Finite Group Databasebeta

← #29645521

Subgroups — #29645521

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444083C211yesmaximal, characteristic
2#21444080C212yesmaximal
3#21444079C212yesmaximal
4#21444078C212yesmaximal
5#21444076C212yesmaximal
6#21444075C211yesmaximal, characteristic
7#21444074C212yesmaximal
8#21444073C212yesmaximal
9C61×#1442C211yesmaximal, characteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758196C2212yes—
13C2×#14519684C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2211yescharacteristic
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2211yescharacteristic
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C22×C4⋊C4×C61C2211yescharacteristic
27C2×#95×C61C2212yes—
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2212yes—
30C2×#95×C61C2211yescharacteristic
31C23×Dic61C2312yes—
32C23×Dic61C2312yes—
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C2×C4⋊Dic61—41no—
36C2×C4⋊Dic61—41no—
37C2×C4⋊Dic61—42no—
38C2×C4⋊Dic61—42no—
39C2×#11758196—24no—
40C2×#11758196—42no—
41C2×#11758196—42no—
42#14519684—24no—
43#14519684—22no—
44#14519684—22no—
45#14519684—24no—
46#14519684—24no—
47#14519684—24no—
48#14519684—42no—
49#14519684—42no—
50#14519684—42no—
51#14519684—42no—
52#14519684—42no—
53#14519684—42no—
54#14519684—42no—
55C23×C4×C61C2312yes—
56C23×C4×C61C2312yes—
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C2×C4⋊C4×C61—41no—
61C2×C4⋊C4×C61—42no—
62#95×C61—22no—
63#95×C61—24no—
64#95×C61—41no—
65#95×C61—42no—
66C24×C61C2411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61#4112yes—
94C22×C4×C61#4112yes—
95C22×C4×C61#4112yes—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—22no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—22no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61#4114yes—
124C4⋊C4×C61—44no—
125C4⋊Dic61—44no—
126C4⋊Dic61—44no—
127#11758196—48no—
128C23×C61C2×#4111yescharacteristic
129C23×C61C2×#4111yescharacteristic
130C23×C61C2×#4111yescharacteristic
131C23×C61C2×#4112yes—
132C23×C61H(5,𝔽2)12yes—
133C23×C61H(5,𝔽2)12yes—
134C23×C61H(5,𝔽2)11yescharacteristic
135C23×C612−1+411yescharacteristic
136C23×C612−1+412yes—
137C23×C612−1+411yescharacteristic
138C23×C612−1+411yescharacteristic
139C2×C4×C61—24no—
140C2×C4×C61—22no—
141C2×C4×C61—24no—
142C2×C4×C61—22no—
143C2×C4×C61—24no—
144C2×C4×C61—22no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×Dic61—24no—
169C2×Dic61—24no—
170C2×Dic61—24no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196#17300—611nomaximal, Sylow
197C22×C61#53812yes—
198C22×C61#53912yes—
199C22×C61#53912yes—
200C22×C61#53911yescharacteristic
201C22×C61#53911yescharacteristic
202C22×C61#53912yes—
203C22×C61#53911yescharacteristic
204C22×C61#54112yes—
205C22×C61#54212yes—
206C22×C61#55212yes—
207C22×C61#55312yes—
208C22×C61#55511yescharacteristic
209C22×C61#55512yes—
210C22×C61#55611yescharacteristic
211C22×C61#55611yescharacteristic
212C22×C61#55611yescharacteristic
213C22×C61#56011yescharacteristic
214C22×C61H(3,𝔽4)11yescharacteristic
215C22×C61#56212yes—
216C22×C61#56312yes—
217C22×C61#56312yes—
218C22×C61#56311yescharacteristic
219C22×C61#56411yescharacteristic
220C4×C61—42no—
221C4×C61—42no—
222C4×C61—42no—
223C4×C61—82no—
224C4×C61—82no—
225Dic61—44no—
226Dic61—82no—
227Dic61—82no—
228Dic61—82no—
229#1444—611no—
230#1443—612no—
231#1443—612no—
232#1442—612no—
233#1442—611no—
234#1442—612no—
235#1442—612no—
236#1442D6111yescharacteristic
237#1441—612no—
238C2×C61#276911yescharacteristic
239C2×C61#277512yes—
240C2×C61#278312yes—
241C2×C61#278511yescharacteristic
242C2×C61#278712yes—
243C2×C61#279511yescharacteristic
244C2×C61#281011yescharacteristic
245C2×C61#282411yescharacteristic
246C2×C61#283411yescharacteristic
247C2×C61#283511yescharacteristic
248C2×C61#283912yes—
249C22×C4⋊C4—612no—
250C22×C4⋊C4—611no—
251C22×C4⋊C4—611no—
252C22×C4⋊C4C2×D6111yescharacteristic
253C2×#95—612no—
254C2×#95—612no—
255C2×#95—611no—
256C2×#95—612no—
257C2×#95—612no—
258C2×#95—611no—
259C2×#95—612no—
260C2×#95—612no—
261C2×#95—612no—
262C2×#95—612no—
263C2×#95—612no—
264C2×#95—612no—
265C2×#95—612no—
266C2×#95C2×D6112yes—
267C2×#95C2×D6111yescharacteristic
268C2×#95C2×D6112yes—
269C2×#95C2×D6111yescharacteristic
270C61#1730011yescharacteristic, complemented, Sylow
271C23×C4—612no—
272C23×C4—612no—
273C23×C4—612no—
274C23×C4—612no—
275C23×C4C22×D6112yes—
276C23×C4C22×D6112yes—
277C23×C4C22×D6111yescharacteristic
278C23×C4C22×D6111yescharacteristic
279C23×C4C22×D6111yescharacteristic
280C2×C4⋊C4—41no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—1224no—
283C2×C4⋊C4—2442no—
284C2×C4⋊C4—2442no—
285C2×C4⋊C4—2441no—
286C2×C4⋊C4—2441no—
287C2×C4⋊C4—2442no—
288C2×C4⋊C4—2442no—
289#95—22no—
290#95—24no—
291#95—41no—
292#95—42no—
293#95—1224no—
294#95—1224no—
295#95—1224no—
296#95—1224no—
297#95—1222no—
298#95—1222no—
299#95—2442no—
300#95—2442no—
301#95—2442no—
302#95—2442no—
303#95—2442no—
304#95—2442no—
305#95—2442no—
306C24C23×D6111yescharacteristic
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—614no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4#1175822212yes—
362C22×C4#1175822412yes—
363C22×C4#1175822612yes—
364C4⋊C4—44no—
365C4⋊C4—2448no—
366C4⋊C4—2444no—
367C4⋊C4—2444no—
368C23#41×D6112yes—
369C23C2×#1175822411yescharacteristic
370C23C2×#1175822211yescharacteristic
371C23C2×#1175822611yescharacteristic
372C23#1451982212yes—
373C23#1451982211yescharacteristic
374C23#1451982312yes—
375C23#1451982412yes—
376C23#1451982411yescharacteristic
377C23#1451982411yescharacteristic
378C23#1451982511yescharacteristic
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—1224no—
409C2×C4—1224no—
410C2×C4—1224no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C22#1684035212yes—
437C22#1684035412yes—
438C22#1684035612yes—
439C22#1684035711yescharacteristic
440C22#1684035911yescharacteristic
441C22#1684036012yes—
442C22#1684036111yescharacteristic
443C22#1684036912yes—
444C22#1684038012yes—
445C22#1684045012yes—
446C22#1684045912yes—
447C22#1684047411yescharacteristic
448C22#1684047512yes—
449C22#1684048211yescharacteristic
450C22#1684048511yescharacteristic
451C22#1684048611yescharacteristic
452C22#1684050111yescharacteristic
453C22#1684050411yescharacteristic
454C22#1684050612yes—
455C22#1684051312yes—
456C22#1684051412yes—
457C22#1684051511yescharacteristic
458C22C61⋊#56411yescharacteristic
459C4—42no—
460C4—42no—
461C4—42no—
462C4—82no—
463C4—82no—
464C4—4882no—
465C4—4882no—
466C4—4882no—
467C4—2444no—
468C2#2145331411yescharacteristic
469C2#2145338912yes—
470C2#2145351012yes—
471C2#2145352511yescharacteristic
472C2#2145355612yes—
473C2#2145365211yescharacteristic
474C2#2145381011yescharacteristic
475C2#2145390311yescharacteristic
476C2#2145400211yescharacteristic
477C2#2145400911yescharacteristic
478C2#2145406012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, prime radical, cosocleC24×C61C24
FittingC61×#1442C2
hypercenter#1442D61
hypocenterC61#17300
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
270. C61#17300semidirect

Maximal subgroups

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

subgroupindex
#214440832
#214440802
#214440792
#214440782
#214440762
#214440752
#214440742
#214440732
C61×#14422
#1730061