Finite Group Databasebeta

← #29834837

Subgroups — #29834837

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×#16839995C211yesmaximal, characteristic
2#427×D61C211yesmaximal, characteristic, complemented
3#21448009C212yesmaximal, complemented
4#21448008C212yesmaximal, complemented
5#21448003C212yesmaximal, complemented
6#21447998C212yesmaximal, complemented
7#21447608C211yesmaximal, characteristic, complemented
8#21447607C211yesmaximal, characteristic, complemented
9#21447535C211yesmaximal, characteristic, complemented
10#21447429C211yesmaximal, characteristic, complemented
11C61×#2140C211yesmaximal, characteristic, complemented
12C22×C8×D61C2211yescharacteristic
13C2×#14519748—21no—
14#117×D61—21no—
15C2×#14519717C2211yescharacteristic
16#16839995—21no—
17#16839995—21no—
18#16839995C2212yes—
19#16839995C2212yes—
20#16839800C2211yescharacteristic
21#16839799C2211yescharacteristic, complemented
22#16839799C2211yescharacteristic, complemented
23#16839798—21no—
24#16839797—21no—
25C2×#14519711C2211yescharacteristic
26#107×D61C2211yescharacteristic, complemented
27#107×D61C2211yescharacteristic, complemented
28#106×D61—21no—
29C2×#14519698—21no—
30#16839590C2212yescomplemented
31#16839589C2212yescomplemented
32#16839588C2212yescomplemented
33#16839587C2212yescomplemented
34#16839563C2212yescomplemented
35#16839563C2212yescomplemented
36#16839541C2212yescomplemented
37#16839541C2212yescomplemented
38C22×D8×C61C2211yescharacteristic
39C2×M32×C61C2211yescharacteristic
40C61×#427C2211yescharacteristic
41C61×#357C2212yescomplemented
42C61×#357C2212yescomplemented
43C22×C22⋊D61—41no—
44C22×C4×D61D411yescharacteristic
45C22×#92418D411yescharacteristic
46C2×C8×D61—22no—
47C2×C8×D61—22no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61D411yescharacteristic
50C2×C8×D61C2311yescharacteristic
51C2×C8×D61C2311yescharacteristic
52#14519748—22no—
53#14519748—22no—
54#14519748—41no—
55#14519748—41no—
56#14519736—21no—
57#14519735—21no—
58#14519735—21no—
59#14519734—41no—
60#14519733—41no—
61C2×C4⋊Dic61—21no—
62C4⋊C4×D61—21no—
63C4⋊C4×D61—21no—
64C2×C22⋊Dic61—41no—
65C22⋊C4×D61—41no—
66C42×D61—41no—
67#14519717—22no—
68C2×#11758185C2312yes—
69#14519711—21no—
70#14519711C2312yes—
71#14519711C2311yescharacteristic
72#14519711C2311yescharacteristic
73#14519710—21no—
74#14519710—21no—
75#14519709—21no—
76#14519708—21no—
77#14519708—21no—
78#14519698—22no—
79#14519698—22no—
80C22×D4×C61—21no—
81C2×D8×C61—21no—
82C2×D8×C61—22no—
83C2×D8×C61—22no—
84C2×D8×C61C2312yes—
85C22×C8×C61C2311yescharacteristic
86#117×C61—21no—
87M32×C61—22no—
88C2×C16×C61C2312yes—
89#107×C61C2311yescharacteristic
90#107×C61C2311yescharacteristic
91#106×C61—21no—
92C24×C61—41no—
93C23×D61D811yescharacteristic
94C2×D4×C61—22no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—42no—
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—42no—
100C2×C22⋊D61—42no—
101C2×C22⋊D61—84no—
102C22×Dic61—41no—
103C22×Dic61D811yescharacteristic
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
112D8×C61—22no—
113D8×C61—22no—
114D8×C61—42no—
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61#4112yes—
117C2×C8×C61#4112yes—
118C2×C8×C61C2411yescharacteristic
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C22⋊C4×C61—41no—
122C42×C61—41no—
123C22⋊Dic61—41no—
124C22⋊Dic61—42no—
125C22⋊Dic61—42no—
126#11758198—41no—
127#11758198—41no—
128C4⋊Dic61—22no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—41no—
132#11758196—41no—
133#11758196—41no—
134C4×Dic61—41no—
135C4×Dic61—41no—
136C4×Dic61—41no—
137C2×#92418—22no—
138C2×#92418C2×D411yescharacteristic
139C2×#92418C2×D411yescharacteristic
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×C61—42no—
149C23×C61—82no—
150C23×C61—82no—
151C23×C61—82no—
152C23×C61C2×D811yescharacteristic
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—41no—
156C22×D61C2×D811yescharacteristic
157C22×D61C2×D811yescharacteristic
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—82no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61#12312yes—
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61#13712yes—
166C2×C4×C61C22×D411yescharacteristic
167C22⋊D61—84no—
168C22⋊D61—84no—
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—82no—
174C2×Dic61C2×D811yescharacteristic
175C2×Dic61C2×D811yescharacteristic
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—82no—
193C22×C61—82no—
194C22×C61—82no—
195C22×C61—164no—
196C22×C61#48012yes—
197C22×C61C22×D811yescharacteristic
198C2×D61—21no—
199C2×D61—21no—
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—44no—
204C2×D61#50912yes—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61#48012yes—
208C4×C61C2×#12311yescharacteristic
209C4×C61C2×#13711yescharacteristic
210Dic61—21no—
211Dic61—21no—
212Dic61—81no—
213Dic61—82no—
214Dic61—81no—
215C2×#466—611no—
216C2×#427—611no—
217#2234—612no—
218#2234—612no—
219#2233—612no—
220#2232—612no—
221#2159—611no—
222#2159—611no—
223#2140—611no—
224#2140D6111yescharacteristic, complemented
225#2112—611no—
226C2×C61—22no—
227C2×C61—162no—
228C2×C61C2×#48011yescharacteristic
229C2×C61C2×#50911yescharacteristic
230C2×C61#341411yescharacteristic
231D61—22no—
232D61—41no—
233C22×D8C2×D6111yescharacteristic
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×#107—611no—
252C2×#106—1221no—
253C2×#102—1221no—
254#367—612no—
255#367—612no—
256#366—612no—
257#366—612no—
258#357—612no—
259#357—612no—
260#357C2×D6112yescomplemented
261#357C2×D6112yescomplemented
262C22⋊C16—612no—
263C22⋊C16—612no—
264C61#3364811yescharacteristic, complemented, Sylow
265C22×D4—21no—
266C22×D4—2441no—
267C23×C4—611no—
268C2×D8—22no—
269C2×D8—21no—
270C2×D8—22no—
271C2×D8C22×D6112yes—
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—1221no—
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—611no—
301#107—611no—
302#107—612no—
303#107—1221no—
304#107—1221no—
305#107—1221no—
306#107C22×D6111yescharacteristic
307#107C22×D6111yescharacteristic
308#106—21no—
309#106—1221no—
310#106—1221no—
311#106—1221no—
312#102—1222no—
313#102—1222no—
314C24—41no—
315C24—611no—
316C2×D4—22no—
317C2×D4—42no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—4884no—
321C2×D4—2442no—
322C2×D4—2442no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—1222no—
329C22×C4—1222no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4D4×D6111yescharacteristic
334D8—22no—
335D8—22no—
336D8—42no—
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#1175822412yes—
349C2×C8C23×D6111yescharacteristic
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—1222no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4—2441no—
356C4⋊C4—2441no—
357C4⋊C4—2441no—
358C22⋊C4—41no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2442no—
362C22⋊C4—2442no—
363C22⋊C4—2441no—
364C42—41no—
365C42—2441no—
366C42—2441no—
367C42—2441no—
368C16—22no—
369C16—1222no—
370C23—42no—
371C23—82no—
372C23—82no—
373C23—82no—
374C23—611no—
375C23—611no—
376C23—1222no—
377C23—1222no—
378C23—2441no—
379C23D8×D6111yescharacteristic
380D4—42no—
381D4—42no—
382D4—82no—
383D4—4884no—
384D4—4884no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—611no—
388C2×C4—611no—
389C2×C4—1222no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—4882no—
397C2×C4—4882no—
398C2×C4—4882no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2442no—
402C2×C4#1451975912yes—
403C2×C4D8×D6111yescharacteristic
404C2×C4#1451980612yes—
405C2×C4C2×D4×D6111yescharacteristic
406C8—1221no—
407C8—1221no—
408C8#1451975912yes—
409C8C2×#1175822411yescharacteristic
410C8C2×#1175822211yescharacteristic
411C22—21no—
412C22—21no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—164no—
417C22—612no—
418C22—1221no—
419C22—1221no—
420C22—1221no—
421C22—1221no—
422C22—1221no—
423C22—2444no—
424C22#1684007412yes—
425C22C2×D8×D6111yescharacteristic
426C4—81no—
427C4—81no—
428C4—1221no—
429C4—1221no—
430C4—4881no—
431C4—4881no—
432C4—4882no—
433C4#1684007412yes—
434C4C2×#1451975911yescharacteristic
435C4C2×#1451980611yescharacteristic
436C2—22no—
437C2—162no—
438C2—1222no—
439C2—2441no—
440C2C2×#1684007411yescharacteristic
441C2#509×D6111yescharacteristic
442C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2140C2
socleC22×C61C22×D8
prime radicalC2×#16839995C2
hypercenter#2140D61
hypocenterC61#33648
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
2. #427×D61C2semidirect
3. #21448009C2semidirect
4. #21448008C2semidirect
5. #21448003C2semidirect
6. #21447998C2semidirect
7. #21447608C2semidirect
8. #21447607C2semidirect
9. #21447535C2semidirect
10. #21447429C2semidirect
11. C61×#2140C2semidirect
21. #16839799C22semidirect
22. #16839799C22semidirect
26. #107×D61C22semidirect
27. #107×D61C22semidirect
30. #16839590C22semidirect
31. #16839589C22semidirect
32. #16839588C22semidirect
33. #16839587C22semidirect
34. #16839563C22semidirect
35. #16839563C22semidirect
36. #16839541C22semidirect
37. #16839541C22semidirect
41. C61×#357C22semidirect
42. C61×#357C22semidirect
224. #2140D61semidirect
260. #357C2×D61semidirect
261. #357C2×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×#168399952
#427×D612
#214480092
#214480082
#214480032
#214479982
#214476082
#214476072
#214475352
#214474292
C61×#21402
#3364861