Finite Group Databasebeta

← #29834841

Subgroups — #29834841

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839999C211yesmaximal, characteristic
2#427×D61C211yesmaximal, characteristic, complemented
3#21448013C212yesmaximal, complemented
4#21448012C212yesmaximal, complemented
5#21448006C212yesmaximal, complemented
6#21448001C212yesmaximal, complemented
7#21447605C211yesmaximal, characteristic, complemented
8#21447536C211yesmaximal, characteristic, complemented
9#21447534C211yesmaximal, characteristic, complemented
10#21447429C211yesmaximal, characteristic, complemented
11C61×#2159C211yesmaximal, characteristic, complemented
12C22×D488C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14C2×#14519752—21no—
15#117×D61—21no—
16C2×#14519717C2211yescharacteristic
17#16839999—21no—
18#16839999—21no—
19#16839999C2212yes—
20#16839999C2212yes—
21#16839800C2211yescharacteristic
22#16839799C2211yescharacteristic, complemented
23#16839799C2211yescharacteristic, complemented
24#16839798—21no—
25#16839797—21no—
26#107×D61C2211yescharacteristic, complemented
27#107×D61C2211yescharacteristic, complemented
28#106×D61—21no—
29C2×#14519697—21no—
30#16839589C2212yescomplemented
31#16839587C2212yescomplemented
32#16839564C2212yescomplemented
33#16839564C2212yescomplemented
34#16839562C2212yescomplemented
35#16839562C2212yescomplemented
36#16839541C2212yescomplemented
37#16839541C2212yescomplemented
38C2×M32×C61C2211yescharacteristic
39C61×#427C2211yescharacteristic
40C2×#107×C61C2211yescharacteristic
41C61×#367C2212yescomplemented
42C61×#366C2212yescomplemented
43C22×D244—21no—
44C22×D244—41no—
45C22×C4×D61D411yescharacteristic
46C2×D488—22no—
47C2×D488—22no—
48C2×D488—21no—
49C2×D488C2312yes—
50C22×#92418D411yescharacteristic
51C2×C8×D61—22no—
52C2×C8×D61—22no—
53C2×C8×D61D411yescharacteristic
54C2×C8×D61D411yescharacteristic
55C2×C8×D61C2311yescharacteristic
56C2×C8×D61C2311yescharacteristic
57#14519752—22no—
58#14519752—22no—
59#14519752—41no—
60#14519752—41no—
61#14519736—21no—
62#14519735—21no—
63#14519735—21no—
64#14519734—41no—
65#14519733—41no—
66C4⋊C4×D61—21no—
67C4⋊C4×D61—21no—
68C2×#11758198—41no—
69C22⋊C4×D61—41no—
70C42×D61—41no—
71#14519717—22no—
72C2×#11758185C2312yes—
73#14519711C2311yescharacteristic
74#14519711C2311yescharacteristic
75#14519710—21no—
76#14519710—21no—
77#14519709—21no—
78#14519708—21no—
79#14519708—21no—
80#14519697—22no—
81#14519697—22no—
82C22×C8×C61C2311yescharacteristic
83#117×C61—21no—
84C2×C4⋊C4×C61—21no—
85M32×C61—22no—
86C2×C16×C61C2312yes—
87#107×C61—21no—
88#107×C61C2312yes—
89#107×C61C2311yescharacteristic
90#107×C61C2311yescharacteristic
91#106×C61—21no—
92C23×D61—41no—
93C23×D61D811yescharacteristic
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×Dic61D811yescharacteristic
97C2×D244—22no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244—42no—
102C2×D244—41no—
103C2×D244—84no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61D811yescharacteristic
109C2×C4×D61D811yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61#4112yes—
114C2×C8×C61#4112yes—
115C2×C8×C61C2411yescharacteristic
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—22no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C42×C61—41no—
122C22⋊Dic61—41no—
123#11758198—41no—
124#11758198—41no—
125#11758198—42no—
126#11758198—42no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C4×Dic61—41no—
134C2×#92418—22no—
135C2×#92418C2×D411yescharacteristic
136C2×#92418C2×D411yescharacteristic
137D488—22no—
138D488—22no—
139D488—42no—
140C8×D61—22no—
141C8×D61—22no—
142C8×D61—21no—
143C8×D61—21no—
144C8×D61—21no—
145C8×D61—21no—
146C16×C61—22no—
147#11758185—22no—
148C23×C61C2×D811yescharacteristic
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—41no—
152C22×D61—42no—
153C22×D61—82no—
154C22×D61—82no—
155C22×D61—82no—
156C22×D61C2×D811yescharacteristic
157C22×D61C2×D811yescharacteristic
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—82no—
162C2×C4×C61#12312yes—
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61#13712yes—
165C2×C4×C61C22×D411yescharacteristic
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61C2×D811yescharacteristic
170C2×Dic61C2×D811yescharacteristic
171D244—42no—
172D244—42no—
173D244—84no—
174D244—84no—
175D244—82no—
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—22no—
181C4×D61—22no—
182C4×D61—82no—
183C4×D61—82no—
184C8×C61#12312yes—
185C8×C61C2×#4111yescharacteristic
186C8×C61C2×#4111yescharacteristic
187#92418—21no—
188#92418—21no—
189#33648—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61#48012yes—
193C22×C61C22×D811yescharacteristic
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—44no—
200C2×D61—82no—
201C2×D61—82no—
202C2×D61—82no—
203C2×D61—164no—
204C2×D61#50912yes—
205C4×C61—81no—
206C4×C61—82no—
207C4×C61—81no—
208C4×C61#48012yes—
209C4×C61C2×#12311yescharacteristic
210C4×C61C2×#13711yescharacteristic
211Dic61—21no—
212Dic61—21no—
213Dic61—81no—
214Dic61—81no—
215C2×#466—611no—
216C2×#427—611no—
217#2234—612no—
218#2234—612no—
219#2233—612no—
220#2232—612no—
221#2159—611no—
222#2159D6111yescharacteristic, complemented
223#2140—611no—
224#2140—611no—
225#2112—611no—
226C2×C61—22no—
227C2×C61C2×#48011yescharacteristic
228C2×C61C2×#50911yescharacteristic
229C2×C61#341411yescharacteristic
230D61—22no—
231D61—41no—
232D61—162no—
233C22×D8—611no—
234C23×C8—611no—
235C2×#121—1221no—
236C2×#117—1221no—
237C2×M32—611no—
238C2×M32C2×D6111yescharacteristic
239#466—612no—
240#466—612no—
241#466—1221no—
242#466—1221no—
243#427—611no—
244#427—611no—
245#427—611no—
246#427—1221no—
247#427—1221no—
248#427C2×D6111yescharacteristic
249C2×#107—611no—
250C2×#107—611no—
251C2×#107C2×D6111yescharacteristic
252C2×#106—1221no—
253C2×#102—1221no—
254#367—612no—
255#367C2×D6112yescomplemented
256#366—612no—
257#366C2×D6112yescomplemented
258#357—612no—
259#357—612no—
260#357—612no—
261#357—612no—
262C22⋊C16—612no—
263C22⋊C16—612no—
264C61#3364811yescharacteristic, complemented, Sylow
265C22×D4—1221no—
266C22×D4—2441no—
267C23×C4—611no—
268C2×D8—612no—
269C2×D8—1222no—
270C2×D8—1221no—
271C2×D8—1222no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—1222no—
278C22×C8—1222no—
279C22×C8C22×D6111yescharacteristic
280#121—1222no—
281#121—1222no—
282#121—2441no—
283#121—2441no—
284#117—21no—
285#117—1221no—
286#117—1221no—
287#117—1221no—
288#117—2441no—
289#117—2441no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C22⋊C4—2441no—
294C2×C22⋊C4—2441no—
295C2×C42—2441no—
296M32—22no—
297M32—1222no—
298C2×C16—612no—
299C2×C16C22×D6112yes—
300#107—21no—
301#107—611no—
302#107—611no—
303#107—1221no—
304#107—1221no—
305#107C22×D6111yescharacteristic
306#107C22×D6111yescharacteristic
307#107C22×D6112yes—
308#106—21no—
309#106—1221no—
310#106—1221no—
311#106—1221no—
312#102—1222no—
313#102—1222no—
314C24—611no—
315C24—2441no—
316C2×D4—1222no—
317C2×D4—4884no—
318C2×D4—2442no—
319C2×D4—2442no—
320C2×D4—2442no—
321C2×D4—2442no—
322C2×D4—2441no—
323C22×C4—41no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4D4×D6111yescharacteristic
334D8—1222no—
335D8—1222no—
336D8—2442no—
337C2×C8—611no—
338C2×C8—611no—
339C2×C8—1222no—
340C2×C8—1221no—
341C2×C8—1221no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—1222no—
345C2×C8—1222no—
346C2×C8#1175822212yes—
347C2×C8D4×D6111yescharacteristic
348C2×C8#1175822612yes—
349C2×C8C23×D6111yescharacteristic
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—41no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—2441no—
357C4⋊C4—2441no—
358C22⋊C4—41no—
359C22⋊C4—2442no—
360C22⋊C4—2442no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C42—41no—
365C42—2441no—
366C42—2441no—
367C42—2441no—
368C16—22no—
369C16—1222no—
370C23—611no—
371C23—611no—
372C23—1222no—
373C23—1222no—
374C23—4882no—
375C23—4882no—
376C23—4882no—
377C23—2441no—
378C23—2442no—
379C23D8×D6111yescharacteristic
380D4—4884no—
381D4—4884no—
382D4—4882no—
383D4—2442no—
384D4—2442no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—1222no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—4882no—
399C2×C4—4882no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4#1451976212yes—
403C2×C4D8×D6111yescharacteristic
404C2×C4#1451980912yes—
405C2×C4C2×D4×D6111yescharacteristic
406C8—1221no—
407C8—1221no—
408C8#1451976212yes—
409C8C2×#1175822211yescharacteristic
410C8C2×#1175822611yescharacteristic
411C22—21no—
412C22—21no—
413C22—612no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—9764no—
420C22—4882no—
421C22—4882no—
422C22—4882no—
423C22—2444no—
424C22#1684007712yes—
425C22C2×D8×D6111yescharacteristic
426C4—81no—
427C4—82no—
428C4—81no—
429C4—1221no—
430C4—1221no—
431C4—4881no—
432C4—4881no—
433C4#1684007712yes—
434C4C2×#1451976211yescharacteristic
435C4C2×#1451980911yescharacteristic
436C2—22no—
437C2—1222no—
438C2—9762no—
439C2—2441no—
440C2C2×#1684007711yescharacteristic
441C2#509×D6111yescharacteristic
442C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2159C2
socleC22×C61C22×D8
prime radicalC2×#16839999C2
hypercenter#2159D61
hypocenterC61#33648
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
2. #427×D61C2semidirect
3. #21448013C2semidirect
4. #21448012C2semidirect
5. #21448006C2semidirect
6. #21448001C2semidirect
7. #21447605C2semidirect
8. #21447536C2semidirect
9. #21447534C2semidirect
10. #21447429C2semidirect
11. C61×#2159C2semidirect
22. #16839799C22semidirect
23. #16839799C22semidirect
26. #107×D61C22semidirect
27. #107×D61C22semidirect
30. #16839589C22semidirect
31. #16839587C22semidirect
32. #16839564C22semidirect
33. #16839564C22semidirect
34. #16839562C22semidirect
35. #16839562C22semidirect
36. #16839541C22semidirect
37. #16839541C22semidirect
41. C61×#367C22semidirect
42. C61×#366C22semidirect
222. #2159D61semidirect
255. #367C2×D61semidirect
257. #366C2×D61semidirect
264. C61#33648semidirect

Maximal subgroups

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

subgroupindex
C2×#168399992
#427×D612
#214480132
#214480122
#214480062
#214480012
#214476052
#214475362
#214475342
#214474292
C61×#21592
#3364861