—
77C24×C61—21no—
78C24×C61—41no—
79C24×C61—41no—
80C24×C61C22⋊C411yescharacteristic
81C24×C61C22⋊C411yescharacteristic
82C24×C61C2×D411yescharacteristic
83C2×D4×C61—22no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—42no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61—42no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—48no—
119C22×C4×C61—48no—
120C22×C4×C61C22⋊C411yescharacteristic
121C22×C4×C61C22⋊C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D412yes—
125C22×C4×C61#4112yes—
126C22×Dic61—24no—
127C22×Dic61—42no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61—42no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—42no—
137C22⋊C4×C61—42no—
138C22⋊C4×C61—42no—
139C22⋊C4×C61—42no—
140C22⋊C4×C61—42no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C22⋊Dic61—48no—
144#11758194—48no—
145C2×#92418—24no—
146C2×#92418—42no—
147C2×#92418—42no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—24no—
153C23×C61—24no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—44no—
167C23×C61—44no—
168C23×C61—44no—
169C23×C61—44no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61#9912yes—
182C23×C61#10412yes—
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61#12112yes—
185C23×C61AGL(1,ℤ/8)11yescharacteristic
186C23×C61AGL(1,ℤ/8)12yes—
187C23×C61#13711yescharacteristic
188D4×C61—82no—
189D4×C61—84no—
190D4×C61—84no—
191D4×C61—82no—
192D4×C61—82no—
193C2×C4×C61—24no—
194C2×C4×C61—24no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—44no—
207C2×C4×C61—44no—
208C2×C4×C61—44no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61#9912yes—
221C2×C4×C61C4×D412yes—
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61#12311yescharacteristic
224C2×Dic61—44no—
225C2×Dic61—44no—
226C2×Dic61—44no—
227C2×Dic61—82no—
228C2×Dic61—82no—
229C2×Dic61—82no—
230C2×Dic61—82no—
231#92418—44no—
232#9117—611nomaximal, Sylow
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—22no—
238C22×C61—22no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—22no—
245C22×C61—22no—
246C22×C61—22no—
247C22×C61—48no—
248C22×C61—48no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61#38611yescharacteristic
265C22×C61C2×#9911yescharacteristic
266C22×C61C2×#9911yescharacteristic
267C22×C61#41711yescharacteristic
268C22×C61#41811yescharacteristic
269C22×C61C2×#10411yescharacteristic
270C22×C61#42111yescharacteristic
271C22×C61#46812yes—
272C22×C61#46912yes—
273C4×C61—21no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—22no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61—81no—
281Dic61—84no—
282C2×#407—611no—
283#2847D6111yescharacteristic
284C2×#327—612no—
285C22⋊#95—611no—
286#1294—612no—
287C2×C61—22no—
288C2×C61—22no—
289C2×C61—42no—
290C2×C61—42no—
291C2×C61—161no—
292C2×C61#150411yescharacteristic
293C2×C61#150711yescharacteristic
294C2×C61#151011yescharacteristic
295C2×C61#151311yescharacteristic
296C2×C61#187111yescharacteristic
297C2×C61#189511yescharacteristic
298C2×C61#189811yescharacteristic
299C24×C4C2×D6111yescharacteristic
300C22×M16—1221no—
301C2×#121Dic6111yescharacteristic, complemented
302C2×#121Dic6111yescharacteristic, complemented
303C2×#121C2×D6111yescharacteristic
304C2×#120—21no—
305C22×C22⋊C4—1221no—
306#407—1224no—
307C2×C22⋊C8—612no—
308C2×C22⋊C8—1221no—
309#386—21no—
310#386—21no—
311#386—21no—
312#380Dic6111yescharacteristic, complemented
313#380Dic6111yescharacteristic, complemented
314#380C2×D6111yescharacteristic
315C2×#95—612no—
316C2×#95—1221no—
317#327—1224no—
318C61#911711yescharacteristic, complemented, Sylow
319C25C22⋊D6111yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C2×Dic6111yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—1222no—
329C23×C4C2×Dic6111yescharacteristic
330C23×C4C2×Dic6111yescharacteristic
331C23×C4C22⋊D6111yescharacteristic
332C23×C4C22⋊D6111yescharacteristic
333C23×C4C22⋊D6111yescharacteristic
334C23×C4C22×D6111yescharacteristic
335C2×M16—1224no—
336C2×M16—2442no—
337C2×M16—2442no—
338C22×C8—1222no—
339#121—22no—
340#121—22no—
341#121—42no—
342#121—42no—
343#120—44no—
344C2×C4⋊C4C2×Dic6111yescharacteristic
345C2×C4⋊C4C2×Dic6111yescharacteristic
346C2×C4⋊C4C2×Dic6111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—1224no—
354C2×C22⋊C4—2442no—
355C2×C22⋊C4—2442no—
356C22⋊C8—614no—
357C22⋊C8—1224no—
358C22⋊C8—1222no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—1222no—
363#95—1222no—
364#95—2442no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊Dic6111yescharacteristic
375C24C22⋊Dic6111yescharacteristic
376C24C2×C22⋊D6111yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—48no—
413C22×C4—48no—
414C22×C4—1224no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4C22⋊Dic6111yescharacteristic
422C22×C4C22⋊Dic6111yescharacteristic
423C22×C4D4×D6112yes—
424C22×C4#1175822412yes—
425C22×C4C22×Dic6111yescharacteristic
426C22×C4C2×C22⋊D6111yescharacteristic
427M16—2448no—
428C2×C8—1224no—
429C2×C8—2442no—
430C2×C8—2442no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—2448no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#1451969212yes—
476C23#1451970412yes—
477C23C2×C22⋊Dic6111yescharacteristic
478C23#1451974912yes—
479C23#1451980211yescharacteristic
480C23#1451980312yes—
481C23#1451980711yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—4882no—
515C2×C4—4882no—
516C2×C4—4882no—
517C2×C4—4882no—
518C2×C4—2444no—
519C2×C4—2444no—
520C2×C4—2444no—
521C2×C4#1451969212yes—
522C2×C4D4×Dic6112yes—
523C2×C4#1451974511yescharacteristic
524C2×C4#1451975811yescharacteristic
525C8—2444no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#1683964211yescharacteristic
558C22C2×#1451969211yescharacteristic
559C22C2×#1451969211yescharacteristic
560C22#1683976311yescharacteristic
561C22#1683976711yescharacteristic
562C22C2×#1451970411yescharacteristic
563C22#1683977911yescharacteristic
564C22#1684000612yes—
565C22#1684001312yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—4884no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2#2144432311yescharacteristic
581C2#2144433511yescharacteristic
582C2#2144434811yescharacteristic
583C2#2144436211yescharacteristic
584C2#2144612211yescharacteristic
585C2#2144625811yescharacteristic
586C2#2144627311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2847C2
socleC23×C61C2×C22⋊C4
cosocleC23×C4×C61C23
hypercenter#2847D61
hypocenterC61#9117
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#16839726C2semidirect
2. C2×#16839496C2semidirect
3. #21444042C2semidirect
4. #21443697C2semidirect
15. C2×#121×C61C4semidirect
16. C2×#121×C61C4semidirect
22. C61×#380C4semidirect
23. C61×#380C4semidirect
35. C22⋊#92418D4semidirect
301. C2×#121Dic61semidirect
302. C2×#121Dic61semidirect
312. #380Dic61semidirect
313. #380Dic61semidirect
318. C61#9117semidirect

Maximal subgroups

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

subgroupindex
C2×#168397262
C2×#168394962
#214440422
#214436972
C61×#28472
#911761