Finite Group Databasebeta

← #29574792

Subgroups — #29574792

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic
2#21448770C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839491C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1957C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×C4×D244C2211yescharacteristic
10C2×#14519735—21no—
11#16839954—22no—
12#16839954C414yescomplemented
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—21no—
16C2×#14519698—21no—
17C2×#14519698—21no—
18#16839663—21no—
19#16839652—22no—
20#16839619—21no—
21C4⋊C4×Dic61—21no—
22C4×C4⋊Dic61C2211yescharacteristic
23#16839491—22no—
24C2×#127×C61C2211yescharacteristic
25C2×#102×C61—22no—
26C2×C4×C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758199—24no—
31C2×#11758199—42no—
32C2×#11758199—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244C2×C412yes—
38C4×D244D412yes—
39#14519735—42no—
40#14519735—42no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—21no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C412yes—
53#14519698—24no—
54#14519698—42no—
55#14519698—42no—
56#14519684—22no—
57#14519684—21no—
58C22×D4×C61—21no—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×C8×C61—21no—
62#127×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61C2×C412yes—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D412yes—
69C2×C42×C61C2311yescharacteristic
70#102×C61—44no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C24×C61—41no—
74C23×D61—21no—
75C2×D4×C61—22no—
76C2×D4×C61—22no—
77C2×D4×C61—22no—
78C2×D4×C61—42no—
79C2×D4×C61—42no—
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×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C22×C4×C61—22no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244C22⋊C412yes—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×C4×D61—41no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C4⋊C4×C61—42no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C42×C61#4111yescharacteristic
122#11758199—48no—
123#11758198—22no—
124#11758198—22no—
125#11758198—44no—
126#11758198—82no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61C22⋊C412yes—
132C4⋊Dic61D812yescomplemented
133C4×Dic61—44no—
134C4×Dic61—41no—
135C4×Dic61—41no—
136C2×#92418—22no—
137C2×#92418—41no—
138C2×#92418—41no—
139C2×#92418—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C23×C61—42no—
143C23×C61—81no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61—81no—
147C23×C61—81no—
148C23×C61—81no—
149C23×C61#12011yescharacteristic
150C22×D61—22no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157D4×C61—44no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—42no—
161D4×C61—42no—
162D4×C61—82no—
163D4×C61—81no—
164D4×C61—81no—
165D4×C61—81no—
166D4×C61—81no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61C2×C22⋊C411yescharacteristic
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12311yescharacteristic
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61#13511yescharacteristic
180C2×C4×C61#13511yescharacteristic
181C2×C4×C61#13511yescharacteristic
182C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195D244—22no—
196D244—22no—
197D244—41no—
198D244—41no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—42no—
203C8×C61—42no—
204#92418—42no—
205#92418—81no—
206#8980—611nomaximal, Sylow
207C22×C61—82no—
208C22×C61—82no—
209C22×C61—82no—
210C22×C61—161no—
211C22×C61—161no—
212C22×C61—161no—
213C22×C61—161no—
214C22×C61#38611yescharacteristic
215C22×C61#44711yescharacteristic
216C22×C61#44911yescharacteristic
217C22×C61#44911yescharacteristic
218C22×C61#44911yescharacteristic
219C22×C61#45311yescharacteristic
220C22×C61#45411yescharacteristic
221C2×D61—42no—
222C2×D61—42no—
223C2×D61—42no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—82no—
231C4×C61#41611yescharacteristic
232C4×C61#41811yescharacteristic
233C4×C61C4×D811yescharacteristic
234C4×C61#44211yescharacteristic
235C4×C61#45911yescharacteristic
236C4×C61#46311yescharacteristic
237C4×C61#48211yescharacteristic
238C4×C61#48211yescharacteristic
239Dic61—42no—
240Dic61—42no—
241Dic61—81no—
242C2×#459—611no—
243#2354—611no—
244#1982—611no—
245#1957D6111yescharacteristic, complemented
246C2×D4⋊C8—611no—
247#1296—611no—
248#1279—611no—
249C2×C61—162no—
250C2×C61#162111yescharacteristic
251C2×C61#162411yescharacteristic
252C2×C61#162511yescharacteristic
253C2×C61#162811yescharacteristic
254C2×C61#187511yescharacteristic
255C2×C61#187911yescharacteristic
256C2×C61#188311yescharacteristic
257D61—82no—
258C22×D8—1221no—
259C2×#127C2×D6111yescharacteristic
260C2×C4×D4—611no—
261C2×#117—1221no—
262#459—614no—
263#459—1222no—
264C2×C4⋊C8—611no—
265C2×C4⋊C8—611no—
266C2×#102—22no—
267C2×#102—1221no—
268C2×#102—1221no—
269C2×#102—1221no—
270C2×C4×C8C2×D6111yescharacteristic
271#390—1221no—
272#388—1222no—
273#384C2×D6111yescharacteristic
274#380—1221no—
275C4×C4⋊C4—611no—
276C4×C4⋊C4—1221no—
277D4⋊C8—1222no—
278C61#898011yescharacteristic, complemented, Sylow
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—611no—
283C23×C4—1221no—
284C2×D8—1224no—
285C2×D8—2442no—
286C2×D8—2442no—
287C22×C8—21no—
288C22×C8—1221no—
289C22×C8—1221no—
290#127—21no—
291#127—21no—
292#127—21no—
293#127C4×D6112yes—
294C4×D4—612no—
295C4×D4—612no—
296C4×D4—1221no—
297C4×D4—1221no—
298#117—2442no—
299#117—2442no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4C22⋊D6112yes—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1222no—
308C2×C22⋊C4—1222no—
309C2×C42—1222no—
310C2×C42—1221no—
311C2×C42C22×D6111yescharacteristic
312C4⋊C8—612no—
313C4⋊C8—1221no—
314C4⋊C8—1221no—
315C4⋊C8—1221no—
316#102—44no—
317#102—1224no—
318#102—2442no—
319#102—2442no—
320C4×C8—21no—
321C4×C8—21no—
322#95—1222no—
323#95—1221no—
324C24—41no—
325C24—1221no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—612no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—1221no—
348C22×C4—22no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1221no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4D4×D6111yescharacteristic
359C22×C4D4×D6111yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361D8—2448no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—1222no—
366C2×C8—2441no—
367C2×C8—2441no—
368C2×C8—2441no—
369C2×C8—2441no—
370C2×C8—2441no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—612no—
377C4⋊C4—612no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—4882no—
385C22⋊C4—2444no—
386C42—2444no—
387C42—2441no—
388C42—2441no—
389C42C2×C4×D6111yescharacteristic
390C42#1175822211yescharacteristic
391C42D4×D6111yescharacteristic
392C42#1175822411yescharacteristic
393C23—42no—
394C23—81no—
395C23—81no—
396C23—81no—
397C23—81no—
398C23—81no—
399C23—81no—
400C23—1222no—
401C23—2441no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23#1451974511yescharacteristic
408D4—44no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418D4—1222no—
419D4—1222no—
420D4—2441no—
421D4—2441no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—1222no—
428C2×C4—1222no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4C22⋊C4×D6111yescharacteristic
441C2×C4#1451973711yescharacteristic
442C2×C4C4×C22⋊D6111yescharacteristic
443C2×C4#1451974811yescharacteristic
444C2×C4#1451975011yescharacteristic
445C2×C4#1451975911yescharacteristic
446C2×C4D8×D6111yescharacteristic
447C2×C4#1451979611yescharacteristic
448C2×C4#1451979811yescharacteristic
449C2×C4#1451979811yescharacteristic
450C2×C4#1451980111yescharacteristic
451C2×C4#1451980111yescharacteristic
452C2×C4#1451980411yescharacteristic
453C2×C4#1451980411yescharacteristic
454C8—42no—
455C8—4881no—
456C8—2442no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22—161no—
461C22—161no—
462C22—161no—
463C22—161no—
464C22—4881no—
465C22—4881no—
466C22—4881no—
467C22—4881no—
468C22—2442no—
469C22—2442no—
470C22—2442no—
471C22#1683963811yescharacteristic
472C22#1683989411yescharacteristic
473C22#1683990411yescharacteristic
474C22#1683990611yescharacteristic
475C22#1683990611yescharacteristic
476C22#1683992911yescharacteristic
477C22#1683993411yescharacteristic
478C4—21no—
479C4—21no—
480C4—82no—
481C4—4881no—
482C4—2442no—
483C4—2442no—
484C4#1683975511yescharacteristic
485C4#1683976511yescharacteristic
486C4#1683984211yescharacteristic
487C4#1683987111yescharacteristic
488C4#1683995611yescharacteristic
489C4#1683997611yescharacteristic
490C4#1684008411yescharacteristic
491C4#1684008511yescharacteristic
492C2—162no—
493C2—4882no—
494C2#2144488111yescharacteristic
495C2#2144490011yescharacteristic
496C2#2144490511yescharacteristic
497C2#2144492611yescharacteristic
498C2#2144613811yescharacteristic
499C2#2144616411yescharacteristic
500C2#2144619811yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1957C2
socleC23×C61#120
prime radicalC2×#16839954C2
cosocleC2×C42×C61C23
hypercenter#1957D61
hypocenterC61#8980
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #21448770C2semidirect
3. #21446747C2semidirect
4. C2×#16839491C2semidirect
5. #21443702C2semidirect
6. #21443659C2semidirect
7. C61×#1957C2semidirect
12. #16839954C4semidirect
132. C4⋊Dic61D8semidirect
245. #1957D61semidirect
278. C61#8980semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
#214487702
#214467472
C2×#168394912
#214437022
#214436592
C61×#19572
#898061