Finite Group Databasebeta

← #29834986

Subgroups — #29834986

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
2C2×C4×D488C211yesmaximal, characteristic, complemented
3#21448022C211yesmaximal, characteristic, complemented
4#21448005C211yesmaximal, characteristic, complemented
5#21447977C212yesmaximal, complemented
6#21447875C212yesmaximal, complemented
7#21447750C211yesmaximal, characteristic, complemented
8#21447733C211yesmaximal, characteristic
9C4×#14519722C212yesmaximal, complemented
10C4×D976C212yesmaximal, complemented
11C61×#2162C211yesmaximal, characteristic, complemented
12C22×D488C2211yescharacteristic
13#16840296—21no—
14C2×C4×D244—21no—
15C2×#14519722C2212yes—
16C2×D976C2212yes—
17#16840164C2211yescharacteristic, complemented
18#16840146C2211yescharacteristic, complemented
19#16840117—21no—
20#16840003C2211yescharacteristic
21#16839998C2211yescharacteristic
22#16839991—21no—
23C4×Dic244C2211yescharacteristic, complemented
24C4×#11758190—21no—
25C4×D488—21no—
26C4×D488—21no—
27C4×D488C2212yes—
28C4×D488C2212yes—
29C4×D488C2211yescharacteristic, complemented
30C2×#14519711C2211yescharacteristic
31C2×#14519699—21no—
32#16839590C2212yescomplemented
33#16839588C2212yescomplemented
34#16839567C2212yescomplemented
35#16839564C2212yes—
36#16839564C2212yes—
37#16839564C2212yescomplemented
38C2×C4×C8×C61C2211yescharacteristic
39C61×C4⋊C16C2212yescomplemented
40C61×C22⋊C16C2211yescharacteristic
41C61×C22⋊C16C2211yescharacteristic
42C4×C16×C61C2212yescomplemented
43C22×D244—21no—
44C22×C4×D61—41no—
45C2×Dic244C2311yescharacteristic
46C2×#11758190—21no—
47C2×D488—21no—
48C2×D488—24no—
49C2×D488C2311yescharacteristic
50C2×D488C2312yes—
51#14519771—41no—
52#14519769—21no—
53#14519765—21no—
54#14519760—41no—
55#14519756—21no—
56#14519751—21no—
57C4×Dic122—21no—
58C4×D244—22no—
59C4×D244—22no—
60C4×D244—21no—
61C4×D244—41no—
62C4×D244—41no—
63C4×C22⋊D61—41no—
64#14519734—41no—
65C2×C4⋊Dic61—21no—
66C2×#11758198—41no—
67#14519722—24no—
68D976—24no—
69#14519711—21no—
70#14519711C2311yescharacteristic
71#14519711C2311yescharacteristic
72#14519711C2312yes—
73#14519709—21no—
74#14519702—21no—
75#14519702—21no—
76#14519699—21no—
77#14519699—21no—
78#14519699—22no—
79#14519699—22no—
80C22×C8×C61D411yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C2×C42×C61D411yescharacteristic
83C2×C16×C61C2312yes—
84C2×C16×C61C2312yes—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C23×D61—41no—
90C22×C4×C61D811yescharacteristic
91C22×C4×C61D811yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—41no—
94C22×Dic61—41no—
95C2×D244—24no—
96C2×D244—22no—
97C2×D244—21no—
98C2×D244—42no—
99C2×D244—41no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—41no—
103C2×C4×D61—84no—
104C2×Dic122—21no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2411yescharacteristic
111C42×C61D811yescharacteristic
112C42×C61D811yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C22⋊Dic61—41no—
116#11758198—42no—
117#11758198—42no—
118#11758198—41no—
119#11758198—41no—
120#11758198—41no—
121#11758198—41no—
122C4⋊Dic61—22no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—41no—
126#11758196—41no—
127#11758196—41no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—41no—
131Dic244—22no—
132D488—24no—
133D488—22no—
134D488—22no—
135D488#4114yes—
136#11758190—42no—
137C16×C61—22no—
138C16×C61—22no—
139C23×C61C2×D811yescharacteristic
140C22×D61—44no—
141C22×D61—42no—
142C22×D61—41no—
143C22×D61—82no—
144C22×D61—82no—
145C2×C4×C61—22no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—22no—
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C22×D411yescharacteristic
155C22⋊D61—82no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—82no—
161D244—24no—
162D244—44no—
163D244—41no—
164D244—42no—
165D244—41no—
166C4×D61—84no—
167C4×D61—82no—
168C4×D61—84no—
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#50812yes—
179C22×C61C22×D811yescharacteristic
180C2×D61—44no—
181C2×D61—88no—
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61#50912yes—
192C4×C61#52511yescharacteristic
193C4×C61#57511yescharacteristic
194Dic61—81no—
195Dic61—81no—
196Dic61—82no—
197Dic61—81no—
198#3168—611no—
199C2×C4×D8—611no—
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#2162D6111yescharacteristic, complemented
209C2×C61—22no—
210C2×C61#310011yescharacteristic
211C2×C61C2×#50811yescharacteristic
212C2×C61C2×#50911yescharacteristic
213D61—84no—
214D61—161no—
215C22×D8—611no—
216#529—1221no—
217C2×C4×D4—1221no—
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—611no—
229C4×D8—612no—
230C4×D8—612no—
231C4×D8—1221no—
232C4×D8—1221no—
233C2×#107—611no—
234C2×#102—1221no—
235C2×C4×C8C2×D6111yescharacteristic
236#367—612no—
237#366—612no—
238C4⋊C16C2×D6112yescomplemented
239#358—612no—
240#357—612no—
241#357—612no—
242#357—612no—
243C22⋊C16C2×D6111yescharacteristic
244C22⋊C16C2×D6111yescharacteristic
245C4×C16C2×D6112yescomplemented
246C61#3366511yescharacteristic, complemented, Sylow
247C22×D4—1221no—
248C23×C4—2441no—
249C2×Q16—611no—
250C2×SD16—1221no—
251C2×D8—612no—
252C2×D8—611no—
253C2×D8—1224no—
254C2×D8—1221no—
255C22×C8D24411yescharacteristic
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—1222no—
265C4×D4—1222no—
266C4×D4—1221no—
267C4×D4—2441no—
268C4×D4—2441no—
269C4×D4—2441no—
270#117—2441no—
271C2×C4⋊C4—1221no—
272C2×C22⋊C4—2441no—
273C2×C42D24411yescharacteristic
274SD32—1224no—
275D16—1224no—
276C2×C16C22×D6112yes—
277C2×C16C22×D6112yes—
278#107—611no—
279#107—611no—
280#107—612no—
281#107—1221no—
282#106—1221no—
283#103—1221no—
284#103—1221no—
285#102—1222no—
286#102—1222no—
287#102—1221no—
288#102—1221no—
289C4×C8D24411yescharacteristic
290C4×C8D24411yescharacteristic
291C4×C8C22×D6111yescharacteristic
292C4×C8C22×D6111yescharacteristic
293C24—2441no—
294C2×Q8—1221no—
295C2×D4—1224no—
296C2×D4—1222no—
297C2×D4—1221no—
298C2×D4—2442no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—4884no—
302C22×C4—2441no—
303C22×C4—2442no—
304C22×C4—2441no—
305C22×C4—2442no—
306C22×C4D48811yescharacteristic
307C22×C4D48811yescharacteristic
308C22×C4C2×D24411yescharacteristic
309Q16—1222no—
310SD16—2442no—
311D8—614no—
312D8—1224no—
313D8—1222no—
314D8—1222no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8C2×D24411yescharacteristic
318C2×C8C2×D24411yescharacteristic
319C2×C8C2×D24411yescharacteristic
320C2×C8C23×D6111yescharacteristic
321C4⋊C4—1222no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C22⋊C4—2441no—
330C22⋊C4—2442no—
331C22⋊C4—2442no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—2441no—
337C42D48811yescharacteristic
338C42D48811yescharacteristic
339C42C2×D24411yescharacteristic
340C42C2×D24411yescharacteristic
341C16—22no—
342C16—22no—
343C23—4882no—
344C23—4882no—
345C23—2444no—
346C23—2441no—
347C23—2442no—
348C23C2×D48811yescharacteristic
349Q8—2441no—
350Q8—2441no—
351D4—1224no—
352D4—4882no—
353D4—2444no—
354D4—2441no—
355D4—2441no—
356D4—2442no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—4884no—
362C2×C4—4882no—
363C2×C4—4884no—
364C2×C4—4882no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2442no—
369C2×C4C2×D48811yescharacteristic
370C2×C4C2×D48811yescharacteristic
371C2×C4C2×D48811yescharacteristic
372C2×C4C2×D48811yescharacteristic
373C2×C4C2×D48811yescharacteristic
374C2×C4C22×D24411yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#41×D6112yes—
379C22—21no—
380C22—21no—
381C22—4888no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—4882no—
386C22—4882no—
387C22—2444no—
388C22#1684019412yes—
389C22C22×D48811yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—4882no—
395C4—4881no—
396C4—4881no—
397C4—4881no—
398C4#1684020012yes—
399C4#1684027411yescharacteristic
400C4#1684056211yescharacteristic
401C2—22no—
402C2—9761no—
403C2—4884no—
404C2#2145582011yescharacteristic
405C2C2×#1684019411yescharacteristic
406C2C2×#1684020011yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2162C2
socleC22×C61C22×D8
prime radical#21447733C2
hypercenter#2162D61
hypocenterC61#33665
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
1. #21456389C2semidirect
2. C2×C4×D488C2semidirect
3. #21448022C2semidirect
4. #21448005C2semidirect
5. #21447977C2semidirect
6. #21447875C2semidirect
7. #21447750C2semidirect
9. C4×#14519722C2semidirect
10. C4×D976C2semidirect
11. C61×#2162C2semidirect
17. #16840164C22semidirect
18. #16840146C22semidirect
23. C4×Dic244C22semidirect
29. C4×D488C22semidirect
32. #16839590C22semidirect
33. #16839588C22semidirect
34. #16839567C22semidirect
37. #16839564C22semidirect
39. C61×C4⋊C16C22semidirect
42. C4×C16×C61C22semidirect
208. #2162D61semidirect
238. C4⋊C16C2×D61semidirect
245. C4×C16C2×D61semidirect
246. C61#33665semidirect

Maximal subgroups

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

subgroupindex
#214563892
C2×C4×D4882
#214480222
#214480052
#214479772
#214478752
#214477502
#214477332
C4×#145197222
C4×D9762
C61×#21622
#3366561