Finite Group Databasebeta

← #29835587

Subgroups — #29835587

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#21448106C211yesmaximal, characteristic, complemented
3#21448086C211yesmaximal, characteristic, complemented
4#21448062C211yesmaximal, characteristic, complemented
5#21448055C211yesmaximal, characteristic, complemented
6#21447934C212yesmaximal, complemented
7#21447920C212yesmaximal, complemented
8C4×#14519720C212yesmaximal, complemented
9C4×#14519718C212yesmaximal, complemented
10C4×#14519717C211yesmaximal, characteristic, complemented
11C61×#3168C211yesmaximal, characteristic, complemented
12#16840312—21no—
13C2×#14519720C2212yes—
14C2×#14519718C2212yes—
15C2×#14519717C2212yes—
16#16840167C2211yescharacteristic
17#16840139C2211yescharacteristic
18#16840109—21no—
19#16839998—21no—
20#16839998C2212yes—
21C4×D488—21no—
22C4×D488C2212yes—
23#16839589C2212yes—
24#16839587C2212yes—
25#16839566C2212yes—
26#16839563C2212yes—
27#16839562C2212yes—
28#16839562C2212yes—
29#16839538C2211yescharacteristic
30#16839538C2211yescharacteristic
31C4×#11758185C2212yes—
32C61×#529—21no—
33C61×#499C2211yescharacteristic
34C61×#495C2211yescharacteristic
35C61×#488—21no—
36C61×#467C2211yescharacteristic
37C61×#466C2211yescharacteristic
38C61×#465—21no—
39C4×Q16×C61C2211yescharacteristic
40C4×SD16×C61—21no—
41C4×D8×C61C2211yescharacteristic
42C2×C4×C8×C61C2211yescharacteristic
43C2×#11758222—41no—
44C2×D488—21no—
45C2×D488C2312yes—
46#14519777—21no—
47#14519774—21no—
48#14519765—41no—
49#14519751—22no—
50#14519751—41no—
51C4×D244—22no—
52C4×D244—41no—
53#14519720—24no—
54#14519718—24no—
55#14519717—24no—
56C2×#11758185C2312yes—
57C2×#11758185C2312yes—
58#14519711—21no—
59#14519711C2312yes—
60#14519699—22no—
61#14519699—22no—
62C2×Q16×C61C2311yescharacteristic
63C2×SD16×C61—21no—
64C2×D8×C61C2311yescharacteristic
65C22×C8×C61D411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67#126×C61—41no—
68#125×C61—21no—
69#124×C61—21no—
70#123×C61—41no—
71C22⋊Q8×C61—21no—
72#121×C61—21no—
73C4×Q8×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61—41no—
76#117×C61—41no—
77C2×C42×C61D411yescharacteristic
78#107×C61C2311yescharacteristic
79#107×C61C2311yescharacteristic
80#106×C61—21no—
81#103×C61—21no—
82#103×C61—21no—
83#102×C61—21no—
84#102×C61—21no—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C2×Q8×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61D811yescharacteristic
94C22×C4×C61D811yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C2×C22⋊D61—42no—
97#11758222—84no—
98C2×D244—22no—
99C2×D244—41no—
100C2×D244—41no—
101C2×C4×D61—42no—
102C2×Dic122—41no—
103Q16×C61—22no—
104SD16×C61—42no—
105D8×C61—22no—
106C2×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2411yescharacteristic
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C42×C61—41no—
124C42×C61D811yescharacteristic
125C42×C61D811yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128#11758198—42no—
129#11758198—42no—
130C4⋊Dic61—22no—
131C4⋊Dic61—41no—
132D488—22no—
133D488—22no—
134D488—42no—
135#11758185—22no—
136#11758185#4114yescomplemented
137C23×C61—41no—
138C23×C61C2×D811yescharacteristic
139C22×D61—42no—
140Q8×C61—41no—
141Q8×C61—41no—
142D4×C61—41no—
143D4×C61—41no—
144D4×C61—82no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—22no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—82no—
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C22×D411yescharacteristic
159C22⋊D61—84no—
160C2×Dic61—42no—
161D244—42no—
162D244—42no—
163D244—82no—
164D244—82no—
165C4×D61—84no—
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×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61C22×D811yescharacteristic
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—82no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—81no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61#50912yes—
190C4×C61#53211yescharacteristic
191C4×C61C2×#13511yescharacteristic
192Dic61—82no—
193#3169—611no—
194#3168D6111yescharacteristic, complemented
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×M32—611no—
204C2×C61—41no—
205C2×C61—161no—
206C2×C61#316911yescharacteristic
207C2×C61C2×#50911yescharacteristic
208C2×C61#341411yescharacteristic
209D61—162no—
210#532—1221no—
211#529—21no—
212C2×SD32—612no—
213C2×D16—612no—
214C2×M32—612no—
215#500—611no—
216#499C2×D6111yescharacteristic
217#495C2×D6111yescharacteristic
218#493—611no—
219#488—21no—
220#486—1221no—
221#467C2×D6111yescharacteristic
222#466—612no—
223#466—1221no—
224#466C2×D6111yescharacteristic
225#465—21no—
226C4×Q16C2×D6111yescharacteristic
227C4×SD16—21no—
228C4×D8—612no—
229C4×D8—1221no—
230C4×D8C2×D6111yescharacteristic
231C2×C4×C8C2×D6111yescharacteristic
232#367—612no—
233#366—612no—
234#358—612no—
235#357—612no—
236#357—612no—
237#357—612no—
238#346—611no—
239#346—611no—
240C4×C16—612no—
241C61#3373711yescharacteristic, complemented, Sylow
242C2×#41—2441no—
243C2×Q16C22×D6111yescharacteristic
244C2×SD16—21no—
245C2×D8—612no—
246C2×D8—1221no—
247C2×D8C22×D6111yescharacteristic
248C22×C8C22⋊D6111yescharacteristic
249C22×C8C22×D6111yescharacteristic
250C4⋊Q8—1221no—
251#127—1221no—
252#126—41no—
253#125—21no—
254#124—21no—
255#124—2441no—
256#123—41no—
257C22⋊Q8—21no—
258#121—21no—
259#121—1222no—
260#121—2441no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—41no—
264C4×D4—1222no—
265C4×D4—2441no—
266#117—41no—
267C2×C42C22⋊D6111yescharacteristic
268SD32—1224no—
269D16—1224no—
270M32—1224no—
271C2×C16—612no—
272C2×C16—612no—
273#107—612no—
274#107—1221no—
275#107C22×D6111yescharacteristic
276#107C22×D6111yescharacteristic
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#102—1222no—
283#102—1222no—
284C4×C8C22⋊D6111yescharacteristic
285C4×C8C22⋊D6111yescharacteristic
286C4×C8C22×D6111yescharacteristic
287C4×C8C22×D6111yescharacteristic
288#41—4884no—
289C2×Q8—21no—
290C2×Q8—2441no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—1222no—
294C2×D4—2442no—
295C2×D4—2441no—
296C2×D4—2441no—
297C22×C4—41no—
298C22×C4—2442no—
299C22×C4#1175819911yescharacteristic
300C22×C4#1175819911yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302Q16—22no—
303SD16—42no—
304D8—22no—
305D8—1222no—
306D8—1222no—
307D8—2442no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D6111yescharacteristic
311C2×C8C2×C22⋊D6111yescharacteristic
312C2×C8C2×C22⋊D6111yescharacteristic
313C2×C8C23×D6111yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—1222no—
321C4⋊C4—2441no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—41no—
330C42#1175819911yescharacteristic
331C42#1175819911yescharacteristic
332C42C2×C22⋊D6111yescharacteristic
333C42C2×C22⋊D6111yescharacteristic
334C16—614no—
335C16—1222no—
336C23—41no—
337C23—2442no—
338C23C2×#1175819911yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—4882no—
342D4—41no—
343D4—41no—
344D4—82no—
345D4—4882no—
346D4—4882no—
347D4—4884no—
348D4—2442no—
349D4—2442no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—4884no—
359C2×C4—2442no—
360C2×C4C2×#1175819911yescharacteristic
361C2×C4C2×#1175819911yescharacteristic
362C2×C4C2×#1175819911yescharacteristic
363C2×C4C2×#1175819911yescharacteristic
364C2×C4C2×#1175819911yescharacteristic
365C2×C4C22×C22⋊D6111yescharacteristic
366C8—21no—
367C8—21no—
368C8#1451979712yes—
369C8#41×D6112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—4882no—
377C22—4882no—
378C22—4882no—
379C22C22×#1175819911yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—4882no—
388C4#1684019712yes—
389C4#1684030811yescharacteristic
390C4C2×#1451979711yescharacteristic
391C2—41no—
392C2—161no—
393C2—9762no—
394C2#2145639411yescharacteristic
395C2C2×#1684019711yescharacteristic
396C2#2145895311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3168C2
socleC22×C61C22×D8
hypercenter#3168D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #21456398C2semidirect
2. #21448106C2semidirect
3. #21448086C2semidirect
4. #21448062C2semidirect
5. #21448055C2semidirect
6. #21447934C2semidirect
7. #21447920C2semidirect
8. C4×#14519720C2semidirect
9. C4×#14519718C2semidirect
10. C4×#14519717C2semidirect
11. C61×#3168C2semidirect
136. #11758185#41semidirect
194. #3168D61semidirect
241. C61#33737semidirect

Maximal subgroups

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

subgroupindex
#214563982
#214481062
#214480862
#214480622
#214480552
#214479342
#214479202
C4×#145197202
C4×#145197182
C4×#145197172
C61×#31682
#3373761