Finite Group Databasebeta

← #29575677

Subgroups — #29575677

Order 15616.

784 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
2#21454165C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519774C2211yescharacteristic
10C2×#14519752—21no—
11C2×#14519752—21no—
12C2×#14519752C412yes—
13C2×C42×D61C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519706—21no—
17C4⋊C8×D61—22no—
18C4⋊C8×D61—22no—
19C2×#14519689—21no—
20#16839663—21no—
21#16839663—21no—
22#16839663C412yes—
23#16839516—21no—
24#16839505—22no—
25#16839505—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#384C2211yescharacteristic
29C22×D244—22no—
30C22×D244—21no—
31C22×D244—21no—
32C22×D244C2×C412yes—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×#92418—21no—
37C22×#92418—21no—
38C2×C8×D61—24no—
39C2×C8×D61—42no—
40C2×C8×D61—42no—
41#14519774—21no—
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519752—44no—
46#14519752—42no—
47#14519752—42no—
48#14519752—42no—
49#14519752—42no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198—22no—
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C42×D61—21no—
57C42×D61—21no—
58C42×D61—21no—
59C42×D61—21no—
60C4⋊#92418—21no—
61C4⋊#92418—21no—
62C4⋊#92418—21no—
63C4⋊#92418D412yescomplemented
64#14519706—24no—
65#14519689—42no—
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61C2×C412yes—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61D412yescomplemented
76C23×D61—22no—
77C23×D61C22⋊C411yescharacteristic
78C22×C4×C61—22no—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—42no—
88C2×D244—42no—
89C2×D244—44no—
90C2×D244—44no—
91C2×D244—44no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—22no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—41no—
116C2×C4×D61D812yes—
117C2×C4×D61D812yes—
118C2×C4×D61SD1612yes—
119C2×C4×D61SD1612yes—
120C2×C8×C61—22no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C4⋊C4×C61—42no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134C42×C61#4111yescharacteristic
135#11758198—44no—
136#11758198—44no—
137#11758198—44no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C2×#92418—22no—
145C2×#92418—41no—
146C2×#92418—41no—
147C2×#92418—41no—
148C2×#92418—41no—
149C2×#92418—41no—
150C8×D61—48no—
151C23×C61C2×C22⋊C411yescharacteristic
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61#10012yes—
164C22×D61#10212yes—
165C22×D61#10212yes—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12311yescharacteristic
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×SD1611yescharacteristic
180C2×C4×C61C2×SD1611yescharacteristic
181C2×C4×C61#13511yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61#13711yescharacteristic
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61#10212yes—
193C2×Dic61#10212yes—
194D244—82no—
195D244—82no—
196D244—88no—
197D244—81no—
198D244—81no—
199D244—81no—
200D244—81no—
201D244—81no—
202D244—81no—
203D244—81no—
204D244—81no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—42no—
214C4×D61—42no—
215C8×C61—42no—
216C8×C61—81no—
217#92418—42no—
218#92418—81no—
219#9133—611nomaximal, Sylow
220C22×C61#38611yescharacteristic
221C22×C61C2×#10011yescharacteristic
222C22×C61#41311yescharacteristic
223C22×C61C2×#10211yescharacteristic
224C22×C61C2×#10211yescharacteristic
225C22×C61#41611yescharacteristic
226C22×C61#41711yescharacteristic
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—82no—
234C2×D61—82no—
235C2×D61—82no—
236C2×D61—82no—
237C2×D61—82no—
238C2×D61—82no—
239C2×D61—82no—
240C2×D61#33114yescomplemented
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—82no—
244C4×C61#44711yescharacteristic
245C4×C61#44811yescharacteristic
246C4×C61#46511yescharacteristic
247C4×C61#46511yescharacteristic
248C4×C61#46611yescharacteristic
249C4×C61#46611yescharacteristic
250C4×C61#48011yescharacteristic
251C4×C61#48111yescharacteristic
252Dic61—22no—
253Dic61—22no—
254Dic61—41no—
255C22×C4⋊C8—611no—
256#2856—611no—
257#1797—611no—
258C2×#331—611no—
259C2×#331—611no—
260#1296—611no—
261#1296D6111yescharacteristic, complemented
262C2×C61C2×#33111yescharacteristic
263C2×C61#154011yescharacteristic
264C2×C61#154711yescharacteristic
265C2×C61#155111yescharacteristic
266C2×C61#187411yescharacteristic
267C2×C61#189311yescharacteristic
268C2×C61#190011yescharacteristic
269D61—24no—
270D61—162no—
271C23×C8—1221no—
272C2×#127—611no—
273C2×#121—612no—
274C2×#121—1221no—
275C2×#121—1221no—
276C22×C42—611no—
277C2×C4⋊C8—611no—
278C2×C4⋊C8—611no—
279C2×C4⋊C8—1222no—
280C2×C4⋊C8—1221no—
281C2×C4⋊C8—1222no—
282C2×C4⋊C8C2×D6111yescharacteristic
283C2×C4⋊C8C2×D6111yescharacteristic
284C2×C22⋊C8—1221no—
285#390—612no—
286#390—1221no—
287#390—1221no—
288#384C2×D6111yescharacteristic
289#336—1221no—
290#331—1222no—
291#331—1222no—
292C61#913311yescharacteristic, complemented, Sylow
293C22×D4—612no—
294C22×D4—1222no—
295C22×D4—1221no—
296C22×D4—1221no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—1224no—
303C22×C8—1221no—
304C22×C8—1221no—
305C22×C8—2442no—
306C22×C8—2442no—
307#127—1221no—
308#127—1221no—
309#127—1221no—
310#127—1221no—
311#121—2442no—
312#121—2442no—
313#121—2442no—
314#121—2442no—
315#121—2444no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4C4×D6112yes—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C42—611no—
323C2×C42—611no—
324C2×C42—611no—
325C2×C42—1221no—
326C2×C42—1221no—
327C2×C42—1221no—
328C2×C42—1221no—
329C2×C42C22×D6111yescharacteristic
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—612no—
334C4⋊C8—1224no—
335C4⋊C8—1221no—
336C4⋊C8—1221no—
337C4⋊C8—1221no—
338C4⋊C8D24412yescomplemented
339C22⋊C8—2442no—
340C24—611no—
341C24—1222no—
342C2×D4—1222no—
343C2×D4—1222no—
344C2×D4—2442no—
345C2×D4—2442no—
346C2×D4—2444no—
347C2×D4—2444no—
348C2×D4—2444no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2441no—
361C22×C4—22no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—611no—
369C22×C4—1222no—
370C22×C4—1221no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—2441no—
381C22×C4C2×C4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C22×C4D4×D6111yescharacteristic
384C2×C8—22no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—1222no—
391C2×C8—2448no—
392C2×C8—2441no—
393C2×C8—2441no—
394C2×C8—2441no—
395C2×C8—2441no—
396C2×C8—2441no—
397C4⋊C4—42no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C22⋊C4—2444no—
403C22⋊C4—2444no—
404C22⋊C4—2444no—
405C42—1221no—
406C42—1221no—
407C42—1221no—
408C42—1221no—
409C42—1221no—
410C42—1221no—
411C42C2×D24411yescharacteristic
412C42#1175822211yescharacteristic
413C42D4×D6111yescharacteristic
414C42#1175822611yescharacteristic
415C23—612no—
416C23—612no—
417C23—612no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—2442no—
423C23—2442no—
424C23—2442no—
425C23—2442no—
426C23—2442no—
427C23—2442no—
428C23—2442no—
429C23C22⋊C4×D6111yescharacteristic
430D4—4882no—
431D4—4882no—
432D4—4888no—
433D4—4881no—
434D4—4881no—
435D4—4881no—
436D4—4881no—
437D4—4881no—
438D4—4881no—
439D4—4881no—
440D4—4881no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—612no—
447C2×C4—612no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—1221no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4#1451973911yescharacteristic
466C2×C4C4×D24411yescharacteristic
467C2×C4#1451974711yescharacteristic
468C2×C4#1451975011yescharacteristic
469C2×C4#1451975211yescharacteristic
470C2×C4#1451976211yescharacteristic
471C2×C4D8×D6111yescharacteristic
472C2×C4D8×D6111yescharacteristic
473C2×C4SD16×D6111yescharacteristic
474C2×C4SD16×D6111yescharacteristic
475C2×C4#1451979811yescharacteristic
476C2×C4#1451980011yescharacteristic
477C2×C4#1451980411yescharacteristic
478C2×C4#1451980911yescharacteristic
479C8—42no—
480C8—81no—
481C8—4881no—
482C8—2442no—
483C22—614no—
484C22—1222no—
485C22—1222no—
486C22—1222no—
487C22—1222no—
488C22—1222no—
489C22—1222no—
490C22—4882no—
491C22—4882no—
492C22—4882no—
493C22—4882no—
494C22—4882no—
495C22—4882no—
496C22—4882no—
497C22#1683964011yescharacteristic
498C22#100×D6111yescharacteristic
499C22#1683974511yescharacteristic
500C22#102×D6111yescharacteristic
501C22#102×D6111yescharacteristic
502C22#1683975711yescharacteristic
503C22#1683976211yescharacteristic
504C4—21no—
505C4—21no—
506C4—82no—
507C4—1222no—
508C4—1222no—
509C4—2441no—
510C4#1683989711yescharacteristic
511C4#1683990211yescharacteristic
512C4#1683999211yescharacteristic
513C4#1683999411yescharacteristic
514C4#1683999711yescharacteristic
515C4#1683999911yescharacteristic
516C4#1684007711yescharacteristic
517C4#1684008211yescharacteristic
518C2—1224no—
519C2—9762no—
520C2#331×D6111yescharacteristic
521C2#2144446711yescharacteristic
522C2#2144449511yescharacteristic
523C2#2144451311yescharacteristic
524C2#2144613511yescharacteristic
525C2#2144624611yescharacteristic
526C2#2144628111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61C2×C22⋊C4
prime radical#21454165C2
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9133
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C8×D61C2semidirect
3. #21445796C2semidirect
4. C2×#16839505C2semidirect
5. C2×#16839505C2semidirect
6. #21443702C2semidirect
7. C61×#1296C2semidirect
63. C4⋊#92418D4semidirect
75. C4⋊C8×C61D4semidirect
240. C2×D61#331semidirect
261. #1296D61semidirect
292. C61#9133semidirect
338. C4⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D612
#214541652
#214457962
C2×#168395052
#214437022
C61×#12962
#913361