Finite Group Databasebeta

← #29656131

Subgroups — #29656131

Order 15616.

982 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#16840498C211yesmaximal, characteristic
2#21455945C212yesmaximal, complemented
3#21445002C218yesmaximal, complemented
4#21444533C211yesmaximal, characteristic
5#21444267C212yesmaximal, complemented
6C61×#3138C211yesmaximal, characteristic
7#16840498—24no—
8#16840498—22no—
9#16840498C2214yes—
10C2×#14519764—22no—
11C2×#14519758—22no—
12C2×C4×Dic122C2212yes—
13C2×D4×Dic61—22no—
14#16840090—22no—
15#16840044C2214yescomplemented
16#16839969C2214yescomplemented
17#16839917—22no—
18#16839867—24no—
19#16839819C2212yes—
20#16839506C2214yes—
21#16839494C2218yescomplemented
22C61×#533C2211yescharacteristic
23C2×#127×C61C2211yescharacteristic
24C61×#490—22no—
25C61×#486C2214yes—
26C61×#418—22no—
27C4×M16×C61C2211yescharacteristic
28C22×Dic122D412yes—
29C23×Dic61—22no—
30C2×#11758202—24no—
31#14519764—28no—
32#14519764—28no—
33#14519758—28no—
34#14519758—28no—
35C4×Dic122—22no—
36C4×Dic122—22no—
37C4×Dic122D414yes—
38C4×Dic122C2314yes—
39D4×Dic61—28no—
40D4×Dic61—28no—
41C2×C4⋊Dic61D412yes—
42C2×#11758196—22no—
43C2×C22⋊Dic61—24no—
44C2×C22⋊Dic61—22no—
45C2×C4×Dic61—22no—
46#14519708—24no—
47C4⋊#92418C2314yes—
48#14519701—24no—
49#14519700—24no—
50C22⋊#92418—22no—
51#14519688—22no—
52C22×D4×C61—22no—
53C22×D4×C61D412yes—
54C2×M16×C61—21no—
55C4⋊Q8×C61C2312yes—
56#127×C61—22no—
57#127×C61D412yes—
58#127×C61C2312yes—
59#125×C61—21no—
60C22⋊Q8×C61—22no—
61C4×Q8×C61—22no—
62#117×C61—21no—
63C2×C42×C61C2311yescharacteristic
64#102×C61—28no—
65#97×C61—21no—
66C4×C8×C61C2312yes—
67C24×C61—22no—
68C2×Q8×C61—22no—
69C2×D4×C61—24no—
70C2×D4×C61—22no—
71C2×D4×C61—24no—
72C2×D4×C61—48no—
73C2×D4×C61—44no—
74C2×D4×C61C2×D414yes—
75C22×C4×C61C2×D412yes—
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—28no—
80C22×Dic61—84no—
81C2×Dic122—22no—
82C2×Dic122—44no—
83C2×Dic122C2×D414yes—
84M16×C61—42no—
85C2×C8×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—42no—
89C22⋊C4×C61—41no—
90C42×C61—41no—
91C42×C61C2×D412yes—
92C42×C61C2×D411yescharacteristic
93C42×C61C2411yescharacteristic
94C22⋊Dic61—216no—
95C22⋊Dic61—28no—
96#11758202—48no—
97C4⋊Dic61—22no—
98C4⋊Dic61C2×D414yes—
99#11758196—24no—
100#11758196—24no—
101C4×Dic61—24no—
102C4×Dic61—24no—
103C2×#92418—24no—
104C23×C61—24no—
105C23×C61—48no—
106C23×C61—44no—
107C23×C61#12011yescharacteristic
108Q8×C61—44no—
109D4×C61—44no—
110D4×C61—48no—
111D4×C61—48no—
112D4×C61—82no—
113C2×C4×C61—22no—
114C2×C4×C61—24no—
115C2×C4×C61—42no—
116C2×C4×C61#12012yes—
117C2×C4×C61#12011yescharacteristic
118C2×C4×C61C22×D411yescharacteristic
119C2×C4×C61C22×D412yes—
120C2×Dic61—24no—
121C2×Dic61—24no—
122C2×Dic61—44no—
123C2×Dic61—44no—
124C2×Dic61—88no—
125Dic122—24no—
126Dic122—24no—
127Dic122—44no—
128C8×C61—42no—
129#92418—44no—
130#18531—611nomaximal, Sylow
131C22×C61—22no—
132C22×C61—48no—
133C22×C61—44no—
134C22×C61—88no—
135C22×C61#45512yes—
136C22×C61C2×#12011yescharacteristic
137C4×C61—22no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—82no—
141C4×C61#57514yes—
142Dic61—44no—
143Dic61—44no—
144C2×#559—611no—
145#3138D6111yescharacteristic
146#3113—612no—
147#1640—618no—
148#1555—611no—
149#1491—612no—
150C2×C61—22no—
151C2×C61—84no—
152C2×C61#300512yes—
153C2×C61C2×#45511yescharacteristic
154#559—614no—
155#559—1224no—
156#559—1222no—
157#533C2×D6111yescharacteristic
158C2×#127C2×D6111yescharacteristic
159C2×#124—1222no—
160C2×#123—1222no—
161C2×C4×Q8—612no—
162C2×C4×D4—1222no—
163#490—22no—
164#486C2×D6114yes—
165#483—1222no—
166#475—614no—
167#462—614no—
168#451—1222no—
169#441—1224no—
170#432—612no—
171#418—22no—
172C4×M16C2×D6111yescharacteristic
173#331—614no—
174Q8⋊C8—618no—
175C61#1853111yescharacteristic, complemented, Sylow
176C22×Q8—612no—
177C22×D4—22no—
178C22×D4C22⋊D6112yes—
179C23×C4—1222no—
180C2×Q16—1224no—
181C2×M16—21no—
182C4⋊Q8C22×D6112yes—
183#127—22no—
184#127C22⋊D6112yes—
185#127C22×D6112yes—
186#125—21no—
187#124—1228no—
188#124—1228no—
189#123—1228no—
190#123—1228no—
191C22⋊Q8—22no—
192C4×Q8—22no—
193C4×Q8—614no—
194C4×Q8—614no—
195C4×Q8—1222no—
196C4×Q8—1222no—
197C4×D4—1228no—
198C4×D4—1228no—
199#117—21no—
200C2×C4⋊C4—612no—
201C2×C4⋊C4—1222no—
202C2×C22⋊C4—1224no—
203C2×C22⋊C4—1222no—
204C2×C42—1222no—
205C2×C42C22×D6111yescharacteristic
206#106—1224no—
207C4⋊C8—614no—
208#103—1224no—
209#103—1224no—
210#102—28no—
211C22⋊C8—1222no—
212#97—21no—
213#97—1222no—
214C4×C8C22×D6112yes—
215C24—22no—
216C2×Q8—22no—
217C2×Q8—614no—
218C2×Q8—1222no—
219C2×Q8—2444no—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—22no—
223C2×D4—48no—
224C2×D4—44no—
225C2×D4C2×C22⋊D6114yes—
226C22×C4—1228no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—4884no—
230C22×C4D4×D6112yes—
231C22×C4C2×C22⋊D6111yescharacteristic
232Q16—2448no—
233M16—42no—
234C2×C8—22no—
235C2×C8—1224no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—614no—
240C4⋊C4—1224no—
241C4⋊C4—1222no—
242C4⋊C4—1224no—
243C22⋊C4—41no—
244C22⋊C4—12216no—
245C22⋊C4—1228no—
246C42—41no—
247C42—1224no—
248C42—1224no—
249C42D4×D6112yes—
250C42C2×C22⋊D6111yescharacteristic
251C42C23×D6111yescharacteristic
252C23—24no—
253C23—48no—
254C23—44no—
255C23#1451974511yescharacteristic
256Q8—44no—
257Q8—1224no—
258Q8—1224no—
259Q8—2444no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—42no—
267C2×C4—1224no—
268C2×C4—1224no—
269C2×C4—4888no—
270C2×C4—2444no—
271C2×C4—2444no—
272C2×C4#1451974511yescharacteristic
273C2×C4#1451974512yes—
274C2×C4C2×D4×D6112yes—
275C2×C4C22×C22⋊D6111yescharacteristic
276C8—42no—
277C8—2444no—
278C22—22no—
279C22—44no—
280C22—48no—
281C22—88no—
282C22#1683993912yes—
283C22C2×#1451974511yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—82no—
288C4—2444no—
289C4—2444no—
290C4#1684055814yes—
291C2—22no—
292C2—84no—
293C2#2145505812yes—
294C2C2×#1683993911yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3138C2
socleC22×C61C2×#120
prime radicalC2×#127×C61C22
hypercenter#3138D61
hypocenterC61#18531
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #21455945C2semidirect
3. #21445002C2semidirect
5. #21444267C2semidirect
15. #16840044C22semidirect
16. #16839969C22semidirect
21. #16839494C22semidirect
175. C61#18531semidirect

Maximal subgroups

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

subgroupindex
C2×#168404982
#214559452
#214450022
#214445332
#214442672
C61×#31382
#1853161