Finite Group Databasebeta

← #29584084

Subgroups — #29584084

Order 15616.

408 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 77 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#21457129C211yesmaximal, characteristic
2#21445972C211yesmaximal, characteristic, complemented
3#21444515C212yesmaximal, complemented
4#21444328C212yesmaximal, complemented
5C61×#1290C211yesmaximal, characteristic, complemented
6#16840312C2212yes—
7#16840043—22no—
8#16839998—22no—
9#16839958—22no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—22no—
12#16839608C2211yescharacteristic
13#16839510—22no—
14#16839505—22no—
15#16839497—24no—
16C61×#432C2212yes—
17C2×C4⋊C8×C61C2211yescharacteristic
18C2×#11758222—22no—
19C2×D488—22no—
20C22×#92418—21no—
21#14519777D412yes—
22#14519774D412yes—
23#14519765—22no—
24#14519751—22no—
25#14519751—22no—
26C4×D244—22no—
27C4×D244—22no—
28C2×C4×Dic61—21no—
29#14519711—22no—
30C4⋊#92418—22no—
31#14519706—44no—
32#14519699—24no—
33#14519684—21no—
34#14519684D412yes—
35C22×C8×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—22no—
38C4⋊C8×C61—22no—
39C22⋊C8×C61—22no—
40#97×C61—22no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61#4111yescharacteristic
44C2×C22⋊D61—42no—
45C22×Dic61—22no—
46#11758222—84no—
47C2×D244—22no—
48C2×D244—22no—
49C2×D244—22no—
50C2×C4×D61—42no—
51C2×Dic122—22no—
52C2×C8×C61—22no—
53C2×C8×C61—42no—
54C2×C8×C61—42no—
55C42×C61C2×D412yes—
56C42×C61#4112yes—
57#11758198—42no—
58#11758198—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4×Dic61—22no—
62C4×Dic61—22no—
63C2×#92418—42no—
64C2×#92418—41no—
65D488—82no—
66C23×C61#12111yescharacteristic
67C22×D61—42no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61#12011yescharacteristic
73C2×C4×C61#12112yes—
74C2×C4×C61#12312yes—
75C2×C4×C61#12411yescharacteristic
76C22⋊D61—84no—
77C2×Dic61—24no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81D244—42no—
82D244—42no—
83D244—82no—
84D244—82no—
85C4×D61—84no—
86Dic122—82no—
87C8×C61—42no—
88C8×C61—82no—
89#92418—81no—
90#10512—611nomaximal, Sylow
91C22×C61—21no—
92C22×C61—21no—
93C22×C61#39411yescharacteristic
94C22×C61#47212yes—
95C2×D61—82no—
96C2×D61—82no—
97C2×D61—82no—
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—22no—
101C4×C61#45311yescharacteristic
102C4×C61#45611yescharacteristic
103Dic61—44no—
104Dic61—82no—
105#3245—611no—
106#1843—611no—
107#1551—612no—
108#1505—612no—
109#1290D6111yescharacteristic, complemented
110C2×C61—22no—
111C2×C61#203911yescharacteristic
112C2×C61#204511yescharacteristic
113C2×C61#205311yescharacteristic
114D61—162no—
115#532—612no—
116#474—1222no—
117#466—1222no—
118#459—1222no—
119#432C2×D6112yes—
120C2×C4⋊C8—611no—
121C2×C4⋊C8—1222no—
122C2×C4⋊C8C2×D6111yescharacteristic
123#376—611no—
124#333—1222no—
125#331—1222no—
126#327—1224no—
127C61#1051211yescharacteristic, complemented, Sylow
128C2×#41—1222no—
129C2×D8—1222no—
130C22×C8—1221no—
131C22×C8D24412yes—
132C4⋊Q8—612no—
133#127—612no—
134#124—1222no—
135#121—1222no—
136#121—1222no—
137C4×D4—1222no—
138C4×D4—1222no—
139C2×C42—1221no—
140C2×C42C22×D6111yescharacteristic
141#107—1222no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—1222no—
145C4⋊C8—2444no—
146#102—1224no—
147C22⋊C8—22no—
148#97—22no—
149#95—612no—
150#95—1221no—
151#41—4884no—
152C2×Q8—1222no—
153C2×D4—1222no—
154C2×D4—1222no—
155C2×D4—1222no—
156C2×D4—2442no—
157C22×C4—1222no—
158C22×C4—2442no—
159C22×C4C2×D24411yescharacteristic
160C22×C4D4×D6111yescharacteristic
161C22×C4#1175822611yescharacteristic
162D8—4882no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—2442no—
167C2×C8—2441no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C22⋊C4—2442no—
171C22⋊C4—2442no—
172C42—1222no—
173C42—1222no—
174C42#1175822212yes—
175C42D4×D6112yes—
176C23—2442no—
177C23#1451975211yescharacteristic
178Q8—4882no—
179D4—4882no—
180D4—4882no—
181D4—4884no—
182D4—2442no—
183D4—2442no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—1224no—
189C2×C4—4884no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4#1451974711yescharacteristic
194C2×C4#1451975012yes—
195C2×C4#1451976212yes—
196C2×C4#1451976511yescharacteristic
197C8—42no—
198C8—82no—
199C8—4881no—
200C22—21no—
201C22—21no—
202C22—4882no—
203C22—4882no—
204C22—4882no—
205C22#1683968011yescharacteristic
206C22#1684003312yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—4882no—
211C4—2444no—
212C4#1683993211yescharacteristic
213C4#1683994711yescharacteristic
214C2—22no—
215C2—9762no—
216C2#2144704411yescharacteristic
217C2#2144707611yescharacteristic
218C2#2144712611yescharacteristic
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#394
prime radical#21457129C2
hypercenter#1290D61
hypocenterC61#10512
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #21445972C2semidirect
3. #21444515C2semidirect
4. #21444328C2semidirect
5. C61×#1290C2semidirect
109. #1290D61semidirect
127. C61#10512semidirect

Maximal subgroups

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

subgroupindex
#214571292
#214459722
#214445152
#214443282
C61×#12902
#1051261