Finite Group Databasebeta

← #29570027

Subgroups — #29570027

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839724C211yesmaximal, characteristic
2#380×D61C211yesmaximal, characteristic
3C2×#16839609C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758189—21no—
10C2×C4⋊C4×D61C412yescomplemented
11C22×#11758198—21no—
12C2×C22⋊C4×D61—21no—
13C22×C4×Dic61—21no—
14#16839724—22no—
15#16839724C414yescomplemented
16C2×C22⋊#92418C2211yescharacteristic
17C2×#14519689—21no—
18#16839622C2211yescharacteristic
19#16839621—21no—
20#16839620—21no—
21#16839619C412yescomplemented
22#16839609—22no—
23#16839609C414yescomplemented
24C2×#14519684C2211yescharacteristic
25#95×D61—21no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C24×D61D411yescharacteristic
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C22×C4×D61—22no—
33C22×C4×D61—44no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61C2×C412yes—
36C22×C4×D61C2×C412yes—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61D412yes—
41C22×C4×D61Q812yes—
42C2×#11758189—24no—
43C2×#11758189—44no—
44C22×#92418—21no—
45C2×C4⋊Dic61C2×C412yes—
46C2×#11758196—22no—
47C4⋊C4×D61—44no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—28no—
50C2×#11758198—24no—
51C2×#11758198—22no—
52C22⋊C4×D61—42no—
53C22⋊C4×D61—42no—
54C2×C4×Dic61—24no—
55C2×C4×Dic61—44no—
56C22⋊#92418—21no—
57C22⋊#92418C2×C412yescomplemented
58#14519689—24no—
59#14519684—21no—
60#14519684—21no—
61#14519684—22no—
62#14519684C2×C412yescomplemented
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C22⋊C4×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61C2×C412yescomplemented
70#95×C61—21no—
71#95×C61—21no—
72#95×C61C2×C412yescomplemented
73C24×C61C2×D411yescharacteristic
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—24no—
79C23×D61—42no—
80C23×D61C22⋊C411yescharacteristic
81C23×D61C22⋊C412yes—
82C23×D61C22⋊C411yescharacteristic
83C23×D61C4⋊C412yes—
84C22×C4×C61—24no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×Q811yescharacteristic
97C22×Dic61—24no—
98C22×Dic61—24no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C412yes—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C4⋊C412yes—
108C2×C4×D61—24no—
109C2×C4×D61—24no—
110C2×C4×D61—44no—
111C2×C4×D61—44no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—44no—
117C2×C4×D61—44no—
118C2×C4×D61—44no—
119C2×C4×D61C4212yes—
120C2×C4×D61C4212yes—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C4⋊C412yes—
124C2×C4×D61C4⋊C412yes—
125C2×C4×D61C4⋊C412yes—
126C2×C4×D61C4⋊C412yes—
127C2×C8×C61—22no—
128C2×C8×C61—42no—
129C4⋊C4×C61—42no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—41no—
134#11758198—216no—
135#11758198—44no—
136C4⋊Dic61—42no—
137#11758196—44no—
138C4×Dic61—48no—
139C2×#92418—22no—
140C2×#92418—42no—
141#11758189—48no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C22⋊C411yescharacteristic
146C23×C61C2×C4⋊C411yescharacteristic
147C23×C61AGL(1,ℤ/8)11yescharacteristic
148C23×C61AGL(1,ℤ/8)11yescharacteristic
149C23×C61#13711yescharacteristic
150C23×C61#13711yescharacteristic
151C22×D61—22no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—24no—
163C22×D61—24no—
164C22×D61—42no—
165C22×D61—42no—
166C22×D61—44no—
167C22×D61—44no—
168C22×D61—44no—
169C22×D61—44no—
170C22×D61#9512yes—
171C22×D61#9512yes—
172C22×D61#10414yes—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—44no—
182C2×C4×C61—44no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61C2×C4211yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C4⋊C411yescharacteristic
190C2×C4×C61C2×C4⋊C411yescharacteristic
191C2×Dic61—22no—
192C2×Dic61—24no—
193C2×Dic61—24no—
194C2×Dic61—24no—
195C2×Dic61—42no—
196C2×Dic61—44no—
197C2×Dic61—44no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61#9512yes—
203C2×Dic61#9512yes—
204C2×Dic61#9914yes—
205C4×D61—24no—
206C4×D61—24no—
207C4×D61—24no—
208C4×D61—24no—
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—42no—
212C4×D61—42no—
213C4×D61—88no—
214C8×C61—42no—
215#92418—42no—
216#8019—611nomaximal, Sylow
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—22no—
225C22×C61C2×#9511yescharacteristic
226C22×C61C2×#9912yes—
227C22×C61#41711yescharacteristic
228C22×C61#41711yescharacteristic
229C22×C61#41811yescharacteristic
230C22×C61#41911yescharacteristic
231C22×C61C2×#10412yes—
232C22×C61#42811yescharacteristic
233C22×C61#42811yescharacteristic
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—24no—
237C2×D61—24no—
238C2×D61—22no—
239C2×D61—22no—
240C2×D61—22no—
241C2×D61—44no—
242C2×D61—44no—
243C2×D61—44no—
244C2×D61—44no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61#33914yes—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—44no—
253C4×C61—82no—
254Dic61—22no—
255Dic61—44no—
256Dic61—82no—
257Dic61#34214yes—
258C2×#407—611no—
259C2×#380—611no—
260C2×C4×C22⋊C4—611no—
261#1294—611no—
262#1294—611no—
263#1294—611no—
264#1294D6111yescharacteristic, complemented
265C2×C61—21no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—21no—
269C2×C61#150712yes—
270C2×C61#150812yes—
271C2×C61C2×#33911yescharacteristic
272C2×C61#173611yescharacteristic
273C2×C61C2×#34211yescharacteristic
274D61—24no—
275D61—42no—
276C24×C4—611no—
277C22×M16—1221no—
278C22×C4⋊C4—612no—
279C22×C22⋊C4—1221no—
280C22×C22⋊C4—1221no—
281C22×C42—1221no—
282#407—614no—
283#407—1222no—
284C2×C22⋊C8—611no—
285C2×C22⋊C8—1221no—
286C2×C22⋊C8C2×D6111yescharacteristic
287#380—611no—
288#380—612no—
289#380—1221no—
290#380—1221no—
291#380C2×D6111yescharacteristic
292C4×C22⋊C4—614no—
293C4×C22⋊C4—1222no—
294C2×#95—611no—
295C2×#95—1221no—
296C2×#95C2×D6111yescharacteristic
297C61#801911yescharacteristic, complemented, Sylow
298C25—611no—
299C23×C4—21no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—612no—
304C23×C4—611no—
305C23×C4—612no—
306C23×C4—611no—
307C23×C4—612no—
308C23×C4—612no—
309C23×C4—1222no—
310C23×C4—1221no—
311C23×C4—2444no—
312C23×C4C22×D6111yescharacteristic
313C2×M16—1224no—
314C2×M16—2444no—
315C22×C8—21no—
316C22×C8—1221no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—2444no—
320C2×C4⋊C4C4×D6112yes—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—1224no—
323C2×C22⋊C4—1228no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—2442no—
327C2×C22⋊C4—2442no—
328C2×C42—1224no—
329C2×C42—2444no—
330C22⋊C8—21no—
331C22⋊C8—612no—
332C22⋊C8—1224no—
333C22⋊C8—1221no—
334C22⋊C8C4×D6112yescomplemented
335#95—21no—
336#95—21no—
337#95—612no—
338#95—1222no—
339#95—1221no—
340#95—1221no—
341#95C4×D6112yescomplemented
342C24—611no—
343C24—611no—
344C24—612no—
345C24—612no—
346C24—1224no—
347C24—1221no—
348C24—1221no—
349C24—1221no—
350C24—1221no—
351C24—2442no—
352C24D4×D6111yescharacteristic
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—611no—
361C22×C4—612no—
362C22×C4—611no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—612no—
369C22×C4—612no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—1224no—
373C22×C4—1224no—
374C22×C4—1224no—
375C22×C4—1224no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2444no—
381C22×C4—2444no—
382C22×C4—2444no—
383C22×C4—2444no—
384C22×C4—2444no—
385C22×C4—2444no—
386C22×C4—2444no—
387C22×C4—2442no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4C2×C4×D6111yescharacteristic
391C22×C4C2×C4×D6111yescharacteristic
392C22×C4C2×C4×D6111yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4Q8×D6111yescharacteristic
396M16—2448no—
397C2×C8—22no—
398C2×C8—42no—
399C2×C8—1222no—
400C2×C8—2442no—
401C4⋊C4—42no—
402C4⋊C4—2442no—
403C4⋊C4—2444no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—12216no—
407C22⋊C4—2444no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42—2448no—
411C23—22no—
412C23—22no—
413C23—614no—
414C23—612no—
415C23—612no—
416C23—1224no—
417C23—1224no—
418C23—1222no—
419C23—1221no—
420C23—1221no—
421C23—1222no—
422C23—1222no—
423C23—1222no—
424C23—1221no—
425C23—1221no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—2442no—
430C23—2442no—
431C23—2444no—
432C23—2444no—
433C23—2444no—
434C23—2444no—
435C23C22⋊C4×D6111yescharacteristic
436C23C22⋊C4×D6111yescharacteristic
437C23C4⋊C4×D6111yescharacteristic
438C23#1451980111yescharacteristic
439C23#1451980411yescharacteristic
440C23#1451980611yescharacteristic
441C23#1451980911yescharacteristic
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—614no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—1224no—
460C2×C4—1224no—
461C2×C4—1224no—
462C2×C4—1224no—
463C2×C4—1224no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—1224no—
467C2×C4—4888no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4—2442no—
474C2×C4—2442no—
475C2×C4—2442no—
476C2×C4—2444no—
477C2×C4—2444no—
478C2×C4—2442no—
479C2×C4C42×D6111yescharacteristic
480C2×C4C22⋊C4×D6111yescharacteristic
481C2×C4C4⋊C4×D6111yescharacteristic
482C2×C4C4⋊C4×D6111yescharacteristic
483C8—42no—
484C8—2442no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—614no—
494C22—1222no—
495C22—1222no—
496C22—1224no—
497C22—1224no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—2444no—
502C22—2444no—
503C22—2444no—
504C22—2444no—
505C22—2442no—
506C22—2442no—
507C22#95×D6111yescharacteristic
508C22#99×D6112yes—
509C22#1683976011yescharacteristic
510C22#1683976211yescharacteristic
511C22#1683976511yescharacteristic
512C22#1683976911yescharacteristic
513C22#104×D6112yes—
514C22#1683980111yescharacteristic
515C22#1683980311yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—44no—
521C4—82no—
522C4—614no—
523C4—1222no—
524C4—4882no—
525C4—2444no—
526C2—21no—
527C2—21no—
528C2—21no—
529C2—21no—
530C2—1224no—
531C2—2442no—
532C2#2144433312yes—
533C2#2144433712yes—
534C2#339×D6111yescharacteristic
535C2#2144553711yescharacteristic
536C2#342×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#8019
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #21443699C2semidirect
5. #21443698C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
10. C2×C4⋊C4×D61C4semidirect
15. #16839724C4semidirect
21. #16839619C4semidirect
23. #16839609C4semidirect
57. C22⋊#92418C2×C4semidirect
62. #14519684C2×C4semidirect
69. C22⋊C8×C61C2×C4semidirect
72. #95×C61C2×C4semidirect
264. #1294D61semidirect
297. C61#8019semidirect
334. C22⋊C8C4×D61semidirect
341. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397242
#380×D612
C2×#168396092
#214436992
#214436982
#214436972
C61×#12942
#801961