Finite Group Databasebeta

← #29594181

Subgroups — #29594181

Order 15616.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447958C211yesmaximal, characteristic
2#21447870C211yesmaximal, characteristic
3#21445417C211yesmaximal, characteristic
4#21444625C211yesmaximal, characteristic
5#21443882C211yesmaximal, characteristic
6#21443867C211yesmaximal, characteristic
7C61×#1364C211yesmaximal, characteristic
8C2×Dic488—21no—
9#16840158—21no—
10#16840142C2211yescharacteristic
11#16840112—21no—
12#16839886—21no—
13C4×Dic244C2211yescharacteristic
14#16839589—21no—
15C4⋊#11758185C2211yescharacteristic
16#16839567—21no—
17#16839565—21no—
18#16839492—21no—
19C8×#92418C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×Dic244D411yescharacteristic
26#14519777—21no—
27C4×Dic122—21no—
28Dic488—42no—
29C2×#11758185—21no—
30#14519711D411yescharacteristic
31#14519708—42no—
32#14519706—41no—
33#14519702—21no—
34#14519701—41no—
35#14519701—41no—
36C4×#92418D411yescharacteristic
37C4×#92418D411yescharacteristic
38C8×Dic61—41no—
39C4⋊Q8×C61—21no—
40C2×C16×C61—21no—
41#107×C61—21no—
42#107×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×Dic122—21no—
47C2×Dic122—41no—
48C2×C8×C61—41no—
49C2×C8×C61C2×D411yescharacteristic
50C2×C8×C61#4111yescharacteristic
51C4⋊C4×C61—41no—
52C4⋊C4×C61—41no—
53C42×C61C2×D411yescharacteristic
54C4⋊Dic61—21no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57#11758196—41no—
58C4×Dic61—41no—
59C2×#92418—21no—
60C2×#92418D811yescharacteristic
61C2×#92418D811yescharacteristic
62Dic244—21no—
63Dic244—41no—
64Dic244—41no—
65Dic244—81no—
66Dic244SD1612yes—
67C16×C61—41no—
68#11758185—41no—
69Q8×C61—81no—
70Q8×C61—81no—
71C2×C4×C61—81no—
72C2×C4×C61#12111yescharacteristic
73C2×C4×C61C2×D811yescharacteristic
74C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78Dic122—22no—
79Dic122—41no—
80Dic122—81no—
81Dic122—81no—
82C8×C61—21no—
83C8×C61—81no—
84C8×C61C2×SD1611yescharacteristic
85C8×C61#13511yescharacteristic
86#92418—22no—
87#92418—21no—
88#92418—21no—
89#12423—611nomaximal, Sylow
90C22×C61#45911yescharacteristic
91C4×C61—21no—
92C4×C61—161no—
93C4×C61#46511yescharacteristic
94C4×C61#47111yescharacteristic
95C4×C61#50811yescharacteristic
96C4×C61#51011yescharacteristic
97Dic61—42no—
98Dic61—81no—
99Dic61—161no—
100#2225—611no—
101#2209—611no—
102#1707—611no—
103C8×Q16—611no—
104#1367—611no—
105#1364D6111yescharacteristic
106#1362—611no—
107C2×C61#166511yescharacteristic
108C2×C61#221111yescharacteristic
109C2×C61#221411yescharacteristic
110C2×Q32—1221no—
111#500C2×D6111yescharacteristic
112#498—1221no—
113#494—611no—
114#487—1221no—
115C8×Q8—1221no—
116C4×Q16—611no—
117#367—1221no—
118C4⋊C16—611no—
119C4⋊C16C2×D6111yescharacteristic
120#358—1221no—
121#358—1221no—
122#335C2×D6111yescharacteristic
123Q8⋊C8—1221no—
124C82—611no—
125C61#1242311yescharacteristic, complemented, Sylow
126C2×Q16—611no—
127C2×Q16—1221no—
128C2×Q16—1221no—
129C4⋊Q8—21no—
130C4⋊Q8—1221no—
131C4×Q8—1221no—
132Q32—2442no—
133C2×C16—21no—
134C2×C16—1221no—
135#107—21no—
136#107—21no—
137#107—611no—
138#106—2442no—
139C4⋊C8—21no—
140C4⋊C8—2441no—
141#103—1221no—
142#103—2441no—
143#103—2441no—
144C4×C8—611no—
145C4×C8—611no—
146C4×C8—2441no—
147C4×C8C22×D6111yescharacteristic
148C2×Q8—41no—
149C2×Q8—1221no—
150C2×Q8—2441no—
151Q16—612no—
152Q16—1221no—
153Q16—4881no—
154Q16—2441no—
155Q16—2441no—
156C2×C8—41no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—1221no—
160C2×C8#1175822211yescharacteristic
161C2×C8D4×D6111yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—1221no—
165C4⋊C4—2441no—
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C42—2441no—
169C42D4×D6111yescharacteristic
170C16—41no—
171C16—2441no—
172Q8—81no—
173Q8—81no—
174Q8—1222no—
175Q8—4881no—
176Q8—4881no—
177Q8—2441no—
178C2×C4—81no—
179C2×C4—4881no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4#1451975011yescharacteristic
183C2×C4D8×D6111yescharacteristic
184C2×C4#1451980411yescharacteristic
185C8—21no—
186C8—81no—
187C8—1222no—
188C8—1221no—
189C8—1221no—
190C8SD16×D6111yescharacteristic
191C8#1451980011yescharacteristic
192C22#1683995611yescharacteristic
193C4—21no—
194C4—161no—
195C4—9761no—
196C4—4881no—
197C4—2442no—
198C4#1683999411yescharacteristic
199C4#1684002811yescharacteristic
200C4#1684019111yescharacteristic
201C4#1684020111yescharacteristic
202C2#2144516311yescharacteristic
203C2#2144788011yescharacteristic
204C2#2144789911yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socle, prime radicalC22×C61#459
hypercenter#1364D61
hypocenterC61#12423
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
125. C61#12423semidirect

Maximal subgroups

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

subgroupindex
#214479582
#214478702
#214454172
#214446252
#214438822
#214438672
C61×#13642
#1242361