Finite Group Databasebeta

← #29593809

Subgroups — #29593809

Order 15616.

350 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×Dic244C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic, complemented
3#21447962C211yesmaximal, characteristic, complemented
4#21445208C211yesmaximal, characteristic
5#21443869C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×D4⋊C16C211yesmaximal, characteristic
8C22×Dic244—21no—
9D4×Dic122—21no—
10#16840167C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840003—21no—
13#16839973—21no—
14#16839967—21no—
15#16839920—22no—
16C4×Dic244C2211yescharacteristic
17#16839590—21no—
18#16839567—21no—
19#16839567—22no—
20#16839515C2211yescharacteristic
21#16839507—21no—
22C8×D4×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C22×Dic122—22no—
26C2×Dic244—22no—
27C2×Dic244—21no—
28C2×Dic244—42no—
29C2×Dic244—42no—
30C2×Dic244D411yescharacteristic
31C2×Dic244D412yes—
32C2×#11758200—41no—
33#14519777—21no—
34#14519777—21no—
35#14519776—41no—
36#14519756—22no—
37#14519754—42no—
38C4×Dic122—21no—
39D4×Dic61—41no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43C4⋊#92418—21no—
44#14519702—22no—
45#14519702—21no—
46#14519700—41no—
47C22×C8×C61—21no—
48C4×D4×C61D411yescharacteristic
49C2×C16×C61—21no—
50C2×C16×C61—21no—
51C4⋊C8×C61D411yescharacteristic
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61D811yescharacteristic
55C22×C4×C61—21no—
56C22×Dic61—42no—
57C2×Dic122—21no—
58C2×Dic122—22no—
59C2×Dic122—44no—
60C2×Dic122—42no—
61C2×Dic122—41no—
62C2×Dic122—82no—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61D811yescharacteristic
69C22⋊C4×C61—21no—
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72#11758200—82no—
73C4⋊Dic61—21no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—42no—
79#11758196—41no—
80C4×Dic61—41no—
81C2×#92418—41no—
82Dic244—21no—
83Dic244—42no—
84Dic244—44no—
85Dic244—41no—
86Dic244—41no—
87Dic244SD1612yescomplemented
88C16×C61—41no—
89C16×C61—41no—
90C23×C61—21no—
91D4×C61—21no—
92D4×C61SD3212yes—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—84no—
103C2×Dic61—81no—
104Dic122—22no—
105Dic122—41no—
106Dic122—42no—
107Dic122—42no—
108Dic122—84no—
109Dic122—81no—
110Dic122—81no—
111C8×C61—21no—
112C8×C61—41no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#92418—81no—
116#12370—611nomaximal, Sylow
117C22×C61—22no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61#44711yescharacteristic
121C4×C61—21no—
122C4×C61—41no—
123C4×C61#45011yescharacteristic
124C4×C61#45511yescharacteristic
125C4×C61C2×SD3211yescharacteristic
126C4×C61#51011yescharacteristic
127Dic61—42no—
128Dic61—82no—
129Dic61—81no—
130Dic61—161no—
131D4×Q16—611no—
132#2241—611no—
133#2225—611no—
134#1673—611no—
135#1362—611no—
136#1332—611no—
137D4⋊C16D6111yescharacteristic
138C2×C61—42no—
139C2×C61#163911yescharacteristic
140C2×C61#218511yescharacteristic
141C2×C61#219511yescharacteristic
142C22×Q16—1221no—
143D4×Q8—1221no—
144#500—611no—
145#494—611no—
146#467—1221no—
147#462—1221no—
148#461—1221no—
149#451—1222no—
150C4×Q16—611no—
151C8×D4C2×D6111yescharacteristic
152#367—1221no—
153C4⋊C16C2×D6111yescharacteristic
154#358—1221no—
155#358—1222no—
156C4×C16C2×D6111yescharacteristic
157#335—611no—
158#332—1221no—
159C61#1237011yescharacteristic, complemented, Sylow
160C22×Q8—1222no—
161C2×Q16—611no—
162C2×Q16—612no—
163C2×Q16—1222no—
164C2×Q16—1221no—
165C2×Q16—2442no—
166C2×Q16—2442no—
167C2×SD16—2441no—
168C22×C8—21no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171C4⋊Q8—2441no—
172C22⋊Q8—1222no—
173C22⋊Q8—2442no—
174C4×Q8—1221no—
175C4×D4—2441no—
176C4×D4D24411yescharacteristic
177C2×C16—21no—
178C2×C16—21no—
179#107—611no—
180#107—1221no—
181#107—1221no—
182C4⋊C8—1221no—
183C4⋊C8D24411yescharacteristic
184#103—1222no—
185#103—1221no—
186#103—2441no—
187C22⋊C8—21no—
188C4×C8C22×D6111yescharacteristic
189C2×Q8—1221no—
190C2×Q8—1222no—
191C2×Q8—4882no—
192C2×Q8—2442no—
193C2×Q8—2444no—
194C2×Q8—2441no—
195C2×D4D48811yescharacteristic
196C22×C4—21no—
197C22×C4—2442no—
198Q16—612no—
199Q16—1221no—
200Q16—2442no—
201Q16—2444no—
202Q16—2441no—
203Q16—2441no—
204SD16—4882no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—2441no—
209C2×C8D4×D6111yescharacteristic
210C2×C8D4×D6111yescharacteristic
211C4⋊C4—1221no—
212C4⋊C4—2442no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4D48811yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—2442no—
221C42—2441no—
222C42C2×D24411yescharacteristic
223C16—41no—
224C16—41no—
225C23—21no—
226Q8—1222no—
227Q8—4884no—
228Q8—4881no—
229Q8—4881no—
230Q8—2442no—
231Q8—2442no—
232Q8—2441no—
233D4—21no—
234D4#1451972212yes—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—4881no—
239C2×C4—4884no—
240C2×C4—2441no—
241C2×C4—2442no—
242C2×C4—2441no—
243C2×C4#1451974711yescharacteristic
244C2×C4C2×D48811yescharacteristic
245C2×C4#1451980511yescharacteristic
246C8—21no—
247C8—41no—
248C8—4881no—
249C8SD16×D6111yescharacteristic
250C8#1451980111yescharacteristic
251C22—22no—
252C22—41no—
253C22—41no—
254C22#1683989811yescharacteristic
255C4—21no—
256C4—41no—
257C4—9761no—
258C4—4881no—
259C4—4882no—
260C4—2442no—
261C4#1683991411yescharacteristic
262C4#1683994111yescharacteristic
263C4C2×#1451972211yescharacteristic
264C4#1684020511yescharacteristic
265C2—42no—
266C2#2144500011yescharacteristic
267C2#2144773811yescharacteristic
268C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×D4⋊C16C2
socleC22×C61#447
prime radicalC2×D4×C61D8
hypercenterD4⋊C16D61
hypocenterC61#12370
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #21448047C2semidirect
3. #21447962C2semidirect
5. #21443869C2semidirect
6. #21443784C2semidirect
87. Dic244SD16semidirect
159. C61#12370semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2442
#214480472
#214479622
#214452082
#214438692
#214437842
C61×D4⋊C162
#1237061