Finite Group Databasebeta

← D61×#2232 #29834767

Subgroups — D61×#2232 #29834767

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D61C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic, complemented
3#21448001C212yesmaximal, complemented
4#21448000C211yesmaximal, characteristic, complemented
5#21447999C211yesmaximal, characteristic, complemented
6#21447998C212yesmaximal, complemented
7#21447997C211yesmaximal, characteristic, complemented
8#366×D61C212yesmaximal, complemented
9#357×D61C212yesmaximal, complemented
10C22⋊C16×D61C211yesmaximal, characteristic, complemented
11C61×#2232C211yesmaximal, characteristic, complemented
12C2×D8×D61C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#121×D61—21no—
15C2×C4⋊C4×D61—21no—
16C2×C16×D61C2212yes—
17#16839999C2211yescharacteristic
18#16839998C2211yescharacteristic
19#16839997—21no—
20#16839996—21no—
21#16839995C2211yescharacteristic
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519710—21no—
24#107×D61—21no—
25#107×D61—21no—
26#107×D61C2211yescharacteristic
27#107×D61C2212yes—
28#107×D61C2212yescomplemented
29#102×D61—21no—
30#16839588C2212yescomplemented
31#16839587C2212yescomplemented
32#16839587C2212yescomplemented
33#16839564C2212yescomplemented
34#16839563C2212yescomplemented
35#16839562C2212yescomplemented
36C22⋊#11758185C2211yescharacteristic, complemented
37#16839541C2212yescomplemented
38C61×#466C2211yescharacteristic
39C2×#107×C61C2211yescharacteristic, complemented
40C61×#366C2212yescomplemented
41C61×#357C2212yescomplemented
42C61×C22⋊C16C2211yescharacteristic, complemented
43C2×D4×D61—21no—
44C2×D4×D61—41no—
45C22×C4×D61—41no—
46C22×C4×D61D411yescharacteristic
47C2×D488C2311yescharacteristic
48C2×#11758199—21no—
49D8×D61—24no—
50C22×#92418D411yescharacteristic
51C2×C8×D61—24no—
52C2×C8×D61D411yescharacteristic
53C2×C8×D61D411yescharacteristic
54C2×C8×D61C2311yescharacteristic
55C2×C8×D61C2311yescharacteristic
56#14519752—21no—
57#14519751—21no—
58#14519750—41no—
59#14519749—41no—
60#14519748—21no—
61C2×C4⋊Dic61—21no—
62C2×#11758196—41no—
63C4⋊C4×D61—22no—
64C4⋊C4×D61—22no—
65C4⋊C4×D61—21no—
66C4⋊C4×D61—41no—
67C4⋊C4×D61—41no—
68C22⋊C4×D61—41no—
69C2×#11758185C2312yes—
70C16×D61—24no—
71#14519711—21no—
72#14519711C2311yescharacteristic
73#14519711C2312yes—
74#14519710—21no—
75#14519710—22no—
76#14519710—22no—
77#14519699—21no—
78#14519698—21no—
79#14519697—21no—
80C2×D8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82#121×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C16×C61C2312yes—
85#107×C61—21no—
86#107×C61C2311yescharacteristic
87#107×C61C2312yes—
88#102×C61—21no—
89C23×D61—41no—
90C23×D61D811yescharacteristic
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C22×Dic61—41no—
99C22×Dic61D811yescharacteristic
100D4×D61—42no—
101D4×D61—42no—
102D4×D61—84no—
103C2×D244—21no—
104C2×D244—41no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—41no—
110C2×C4×D61—84no—
111C2×C4×D61D811yescharacteristic
112C2×C4×D61D811yescharacteristic
113C2×C4×D61C2×D411yescharacteristic
114C2×C4×D61C2×D411yescharacteristic
115D8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2411yescharacteristic
119C4⋊C4×C61—21no—
120C4⋊C4×C61—22no—
121C4⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊Dic61—41no—
124#11758199—42no—
125#11758198—41no—
126#11758198—41no—
127C4⋊Dic61—21no—
128C4⋊Dic61—22no—
129C4⋊Dic61—41no—
130#11758196—42no—
131#11758196—42no—
132#11758196—41no—
133C2×#92418—22no—
134C2×#92418C2×D411yescharacteristic
135C2×#92418C2×D411yescharacteristic
136D488—22no—
137C8×D61—22no—
138C8×D61—22no—
139C8×D61—22no—
140C8×D61#4114yes—
141C16×C61—22no—
142#11758185—22no—
143C23×C61—41no—
144C23×C61C2×D811yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—41no—
148C22×D61—82no—
149C22×D61—82no—
150C22×D61—82no—
151C22×D61D1614yes—
152C22×D61C2×D811yescharacteristic
153C22×D61C2×D811yescharacteristic
154D4×C61—41no—
155D4×C61—41no—
156D4×C61—82no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—82no—
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61C22×D411yescharacteristic
164C22⋊D61—82no—
165C22⋊D61—82no—
166C22⋊D61—82no—
167C2×Dic61—22no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—82no—
171C2×Dic61C2×D811yescharacteristic
172C2×Dic61C2×D811yescharacteristic
173D244—41no—
174D244—41no—
175D244—82no—
176C4×D61—22no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—22no—
180C4×D61—84no—
181C4×D61—84no—
182C4×D61—82no—
183C4×D61#12312yes—
184C4×D61#13712yes—
185C8×C61—21no—
186C8×C61C2×#4112yes—
187#92418—21no—
188#92418#12312yes—
189C2×#2232—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61C2×D1612yes—
196C22×C61C22×D811yescharacteristic
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—28no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—164no—
204C2×D61#48012yes—
205C2×D61C2×D1612yes—
206C2×D61C2×D1612yes—
207C2×D61#51012yes—
208C4×C61—21no—
209C4×C61—82no—
210C4×C61—81no—
211C4×C61C2×#12311yescharacteristic
212C4×C61C2×#13711yescharacteristic
213Dic61—21no—
214Dic61—82no—
215Dic61—81no—
216Dic61#48012yes—
217C2×#466—611no—
218C22×#107—611no—
219#2232—611no—
220#2232—611no—
221#2232—612no—
222#2232—612no—
223#2232—611no—
224#2232D6111yescharacteristic, direct product factor
225C2×#366—612no—
226C2×#357—612no—
227C2×C22⋊C16—611no—
228C2×C61—22no—
229C2×C61—161no—
230C2×C61C2×#48011yescharacteristic
231C2×C61C22×D1611yescharacteristic
232C2×C61C2×#51011yescharacteristic
233D61—22no—
234D61—161no—
235D61#223214yesdirect product factor
236C22×D8—611no—
237C23×C8—611no—
238C2×#121—1221no—
239C22×C4⋊C4—1221no—
240C22×C16—612no—
241#466—611no—
242#466—611no—
243#466—611no—
244#466—1221no—
245#466—1221no—
246#466C2×D6111yescharacteristic
247C2×#107—611no—
248C2×#107—612no—
249C2×#107—612no—
250C2×#107—611no—
251C2×#107—1221no—
252C2×#107—1221no—
253C2×#107—1221no—
254C2×#107C2×D6111yescharacteristic, complemented
255C2×#102—1221no—
256#366—612no—
257#366—612no—
258#366—612no—
259#366C2×D6112yescomplemented
260#357—612no—
261#357—612no—
262#357—612no—
263#357C2×D6112yescomplemented
264C22⋊C16—611no—
265C22⋊C16—612no—
266C22⋊C16C2×D6111yescharacteristic, complemented
267C61C2×#223211yescharacteristic, complemented, Sylow
268C22×D4—1221no—
269C22×D4—2441no—
270C23×C4—611no—
271C23×C4—2441no—
272C2×D8—611no—
273C2×D8—1224no—
274C2×D8—1221no—
275C2×D8C22×D6111yescharacteristic
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—611no—
279C22×C8—611no—
280C22×C8—611no—
281C22×C8—1224no—
282C22×C8C22×D6111yescharacteristic
283#121—21no—
284#121—1221no—
285#121—1221no—
286#121—1221no—
287#121—2441no—
288#121—2441no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—1222no—
291C2×C4⋊C4—1222no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—2441no—
295C2×C4⋊C4—2441no—
296C2×C4⋊C4—2441no—
297C2×C22⋊C4—2441no—
298C2×C16—612no—
299C2×C16—1224no—
300C2×C16C22×D6112yes—
301#107—21no—
302#107—612no—
303#107—611no—
304#107—1222no—
305#107—1222no—
306#107—1221no—
307#107—1221no—
308#107C22×D6112yes—
309#107C22×D6111yescharacteristic
310#102—21no—
311#102—1221no—
312#102—1221no—
313#102—1221no—
314C24—611no—
315C24—2441no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—1221no—
319C2×D4—4884no—
320C2×D4—2441no—
321C2×D4—2442no—
322C2×D4—2442no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C22×C4—41no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—4884no—
335C22×C4—2441no—
336C22×C4—2442no—
337C22×C4—2442no—
338C22×C4—2441no—
339C22×C4D4×D6111yescharacteristic
340D8—22no—
341D8—1222no—
342D8—2442no—
343C2×C8—22no—
344C2×C8—611no—
345C2×C8—614no—
346C2×C8—611no—
347C2×C8—1222no—
348C2×C8—1222no—
349C2×C8—1222no—
350C2×C8—1222no—
351C2×C8D4×D6111yescharacteristic
352C2×C8C23×D6111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—41no—
356C4⋊C4—1221no—
357C4⋊C4—1222no—
358C4⋊C4—2442no—
359C4⋊C4—2442no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C22⋊C4—41no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C22⋊C4—2441no—
366C16—22no—
367C16—1222no—
368C23—41no—
369C23—611no—
370C23—611no—
371C23—614no—
372C23—1222no—
373C23—1222no—
374C23—4882no—
375C23—4882no—
376C23—4882no—
377C23—2441no—
378C23D8×D6111yescharacteristic
379D4—41no—
380D4—41no—
381D4—82no—
382D4—4882no—
383D4—4882no—
384D4—4882no—
385D4—4882no—
386D4—2441no—
387D4—2441no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—611no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—611no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—4884no—
403C2×C4—4884no—
404C2×C4—4882no—
405C2×C4—4882no—
406C2×C4—2441no—
407C2×C4—2442no—
408C2×C4D8×D6111yescharacteristic
409C2×C4C2×D4×D6111yescharacteristic
410C8—21no—
411C8—612no—
412C8—1221no—
413C8#41×D6112yes—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—612no—
420C22—612no—
421C22—612no—
422C22—612no—
423C22—1228no—
424C22—1221no—
425C22—1221no—
426C22—9764no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22D16×D6112yes—
431C22C2×D8×D6111yescharacteristic
432C4—21no—
433C4—82no—
434C4—81no—
435C4—612no—
436C4—1221no—
437C4—4882no—
438C4—4881no—
439C4#123×D6111yescharacteristic
440C4#137×D6111yescharacteristic
441C2—22no—
442C2—161no—
443C2—614no—
444C2—1222no—
445C2—9761no—
446C2#480×D6111yescharacteristic
447C2C2×D16×D6111yescharacteristic
448C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2232C2
socleC22×C61C22×D8
prime radical#466×D61C2
hypercenter#2232D61
hypocenterC61C2×#2232
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. C2×#107×D61C2semidirect
3. #21448001C2semidirect
4. #21448000C2semidirect
5. #21447999C2semidirect
6. #21447998C2semidirect
7. #21447997C2semidirect
8. #366×D61C2semidirect
9. #357×D61C2semidirect
10. C22⋊C16×D61C2semidirect
11. C61×#2232C2semidirect
22. C2×#14519711C22semidirect
28. #107×D61C22semidirect
30. #16839588C22semidirect
31. #16839587C22semidirect
32. #16839587C22semidirect
33. #16839564C22semidirect
34. #16839563C22semidirect
35. #16839562C22semidirect
36. C22⋊#11758185C22semidirect
37. #16839541C22semidirect
39. C2×#107×C61C22semidirect
40. C61×#366C22semidirect
41. C61×#357C22semidirect
42. C61×C22⋊C16C22semidirect
224. #2232D61direct (N × H)
235. D61#2232direct (N × H)
254. C2×#107C2×D61semidirect
259. #366C2×D61semidirect
263. #357C2×D61semidirect
266. C22⋊C16C2×D61semidirect
267. C61C2×#2232semidirect

Maximal subgroups

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

subgroupindex
#466×D612
C2×#107×D612
#214480012
#214480002
#214479992
#214479982
#214479972
#366×D612
#357×D612
C22⋊C16×D612
C61×#22322
C2×#223261