Finite Group Databasebeta

← #29834936

Subgroups — #29834936

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456396C211yesmaximal, characteristic, complemented
2C4×D8×D61C211yesmaximal, characteristic, complemented
3#21447998C212yesmaximal, complemented
4#21447957C211yesmaximal, characteristic, complemented
5#21447956C211yesmaximal, characteristic, complemented
6#21447851C211yesmaximal, characteristic, complemented
7#21447729C212yesmaximal, complemented
8D16×Dic61C212yesmaximal, complemented
9#21447663C212yesmaximal, complemented
10#21447617C211yesmaximal, characteristic, complemented
11C61×#2206C211yesmaximal, characteristic, complemented
12C2×D8×D61C2211yescharacteristic
13#16840310—21no—
14C4×D4×D61—21no—
15C2×#14519718C2212yes—
16#16840167C2211yescharacteristic, complemented
17#16840108—21no—
18#16839995—21no—
19#16839995C2212yes—
20C4×D488C2211yescharacteristic
21D8×Dic61—21no—
22D8×Dic61C2211yescharacteristic
23D8×Dic61C2212yescomplemented
24#16839844C2211yescharacteristic
25C4×#11758199—21no—
26#16839842—21no—
27#107×D61C2211yescharacteristic
28#102×D61—21no—
29C4×C8×D61C2211yescharacteristic
30#16839588C2212yescomplemented
31#16839587C2212yescomplemented
32C4⋊#11758185C2211yescharacteristic, complemented
33#16839564C2212yes—
34#16839563C2212yes—
35#16839563C2212yescomplemented
36#16839541C2212yes—
37C16×Dic61C2212yescomplemented
38C2×D16×C61C2212yes—
39C61×#493C2211yescharacteristic, complemented
40C4×D8×C61C2211yescharacteristic
41C61×C4⋊C16C2211yescharacteristic, complemented
42C61×#357C2212yescomplemented
43C2×#11758224—41no—
44C2×D4×D61—21no—
45C22×C4×D61—41no—
46C2×D488C2311yescharacteristic
47C2×#11758199—21no—
48D8×D61—22no—
49D8×D61—22no—
50C2×C8×D61D411yescharacteristic
51C2×C8×D61C2311yescharacteristic
52#14519777—21no—
53#14519764—41no—
54#14519748—22no—
55#14519748—41no—
56C4×D244—21no—
57D4×Dic61—21no—
58D4×Dic61—22no—
59D4×Dic61—41no—
60#14519739—21no—
61C4×C22⋊D61—41no—
62#14519737—41no—
63C4⋊C4×D61—21no—
64C22⋊C4×D61—41no—
65C42×D61D411yescharacteristic
66#14519718—24no—
67C2×#11758185C2312yes—
68#14519711—21no—
69#14519711C2312yes—
70#14519711C2311yescharacteristic
71#14519710—21no—
72#14519699—21no—
73#14519698—22no—
74#14519698—22no—
75#14519698—21no—
76#14519697—21no—
77C4×#92418D411yescharacteristic
78C8×Dic61D411yescharacteristic
79C8×Dic61C2311yescharacteristic
80C2×D8×C61—21no—
81C2×D8×C61C2312yes—
82C2×D8×C61C2311yescharacteristic
83#127×C61—21no—
84C4×D4×C61—21no—
85D16×C61—24no—
86C2×C16×C61C2312yes—
87#107×C61C2311yescharacteristic
88#102×C61—21no—
89C4×C8×C61C2311yescharacteristic
90C23×D61—41no—
91C2×D4×C61—21no—
92C2×D4×C61—22no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C22×C4×C61—41no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—41no—
98C22×Dic61—41no—
99C22×Dic61—42no—
100#11758224—84no—
101D4×D61—24no—
102D4×D61—42no—
103C2×D244—21no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—84no—
108C2×C4×D61D811yescharacteristic
109C2×C4×D61D811yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×Dic122—41no—
112D8×C61—21no—
113D8×C61—22no—
114D8×C61—22no—
115D8×C61—42no—
116D8×C61#4112yescomplemented
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2411yescharacteristic
119C4⋊C4×C61—21no—
120C22⋊C4×C61—41no—
121C42×C61C2×D411yescharacteristic
122C22⋊Dic61—41no—
123C22⋊Dic61—42no—
124C22⋊Dic61—42no—
125#11758199—24no—
126#11758198—41no—
127#11758198—41no—
128C4⋊Dic61—22no—
129C4⋊Dic61—21no—
130C4⋊Dic61—41no—
131#11758196—41no—
132C4×Dic61D811yescharacteristic
133C4×Dic61D811yescharacteristic
134C4×Dic61C2×D411yescharacteristic
135C2×#92418C2×D411yescharacteristic
136C2×#92418C2×D411yescharacteristic
137D488—21no—
138D488#4112yescomplemented
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—41no—
142C16×C61—22no—
143#11758185—22no—
144C23×C61—41no—
145C23×C61—42no—
146C22×D61—44no—
147C22×D61—41no—
148C22×D61—82no—
149C22×D61—82no—
150C22×D61C2×D811yescharacteristic
151D4×C61—22no—
152D4×C61—42no—
153D4×C61—41no—
154D4×C61—42no—
155D4×C61—82no—
156D4×C61—82no—
157C2×C4×C61—41no—
158C2×C4×C61—82no—
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C22⋊D61—44no—
163C22⋊D61—84no—
164C2×Dic61—41no—
165C2×Dic61—42no—
166C2×Dic61—82no—
167C2×Dic61—84no—
168C2×Dic61C2×D811yescharacteristic
169C2×Dic61C2×D811yescharacteristic
170C2×Dic61C2×D811yescharacteristic
171D244—22no—
172D244—41no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—41no—
176C4×D61—82no—
177C4×D61—82no—
178C4×D61—82no—
179C4×D61D1614yescomplemented
180Dic122—82no—
181C8×C61—21no—
182C8×C61C2×#4111yescharacteristic
183C8×C61C2×#4111yescharacteristic
184#92418—21no—
185#92418—21no—
186#33660—611nomaximal, Sylow
187C22×C61—42no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—82no—
191C22×C61—82no—
192C22×C61—82no—
193C22×C61C22×D811yescharacteristic
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—42no—
197C2×D61—88no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61C2×D1612yes—
201C4×C61—21no—
202C4×C61—81no—
203C4×C61C2×D1612yes—
204C4×C61#52511yescharacteristic
205C4×C61#57511yescharacteristic
206Dic61—21no—
207Dic61—21no—
208Dic61—82no—
209Dic61—81no—
210Dic61C2×D1612yes—
211#3169—611no—
212C2×C4×D8—611no—
213#2232—612no—
214#2224—611no—
215#2224—611no—
216#2206—611no—
217#2206D6111yescharacteristic, complemented
218#2184—612no—
219C4×D16—612no—
220C4×D16—612no—
221#2162—611no—
222C2×C61—82no—
223C2×C61—162no—
224C2×C61#310011yescharacteristic
225C2×C61C22×D1611yescharacteristic
226C2×C61#341411yescharacteristic
227D61—22no—
228D61—82no—
229C22×D8—611no—
230#532—1221no—
231C2×C4×D4—1221no—
232C2×D16—612no—
233C2×D16C2×D6112yes—
234#500—611no—
235#493C2×D6111yescharacteristic, complemented
236#486—1221no—
237#466—612no—
238#466—1221no—
239C4×D8—612no—
240C4×D8—611no—
241C4×D8—611no—
242C4×D8—611no—
243C4×D8—1221no—
244C4×D8—1221no—
245C4×D8—1221no—
246C4×D8C2×D6111yescharacteristic
247C2×#107—611no—
248C2×#102—1221no—
249C2×C4×C8—611no—
250#366—612no—
251#366—612no—
252C4⋊C16—611no—
253C4⋊C16C2×D6111yescharacteristic, complemented
254#357—612no—
255#357—612no—
256#357—612no—
257#357C2×D6112yescomplemented
258C22⋊C16—612no—
259C4×C16—612no—
260C61#3366011yescharacteristic, complemented, Sylow
261C2×#41—2441no—
262C22×D4—1221no—
263C23×C4—2441no—
264C2×D8—21no—
265C2×D8—611no—
266C2×D8—1221no—
267C2×D8—1222no—
268C2×D8—1222no—
269C2×D8C22×D6112yes—
270C2×D8C22×D6111yescharacteristic
271C22×C8—611no—
272C22×C8—611no—
273C4⋊Q8—1221no—
274#127—21no—
275#124—2441no—
276#121—1222no—
277#121—2441no—
278C4×D4—21no—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—1222no—
282C4×D4—1221no—
283C4×D4—2441no—
284C4×D4—2441no—
285C4×D4—2441no—
286C2×C4⋊C4—1221no—
287C2×C22⋊C4—2441no—
288C2×C42—611no—
289D16—24no—
290D16—1224no—
291C2×C16—612no—
292C2×C16C22×D6112yes—
293#107—611no—
294#107—612no—
295#107—1221no—
296#107—1221no—
297#107C22×D6111yescharacteristic
298#102—21no—
299#102—1221no—
300#102—1221no—
301#102—1222no—
302#102—1222no—
303#102—1221no—
304C4×C8—611no—
305C4×C8—611no—
306C4×C8—611no—
307C4×C8C22×D6111yescharacteristic
308C24—2441no—
309#41—4884no—
310C2×Q8—2441no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—1224no—
316C2×D4—1221no—
317C2×D4—2441no—
318C2×D4—2442no—
319C2×D4—2442no—
320C22×C4—41no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—4884no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2442no—
329C22×C4—2441no—
330D8—21no—
331D8—22no—
332D8—22no—
333D8—42no—
334D8—612no—
335D8—1224no—
336D8—1221no—
337D8#1175822412yescomplemented
338C2×C8—611no—
339C2×C8—611no—
340C2×C8—1221no—
341C2×C8—1221no—
342C2×C8—2441no—
343C2×C8D4×D6111yescharacteristic
344C2×C8C23×D6111yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—1221no—
347C4⋊C4—1222no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C22⋊C4—41no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C42—611no—
357C42—611no—
358C42—611no—
359C42D4×D6111yescharacteristic
360C16—22no—
361C16—1222no—
362C23—41no—
363C23—42no—
364C23—611no—
365C23—4882no—
366C23—4882no—
367C23—2444no—
368C23—2441no—
369Q8—4882no—
370D4—22no—
371D4—42no—
372D4—41no—
373D4—42no—
374D4—82no—
375D4—82no—
376D4—1222no—
377D4—4884no—
378D4—2444no—
379D4—2441no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—611no—
383C2×C4—614no—
384C2×C4—611no—
385C2×C4—611no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—4882no—
389C2×C4—4882no—
390C2×C4—4882no—
391C2×C4—4884no—
392C2×C4—4882no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2442no—
396C2×C4D8×D6111yescharacteristic
397C2×C4D8×D6111yescharacteristic
398C2×C4C2×D4×D6111yescharacteristic
399C8—21no—
400C8—1221no—
401C8—1221no—
402C8#41×D6111yescharacteristic
403C8C2×#1175822411yescharacteristic
404C22—42no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22—612no—
411C22—1221no—
412C22—1221no—
413C22—4888no—
414C22—4881no—
415C22—4881no—
416C22—2442no—
417C22C2×D8×D6111yescharacteristic
418C4—21no—
419C4—81no—
420C4—612no—
421C4—1221no—
422C4—1221no—
423C4—4881no—
424C4—4882no—
425C4D16×D6112yes—
426C4#1684027211yescharacteristic
427C4#1684055811yescharacteristic
428C2—82no—
429C2—162no—
430C2—1222no—
431C2—4882no—
432C2#2145581811yescharacteristic
433C2C2×D16×D6111yescharacteristic
434C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2206C2
socleC22×C61C22×D8
hypercenter#2206D61
hypocenterC61#33660
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21456396C2semidirect
2. C4×D8×D61C2semidirect
3. #21447998C2semidirect
4. #21447957C2semidirect
5. #21447956C2semidirect
6. #21447851C2semidirect
7. #21447729C2semidirect
8. D16×Dic61C2semidirect
9. #21447663C2semidirect
10. #21447617C2semidirect
11. C61×#2206C2semidirect
16. #16840167C22semidirect
23. D8×Dic61C22semidirect
30. #16839588C22semidirect
31. #16839587C22semidirect
32. C4⋊#11758185C22semidirect
35. #16839563C22semidirect
37. C16×Dic61C22semidirect
39. C61×#493C22semidirect
41. C61×C4⋊C16C22semidirect
42. C61×#357C22semidirect
116. D8×C61#41semidirect
138. D488#41semidirect
179. C4×D61D16semidirect
217. #2206D61semidirect
235. #493C2×D61semidirect
253. C4⋊C16C2×D61semidirect
257. #357C2×D61semidirect
260. C61#33660semidirect
337. D8#11758224semidirect

Maximal subgroups

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

subgroupindex
#214563962
C4×D8×D612
#214479982
#214479572
#214479562
#214478512
#214477292
D16×Dic612
#214476632
#214476172
C61×#22062
#3366061