Finite Group Databasebeta

← #29594985

Subgroups — #29594985

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519692C211yesmaximal, characteristic
2#21448401C211yesmaximal, characteristic
3#21443943C214yesmaximal, complemented
4C22×#99×C61C211yesmaximal, characteristic
5C2×#14519736C411yescharacteristic, complemented
6C2×#14519736C411yescharacteristic, complemented
7C22×C22⋊Dic61—21no—
8C2×#14519692—21no—
9C2×#14519692—22no—
10C2×#14519692C414yescomplemented
11C2×#14519692C2212yes—
12#16839665—21no—
13#16839665—21no—
14#16839665C412yescomplemented
15#16839665C2212yes—
16#16839618—21no—
17#16839618—21no—
18C23×D4×C61C2211yescharacteristic
19C22×C22⋊C4×C61—21no—
20C2×#99×C61—21no—
21C2×#99×C61—22no—
22C2×#99×C61C414yescomplemented
23C2×#99×C61C2212yes—
24C23×Dic61—41no—
25#14519736—41no—
26#14519736—41no—
27#14519736—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C412yescomplemented
30C2×C22⋊Dic61—24no—
31C2×C22⋊Dic61—22no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—22no—
38C2×C22⋊Dic61—41no—
39C2×C22⋊Dic61—42no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C412yescomplemented
42#14519692—24no—
43#14519692—22no—
44#14519692C2×C414yescomplemented
45C25×C61D411yescharacteristic
46C25×C61D411yescharacteristic
47C22×D4×C61—41no—
48C22×D4×C61—41no—
49C22×D4×C61—42no—
50C22×D4×C61C2×C412yes—
51C22×D4×C61C2×C411yescharacteristic
52C22×D4×C61C2×C412yes—
53C22×D4×C61D411yescharacteristic
54C22×D4×C61D411yescharacteristic
55C22×D4×C61D412yes—
56C22×D4×C61Q812yes—
57C22×D4×C61C2311yescharacteristic
58C23×C4×C61—41no—
59C23×C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—24no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—41no—
63C2×C22⋊C4×C61—42no—
64#99×C61—24no—
65#99×C61—22no—
66#99×C61C2×C414yescomplemented
67C24×C61—21no—
68C24×C61—21no—
69C24×C61—22no—
70C24×C61—21no—
71C24×C61—22no—
72C24×C61—21no—
73C24×C61—82no—
74C24×C61—82no—
75C24×C61C22⋊C411yescharacteristic
76C24×C61C22⋊C411yescharacteristic
77C24×C61C22⋊C412yes—
78C24×C61C22⋊C412yes—
79C24×C61C22⋊C411yescharacteristic
80C24×C61C4⋊C412yes—
81C24×C61C4⋊C412yes—
82C24×C61C2×D411yescharacteristic
83C24×C61C2×D411yescharacteristic
84C2×D4×C61—42no—
85C2×D4×C61—42no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—42no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61C4212yes—
101C2×D4×C61C22⋊C412yes—
102C2×D4×C61C22⋊C412yes—
103C2×D4×C61C4⋊C412yes—
104C2×D4×C61C4⋊C412yes—
105C2×D4×C61C4⋊C412yes—
106C2×D4×C61C22×C411yescharacteristic
107C2×D4×C61C22×C411yescharacteristic
108C2×D4×C61C2×D411yescharacteristic
109C2×D4×C61C2×Q811yescharacteristic
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—44no—
114C22×C4×C61—42no—
115C22×C4×C61—84no—
116C22×C4×C61C4212yes—
117C22×C4×C61C22⋊C411yescharacteristic
118C22×C4×C61C4⋊C412yes—
119C22×C4×C61C22×C411yescharacteristic
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—44no—
123C22×Dic61—42no—
124C22×Dic61—84no—
125C22⋊C4×C61—24no—
126C22⋊C4×C61—44no—
127C22⋊C4×C61—42no—
128C22⋊Dic61—24no—
129C22⋊Dic61—44no—
130C22⋊Dic61—42no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—42no—
134C22⋊Dic61—82no—
135C22⋊Dic61—82no—
136C22⋊Dic61—82no—
137C22⋊Dic61—82no—
138C4⋊Dic61—42no—
139C4⋊Dic61—42no—
140C4×Dic61—42no—
141C4×Dic61—42no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—22no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—42no—
159C23×C61—44no—
160C23×C61—44no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—82no—
166C23×C61—82no—
167C23×C61—82no—
168C23×C61—82no—
169C23×C61—82no—
170C23×C61—82no—
171C23×C61—84no—
172C23×C61—84no—
173C23×C61#9512yes—
174C23×C61#9512yes—
175C23×C61#9512yes—
176C23×C61#9911yescharacteristic
177C23×C61#9911yescharacteristic
178C23×C61#9912yes—
179C23×C61C2×C22⋊C411yescharacteristic
180C23×C61C2×C22⋊C411yescharacteristic
181C23×C61C2×C22⋊C411yescharacteristic
182C23×C61C2×C4⋊C411yescharacteristic
183C23×C61C2×C4⋊C411yescharacteristic
184D4×C61—42no—
185D4×C61—42no—
186D4×C61—42no—
187D4×C61—42no—
188D4×C61—42no—
189D4×C61—42no—
190D4×C61—41no—
191D4×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—44no—
203C2×C4×C61—88no—
204C2×C4×C61—84no—
205C2×C4×C61#9512yes—
206C2×C4×C61C2×C4211yescharacteristic
207C2×C4×C61C2×C4⋊C411yescharacteristic
208C2×Dic61—44no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—88no—
216C2×Dic61—84no—
217#12582—611nomaximal, Sylow
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—22no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—22no—
224C22×C61—22no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—42no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—44no—
236C22×C61—44no—
237C22×C61—44no—
238C22×C61—44no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61—81no—
247C22×C61—82no—
248C22×C61—82no—
249C22×C61—82no—
250C22×C61—82no—
251C22×C61#34212yes—
252C22×C61#34212yes—
253C22×C61C2×#9511yescharacteristic
254C22×C61C2×#9911yescharacteristic
255C22×C61C2×#9911yescharacteristic
256C4×C61—22no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—84no—
260Dic61—82no—
261Dic61—84no—
262Dic61—82no—
263C22×#99—611no—
264C22×#99D6111yescharacteristic
265#2309—611no—
266#1393—614no—
267C2×C61—21no—
268C2×C61—21no—
269C2×C61—22no—
270C2×C61—22no—
271C2×C61—41no—
272C2×C61—41no—
273C2×C61—42no—
274C2×C61—42no—
275C2×C61—41no—
276C2×C61—41no—
277C2×C61C2×#34211yescharacteristic
278C2×C61#212712yes—
279C23×D4C2×D6111yescharacteristic
280C2×#117—611no—
281C2×#117—611no—
282C22×C22⋊C4—21no—
283C22×C22⋊C4—1221no—
284C2×#99—21no—
285C2×#99—22no—
286C2×#99—614no—
287C2×#99—612no—
288C2×#99—1221no—
289C2×#99—1222no—
290C2×#99Dic6114yescomplemented
291C2×#99C2×D6112yes—
292#390—612no—
293#390—612no—
294#390—1221no—
295#390—1221no—
296#379—1221no—
297#379—1221no—
298C61#1258211yescharacteristic, complemented, Sylow
299C25D24411yescharacteristic
300C25C22⋊D6111yescharacteristic
301C22×D4—41no—
302C22×D4—41no—
303C22×D4—42no—
304C22×D4Dic12212yes—
305C22×D4C4×D6112yes—
306C22×D4C4×D6111yescharacteristic
307C22×D4D24411yescharacteristic
308C22×D4C2×Dic6112yes—
309C22×D4C22⋊D6112yes—
310C22×D4C22⋊D6111yescharacteristic
311C22×D4C22×D6111yescharacteristic
312C23×C4—41no—
313C23×C4—2441no—
314C23×C4C4×D6111yescharacteristic
315#117—2442no—
316#117—2441no—
317#117—2441no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4—1221no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—1224no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—2442no—
333C2×C22⋊C4—2441no—
334C2×C42—612no—
335C2×C42—1221no—
336#99—24no—
337#99—22no—
338#99—614no—
339#99—1224no—
340#99—1222no—
341#99C2×Dic6114yescomplemented
342C24—21no—
343C24—21no—
344C24—21no—
345C24—22no—
346C24—21no—
347C24—22no—
348C24—82no—
349C24—82no—
350C24#1175819612yes—
351C24C4⋊Dic6112yes—
352C24#1175819811yescharacteristic
353C24#1175819811yescharacteristic
354C24#1175819812yes—
355C24#1175819811yescharacteristic
356C24C22⋊Dic6112yes—
357C24C2×D24411yescharacteristic
358C24C2×C22⋊D6111yescharacteristic
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4C4×Dic6112yes—
376C2×D4#1175819612yes—
377C2×D4#1175819612yes—
378C2×D4C4⋊Dic6112yes—
379C2×D4#1175819812yes—
380C2×D4C22⋊Dic6112yes—
381C2×D4C2×Dic12211yescharacteristic
382C2×D4C2×C4×D6111yescharacteristic
383C2×D4C22×Dic6111yescharacteristic
384C2×D4C2×C22⋊D6111yescharacteristic
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—42no—
389C22×C4—44no—
390C22×C4—84no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—4884no—
394C22×C4—2442no—
395C22×C4—2444no—
396C22×C4C4×Dic6112yes—
397C22×C4#1175819612yes—
398C22×C4#1175819811yescharacteristic
399C22×C4C2×C4×D6111yescharacteristic
400C4⋊C4—2442no—
401C4⋊C4—2442no—
402C22⋊C4—24no—
403C22⋊C4—42no—
404C22⋊C4—44no—
405C22⋊C4—1224no—
406C22⋊C4—4882no—
407C22⋊C4—4882no—
408C22⋊C4—4882no—
409C22⋊C4—4882no—
410C22⋊C4—2442no—
411C22⋊C4—2444no—
412C22⋊C4—2442no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C42—2442no—
416C42—2442no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—42no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—82no—
441C23—82no—
442C23—82no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—84no—
447C23—84no—
448C23#1451968412yes—
449C23#1451968412yes—
450C23#1451968412yes—
451C23#1451969111yescharacteristic
452C23#1451969111yescharacteristic
453C23#1451969112yes—
454C23C2×#1175819811yescharacteristic
455C23C2×#1175819811yescharacteristic
456C23C2×C22⋊Dic6111yescharacteristic
457C23C2×#1175819611yescharacteristic
458C23C2×C4⋊Dic6111yescharacteristic
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—42no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—44no—
478C2×C4—88no—
479C2×C4—84no—
480C2×C4—4888no—
481C2×C4—4884no—
482C2×C4—2444no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4#1451968412yes—
490C2×C4C2×C4×Dic6111yescharacteristic
491C2×C4C2×#1175819611yescharacteristic
492C22—22no—
493C22—22no—
494C22—22no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—22no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22#1683952812yes—
526C22#1683952812yes—
527C22C2×#1451968411yescharacteristic
528C22C2×#1451969111yescharacteristic
529C22C2×#1451969111yescharacteristic
530C4—22no—
531C4—21no—
532C4—21no—
533C4—84no—
534C4—4882no—
535C4—4884no—
536C4—4882no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—22no—
541C2—41no—
542C2—41no—
543C2—42no—
544C2—42no—
545C2—41no—
546C2—41no—
547C2C2×#1683952811yescharacteristic
548C2#2144748612yes—
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC22×#99×C61C2
socleC22×C61C2×#99
prime radicalC23×D4×C61C22
cosocleC22×D4×C61C23
hypercenterC22×#99D61
hypocenterC61#12582
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #21443943C2semidirect
5. C2×#14519736C4semidirect
6. C2×#14519736C4semidirect
10. C2×#14519692C4semidirect
14. #16839665C4semidirect
22. C2×#99×C61C4semidirect
29. C2×C4⋊Dic61C2×C4semidirect
41. C2×C4×Dic61C2×C4semidirect
44. #14519692C2×C4semidirect
66. #99×C61C2×C4semidirect
290. C2×#99Dic61semidirect
298. C61#12582semidirect
341. #99C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C22×#145196922
#214484012
#214439432
C22×#99×C612
#1258261