Finite Group Databasebeta

← #29645569

Subgroups — #29645569

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444090C211yesmaximal, characteristic
2#21444090C211yesmaximal, characteristic
3#21444085C212yesmaximal
4#21444083C212yesmaximal
5#21444073C212yesmaximal
6#21444071C212yesmaximal
7#21444070C212yesmaximal
8#21444070C212yesmaximal
9C61×#1446C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×#11758196C2212yes—
12C22×#11758196C2212yes—
13C22×#11758196C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2212yes—
16C2×#14519684C2211yescharacteristic
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2212yes—
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—42no—
37C2×C4⋊Dic61—42no—
38C2×#11758196—24no—
39C2×#11758196—42no—
40C2×#11758196—42no—
41C2×#11758196—42no—
42C2×#11758196—42no—
43C2×#11758196—42no—
44C2×#11758196—42no—
45C2×#11758196—42no—
46C2×#11758196Q818yescomplemented
47#14519684—24no—
48#14519684—42no—
49#14519684—42no—
50#14519684—42no—
51#14519684—42no—
52#14519684—42no—
53#14519684—41no—
54#14519684—41no—
55#14519684—41no—
56#14519684—42no—
57#14519684—42no—
58#14519684—41no—
59C22×Q8×C61—42no—
60C22×Q8×C61—42no—
61C22×Q8×C61—41no—
62C22×Q8×C61—41no—
63C22×Q8×C61Q814yes—
64C23×C4×C61C2312yes—
65C23×C4×C61C2312yes—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69#95×C61—42no—
70#95×C61—41no—
71#95×C61—42no—
72#95×C61—41no—
73C24×C61C2411yescharacteristic
74C2×Q8×C61—44no—
75C2×Q8×C61—44no—
76C2×Q8×C61—44no—
77C2×Q8×C61—48no—
78C2×Q8×C61—48no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
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—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61C2×Q812yes—
105C22×C4×C61C2×Q812yes—
106C22×C4×C61C2×Q812yes—
107C22×C4×C61C2×Q814yes—
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—22no—
132C22×Dic61—22no—
133C22×Dic61C2×Q814yes—
134C22×Dic61C2×Q814yes—
135C22×Dic61#4114yes—
136C4⋊Dic61—48no—
137#11758196—48no—
138#11758196—48no—
139#11758196—48no—
140C23×C61C22×Q811yescharacteristic
141C23×C61C22×Q812yes—
142C23×C61C2×#4112yes—
143C23×C61H(5,𝔽2)12yes—
144C23×C61H(5,𝔽2)12yes—
145C23×C61H(5,𝔽2)12yes—
146C23×C61H(5,𝔽2)11yescharacteristic
147C23×C61H(5,𝔽2)11yescharacteristic
148C23×C612−1+412yes—
149Q8×C61—416no—
150C2×C4×C61—24no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
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×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×Dic61—24no—
180C2×Dic61—24no—
181C2×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—24no—
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—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207#17306—611nomaximal, Sylow
208C22×C61#53812yes—
209C22×C61#53812yes—
210C22×C61#53912yes—
211C22×C61#54312yes—
212C22×C61#54311yescharacteristic
213C22×C61#54311yescharacteristic
214C22×C61#54311yescharacteristic
215C22×C61#54412yes—
216C22×C61#54412yes—
217C22×C61#55412yes—
218C22×C61#55412yes—
219C22×C61#55511yescharacteristic
220C22×C61#55712yes—
221C22×C61Q8211yescharacteristic
222C22×C61Q8212yes—
223C22×C61#56012yes—
224C22×C61#56012yes—
225C22×C61H(3,𝔽4)11yescharacteristic
226C22×C61#56212yes—
227C22×C61#56212yes—
228C22×C61#56311yescharacteristic
229C4×C61—42no—
230C4×C61—42no—
231C4×C61—42no—
232C4×C61—44no—
233C4×C61—82no—
234Dic61—44no—
235Dic61—44no—
236Dic61—44no—
237Dic61—82no—
238#1446—611no—
239#1446—611no—
240#1446D6111yescharacteristic
241#1445—612no—
242#1444—612no—
243#1441—612no—
244#1441—612no—
245#1441—612no—
246#1441—612no—
247C2×C61#278412yes—
248C2×C61#279212yes—
249C2×C61#280612yes—
250C2×C61#280612yes—
251C2×C61#280911yescharacteristic
252C2×C61#281111yescharacteristic
253C2×C61#282412yes—
254C2×C61#284112yes—
255C2×C61#284211yescharacteristic
256C23×Q8C2×D6111yescharacteristic
257C22×C4⋊C4—612no—
258C22×C4⋊C4—612no—
259C22×C4⋊C4—612no—
260C22×C4⋊C4—612no—
261C2×#95—612no—
262C2×#95—612no—
263C2×#95—612no—
264C2×#95—612no—
265C2×#95—612no—
266C2×#95—612no—
267C2×#95—611no—
268C2×#95—612no—
269C2×#95—611no—
270C2×#95—611no—
271C2×#95—612no—
272C2×#95—611no—
273C2×#95C2×D6111yescharacteristic
274C2×#95C2×D6112yes—
275C2×#95C2×D6111yescharacteristic
276C2×#95C2×D6112yes—
277C61#1730611yescharacteristic, complemented, Sylow
278C22×Q8—42no—
279C22×Q8—42no—
280C22×Q8—41no—
281C22×Q8—41no—
282C22×Q8Dic12214yes—
283C23×C4—612no—
284C23×C4—612no—
285C23×C4—612no—
286C23×C4—612no—
287C23×C4C22×D6112yes—
288C23×C4C22×D6111yescharacteristic
289C23×C4C22×D6111yescharacteristic
290C23×C4C22×D6111yescharacteristic
291C23×C4C22×D6112yes—
292C2×C4⋊C4—618no—
293C2×C4⋊C4—1224no—
294C2×C4⋊C4—1224no—
295C2×C4⋊C4—2442no—
296C2×C4⋊C4—2442no—
297C2×C4⋊C4—2442no—
298C2×C4⋊C4—2442no—
299C2×C4⋊C4—2442no—
300C2×C4⋊C4—2442no—
301C2×C4⋊C4—2442no—
302C2×C4⋊C4—2442no—
303C2×C4⋊C4—2442no—
304#95—42no—
305#95—41no—
306#95—42no—
307#95—41no—
308#95—1224no—
309#95—2442no—
310#95—2442no—
311#95—2442no—
312#95—2442no—
313#95—2441no—
314#95—2441no—
315#95—2441no—
316#95—2442no—
317#95—2441no—
318#95—2442no—
319#95—2442no—
320C24C23×D6111yescharacteristic
321C2×Q8—44no—
322C2×Q8—44no—
323C2×Q8—44no—
324C2×Q8—48no—
325C2×Q8—48no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—614no—
352C22×C4—614no—
353C22×C4—614no—
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×C4—1222no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4C2×Dic12212yes—
380C22×C4C2×Dic12212yes—
381C22×C4C2×Dic12212yes—
382C22×C4Q8×D6114yes—
383C4⋊C4—2448no—
384C4⋊C4—2448no—
385C4⋊C4—2448no—
386C4⋊C4—2448no—
387C23C2×Q8×D6112yes—
388C23C22×Dic12211yescharacteristic
389C23#41×D6112yes—
390C23#1451982212yes—
391C23#1451982212yes—
392C23#1451982211yescharacteristic
393C23#1451982211yescharacteristic
394C23#1451982312yes—
395C23#1451982512yes—
396Q8—416no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C22#1684034612yes—
455C22#1684034612yes—
456C22#1684035812yes—
457C22#1684038712yes—
458C22#1684038811yescharacteristic
459C22#1684038811yescharacteristic
460C22#1684038811yescharacteristic
461C22#1684038912yes—
462C22#1684038912yes—
463C22#1684046612yes—
464C22#1684046612yes—
465C22#1684047411yescharacteristic
466C22#1684048812yes—
467C22#1684049211yescharacteristic
468C22Q8×Dic12212yes—
469C22#1684050112yes—
470C22#1684050112yes—
471C22#1684050411yescharacteristic
472C22#1684050812yes—
473C22#1684050812yes—
474C22#1684051111yescharacteristic
475C4—42no—
476C4—42no—
477C4—42no—
478C4—44no—
479C4—82no—
480C4—4882no—
481C4—2444no—
482C4—2444no—
483C4—2444no—
484C2#2145351412yes—
485C2#2145361212yes—
486C2#2145377912yes—
487C2#2145377912yes—
488C2#2145380511yescharacteristic
489C2#2145381211yescharacteristic
490C2#2145389812yes—
491C2#2145407312yes—
492C2#2145408311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, prime radical, cosocleC24×C61C24
FittingC61×#1446C2
hypercenter#1446D61
hypocenterC61#17306
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
46. C2×#11758196Q8semidirect
277. C61#17306semidirect

Maximal subgroups

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

subgroupindex
#214440902
#214440852
#214440832
#214440732
#214440712
#214440702
C61×#14462
#1730661