Finite Group Databasebeta

← #29835586

Subgroups — #29835586

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456398C211yesmaximal, characteristic, complemented
2#21456389C211yesmaximal, characteristic, complemented
3#21448105C211yesmaximal, characteristic, complemented
4#21448085C211yesmaximal, characteristic, complemented
5#21448061C211yesmaximal, characteristic, complemented
6#21448056C211yesmaximal, characteristic, complemented
7#21447932C212yesmaximal, complemented
8#21447922C212yesmaximal, complemented
9C4×#14519722C212yesmaximal, complemented
10C4×D976C212yesmaximal, complemented
11C4×M32×C61C211yesmaximal, characteristic, complemented
12#16840312—21no—
13#16840296—21no—
14C2×#14519722C2212yes—
15C2×D976C2212yes—
16#16840167C2211yescharacteristic
17#16840164C2211yescharacteristic
18#16840146C2211yescharacteristic
19#16840139C2211yescharacteristic
20#16840117—21no—
21#16840109—21no—
22#16840003C2211yescharacteristic
23#16839998—21no—
24#16839998C2211yescharacteristic
25#16839998C2212yes—
26#16839991—21no—
27C4×Dic244C2211yescharacteristic
28C4×#11758190—21no—
29C4×D488—21no—
30C4×D488C2211yescharacteristic
31C4×D488C2212yes—
32#16839590C2212yes—
33#16839588C2212yes—
34#16839567C2212yes—
35#16839564C2212yes—
36#16839564C2212yes—
37#16839564C2212yes—
38C2×M32×C61C2212yes—
39C2×C4×C8×C61C2211yescharacteristic
40C61×#346C2211yescharacteristic
41C61×#346C2211yescharacteristic
42C4×C16×C61C2212yes—
43C2×#11758222—41no—
44C2×Dic244C2311yescharacteristic
45C2×#11758190—21no—
46C2×D488—21no—
47C2×D488C2312yes—
48C2×D488C2311yescharacteristic
49#14519777—21no—
50#14519774—21no—
51#14519771—41no—
52#14519769—21no—
53#14519765—21no—
54#14519765—41no—
55#14519760—41no—
56#14519756—21no—
57#14519751—21no—
58#14519751—22no—
59#14519751—41no—
60C4×Dic122—21no—
61C4×D244—21no—
62C4×D244—22no—
63C4×D244—41no—
64C4×C22⋊D61—41no—
65#14519734—41no—
66#14519722—24no—
67D976—24no—
68#14519711—21no—
69#14519711C2311yescharacteristic
70#14519711C2312yes—
71#14519711C2311yescharacteristic
72#14519709—21no—
73#14519702—21no—
74#14519702—21no—
75#14519699—21no—
76#14519699—22no—
77#14519699—22no—
78#14519699—21no—
79C22×C8×C61D411yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C2×C42×C61D411yescharacteristic
82M32×C61—24no—
83C2×C16×C61C2312yes—
84C2×C16×C61C2312yes—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C22×C4×C61D811yescharacteristic
90C22×C4×C61D811yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—42no—
93C2×C22⋊D61—41no—
94#11758222—84no—
95C2×D244—21no—
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99C2×C4×D61—42no—
100C2×C4×D61—41no—
101C2×Dic122—21no—
102C2×Dic122—41no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2411yescharacteristic
109C42×C61D811yescharacteristic
110C42×C61D811yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C22⋊Dic61—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117#11758198—42no—
118#11758198—41no—
119#11758198—42no—
120C4⋊Dic61—22no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—41no—
129Dic244—22no—
130D488—22no—
131D488—22no—
132D488—22no—
133D488—42no—
134#11758190—42no—
135C16×C61—22no—
136C16×C61#4114yescomplemented
137C23×C61C2×D811yescharacteristic
138C22×D61—41no—
139C22×D61—42no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61C2×D811yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C22×D411yescharacteristic
150C22⋊D61—84no—
151C22⋊D61—82no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156D244—41no—
157D244—42no—
158D244—41no—
159D244—42no—
160D244—82no—
161D244—82no—
162C4×D61—82no—
163C4×D61—84no—
164Dic122—41no—
165Dic122—41no—
166Dic122—82no—
167C8×C61—21no—
168C8×C61—21no—
169C8×C61#13512yes—
170C8×C61C2×#4112yes—
171#33737—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61C22×D811yescharacteristic
176C2×D61—82no—
177C2×D61—81no—
178C2×D61—82no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—82no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61#50912yes—
187C4×C61#53211yescharacteristic
188C4×C61C2×#13511yescharacteristic
189Dic61—82no—
190Dic61—81no—
191Dic61—81no—
192Dic61—81no—
193#3169—611no—
194#3168—611no—
195#2255—611no—
196#2250—611no—
197#2244—611no—
198#2243—611no—
199#2220—612no—
200#2218—612no—
201C4×SD32—612no—
202C4×D16—612no—
203C4×M32D6111yescharacteristic, complemented
204C2×C61—41no—
205C2×C61#316911yescharacteristic
206C2×C61C2×#50911yescharacteristic
207C2×C61#341411yescharacteristic
208D61—162no—
209D61—161no—
210#532—1221no—
211#529—1221no—
212C2×SD32—612no—
213C2×D16—612no—
214C2×M32C2×D6112yes—
215#500—611no—
216#499—611no—
217#495—611no—
218#493—611no—
219#488—1221no—
220#486—1221no—
221#467—611no—
222#466—611no—
223#466—612no—
224#466—1221no—
225#465—1221no—
226C4×Q16—611no—
227C4×SD16—1221no—
228C4×D8—611no—
229C4×D8—612no—
230C4×D8—1221no—
231C2×C4×C8C2×D6111yescharacteristic
232#367—612no—
233#366—612no—
234#358—612no—
235#357—612no—
236#357—612no—
237#357—612no—
238#346C2×D6111yescharacteristic
239#346C2×D6111yescharacteristic
240C4×C16C2×D6112yes—
241C61#3373711yescharacteristic, complemented, Sylow
242C2×#41—2441no—
243C2×Q16—611no—
244C2×SD16—1221no—
245C2×D8—612no—
246C2×D8—611no—
247C2×D8—1221no—
248C22×C8D24411yescharacteristic
249C22×C8C22×D6111yescharacteristic
250C4⋊Q8—1221no—
251#127—1221no—
252#126—2441no—
253#125—1221no—
254#124—1221no—
255#124—2441no—
256#123—2441no—
257C22⋊Q8—1221no—
258#121—1221no—
259#121—1222no—
260#121—2441no—
261C4×Q8—1221no—
262C4×D4—1221no—
263C4×D4—1222no—
264C4×D4—2441no—
265C4×D4—2441no—
266#117—2441no—
267C2×C42D24411yescharacteristic
268SD32—1224no—
269D16—1224no—
270M32—24no—
271C2×C16C22×D6112yes—
272C2×C16C22×D6112yes—
273#107—611no—
274#107—611no—
275#107—612no—
276#107—1221no—
277#106—1221no—
278#103—1221no—
279#103—1221no—
280#102—1221no—
281#102—1222no—
282#102—1222no—
283#102—1221no—
284C4×C8D24411yescharacteristic
285C4×C8D24411yescharacteristic
286C4×C8C22×D6111yescharacteristic
287C4×C8C22×D6111yescharacteristic
288#41—4884no—
289C2×Q8—1221no—
290C2×Q8—2441no—
291C2×D4—1221no—
292C2×D4—1222no—
293C2×D4—2441no—
294C2×D4—2442no—
295C2×D4—2441no—
296C2×D4—2441no—
297C22×C4—2441no—
298C22×C4—2442no—
299C22×C4D48811yescharacteristic
300C22×C4D48811yescharacteristic
301C22×C4C2×D24411yescharacteristic
302Q16—1222no—
303SD16—2442no—
304D8—1222no—
305D8—1222no—
306D8—1222no—
307D8—2442no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×D24411yescharacteristic
311C2×C8C2×D24411yescharacteristic
312C2×C8C2×D24411yescharacteristic
313C2×C8C23×D6111yescharacteristic
314C4⋊C4—1222no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2442no—
326C22⋊C4—2441no—
327C22⋊C4—2442no—
328C22⋊C4—2441no—
329C42—2441no—
330C42D48811yescharacteristic
331C42D48811yescharacteristic
332C42C2×D24411yescharacteristic
333C42C2×D24411yescharacteristic
334C16—22no—
335C16#1175822214yescomplemented
336C23—2441no—
337C23—2442no—
338C23C2×D48811yescharacteristic
339Q8—4882no—
340Q8—2441no—
341Q8—2441no—
342D4—4882no—
343D4—4882no—
344D4—4882no—
345D4—4884no—
346D4—2442no—
347D4—2441no—
348D4—2441no—
349D4—2442no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—4882no—
355C2×C4—4884no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2442no—
360C2×C4C2×D48811yescharacteristic
361C2×C4C2×D48811yescharacteristic
362C2×C4C2×D48811yescharacteristic
363C2×C4C2×D48811yescharacteristic
364C2×C4C2×D48811yescharacteristic
365C2×C4C22×D24411yescharacteristic
366C8—21no—
367C8—21no—
368C8#1451979912yes—
369C8C2×#1175822212yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—4882no—
374C22—4881no—
375C22—4882no—
376C22—4881no—
377C22—4882no—
378C22—4881no—
379C22C22×D48811yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—4881no—
385C4—4882no—
386C4—4881no—
387C4—4881no—
388C4#1684020012yes—
389C4#1684031211yescharacteristic
390C4C2×#1451979911yescharacteristic
391C2—41no—
392C2—9762no—
393C2—9761no—
394C2#2145639811yescharacteristic
395C2C2×#1684020011yescharacteristic
396C2#2145895511yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×M32×C61C2
socleC22×C61C22×D8
hypercenterC4×M32D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
1. #21456398C2semidirect
2. #21456389C2semidirect
3. #21448105C2semidirect
4. #21448085C2semidirect
5. #21448061C2semidirect
6. #21448056C2semidirect
7. #21447932C2semidirect
8. #21447922C2semidirect
9. C4×#14519722C2semidirect
10. C4×D976C2semidirect
11. C4×M32×C61C2semidirect
136. C16×C61#41semidirect
203. C4×M32D61semidirect
241. C61#33737semidirect
335. C16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214563982
#214563892
#214481052
#214480852
#214480612
#214480562
#214479322
#214479222
C4×#145197222
C4×D9762
C4×M32×C612
#3373761