Finite Group Databasebeta

← #29575346

Subgroups — #29575346

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C8×D61C211yesmaximal, characteristic, complemented
2C4×#14519748C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519748C411yescharacteristic
10C2×C4×C22⋊D61—21no—
11C2×C42×D61C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519689—21no—
14C2×C4×#92418C2211yescharacteristic
15C2×C8×Dic61—21no—
16C4×C8×D61—22no—
17C4×C8×D61—22no—
18#16839665C411yescharacteristic
19#16839658C411yescharacteristic
20#16839650—21no—
21#16839638—21no—
22#16839619C411yescharacteristic
23C4×C4⋊Dic61C2211yescharacteristic
24C4×C22⋊Dic61—21no—
25#16839516—21no—
26D4⋊#92418—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37C2×C8×D61—24no—
38C2×C8×D61—24no—
39C2×C8×D61—24no—
40#14519748—22no—
41#14519748C814yescomplemented
42C4×C22⋊D61—42no—
43C4×C22⋊D61—42no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C42×D61—21no—
56C42×D61—21no—
57C42×D61—21no—
58C42×D61—21no—
59C4⋊#92418—21no—
60C4⋊#92418—21no—
61#14519689—42no—
62C4×#92418—21no—
63C4×#92418D412yescomplemented
64C8×Dic61—24no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C22×D4×C61C2×C411yescharacteristic
69C23×C4×C61—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C2×C4⋊C4×C61C2×C411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C2×C42×C61C2311yescharacteristic
79C4⋊C8×C61—21no—
80C4⋊C8×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61D412yescomplemented
83C24×C61—21no—
84C23×D61C22⋊C411yescharacteristic
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61C2×C812yescomplemented
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—24no—
102C2×C22⋊D61—42no—
103C2×C22⋊D61—42no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C2×C4×D61—22no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—21no—
120C2×C4×D61—22no—
121C2×C4×D61C2×C812yes—
122C2×C4×D61M1612yes—
123C2×C4×D61D812yes—
124C2×C4×D61SD1612yes—
125C2×C8×C61—22no—
126C2×C8×C61—22no—
127C2×C8×C61—22no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C42×C61#4111yescharacteristic
139C22⋊Dic61—24no—
140C22⋊Dic61—42no—
141C22⋊Dic61—42no—
142#11758198—42no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61C2×C812yescomplemented
147#11758196—42no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C4×Dic61—21no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—41no—
160C2×#92418—41no—
161C2×#92418—41no—
162C8×D61—216no—
163C23×C61—22no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61C2×C22⋊C411yescharacteristic
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61C22⋊C812yes—
176C22×D61#10212yes—
177C22×D61#10412yes—
178D4×C61—22no—
179D4×C61—22no—
180D4×C61—41no—
181D4×C61—41no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61C4×D411yescharacteristic
192C2×C4×C61C4×D411yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12311yescharacteristic
197C2×C4×C61C22×C811yescharacteristic
198C2×C4×C61C2×M1611yescharacteristic
199C2×C4×C61#13111yescharacteristic
200C2×C4×C61#13111yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C2×SD1611yescharacteristic
203C2×C4×C61#13511yescharacteristic
204C2×C4×C61#13511yescharacteristic
205C22⋊D61—48no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—22no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61C22⋊C812yes—
219C2×Dic61#10212yes—
220C2×Dic61#10412yes—
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—22no—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—22no—
230C4×D61—22no—
231C8×C61—24no—
232C8×C61—81no—
233#92418—24no—
234#92418—81no—
235#9072—611nomaximal, Sylow
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61—81no—
243C22×C61#38611yescharacteristic
244C22×C61C2×C22⋊C811yescharacteristic
245C22×C61#40811yescharacteristic
246C22×C61C2×#10211yescharacteristic
247C22×C61#41611yescharacteristic
248C22×C61C2×#10411yescharacteristic
249C22×C61C2×#10411yescharacteristic
250C2×D61—22no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61D4⋊C814yescomplemented
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—81no—
260C4×C61C8×D411yescharacteristic
261C4×C61C8×D411yescharacteristic
262C4×C61#43511yescharacteristic
263C4×C61#43511yescharacteristic
264C4×C61#46511yescharacteristic
265C4×C61#46511yescharacteristic
266C4×C61#46611yescharacteristic
267C4×C61#46611yescharacteristic
268Dic61—22no—
269Dic61—22no—
270Dic61—22no—
271Dic61—42no—
272Dic61—81no—
273C22×C4×C8—611no—
274C4×#121—611no—
275#1797—611no—
276C2×D4⋊C8—611no—
277C2×D4⋊C8D6111yescharacteristic, complemented
278#1279—611no—
279#1279—611no—
280C2×C61—82no—
281C2×C61C2×D4⋊C811yescharacteristic
282C2×C61#147611yescharacteristic
283C2×C61#149211yescharacteristic
284C2×C61#149411yescharacteristic
285C2×C61#186911yescharacteristic
286C2×C61#189311yescharacteristic
287C2×C61#189611yescharacteristic
288D61—24no—
289C23×C8—1221no—
290C2×#121—611no—
291C2×C4×D4—1221no—
292C2×C4×D4C2×D6111yescharacteristic
293C22×C42—611no—
294C2×C4⋊C8—611no—
295C2×C4⋊C8C2×D6111yescharacteristic
296C2×C22⋊C8—1221no—
297C2×C4×C8—611no—
298C2×C4×C8—1222no—
299C2×C4×C8—1221no—
300C2×C4×C8—1222no—
301C2×C4×C8C2×D6111yescharacteristic
302#390—611no—
303#389—611no—
304#388—1221no—
305#386—1221no—
306#380—611no—
307C4×C4⋊C4—611no—
308C4×C22⋊C4—1221no—
309#336—1221no—
310D4⋊C8—22no—
311D4⋊C8—1222no—
312C61#907211yescharacteristic, complemented, Sylow
313C22×D4—1221no—
314C22×D4C4×D6111yescharacteristic
315C23×C4—21no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—1224no—
322C22×C8—1224no—
323C22×C8—1224no—
324C22×C8—1221no—
325C22×C8—1221no—
326#121—614no—
327#121—1222no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—2442no—
333C4×D4—2442no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—611no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4C4×D6111yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C42—611no—
344C2×C42—611no—
345C2×C42—611no—
346C2×C42—1221no—
347C2×C42—1221no—
348C2×C42—1221no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42C22×D6111yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—1221no—
355C4⋊C8—1221no—
356C22⋊C8—2442no—
357C4×C8—21no—
358C4×C8—612no—
359C4×C8—1224no—
360C4×C8—1221no—
361C4×C8C22⋊D6112yescomplemented
362#95—1221no—
363#95—1221no—
364#95—1221no—
365C24—21no—
366C24—611no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—1224no—
373C2×D4—2442no—
374C2×D4—2442no—
375C2×D4C8×D6112yescomplemented
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—612no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4C2×C4×D6111yescharacteristic
405C22×C4D4×D6111yescharacteristic
406C22×C4D4×D6111yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—12216no—
414C2×C8—1222no—
415C2×C8—1222no—
416C2×C8—1222no—
417C2×C8—2441no—
418C2×C8—2441no—
419C2×C8—2441no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—612no—
423C4⋊C4—1221no—
424C4⋊C4—1221no—
425C4⋊C4—1221no—
426C4⋊C4—2442no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—1224no—
430C22⋊C4—2442no—
431C22⋊C4—2442no—
432C22⋊C4—2442no—
433C42—1221no—
434C42—1221no—
435C42—1221no—
436C42—1221no—
437C42—1221no—
438C42—1221no—
439C42—2441no—
440C42—2441no—
441C42#1175822211yescharacteristic
442C42D4×D6111yescharacteristic
443C42#1175822411yescharacteristic
444C42C2×C22⋊D6111yescharacteristic
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—612no—
453C23—612no—
454C23—612no—
455C23—1221no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23C22⋊C4×D6111yescharacteristic
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—2448no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—612no—
477C2×C4—1224no—
478C2×C4—1224no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4#1451973711yescharacteristic
500C2×C4C4×C22⋊D6111yescharacteristic
501C2×C4#1451974511yescharacteristic
502C2×C4#1451974811yescharacteristic
503C2×C4#1451975011yescharacteristic
504C2×C4#1451975911yescharacteristic
505C2×C4C2×C8×D6111yescharacteristic
506C2×C4M16×D6111yescharacteristic
507C2×C4#1451978311yescharacteristic
508C2×C4#1451978511yescharacteristic
509C2×C4D8×D6111yescharacteristic
510C2×C4SD16×D6111yescharacteristic
511C2×C4#1451979611yescharacteristic
512C2×C4#1451979811yescharacteristic
513C8—24no—
514C8—81no—
515C8—1224no—
516C8—4881no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—614no—
525C22—1222no—
526C22—1222no—
527C22—1222no—
528C22—1222no—
529C22—1222no—
530C22—1222no—
531C22#1683963811yescharacteristic
532C22C22⋊C8×D6111yescharacteristic
533C22#1683972711yescharacteristic
534C22#102×D6111yescharacteristic
535C22#1683975511yescharacteristic
536C22#104×D6111yescharacteristic
537C22#104×D6111yescharacteristic
538C4—21no—
539C4—21no—
540C4—81no—
541C4—1222no—
542C4—1222no—
543C4—1222no—
544C4—4881no—
545C4—2442no—
546C4#1683982511yescharacteristic
547C4C8×C22⋊D6111yescharacteristic
548C4#1683983111yescharacteristic
549C4#1683983611yescharacteristic
550C4#1683998811yescharacteristic
551C4#1683999011yescharacteristic
552C4#1683999511yescharacteristic
553C4#1683999711yescharacteristic
554C2—82no—
555C2—1224no—
556C2D4⋊C8×D6111yescharacteristic
557C2#2144419811yescharacteristic
558C2#2144426811yescharacteristic
559C2#2144427611yescharacteristic
560C2#2144610811yescharacteristic
561C2#2144624411yescharacteristic
562C2#2144625911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#9072
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×C4×C8×D61C2semidirect
3. #21445796C2semidirect
4. C2×D4⋊#92418C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C2×C61×D4⋊C8C2semidirect
41. #14519748C8semidirect
63. C4×#92418D4semidirect
82. C4×C8×C61D4semidirect
90. C2×D4×C61C2×C8semidirect
146. C4⋊Dic61C2×C8semidirect
256. C2×D61D4⋊C8semidirect
277. C2×D4⋊C8D61semidirect
312. C61#9072semidirect
361. C4×C8C22⋊D61semidirect
375. C2×D4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D612
C4×#145197482
#214457962
C2×D4⋊#924182
#214436592
#214436582
C2×C61×D4⋊C82
#907261