Finite Group Databasebeta

← #29571461

Subgroups — #29571461

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic, complemented
3C2×#16839498C212yesmaximal, complemented
4C2×#16839495C212yesmaximal
5C61×#1434C211yesmaximal, characteristic, complemented
6#16840296—24no—
7#16840296—24no—
8C2×#14519771—21no—
9C2×#14519769C411yescharacteristic, complemented
10C2×#14519765C411yescharacteristic, complemented
11C2×#14519760—21no—
12C2×#14519756C2211yescharacteristic
13C2×#14519751C2211yescharacteristic
14C2×C4×Dic122C411yescharacteristic, complemented
15C2×C4×D244C411yescharacteristic, complemented
16C2×C4×C22⋊D61—21no—
17C2×#14519734—21no—
18C2×C22⋊#92418C2212yes—
19#16839517—21no—
20#16839517—21no—
21#16839498—24no—
22#16839495—24no—
23C22×C42×C61C2211yescharacteristic
24C2×#95×C61—21no—
25C2×#95×C61—21no—
26C2×#95×C61C2212yes—
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C4×D61—21no—
31C22×#92418—22no—
32#14519771—28no—
33#14519769—22no—
34#14519769—22no—
35#14519765—22no—
36#14519765—22no—
37#14519760—28no—
38#14519756—22no—
39#14519756D414yes—
40#14519751—22no—
41#14519751D414yes—
42C4×Dic122—22no—
43C4×Dic122—22no—
44C4×D244—22no—
45C4×D244—22no—
46C4×C22⋊D61—28no—
47#14519734—28no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×C4⋊Dic61C2×C411yescharacteristic
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×C22⋊Dic61—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×C4×Dic61—21no—
60C22⋊#92418—22no—
61C22⋊#92418—22no—
62C23×C4×C61—22no—
63C23×C4×C61D411yescharacteristic
64C23×C4×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×C42×C61—22no—
67C2×C42×C61—22no—
68C2×C42×C61C2×C411yescharacteristic
69C2×C42×C61C2×C411yescharacteristic
70C2×C42×C61D411yescharacteristic
71C2×C42×C61D411yescharacteristic
72#95×C61—24no—
73#95×C61—22no—
74#95×C61—22no—
75#95×C61—42no—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—24no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D412yes—
101C22×C4×C61C2×D412yes—
102C2×C22⋊D61—24no—
103C2×C22⋊D61—42no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C2×D244—21no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244C22⋊C412yes—
113C2×C4×D61—24no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×Dic122—21no—
117C2×Dic122—41no—
118C2×Dic122—41no—
119C2×Dic122C22⋊C412yes—
120C42×C61—21no—
121C42×C61—21no—
122C42×C61—21no—
123C42×C61—21no—
124C42×C61—22no—
125C42×C61—22no—
126C22⋊Dic61—24no—
127#11758198—24no—
128#11758198—24no—
129#11758198—24no—
130#11758198—24no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61C22⋊C412yes—
134C4⋊Dic61C22⋊C412yes—
135#11758196—24no—
136#11758196—24no—
137#11758196—24no—
138#11758196—24no—
139C4×Dic61—24no—
140C2×#92418—42no—
141C2×#92418—42no—
142C2×#92418—42no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61C2×C22⋊C411yescharacteristic
148C23×C61#12012yes—
149C23×C61#13512yes—
150C23×C61AGL(1,ℤ/8)11yescharacteristic
151C23×C61#13711yescharacteristic
152C22×D61—22no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—44no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—44no—
180C2×C4×C61—44no—
181C2×C4×C61—44no—
182C2×C4×C61—82no—
183C2×C4×C61—82no—
184C2×C4×C61—82no—
185C2×C4×C61—82no—
186C2×C4×C61#10412yes—
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61#12012yes—
190C22⋊D61—44no—
191C22⋊D61—44no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201D244—42no—
202D244—42no—
203C4×D61—48no—
204Dic122—42no—
205Dic122—42no—
206#92418—82no—
207#8330—611nomaximal, Sylow
208C22×C61—22no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61#37911yescharacteristic
217C22×C61#41011yescharacteristic
218C22×C61#41011yescharacteristic
219C22×C61#41611yescharacteristic
220C22×C61#41711yescharacteristic
221C22×C61C2×#10411yescharacteristic
222C22×C61#42111yescharacteristic
223C22×C61#44912yes—
224C22×C61#45212yes—
225C2×D61—42no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—22no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—22no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61—84no—
240Dic61—42no—
241Dic61—42no—
242Dic61—42no—
243C2×#529—611no—
244#1817—611no—
245C2×#328—612no—
246C2×#327—612no—
247#1434D6111yescharacteristic, complemented
248C2×C61—22no—
249C2×C61—22no—
250C2×C61#150011yescharacteristic
251C2×C61#150911yescharacteristic
252C2×C61#151211yescharacteristic
253C2×C61#152111yescharacteristic
254C2×C61#178211yescharacteristic
255C2×C61#178811yescharacteristic
256C2×C61#178911yescharacteristic
257D61—82no—
258#529—1224no—
259#529—1224no—
260C2×#126—1221no—
261C2×#125—611no—
262C2×#124—611no—
263C2×#123—1221no—
264C2×C22⋊Q8—611no—
265C2×#121—611no—
266C2×C4×Q8—611no—
267C2×C4×D4—611no—
268C2×C4×D4—1221no—
269C2×#117—1221no—
270C22×C42C2×D6111yescharacteristic
271C2×C22⋊C8—612no—
272C2×#95—21no—
273C2×#95—21no—
274C2×#95C2×D6112yes—
275#336—1221no—
276#336—1221no—
277#328—1224no—
278#327—1224no—
279C61#833011yescharacteristic, complemented, Sylow
280C22×Q8—611no—
281C22×D4—611no—
282C22×D4—1221no—
283C23×C4—22no—
284C23×C4—1221no—
285C23×C4C22⋊D6111yescharacteristic
286C23×C4C22⋊D6111yescharacteristic
287C23×C4C22×D6111yescharacteristic
288C22×C8—1222no—
289#126—1228no—
290#125—1222no—
291#125—1222no—
292#124—1222no—
293#124—1222no—
294#123—1228no—
295C22⋊Q8—614no—
296C22⋊Q8—1222no—
297#121—614no—
298#121—1222no—
299C4×Q8—1222no—
300C4×Q8—1222no—
301C4×D4—1222no—
302C4×D4—1222no—
303C4×D4—1228no—
304#117—1228no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—1221no—
319C2×C42C4×D6111yescharacteristic
320C2×C42C4×D6111yescharacteristic
321C2×C42D24411yescharacteristic
322C2×C42D24411yescharacteristic
323C22⋊C8—1222no—
324C22⋊C8—1222no—
325#95—24no—
326#95—22no—
327#95—22no—
328#95—42no—
329C24—1221no—
330C24C2×C22⋊D6111yescharacteristic
331C2×Q8—612no—
332C2×Q8—1221no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×D4—612no—
336C2×D4—1224no—
337C2×D4—1221no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2441no—
341C2×D4—2442no—
342C2×D4—2441no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—1224no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4#1175819811yescharacteristic
366C22×C4#1175819811yescharacteristic
367C22×C4#1175819811yescharacteristic
368C22×C4#1175819811yescharacteristic
369C22×C4C2×C4×D6111yescharacteristic
370C22×C4C2×D24411yescharacteristic
371C22×C4D4×D6112yes—
372C22×C4D4×D6112yes—
373C2×C8—2442no—
374C2×C8—2442no—
375C2×C8—2442no—
376C4⋊C4—612no—
377C4⋊C4—612no—
378C4⋊C4—1224no—
379C4⋊C4—1224no—
380C4⋊C4—1224no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1224no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—22no—
394C42—22no—
395C42—1224no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—1222no—
401C23—2441no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23C2×#1175819811yescharacteristic
408C23#1451974512yes—
409C23#1451979712yes—
410C23#1451980311yescharacteristic
411C23#1451980811yescharacteristic
412Q8—2442no—
413Q8—2442no—
414D4—2442no—
415D4—2442no—
416D4—2444no—
417D4—2444no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—2448no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4#1451970512yes—
456C2×C4C22⋊C4×D6111yescharacteristic
457C2×C4C22⋊C4×D6111yescharacteristic
458C2×C4#1451974712yes—
459C8—4882no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—21no—
467C22—21no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—2442no—
473C22—2442no—
474C22—2442no—
475C22#1683961711yescharacteristic
476C22#1683973511yescharacteristic
477C22#1683973511yescharacteristic
478C22#1683975611yescharacteristic
479C22#1683976111yescharacteristic
480C22C2×#1451970511yescharacteristic
481C22#1683978011yescharacteristic
482C22#1683990512yes—
483C22#1683992212yes—
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—84no—
492C4—2442no—
493C4—2442no—
494C4—2442no—
495C2—22no—
496C2—22no—
497C2—4882no—
498C2#2144430311yescharacteristic
499C2#2144434211yescharacteristic
500C2#2144435511yescharacteristic
501C2#2144439411yescharacteristic
502C2#2144573611yescharacteristic
503C2#2144575711yescharacteristic
504C2#2144576411yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1434C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1434D61
hypocenterC61#8330
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #21445887C2semidirect
3. C2×#16839498C2semidirect
5. C61×#1434C2semidirect
9. C2×#14519769C4semidirect
10. C2×#14519765C4semidirect
14. C2×C4×Dic122C4semidirect
15. C2×C4×D244C4semidirect
247. #1434D61semidirect
279. C61#8330semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
#214458872
C2×#168394982
C2×#168394952
C61×#14342
#833061