Finite Group Databasebeta

← #29570919

Subgroups — #29570919

Order 15616.

724 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic61C211yesmaximal, characteristic
2C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
3C2×#16839496C211yesmaximal, characteristic
4#21444044C211yesmaximal, characteristic, complemented
5#21443699C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic
8C2×D4×Dic61—21no—
9C2×D4×Dic61C411yescharacteristic, complemented
10C22×C4×Dic61C2211yescharacteristic
11C2×C22⋊#92418C2211yescharacteristic
12C2×C8×Dic61—21no—
13#16839665C411yescharacteristic, complemented
14#16839661C411yescharacteristic, complemented
15#16839655—21no—
16#16839642—21no—
17#16839622C2211yescharacteristic
18C4⋊C4×Dic61C411yescharacteristic, complemented
19C22⋊C4×Dic61—21no—
20C2×#14519684—21no—
21C2×#14519684—21no—
22C2×#14519684C2211yescharacteristic
23#16839516—21no—
24#16839496C414yescomplemented
25C2×#121×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C61×#327C414yescomplemented
29C23×Dic61—21no—
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×#92418—21no—
34D4×Dic61—42no—
35D4×Dic61—42no—
36D4×Dic61—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C22⋊#92418—21no—
51C22⋊#92418C2×C412yescomplemented
52C8×Dic61—42no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—42no—
58#14519684—42no—
59#14519684C2×C412yescomplemented
60C22×D4×C61—21no—
61C22×D4×C61C2×C411yescharacteristic
62C23×C4×C61—21no—
63C23×C4×C61C2311yescharacteristic
64C22×C8×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67#121×C61C2×C412yes—
68#121×C61C2×C412yes—
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61C2×C412yescomplemented
73#95×C61—21no—
74#95×C61C2×C412yescomplemented
75C24×C61—21no—
76C24×C61C2×D411yescharacteristic
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—21no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61C4212yes—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—22no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—22no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—42no—
113C22×Dic61—42no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—42no—
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61D812yes—
126C22×Dic61SD1612yes—
127C2×C8×C61—22no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61C4212yes—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—22no—
134C22⋊Dic61—42no—
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61—42no—
138C22⋊Dic61—42no—
139C4⋊Dic61—42no—
140C4⋊Dic61—41no—
141C4⋊Dic61—41no—
142C4×Dic61—22no—
143C4×Dic61—22no—
144C4×Dic61—41no—
145C4×Dic61—41no—
146C4×Dic61—42no—
147C2×#92418—22no—
148C2×#92418—41no—
149C2×#92418—41no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—22no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61C4×D411yescharacteristic
163C23×C61C4×D411yescharacteristic
164C23×C61C2×D811yescharacteristic
165C23×C61C2×SD1611yescharacteristic
166C23×C61#13511yescharacteristic
167C23×C61#13511yescharacteristic
168D4×C61—42no—
169D4×C61—42no—
170D4×C61—42no—
171D4×C61—42no—
172D4×C61—42no—
173D4×C61—42no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—22no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61—81no—
192C2×C4×C61C2×C4211yescharacteristic
193C2×C4×C61#11711yescharacteristic
194C2×C4×C61C4×D411yescharacteristic
195C2×C4×C61C4×D411yescharacteristic
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—42no—
218C2×Dic61—84no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222C2×Dic61—81no—
223C2×Dic61#9912yes—
224C2×Dic61#10212yes—
225C2×Dic61#10212yes—
226C8×C61—42no—
227#92418—42no—
228#8220—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—42no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61—81no—
247C22×C61—81no—
248C22×C61C4×C22⋊C411yescharacteristic
249C22×C61C2×#9911yescharacteristic
250C22×C61#41011yescharacteristic
251C22×C61C2×#10211yescharacteristic
252C22×C61#41611yescharacteristic
253C22×C61#42111yescharacteristic
254C22×C61#42111yescharacteristic
255C22×C61C4×D811yescharacteristic
256C22×C61C4×D811yescharacteristic
257C22×C61C4×SD1611yescharacteristic
258C22×C61C4×SD1611yescharacteristic
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—42no—
264C4×C61—82no—
265Dic61—22no—
266Dic61—22no—
267Dic61—22no—
268Dic61—41no—
269Dic61—82no—
270Dic61—81no—
271Dic61—81no—
272C4×#121—611no—
273C4×C22⋊C8—611no—
274C2×#327—611no—
275C2×#327D6111yescharacteristic
276#1434—611no—
277#1294—611no—
278#1294—611no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—21no—
283C2×C61—82no—
284C2×C61#151611yescharacteristic
285C2×C61#151711yescharacteristic
286C2×C61#151911yescharacteristic
287C2×C61#152111yescharacteristic
288C2×C61C4×#9911yescharacteristic
289C2×C61#175911yescharacteristic
290C2×C61C4×#10211yescharacteristic
291C2×#121C2×D6111yescharacteristic
292C2×C4×D4—611no—
293C2×C4×D4—1221no—
294C22×C42—611no—
295C2×C22⋊C8—611no—
296C2×C22⋊C8C2×D6111yescharacteristic
297C2×C4×C8—1221no—
298#390—611no—
299#389—611no—
300#388—1221no—
301#386—1221no—
302#380—611no—
303C4×C4⋊C4—611no—
304C4×C22⋊C4—1221no—
305C2×#95—611no—
306C2×#95—1221no—
307C2×#95—1221no—
308C2×#95C2×D6111yescharacteristic
309#336—1221no—
310#327—614no—
311#327Dic6114yescomplemented
312C61#822011yescharacteristic, complemented, Sylow
313C22×D4—21no—
314C22×D4C4×D6111yescharacteristic
315C23×C4—21no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—1221no—
319C23×C4—1221no—
320C23×C4C22×D6111yescharacteristic
321C22×C8—21no—
322C22×C8—1221no—
323#121—21no—
324#121—21no—
325#121C4×D6112yes—
326#121C2×Dic6112yes—
327C4×D4—2442no—
328C4×D4—2442no—
329C4×D4—2442no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4C4×D6111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C42—611no—
340C2×C42—611no—
341C2×C42—611no—
342C2×C42—611no—
343C2×C42—1221no—
344C2×C42—2442no—
345C22⋊C8—21no—
346C22⋊C8—612no—
347C22⋊C8—1221no—
348C22⋊C8C2×Dic6112yescomplemented
349C4×C8—2442no—
350#95—21no—
351#95—612no—
352#95—1221no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356#95—2442no—
357#95—2442no—
358#95C2×Dic6112yescomplemented
359C24—21no—
360C24D4×D6111yescharacteristic
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4C4×Dic6112yes—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—612no—
385C22×C4—612no—
386C22×C4—611no—
387C22×C4—1222no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1222no—
393C22×C4—2442no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4C2×C4×D6111yescharacteristic
406C22×C4C2×C4×D6111yescharacteristic
407C22×C4D4×D6111yescharacteristic
408C22×C4#1175822411yescharacteristic
409C22×C4#1175822411yescharacteristic
410C22×C4C22×Dic6111yescharacteristic
411C2×C8—22no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—1222no—
415C2×C8—2441no—
416C2×C8—2441no—
417C4⋊C4—21no—
418C4⋊C4—2441no—
419C4⋊C4—2441no—
420C4⋊C4—2442no—
421C4⋊C4C4×Dic6112yes—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C42—1222no—
430C42—1222no—
431C42—2441no—
432C42—2441no—
433C42—2442no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23C22⋊C4×D6111yescharacteristic
446C23#1451973711yescharacteristic
447C23D4×Dic6111yescharacteristic
448C23D8×D6111yescharacteristic
449C23SD16×D6111yescharacteristic
450C23#1451979611yescharacteristic
451C23#1451979811yescharacteristic
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—612no—
477C2×C4—612no—
478C2×C4—612no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—1221no—
486C2×C4—1221no—
487C2×C4—1221no—
488C2×C4—4884no—
489C2×C4—4881no—
490C2×C4—4881no—
491C2×C4—4881no—
492C2×C4—4881no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2442no—
506C2×C4C2×C4×Dic6111yescharacteristic
507C2×C4#1451973311yescharacteristic
508C2×C4#1451973711yescharacteristic
509C2×C4D4×Dic6111yescharacteristic
510C8—42no—
511C8—2442no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22C22⋊C4×Dic6111yescharacteristic
532C22#99×D6111yescharacteristic
533C22#1683973411yescharacteristic
534C22#102×D6111yescharacteristic
535C22#1683975511yescharacteristic
536C22#1683977711yescharacteristic
537C22#1683977711yescharacteristic
538C22#1683984211yescharacteristic
539C22D8×Dic6111yescharacteristic
540C22SD16×Dic6111yescharacteristic
541C22#1683985311yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—82no—
548C4—1222no—
549C4—1222no—
550C4—1222no—
551C4—4882no—
552C4—4881no—
553C4—4881no—
554C4—2441no—
555C2—21no—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—82no—
560C2#2144437211yescharacteristic
561C2#2144437711yescharacteristic
562C2#2144438511yescharacteristic
563C2#2144439311yescharacteristic
564C2#99×Dic6111yescharacteristic
565C2#2144563111yescharacteristic
566C2#102×Dic6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenterC2×#327D61
hypocenterC61#8220
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×Dic61C2semidirect
4. #21444044C2semidirect
5. #21443699C2semidirect
6. #21443698C2semidirect
9. C2×D4×Dic61C4semidirect
13. #16839665C4semidirect
14. #16839661C4semidirect
18. C4⋊C4×Dic61C4semidirect
24. #16839496C4semidirect
28. C61×#327C4semidirect
51. C22⋊#92418C2×C4semidirect
59. #14519684C2×C4semidirect
72. C22⋊C8×C61C2×C4semidirect
74. #95×C61C2×C4semidirect
311. #327Dic61semidirect
312. C61#8220semidirect
348. C22⋊C8C2×Dic61semidirect
358. #95C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#121×Dic612
C22⋊C8×Dic612
C2×#168394962
#214440442
#214436992
#214436982
C2×C61×#3272
#822061