Finite Group Databasebeta

← #29574789

Subgroups — #29574789

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839963C211yesmaximal, characteristic
2#21448731C211yesmaximal, characteristic, complemented
3#21446745C211yesmaximal, characteristic
4#21446624C211yesmaximal, characteristic
5C2×#16839492C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11C2×#14519742—21no—
12#16839963—22no—
13#16839963C414yescomplemented
14C2×#14519699—21no—
15C2×#14519699—21no—
16C2×#14519699—21no—
17C2×#14519697—22no—
18C2×C4×#92418C2211yescharacteristic
19#16839658—21no—
20#16839657—22no—
21#16839631—21no—
22C4⋊C4×Dic61—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839492—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—21no—
32C2×#11758190—24no—
33C2×#11758190—42no—
34C2×#11758190—42no—
35C22×#92418—21no—
36#14519774—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774C2×C412yes—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122C2×C412yes—
43C4×Dic122D412yes—
44#14519742—42no—
45#14519742—42no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61D411yescharacteristic
48C2×C4⋊Dic61D411yescharacteristic
49C2×#11758196—21no—
50C2×#11758196—22no—
51C2×#11758196—22no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—21no—
55#14519699—24no—
56#14519699—42no—
57#14519699—42no—
58#14519697—44no—
59C4×#92418—21no—
60C4×#92418—21no—
61#14519684—22no—
62#14519684—21no—
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D412yes—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61C2×C412yes—
73C23×D61—41no—
74C22×C4×C61—22no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122C22⋊C412yes—
102C2×Dic122D812yes—
103C2×Dic122SD1612yes—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C42×C61C22×C411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61C22⋊C412yes—
124C4⋊Dic61SD1612yescomplemented
125#11758196—22no—
126#11758196—22no—
127#11758196—44no—
128#11758196—82no—
129C4×Dic61—22no—
130C4×Dic61—22no—
131C4×Dic61—44no—
132C4×Dic61—41no—
133C4×Dic61—41no—
134C2×#92418—22no—
135C2×#92418—41no—
136C2×#92418—41no—
137#11758190—48no—
138C23×C61#12011yescharacteristic
139C22×D61—42no—
140C22×D61—81no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12311yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×SD1611yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177D244—44no—
178D244—42no—
179D244—42no—
180D244—42no—
181D244—42no—
182D244—82no—
183D244—81no—
184D244—81no—
185D244—81no—
186D244—81no—
187Dic122—22no—
188Dic122—22no—
189Dic122—22no—
190Dic122#10214yescomplemented
191C8×C61—42no—
192C8×C61—81no—
193#92418—42no—
194#8979—611nomaximal, Sylow
195C22×C61#38611yescharacteristic
196C22×C61#44711yescharacteristic
197C22×C61#44811yescharacteristic
198C22×C61#44811yescharacteristic
199C22×C61#44911yescharacteristic
200C22×C61#45311yescharacteristic
201C22×C61#45411yescharacteristic
202C2×D61—82no—
203C2×D61—82no—
204C2×D61—82no—
205C2×D61—161no—
206C2×D61—161no—
207C2×D61—161no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—82no—
212C4×C61C2×#10211yescharacteristic
213C4×C61#41711yescharacteristic
214C4×C61C4×SD1611yescharacteristic
215C4×C61#44011yescharacteristic
216C4×C61#46011yescharacteristic
217C4×C61#46411yescharacteristic
218C4×C61#48011yescharacteristic
219C4×C61#48111yescharacteristic
220Dic61—24no—
221Dic61—42no—
222Dic61—42no—
223Dic61—81no—
224C2×#460—611no—
225Q8×C4⋊C4—611no—
226#1982—611no—
227#1957—611no—
228C2×Q8⋊C8—611no—
229#1296D6111yescharacteristic, complemented
230#1279—611no—
231C2×C61#162111yescharacteristic
232C2×C61#162311yescharacteristic
233C2×C61#162611yescharacteristic
234C2×C61#162711yescharacteristic
235C2×C61#187411yescharacteristic
236C2×C61#188011yescharacteristic
237C2×C61#188311yescharacteristic
238D61—162no—
239C22×SD16—1221no—
240C2×#127—611no—
241C2×C4×Q8—611no—
242C2×C4×Q8—1221no—
243#460—614no—
244#460—1222no—
245C2×C4⋊C8C2×D6111yescharacteristic
246C2×C4⋊C8C2×D6111yescharacteristic
247C2×#102—1221no—
248C2×#102—1221no—
249C2×#102—1221no—
250C2×#102—1222no—
251C2×C4×C8—611no—
252#389—1221no—
253#389—1222no—
254#384—1221no—
255#384C2×D6111yescharacteristic
256C4×C4⋊C4—611no—
257C4×C4⋊C4—1221no—
258Q8⋊C8—1222no—
259C61#897911yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×D4—1221no—
262C22×D4—1221no—
263C22×D4—1221no—
264C2×SD16—1224no—
265C2×SD16—2442no—
266C2×SD16—2442no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—1221no—
270#127—612no—
271#127—1221no—
272#127—1221no—
273#127—1221no—
274C4×Q8—612no—
275C4×Q8—612no—
276C4×Q8—1221no—
277C4×Q8—1221no—
278C4×Q8—2442no—
279C4×Q8—2442no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4—611no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1222no—
287C2×C4⋊C4—1222no—
288C2×C4⋊C4D24412yes—
289C2×C42—1221no—
290C2×C42—1222no—
291C2×C42—1221no—
292C2×C42C22×D6111yescharacteristic
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8C4×D6112yes—
297#102—1224no—
298#102—2444no—
299#102—2442no—
300#102—2442no—
301C4×C8—1221no—
302C4×C8—1221no—
303#95—1222no—
304#95—1221no—
305C24—2441no—
306C2×Q8—612no—
307C2×Q8—612no—
308C2×Q8—612no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×D4—1222no—
313C2×D4—1222no—
314C2×D4—1222no—
315C2×D4—2442no—
316C2×D4—2442no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C22×C4—22no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4C2×D24411yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336SD16—2448no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—1222no—
344C2×C8—2441no—
345C2×C8—2441no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—612no—
352C4⋊C4—612no—
353C4⋊C4—1221no—
354C4⋊C4—1222no—
355C4⋊C4—1222no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—4882no—
360C4⋊C4—2444no—
361C42—1222no—
362C42—1222no—
363C42—2444no—
364C42—2441no—
365C42—2441no—
366C42C2×C4×D6111yescharacteristic
367C42#1175822211yescharacteristic
368C42D4×D6111yescharacteristic
369C42#1175822611yescharacteristic
370C23—4881no—
371C23—4881no—
372C23—4881no—
373C23—4881no—
374C23—4881no—
375C23—4881no—
376C23—2442no—
377C23#1451974711yescharacteristic
378Q8—614no—
379Q8—1222no—
380Q8—1222no—
381Q8—1222no—
382D4—4882no—
383D4—4881no—
384D4—4881no—
385D4—4881no—
386D4—4881no—
387D4—2444no—
388D4—2442no—
389D4—2442no—
390D4—2442no—
391D4—2442no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4C22⋊C4×D6111yescharacteristic
410C2×C4#1451973911yescharacteristic
411C2×C4C4×D24411yescharacteristic
412C2×C4#1451975011yescharacteristic
413C2×C4#1451975211yescharacteristic
414C2×C4#1451976211yescharacteristic
415C2×C4D8×D6111yescharacteristic
416C2×C4SD16×D6111yescharacteristic
417C2×C4SD16×D6111yescharacteristic
418C2×C4#1451979811yescharacteristic
419C2×C4#1451980111yescharacteristic
420C2×C4#1451980411yescharacteristic
421C2×C4#1451980911yescharacteristic
422C2×C4#1451980911yescharacteristic
423C8—42no—
424C8—81no—
425C8—2442no—
426C22—9761no—
427C22—9761no—
428C22—9761no—
429C22—9761no—
430C22—4882no—
431C22—4882no—
432C22—4882no—
433C22#1683964011yescharacteristic
434C22#1683989711yescharacteristic
435C22#1683990211yescharacteristic
436C22#1683990211yescharacteristic
437C22#1683990811yescharacteristic
438C22#1683993211yescharacteristic
439C22#1683993711yescharacteristic
440C4—21no—
441C4—21no—
442C4—82no—
443C4—1224no—
444C4—4881no—
445C4—2442no—
446C4—2442no—
447C4#102×D6111yescharacteristic
448C4#1683976211yescharacteristic
449C4#1683984911yescharacteristic
450C4#1683986111yescharacteristic
451C4#1683996111yescharacteristic
452C4#1683998711yescharacteristic
453C4#1684007711yescharacteristic
454C4#1684008211yescharacteristic
455C2—9762no—
456C2#2144488511yescharacteristic
457C2#2144489811yescharacteristic
458C2#2144491611yescharacteristic
459C2#2144492311yescharacteristic
460C2#2144613511yescharacteristic
461C2#2144617511yescharacteristic
462C2#2144619411yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#8979
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21448731C2semidirect
5. C2×#16839492C2semidirect
6. #21443658C2semidirect
7. C61×#1296C2semidirect
13. #16839963C4semidirect
124. C4⋊Dic61SD16semidirect
190. Dic122#102semidirect
229. #1296D61semidirect
259. C61#8979semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
#214487312
#214467452
#214466242
C2×#168394922
#214436582
C61×#12962
#897961