Finite Group Databasebeta

← #29645378

Subgroups — #29645378

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444090C211yesmaximal, characteristic
2#21444090C211yesmaximal, characteristic
3#21444088C212yesmaximal
4#21444085C212yesmaximal
5#21444080C212yesmaximal
6#21444080C212yesmaximal
7#21444073C212yesmaximal
8#21444071C212yesmaximal
9C61×#1446C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×#11758196C2212yes—
12C2×#14519684C2212yes—
13C2×#14519684C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2211yescharacteristic
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C23×Q8×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2212yes—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C23×Dic61C2312yes—
32C23×Dic61C2312yes—
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C2×C4⋊Dic61—24no—
36C2×C4⋊Dic61—24no—
37C2×C4⋊Dic61—42no—
38C2×#11758196—24no—
39C2×#11758196—24no—
40C2×#11758196—42no—
41#14519684—24no—
42#14519684—24no—
43#14519684—41no—
44#14519684—42no—
45#14519684—42no—
46#14519684—42no—
47#14519684—42no—
48#14519684—41no—
49#14519684—41no—
50#14519684—41no—
51#14519684—42no—
52#14519684—42no—
53#14519684—42no—
54#14519684—42no—
55C22×Q8×C61—41no—
56C22×Q8×C61—41no—
57C22×Q8×C61—42no—
58C22×Q8×C61—42no—
59C22×Q8×C61Q814yes—
60C23×C4×C61C2312yes—
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2312yes—
65#95×C61—41no—
66#95×C61—42no—
67#95×C61—42no—
68#95×C61—41no—
69C24×C61C2411yescharacteristic
70C2×Q8×C61—44no—
71C2×Q8×C61—44no—
72C2×Q8×C61—44no—
73C2×Q8×C61—48no—
74C2×Q8×C61—48no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—21no—
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—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61C2×Q812yes—
101C22×C4×C61C2×Q812yes—
102C22×C4×C61C2×Q812yes—
103C22×C4×C61#4114yes—
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—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61#4114yes—
132C4⋊Dic61—48no—
133#11758196—48no—
134C23×C61C22×Q811yescharacteristic
135C23×C61C2×#4112yes—
136C23×C61C2×#4112yes—
137C23×C61H(5,𝔽2)11yescharacteristic
138C23×C61H(5,𝔽2)11yescharacteristic
139C23×C61H(5,𝔽2)12yes—
140C23×C61H(5,𝔽2)12yes—
141C23×C612−1+412yes—
142C23×C612−1+412yes—
143Q8×C61—416no—
144C2×C4×C61—24no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—24no—
155C2×C4×C61—24no—
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×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×Dic61—24no—
174C2×Dic61—24no—
175C2×Dic61—24no—
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—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201#17289—611nomaximal, Sylow
202C22×C61#53912yes—
203C22×C61#53912yes—
204C22×C61#54212yes—
205C22×C61#54212yes—
206C22×C61#54212yes—
207C22×C61#54212yes—
208C22×C61#54311yescharacteristic
209C22×C61#54311yescharacteristic
210C22×C61#54311yescharacteristic
211C22×C61#55112yes—
212C22×C61#55112yes—
213C22×C61#55511yescharacteristic
214C22×C61#55511yescharacteristic
215C22×C61#55712yes—
216C22×C61#55712yes—
217C22×C61#56012yes—
218C22×C61#56012yes—
219C22×C61#56311yescharacteristic
220C22×C61#56311yescharacteristic
221C22×C61#56312yes—
222C22×C61#56312yes—
223C4×C61—42no—
224C4×C61—42no—
225C4×C61—42no—
226C4×C61—44no—
227C4×C61—82no—
228Dic61—44no—
229Dic61—82no—
230Dic61—82no—
231Dic61—82no—
232#1446—611no—
233#1446—611no—
234#1446D6111yescharacteristic
235#1445—612no—
236#1445—612no—
237#1443—612no—
238#1443—612no—
239#1441—612no—
240#1441—612no—
241C2×C61#273712yes—
242C2×C61#273712yes—
243C2×C61#279912yes—
244C2×C61#279912yes—
245C2×C61#280911yescharacteristic
246C2×C61#280911yescharacteristic
247C2×C61#283812yes—
248C2×C61#283812yes—
249C2×C61#284211yescharacteristic
250C23×Q8C2×D6111yescharacteristic
251C22×C4⋊C4—612no—
252C22×C4⋊C4—612no—
253C2×#95—612no—
254C2×#95—612no—
255C2×#95—611no—
256C2×#95—612no—
257C2×#95—612no—
258C2×#95—612no—
259C2×#95—612no—
260C2×#95—612no—
261C2×#95—612no—
262C2×#95—612no—
263C2×#95—611no—
264C2×#95—612no—
265C2×#95—611no—
266C2×#95—611no—
267C2×#95C2×D6111yescharacteristic
268C2×#95C2×D6112yes—
269C2×#95C2×D6111yescharacteristic
270C2×#95C2×D6112yes—
271C61#1728911yescharacteristic, complemented, Sylow
272C22×Q8—41no—
273C22×Q8—41no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8Dic12214yes—
277C23×C4—612no—
278C23×C4—612no—
279C23×C4—612no—
280C23×C4—612no—
281C23×C4C22×D6112yes—
282C23×C4C22×D6111yescharacteristic
283C23×C4C22×D6111yescharacteristic
284C23×C4C22×D6111yescharacteristic
285C23×C4C22×D6112yes—
286C2×C4⋊C4—1224no—
287C2×C4⋊C4—1224no—
288C2×C4⋊C4—1224no—
289C2×C4⋊C4—1224no—
290C2×C4⋊C4—2442no—
291C2×C4⋊C4—2442no—
292#95—41no—
293#95—42no—
294#95—42no—
295#95—41no—
296#95—1224no—
297#95—1224no—
298#95—2442no—
299#95—2441no—
300#95—2442no—
301#95—2442no—
302#95—2441no—
303#95—2441no—
304#95—2441no—
305#95—2442no—
306#95—2442no—
307#95—2442no—
308#95—2442no—
309#95—2442no—
310C24C23×D6111yescharacteristic
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8—48no—
315C2×Q8—48no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—614no—
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—1222no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4C2×Dic12212yes—
370C22×C4C2×Dic12212yes—
371C22×C4C2×Dic12212yes—
372C22×C4#1175822614yes—
373C4⋊C4—2448no—
374C4⋊C4—2448no—
375C23C22×Dic12211yescharacteristic
376C23#41×D6112yes—
377C23C2×#1175822612yes—
378C23#1451982211yescharacteristic
379C23#1451982211yescharacteristic
380C23#1451982212yes—
381C23#1451982212yes—
382C23#1451982412yes—
383C23#1451982512yes—
384Q8—416no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—24no—
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—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—1224no—
415C2×C4—1224no—
416C2×C4—1224no—
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—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C22#1684035812yes—
443C22#1684036112yes—
444C22#1684037612yes—
445C22#1684037612yes—
446C22#1684038612yes—
447C22#1684038612yes—
448C22#1684038811yescharacteristic
449C22#1684038811yescharacteristic
450C22#1684038811yescharacteristic
451C22#1684043912yes—
452C22#1684043912yes—
453C22#1684047411yescharacteristic
454C22#1684047811yescharacteristic
455C22#1684048812yes—
456C22#1684049112yes—
457C22#1684050112yes—
458C22#1684050112yes—
459C22#1684051111yescharacteristic
460C22#1684051211yescharacteristic
461C22#1684051312yes—
462C22#1684051312yes—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—82no—
468C4—4882no—
469C4—4882no—
470C4—4882no—
471C4—2444no—
472C2#2145288012yes—
473C2#2145288112yes—
474C2#2145370512yes—
475C2#2145370512yes—
476C2#2145380511yescharacteristic
477C2#2145380711yescharacteristic
478C2#2145405312yes—
479C2#2145405412yes—
480C2#2145408311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, prime radical, cosocleC24×C61C24
FittingC61×#1446C2
hypercenter#1446D61
hypocenterC61#17289
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
271. C61#17289semidirect

Maximal subgroups

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

subgroupindex
#214440902
#214440882
#214440852
#214440802
#214440732
#214440712
C61×#14462
#1728961