Finite Group Databasebeta

← #29580854

Subgroups — #29580854

Order 15616.

734 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455819C212yesmaximal, complemented
2#21446651C211yesmaximal, characteristic, complemented
3#21444244C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#2397C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16840075—22no—
8#16840042—22no—
9#16839957—22no—
10#16839896—22no—
11C4×#11758199—24no—
12#16839815C2212yes—
13#16839786C2211yescharacteristic
14C2×#14519705—22no—
15D4⋊#92418—24no—
16C2×C4×D4×C61—22no—
17C2×C4×D4×C61C2212yes—
18C61×#399—22no—
19C61×#392—22no—
20C61×#376C2211yescharacteristic
21C2×#11758222—21no—
22C2×#11758199—24no—
23C2×#11758194—21no—
24#14519777D411yescharacteristic, complemented
25#14519774D411yescharacteristic, complemented
26#14519765—21no—
27#14519751—22no—
28C4×D244—22no—
29#14519710—24no—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32#14519705—44no—
33#14519698—24no—
34#14519697—24no—
35C22⋊#92418—22no—
36C4×#92418D414yescomplemented
37C22×D4×C61—22no—
38C22×D4×C61D412yes—
39C23×C4×C61—22no—
40C4×D4×C61—22no—
41C4×D4×C61—22no—
42C4×D4×C61—22no—
43C4×D4×C61—22no—
44C4×D4×C61—44no—
45C4×D4×C61—44no—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61D412yes—
48C2×C22⋊C4×C61—24no—
49C2×C22⋊C4×C61—22no—
50C2×C42×C61D412yes—
51C2×C42×C61C2311yescharacteristic
52#95×C61—22no—
53C24×C61—22no—
54C2×D4×C61—22no—
55C2×D4×C61—22no—
56C2×D4×C61—44no—
57C2×D4×C61—44no—
58C2×D4×C61—48no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61—44no—
64C22×C4×C61—44no—
65C22×C4×C61C2×D412yes—
66C22×C4×C61C2×D411yescharacteristic
67C2×C22⋊D61—41no—
68#11758222—42no—
69#11758222—42no—
70C2×D244—22no—
71C2×D244—21no—
72C2×C4×D61—41no—
73C2×Dic122—21no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—44no—
77C22⋊C4×C61—48no—
78C22⋊C4×C61—42no—
79C22⋊C4×C61—42no—
80C42×C61—22no—
81C42×C61D814yescomplemented
82C42×C61C2×D411yescharacteristic
83C42×C61C2×D412yes—
84C42×C61#4111yescharacteristic
85#11758199—48no—
86#11758198—42no—
87C4⋊Dic61—22no—
88#11758194—42no—
89C2×#92418—24no—
90C2×#92418—41no—
91C23×C61—24no—
92C23×C61—44no—
93C23×C61—42no—
94C23×C61—42no—
95C23×C61—44no—
96C23×C61#12011yescharacteristic
97C22×D61—41no—
98D4×C61—24no—
99D4×C61—24no—
100D4×C61—42no—
101D4×C61—42no—
102D4×C61—416no—
103C2×C4×C61—24no—
104C2×C4×C61—42no—
105C2×C4×C61—44no—
106C2×C4×C61—42no—
107C2×C4×C61—44no—
108C2×C4×C61—84no—
109C2×C4×C61—82no—
110C2×C4×C61—82no—
111C2×C4×C61#12012yes—
112C2×C4×C61#12112yes—
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61#12711yescharacteristic
115C2×C4×C61C2×D812yes—
116C2×C4×C61AGL(1,ℤ/8)12yes—
117C22⋊D61—82no—
118C2×Dic61—41no—
119D244—44no—
120D244—42no—
121C4×D61—81no—
122C4×D61—81no—
123Dic122—42no—
124#92418—44no—
125#92418—81no—
126#10012—611nomaximal, Sylow
127C22×C61—22no—
128C22×C61—48no—
129C22×C61—44no—
130C22×C61—84no—
131C22×C61—82no—
132C22×C61—82no—
133C22×C61#39211yescharacteristic
134C22×C61#44712yes—
135C2×D61—82no—
136C2×D61—81no—
137C4×C61—22no—
138C4×C61—22no—
139C4×C61—44no—
140C4×C61—82no—
141C4×C61#45912yes—
142C4×C61#49311yescharacteristic
143C4×C61#49611yescharacteristic
144Dic61—81no—
145#3100—612no—
146#2397D6111yescharacteristic, complemented
147#1963—611no—
148#1486—612no—
149#1274—611no—
150C2×C61—22no—
151C2×C61—84no—
152C2×C61#201012yes—
153C2×C61#201111yescharacteristic
154D61—161no—
155#532—611no—
156C2×C4×D4—22no—
157C2×C4×D4C2×D6112yes—
158#480—1222no—
159#474—1222no—
160#459—1222no—
161#447—1222no—
162C4×D8—1224no—
163#431—612no—
164#423—611no—
165C2×#104—1222no—
166#399—22no—
167#392—22no—
168#376C2×D6111yescharacteristic
169D4⋊C8—1224no—
170C61#1001211yescharacteristic, complemented, Sylow
171C2×#41—1221no—
172C22×D4—22no—
173C22×D4C22⋊D6112yes—
174C23×C4—22no—
175C2×D8—1224no—
176C2×M16—1221no—
177C4⋊Q8—611no—
178#127—611no—
179#124—1221no—
180#121—1222no—
181C4×D4—22no—
182C4×D4—22no—
183C4×D4—22no—
184C4×D4—22no—
185C4×D4—44no—
186C4×D4—44no—
187C4×D4—1222no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4C22⋊D6112yes—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—22no—
192C2×C42C22⋊D6112yes—
193C2×C42C22×D6111yescharacteristic
194#107—1224no—
195C4⋊C8—1222no—
196C4⋊C8—1222no—
197#104—2444no—
198#102—1224no—
199#102—1224no—
200C22⋊C8—1222no—
201C4×C8—614no—
202#95—22no—
203C24—22no—
204#41—2442no—
205#41—2442no—
206C2×Q8—1221no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—44no—
210C2×D4—44no—
211C2×D4—48no—
212C2×D4—1222no—
213C2×D4—1221no—
214C2×D4—2441no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—2441no—
222C22×C4C2×C22⋊D6112yes—
223C22×C4C2×C22⋊D6111yescharacteristic
224D8—2448no—
225M16—2442no—
226C2×C8—1224no—
227C2×C8—2441no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—44no—
231C4⋊C4—1222no—
232C22⋊C4—48no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—2442no—
236C42—22no—
237C42#1175819914yescomplemented
238C42D4×D6111yescharacteristic
239C42D4×D6112yes—
240C42#1175822411yescharacteristic
241C23—24no—
242C23—44no—
243C23—42no—
244C23—44no—
245C23—42no—
246C23—2441no—
247C23#1451974611yescharacteristic
248Q8—2442no—
249D4—24no—
250D4—24no—
251D4—42no—
252D4—42no—
253D4—416no—
254D4—4882no—
255D4—2444no—
256D4—2442no—
257C2×C4—24no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—84no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—4881no—
266C2×C4—4881no—
267C2×C4—2441no—
268C2×C4#1451974512yes—
269C2×C4#1451974811yescharacteristic
270C2×C4#1451974912yes—
271C2×C4#1451977311yescharacteristic
272C2×C4C2×#1175819912yes—
273C2×C4#1451980312yes—
274C8—4881no—
275C8—2444no—
276C22—22no—
277C22—48no—
278C22—44no—
279C22—84no—
280C22—82no—
281C22—82no—
282C22—4882no—
283C22—4881no—
284C22#1683967011yescharacteristic
285C22#1683989612yes—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—82no—
290C4—4881no—
291C4#1683995412yes—
292C4#1684013811yescharacteristic
293C4#1684014911yescharacteristic
294C2—22no—
295C2—84no—
296C2—9761no—
297C2#2144688412yes—
298C2#2144689011yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2397C2
socleC22×C61#392
hypercenter#2397D61
hypocenterC61#10012
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #21455819C2semidirect
2. #21446651C2semidirect
3. #21444244C2semidirect
4. #21443648C2semidirect
5. C61×#2397C2semidirect
24. #14519777D4semidirect
25. #14519774D4semidirect
36. C4×#92418D4semidirect
81. C42×C61D8semidirect
146. #2397D61semidirect
170. C61#10012semidirect
237. C42#11758199semidirect

Maximal subgroups

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

subgroupindex
#214558192
#214466512
#214442442
#214436482
C61×#23972
#1001261