Finite Group Databasebeta

← #29575598

Subgroups — #29575598

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
1#21454101C211yesmaximal, characteristic
2C2×#16839497C212yesmaximal, complemented
3#21444042C211yesmaximal, characteristic, complemented
4#21443699C212yesmaximal, complemented
5C2×C61×#407C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic, complemented
7C2×#14519751C411yescharacteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519746—21no—
10C22×C22⋊Dic61—21no—
11#16839641—21no—
12#16839641—21no—
13#16839641—21no—
14#16839622C411yescharacteristic, complemented
15#16839622C411yescharacteristic, complemented
16#16839622C2211yescharacteristic
17C2×#14519684—21no—
18C2×#14519684C2212yes—
19#16839497—24no—
20C24×C4×C61C2211yescharacteristic
21C22×M16×C61—21no—
22C61×#407—24no—
23C2×C22⋊C8×C61—21no—
24C2×C22⋊C8×C61C2212yes—
25C22×D244C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C22×C22⋊D61—21no—
28C22×C22⋊D61—21no—
29C23×Dic61—22no—
30#14519751—22no—
31#14519751—22no—
32#14519751—42no—
33#14519751—42no—
34#14519746—44no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61—24no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—42no—
43C2×C22⋊Dic61—42no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—22no—
51#14519684—22no—
52#14519684—42no—
53C25×C61D411yescharacteristic
54C23×C4×C61—22no—
55C23×C4×C61—22no—
56C23×C4×C61—42no—
57C23×C4×C61—42no—
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C23×C4×C61D411yescharacteristic
61C23×C4×C61D411yescharacteristic
62C23×C4×C61D411yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C2×M16×C61—24no—
65C2×M16×C61—42no—
66C2×M16×C61—42no—
67C22×C8×C61—22no—
68C22⋊C8×C61—24no—
69C22⋊C8×C61—22no—
70C22⋊C8×C61D414yescomplemented
71C24×C61—22no—
72C24×C61—22no—
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—22no—
76C24×C61—22no—
77C24×C61—41no—
78C24×C61—41no—
79C24×C61C22⋊C411yescharacteristic
80C24×C61C22⋊C411yescharacteristic
81C24×C61C2×D411yescharacteristic
82C23×D61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—48no—
103C22×C4×C61—48no—
104C22×C4×C61C22⋊C411yescharacteristic
105C22×C4×C61C22⋊C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D412yes—
109C22×C4×C61#4112yes—
110C2×C22⋊D61—42no—
111C2×C22⋊D61—42no—
112C2×C22⋊D61—42no—
113C2×C22⋊D61—42no—
114C2×C22⋊D61—42no—
115C2×C22⋊D61—42no—
116C2×C22⋊D61—42no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—42no—
119C2×C22⋊D61—41no—
120C22×Dic61—24no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—42no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61—42no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C2×D244—22no—
131C2×D244—41no—
132C2×D244—41no—
133M16×C61—48no—
134C2×C8×C61—24no—
135C2×C8×C61—42no—
136C2×C8×C61—42no—
137C22⋊Dic61—48no—
138C22⋊Dic61—42no—
139C22⋊Dic61—42no—
140C22⋊Dic61—42no—
141#11758198—42no—
142#11758198—42no—
143#11758198—41no—
144#11758198—41no—
145C4⋊Dic61—22no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
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#9912yes—
175C23×C61#10412yes—
176C23×C61C2×C22⋊C411yescharacteristic
177C23×C61#12112yes—
178C23×C61AGL(1,ℤ/8)11yescharacteristic
179C23×C61AGL(1,ℤ/8)12yes—
180C23×C61#13711yescharacteristic
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—44no—
202C2×C4×C61—44no—
203C2×C4×C61—44no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61#9912yes—
207C2×C4×C61C4×D412yes—
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12311yescharacteristic
210C22⋊D61—84no—
211C22⋊D61—84no—
212C22⋊D61—82no—
213C22⋊D61—82no—
214C2×Dic61—44no—
215C2×Dic61—44no—
216C2×Dic61—44no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—82no—
227C2×Dic61—82no—
228C2×Dic61—82no—
229C2×Dic61—82no—
230D244—82no—
231C8×C61—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#38611yescharacteristic
258C22×C61C2×#9911yescharacteristic
259C22×C61C2×#9911yescharacteristic
260C22×C61#41711yescharacteristic
261C22×C61#41811yescharacteristic
262C22×C61C2×#10411yescharacteristic
263C22×C61#42111yescharacteristic
264C22×C61#46812yes—
265C22×C61#46912yes—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C2×D61—81no—
273C4×C61—21no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—41no—
278Dic61—84no—
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282C2×#407D6111yescharacteristic, complemented
283#2847—611no—
284C2×#327—612no—
285C22⋊#95—611no—
286#1294—612no—
287C2×C61—22no—
288C2×C61—22no—
289C2×C61—42no—
290C2×C61—42no—
291C2×C61#150411yescharacteristic
292C2×C61#150711yescharacteristic
293C2×C61#151011yescharacteristic
294C2×C61#151311yescharacteristic
295C2×C61#187111yescharacteristic
296C2×C61#189511yescharacteristic
297C2×C61#189811yescharacteristic
298D61—161no—
299C24×C4C2×D6111yescharacteristic
300C22×M16—21no—
301C2×#121—611no—
302C2×#121—611no—
303C2×#121—611no—
304C2×#120—1221no—
305C22×C22⋊C4—1221no—
306#407—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8C2×D6112yes—
309#386—1221no—
310#386—1221no—
311#386—1221no—
312#380—611no—
313#380—611no—
314#380—611no—
315C2×#95—612no—
316C2×#95—1221no—
317#327—1224no—
318C61#911711yescharacteristic, complemented, Sylow
319C25D24411yescharacteristic
320C22×D4—611no—
321C22×D4—1221no—
322C22×D4—1221no—
323C22×D4—1221no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—1222no—
329C23×C4C4×D6111yescharacteristic
330C23×C4C4×D6111yescharacteristic
331C23×C4D24411yescharacteristic
332C23×C4C22⋊D6111yescharacteristic
333C23×C4C22⋊D6111yescharacteristic
334C23×C4C22×D6111yescharacteristic
335C2×M16—24no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—22no—
339#121—1222no—
340#121—1222no—
341#121—2442no—
342#121—2442no—
343#120—2444no—
344C2×C4⋊C4—611no—
345C2×C4⋊C4—611no—
346C2×C4⋊C4—611no—
347C2×C22⋊C4—1224no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1221no—
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1221no—
352C2×C22⋊C4—1221no—
353C2×C22⋊C4—1221no—
354C2×C22⋊C4—2442no—
355C2×C22⋊C4—2442no—
356C22⋊C8—24no—
357C22⋊C8—22no—
358C22⋊C8C22⋊D6114yescomplemented
359#95—1221no—
360#95—1221no—
361#95—1221no—
362#95—1222no—
363#95—1222no—
364#95—2442no—
365C24—21no—
366C24—22no—
367C24—22no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—1221no—
374C24#1175819811yescharacteristic
375C24#1175819811yescharacteristic
376C24C2×D24411yescharacteristic
377C2×D4—1222no—
378C2×D4—2441no—
379C2×D4—2441no—
380C2×D4—2442no—
381C2×D4—2442no—
382C2×D4—2442no—
383C2×D4—2442no—
384C2×D4—2441no—
385C2×D4—2442no—
386C2×D4—2442no—
387C2×D4—2442no—
388C2×D4—2442no—
389C2×D4—2441no—
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—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—1224no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—1221no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4#1175819811yescharacteristic
422C22×C4#1175819811yescharacteristic
423C22×C4C2×C4×D6111yescharacteristic
424C22×C4#1175822212yes—
425C22×C4C2×C22⋊D6111yescharacteristic
426C22×C4C2×C22⋊D6112yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—1222no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C22⋊C4—2442no—
435C22⋊C4—2448no—
436C22⋊C4—2442no—
437C22⋊C4—2442no—
438C22⋊C4—2442no—
439C22⋊C4—2442no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
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—2441no—
469C23—2441no—
470C23—2441no—
471C23—2441no—
472C23—2441no—
473C23—2441no—
474C23—2441no—
475C23#1451969112yes—
476C23#1451970312yes—
477C23C2×#1175819811yescharacteristic
478C23#1451975112yes—
479C23#1451980512yes—
480C23#1451980511yescharacteristic
481C23#1451981011yescharacteristic
482D4—4882no—
483D4—4884no—
484D4—4884no—
485D4—4882no—
486D4—4882no—
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—4882no—
506C2×C4—4882no—
507C2×C4—4882no—
508C2×C4—4882no—
509C2×C4—2444no—
510C2×C4—2444no—
511C2×C4—2444no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4#1451969112yes—
522C2×C4C4×C22⋊D6112yes—
523C2×C4#1451974611yescharacteristic
524C2×C4#1451976011yescharacteristic
525C8—44no—
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—4881no—
551C22—4881no—
552C22—4881no—
553C22—4881no—
554C22—4881no—
555C22—4881no—
556C22—4881no—
557C22#1683964111yescharacteristic
558C22C2×#1451969111yescharacteristic
559C22C2×#1451969111yescharacteristic
560C22#1683976411yescharacteristic
561C22#1683976811yescharacteristic
562C22C2×#1451970311yescharacteristic
563C22#1683977811yescharacteristic
564C22#1684000812yes—
565C22#1684001512yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—4884no—
572C4—4881no—
573C4—4881no—
574C4—4881no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—9761no—
580C2#2144432411yescharacteristic
581C2#2144433611yescharacteristic
582C2#2144434911yescharacteristic
583C2#2144436311yescharacteristic
584C2#2144612111yescharacteristic
585C2#2144625711yescharacteristic
586C2#2144627211yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#407C2
socleC23×C61C2×C22⋊C4
prime radical#21454101C2
cosocleC23×C4×C61C23
hypercenterC2×#407D61
hypocenterC61#9117
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16839497C2semidirect
3. #21444042C2semidirect
4. #21443699C2semidirect
5. C2×C61×#407C2semidirect
6. C2×#14519751C4semidirect
7. C2×#14519751C4semidirect
14. #16839622C4semidirect
15. #16839622C4semidirect
70. C22⋊C8×C61D4semidirect
282. C2×#407D61semidirect
318. C61#9117semidirect
358. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214541012
C2×#168394972
#214440422
#214436992
C2×C61×#4072
#911761