Finite Group Databasebeta

← #29834984

Subgroups — #29834984

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456389C211yesmaximal, characteristic, complemented
2#21448021C211yesmaximal, characteristic, complemented
3#21448004C211yesmaximal, characteristic, complemented
4#21447976C212yesmaximal, complemented
5#21447874C212yesmaximal, complemented
6#21447748C211yesmaximal, characteristic, complemented
7#21447731C211yesmaximal, characteristic
8C4×#14519721C212yesmaximal, complemented
9C4×#14519718C212yesmaximal, complemented
10#21447618C211yesmaximal, characteristic, complemented
11C2×C4×D8×C61C211yesmaximal, characteristic, complemented
12#16840296—21no—
13C2×#14519721C2212yes—
14C2×#14519718C2212yes—
15#16840164C2211yescharacteristic, complemented
16#16840146C2211yescharacteristic, complemented
17#16840117—21no—
18#16840003C2211yescharacteristic
19#16839998C2211yescharacteristic
20#16839991—21no—
21C4×Dic244C2211yescharacteristic, complemented
22C4×#11758190—21no—
23C4×D488C2211yescharacteristic, complemented
24#16839589C2212yescomplemented
25#16839587C2212yescomplemented
26C4⋊#11758185C2212yescomplemented
27#16839565C2212yescomplemented
28#16839563C2212yes—
29#16839563C2212yes—
30#16839562C2212yescomplemented
31C22⋊#11758185C2211yescharacteristic
32C22⋊#11758185C2211yescharacteristic
33C4×#11758185C2212yescomplemented
34C22×D8×C61C2211yescharacteristic
35C2×C4×D4×C61—21no—
36C4×D8×C61—21no—
37C4×D8×C61—21no—
38C4×D8×C61C2212yes—
39C4×D8×C61C2212yes—
40C2×#107×C61C2211yescharacteristic
41C2×#102×C61—21no—
42C2×C4×C8×C61C2211yescharacteristic
43C2×Dic244C2311yescharacteristic
44C2×#11758190—21no—
45C2×D488C2311yescharacteristic
46#14519771—41no—
47#14519769—21no—
48#14519765—21no—
49#14519760—41no—
50#14519756—21no—
51#14519751—21no—
52C4×Dic122—21no—
53C4×D244—21no—
54C4×C22⋊D61—41no—
55#14519734—41no—
56#14519721—24no—
57#14519718—24no—
58C2×#11758185C2312yes—
59C2×#11758185C2312yes—
60#14519711C2311yescharacteristic
61#14519711C2311yescharacteristic
62#14519709—21no—
63#14519702—21no—
64#14519702—21no—
65#14519699—21no—
66#14519699—21no—
67C22×D4×C61—21no—
68C23×C4×C61—41no—
69C2×D8×C61—24no—
70C2×D8×C61—21no—
71C2×D8×C61C2312yes—
72C22×C8×C61D411yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C4×D4×C61—22no—
75C4×D4×C61—22no—
76C4×D4×C61—41no—
77C4×D4×C61—41no—
78C2×C4⋊C4×C61—21no—
79C2×C22⋊C4×C61—41no—
80C2×C42×C61D411yescharacteristic
81#107×C61—21no—
82#107×C61C2312yes—
83#102×C61—22no—
84#102×C61—22no—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C24×C61—41no—
90C2×D4×C61—24no—
91C2×D4×C61—22no—
92C2×D4×C61—42no—
93C2×D4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—84no—
98C22×C4×C61D811yescharacteristic
99C22×C4×C61D811yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102C2×D244—21no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105D8×C61—24no—
106D8×C61—22no—
107D8×C61#4114yes—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2411yescharacteristic
114C4⋊C4×C61—22no—
115C4⋊C4×C61—41no—
116C22⋊C4×C61—42no—
117C22⋊C4×C61—42no—
118C42×C61D811yescharacteristic
119C42×C61D811yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C22⋊Dic61—41no—
123#11758198—41no—
124#11758198—41no—
125#11758198—41no—
126#11758198—41no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129#11758196—41no—
130#11758196—41no—
131#11758196—41no—
132#11758196—41no—
133C4×Dic61—41no—
134Dic244—22no—
135D488—22no—
136#11758190—42no—
137#11758185—22no—
138#11758185—22no—
139C23×C61—44no—
140C23×C61—42no—
141C23×C61—82no—
142C23×C61—82no—
143C23×C61C2×D811yescharacteristic
144C22×D61—41no—
145D4×C61—24no—
146D4×C61—44no—
147D4×C61—42no—
148C2×C4×C61—22no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—42no—
153C2×C4×C61—84no—
154C2×C4×C61—82no—
155C2×C4×C61—84no—
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C22⋊D61—82no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166D244—41no—
167D244—41no—
168C4×D61—82no—
169Dic122—41no—
170Dic122—41no—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61—21no—
174C8×C61C2×#4112yes—
175#33665—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—44no—
179C22×C61—88no—
180C22×C61—82no—
181C22×C61—82no—
182C22×C61#50812yes—
183C22×C61C22×D811yescharacteristic
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—82no—
192C4×C61#50912yes—
193C4×C61#52511yescharacteristic
194C4×C61#57511yescharacteristic
195Dic61—81no—
196Dic61—81no—
197Dic61—81no—
198#3168—611no—
199C2×C4×D8D6111yescharacteristic, complemented
200#2236—611no—
201#2233—611no—
202#2228—612no—
203#2210—612no—
204#2187—611no—
205#2184—611no—
206C4×SD32—612no—
207C4×D16—612no—
208#2162—611no—
209C2×C61—22no—
210C2×C61—84no—
211C2×C61#310011yescharacteristic
212C2×C61C2×#50811yescharacteristic
213C2×C61C2×#50911yescharacteristic
214D61—161no—
215C22×D8C2×D6111yescharacteristic
216#529—1221no—
217C2×C4×D4—21no—
218C2×SD32—612no—
219C2×D16—612no—
220#499—611no—
221#495—611no—
222#488—1221no—
223#467—611no—
224#466—611no—
225#465—1221no—
226C4×Q16—611no—
227C4×SD16—1221no—
228C4×D8—21no—
229C4×D8—21no—
230C4×D8—611no—
231C4×D8C2×D6112yes—
232C4×D8C2×D6112yes—
233C2×#107C2×D6111yescharacteristic
234C2×#102—21no—
235C2×C4×C8C2×D6111yescharacteristic
236#367—612no—
237#366—612no—
238C4⋊C16—612no—
239#358—612no—
240#357—612no—
241#357—612no—
242#357—612no—
243C22⋊C16—611no—
244C22⋊C16—611no—
245C4×C16—612no—
246C61#3366511yescharacteristic, complemented, Sylow
247C22×D4—21no—
248C23×C4—41no—
249C2×Q16—611no—
250C2×SD16—1221no—
251C2×D8—24no—
252C2×D8—21no—
253C2×D8—611no—
254C2×D8C22×D6112yes—
255C22×C8C22⋊D6111yescharacteristic
256C22×C8C22×D6111yescharacteristic
257#126—2441no—
258#125—1221no—
259#124—1221no—
260#123—2441no—
261C22⋊Q8—1221no—
262#121—1221no—
263C4×Q8—1221no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—41no—
267C4×D4—41no—
268C4×D4—1221no—
269C4×D4—2441no—
270#117—2441no—
271C2×C4⋊C4—21no—
272C2×C22⋊C4—41no—
273C2×C42C22⋊D6111yescharacteristic
274SD32—1224no—
275D16—1224no—
276C2×C16—612no—
277C2×C16—612no—
278#107—21no—
279#107—611no—
280#107—611no—
281#107C22×D6112yes—
282#106—1221no—
283#103—1221no—
284#103—1221no—
285#102—22no—
286#102—22no—
287#102—1221no—
288#102—1221no—
289C4×C8C22⋊D6111yescharacteristic
290C4×C8C22⋊D6111yescharacteristic
291C4×C8C22×D6111yescharacteristic
292C4×C8C22×D6111yescharacteristic
293C24—41no—
294C2×Q8—1221no—
295C2×D4—24no—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—1221no—
300C2×D4—2441no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—84no—
305C22×C4—2441no—
306C22×C4#1175819911yescharacteristic
307C22×C4#1175819911yescharacteristic
308C22×C4C2×C22⋊D6111yescharacteristic
309Q16—1222no—
310SD16—2442no—
311D8—24no—
312D8—22no—
313D8—1222no—
314D8#1175822214yes—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8C2×C22⋊D6111yescharacteristic
318C2×C8C2×C22⋊D6111yescharacteristic
319C2×C8C2×C22⋊D6111yescharacteristic
320C2×C8C23×D6111yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—2441no—
337C42#1175819911yescharacteristic
338C42#1175819911yescharacteristic
339C42C2×C22⋊D6111yescharacteristic
340C42C2×C22⋊D6111yescharacteristic
341C16—1222no—
342C16—1222no—
343C23—44no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—2441no—
348C23C2×#1175819911yescharacteristic
349Q8—2441no—
350Q8—2441no—
351D4—24no—
352D4—44no—
353D4—42no—
354D4—4882no—
355D4—2441no—
356D4—2441no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—84no—
363C2×C4—82no—
364C2×C4—84no—
365C2×C4—4882no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4C2×#1175819911yescharacteristic
370C2×C4C2×#1175819911yescharacteristic
371C2×C4C2×#1175819911yescharacteristic
372C2×C4C2×#1175819911yescharacteristic
373C2×C4C2×#1175819911yescharacteristic
374C2×C4C22×C22⋊D6111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8C2×#1175822212yes—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—88no—
383C22—82no—
384C22—82no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22#1684019212yes—
389C22C22×#1175819911yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—4881no—
396C4—4881no—
397C4—4881no—
398C4#1684019812yes—
399C4#1684027311yescharacteristic
400C4#1684056011yescharacteristic
401C2—22no—
402C2—84no—
403C2—9761no—
404C2#2145581911yescharacteristic
405C2C2×#1684019211yescharacteristic
406C2C2×#1684019811yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C4×D8×C61C2
socleC22×C61C22×D8
prime radical#21447731C2
hypercenterC2×C4×D8D61
hypocenterC61#33665
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #21456389C2semidirect
2. #21448021C2semidirect
3. #21448004C2semidirect
4. #21447976C2semidirect
5. #21447874C2semidirect
6. #21447748C2semidirect
8. C4×#14519721C2semidirect
9. C4×#14519718C2semidirect
10. #21447618C2semidirect
11. C2×C4×D8×C61C2semidirect
15. #16840164C22semidirect
16. #16840146C22semidirect
21. C4×Dic244C22semidirect
23. C4×D488C22semidirect
24. #16839589C22semidirect
25. #16839587C22semidirect
26. C4⋊#11758185C22semidirect
27. #16839565C22semidirect
30. #16839562C22semidirect
33. C4×#11758185C22semidirect
199. C2×C4×D8D61semidirect
246. C61#33665semidirect

Maximal subgroups

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

subgroupindex
#214563892
#214480212
#214480042
#214479762
#214478742
#214477482
#214477312
C4×#145197212
C4×#145197182
#214476182
C2×C4×D8×C612
#3366561