Finite Group Databasebeta

← #29593569

Subgroups — #29593569

Order 15616.

312 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458805C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic, complemented
3#21445186C211yesmaximal, characteristic, complemented
4#21443869C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic
7C61×#2208C211yesmaximal, characteristic
8#16840482—21no—
9C2×#14519723—22no—
10#16840145—21no—
11#16840142C2211yescharacteristic
12#16840044—21no—
13#16839983—22no—
14#16839967—21no—
15C8×Dic122C2211yescharacteristic
16#16839856—21no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C2×SD32×C61—21no—
21C61×#494C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758200—22no—
28#14519777—21no—
29#14519770—42no—
30#14519764—22no—
31#14519756—41no—
32C4×Dic122D411yescharacteristic
33#14519742—22no—
34#14519736—41no—
35#14519723—44no—
36C2×#11758185—21no—
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519700—22no—
42#14519700—41no—
43C8×Dic61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61—21no—
46C2×D8×C61D411yescharacteristic
47C4⋊Q8×C61—21no—
48C4×D4×C61—21no—
49SD32×C61—42no—
50C2×C16×C61—21no—
51#107×C61D411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61—21no—
56C22×C4×C61—41no—
57C2×Dic122—22no—
58C2×Dic122D811yescharacteristic
59Q16×C61—42no—
60Q16×C61—41no—
61Q16×C61—41no—
62D8×C61—21no—
63D8×C61—21no—
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72C22⋊Dic61—42no—
73#11758200—82no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4⋊Dic61D811yescharacteristic
77#11758196—21no—
78#11758196—42no—
79C4×Dic61—21no—
80C4×Dic61—42no—
81C2×#92418—21no—
82C2×#92418—41no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86C16×C61—41no—
87#11758185—22no—
88C23×C61—41no—
89Q8×C61—81no—
90Q8×C61—81no—
91D4×C61—41no—
92D4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×C4×C61—81no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103Dic122—21no—
104Dic122—21no—
105Dic122—42no—
106Dic122—42no—
107C8×C61—21no—
108C8×C61#13511yescharacteristic
109C8×C61AGL(1,ℤ/8)11yescharacteristic
110#92418—41no—
111#92418—81no—
112#12335—611nomaximal, Sylow
113C22×C61—81no—
114C22×C61—81no—
115C22×C61—81no—
116C22×C61#44711yescharacteristic
117C4×C61—21no—
118C4×C61—81no—
119C4×C61—161no—
120C4×C61#44911yescharacteristic
121C4×C61#45311yescharacteristic
122C4×C61#50811yescharacteristic
123C4×C61#51011yescharacteristic
124Dic61—41no—
125Dic61—41no—
126Dic61—82no—
127#3393—611no—
128#2247—611no—
129#2208D6111yescharacteristic
130#1670—611no—
131#1362—611no—
132Q8⋊C16—611no—
133#1331—611no—
134C2×C61—161no—
135C2×C61#162111yescharacteristic
136C2×C61#218911yescharacteristic
137C2×C61#219511yescharacteristic
138#556—1221no—
139C2×Q32—1222no—
140C2×SD32—21no—
141#495—1221no—
142#494—611no—
143#494C2×D6111yescharacteristic
144#475—1221no—
145#464—1222no—
146#461—1221no—
147C8×Q8—611no—
148C4×Q16—1221no—
149C4×D8C2×D6111yescharacteristic
150C4⋊C16C2×D6111yescharacteristic
151#358—21no—
152C4×C16—611no—
153#335—611no—
154#332—1221no—
155C61#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—612no—
159C2×Q16—1221no—
160C2×SD16—1222no—
161C2×D8C22⋊D6111yescharacteristic
162C4⋊Q8—21no—
163C4⋊Q8—1221no—
164#126—2442no—
165#124—1222no—
166C22⋊Q8—2441no—
167C4×Q8—611no—
168C4×Q8—1222no—
169C4×D4—21no—
170#117—2441no—
171Q32—2444no—
172SD32—42no—
173C2×C16—21no—
174C2×C16—1221no—
175#107C22⋊D6111yescharacteristic
176#106—2441no—
177C4⋊C8—611no—
178C4⋊C8—1221no—
179C4⋊C8—1221no—
180#103—1222no—
181#103—2441no—
182#102—21no—
183C4×C8—1221no—
184C4×C8C22×D6111yescharacteristic
185C2×Q8—41no—
186C2×Q8—611no—
187C2×Q8—1222no—
188C2×D4—21no—
189C22×C4—41no—
190Q16—42no—
191Q16—41no—
192Q16—41no—
193Q16—2442no—
194Q16—2441no—
195Q16—2441no—
196SD16—4882no—
197D8—21no—
198D8—21no—
199C2×C8—1221no—
200C2×C8—2441no—
201C2×C8D4×D6111yescharacteristic
202C2×C8C2×C22⋊D6111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—41no—
212C22⋊C4—2442no—
213C22⋊C4—2442no—
214C42—1221no—
215C42—2442no—
216C42D4×D6111yescharacteristic
217C16—41no—
218C16—1222no—
219C23—41no—
220Q8—81no—
221Q8—81no—
222Q8—1221no—
223Q8—1221no—
224Q8—2442no—
225Q8—2442no—
226D4—41no—
227D4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2442no—
235C2×C4#1451974511yescharacteristic
236C2×C4D8×D6111yescharacteristic
237C2×C4#1451980111yescharacteristic
238C8—21no—
239C8—4881no—
240C8—2441no—
241C8#1451979711yescharacteristic
242C8#1451980311yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1683989411yescharacteristic
247C4—21no—
248C4—81no—
249C4—161no—
250C4—4882no—
251C4—2441no—
252C4—2441no—
253C4#1683990511yescharacteristic
254C4#1683992811yescharacteristic
255C4#1684019311yescharacteristic
256C4#1684020111yescharacteristic
257C2—161no—
258C2#2144488311yescharacteristic
259C2#2144775611yescharacteristic
260C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2208C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#2208D61
hypocenterC61#12335
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #21448071C2semidirect
3. #21445186C2semidirect
4. #21443869C2semidirect
5. #21443797C2semidirect
155. C61#12335semidirect

Maximal subgroups

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

subgroupindex
#214588052
#214480712
#214451862
#214438692
#214437972
#214437802
C61×#22082
#1233561