Finite Group Databasebeta

← #29594165

Subgroups — #29594165

Order 15616.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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#21447972C211yesmaximal, characteristic
2#21447870C211yesmaximal, characteristic
3#21445416C211yesmaximal, characteristic
4C8×Dic244C211yesmaximal, characteristic
5#21443876C211yesmaximal, characteristic
6#21443869C211yesmaximal, characteristic
7C61×#1367C211yesmaximal, characteristic
8C2×Dic488—21no—
9#16840167C2211yescharacteristic
10#16840160—21no—
11#16840142C2211yescharacteristic
12#16840113—21no—
13C8×Dic122—21no—
14C4×Dic244C2211yescharacteristic
15#16839588—21no—
16#16839567—21no—
17#16839567—21no—
18#16839515C2211yescharacteristic
19#16839494—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C82×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×Dic244D411yescharacteristic
26#14519777—21no—
27#14519777—21no—
28C4×Dic122—21no—
29Dic488—42no—
30#14519711—21no—
31#14519711—21no—
32#14519711D411yescharacteristic
33#14519709—41no—
34#14519709—41no—
35C4⋊#92418—21no—
36#14519706—41no—
37#14519702—21no—
38#14519702—42no—
39C8×Dic61—41no—
40C2×C16×C61—21no—
41C2×C16×C61—21no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×Dic122—21no—
46C2×Dic122—41no—
47C2×Dic122—41no—
48C2×C8×C61—21no—
49C2×C8×C61D811yescharacteristic
50C2×C8×C61D811yescharacteristic
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C42×C61C2×D411yescharacteristic
54C4⋊Dic61—21no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59#11758196—41no—
60C4×Dic61—41no—
61C2×#92418—41no—
62Dic244—21no—
63Dic244—41no—
64Dic244—41no—
65Dic244—81no—
66Dic244SD1612yes—
67C16×C61—41no—
68C16×C61—41no—
69C2×C4×C61#12111yescharacteristic
70C2×C4×C61C2×D811yescharacteristic
71C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—81no—
75C2×Dic61—81no—
76Dic122—22no—
77Dic122—41no—
78Dic122—82no—
79Dic122—81no—
80Dic122—81no—
81C8×C61—21no—
82C8×C61—21no—
83C8×C61—41no—
84C8×C61Q3212yescomplemented
85C8×C61C2×SD1611yescharacteristic
86C8×C61#13511yescharacteristic
87#92418—81no—
88#12421—611nomaximal, Sylow
89C22×C61#45911yescharacteristic
90C4×C61—21no—
91C4×C61#46511yescharacteristic
92C4×C61#47111yescharacteristic
93C4×C61C2×Q3211yescharacteristic
94C4×C61#51011yescharacteristic
95Dic61—42no—
96Dic61—81no—
97Dic61—161no—
98Dic61—161no—
99#2227—611no—
100#2209—611no—
101#1707—611no—
102C8×Q16—611no—
103#1367D6111yescharacteristic
104#1365—611no—
105#1362—611no—
106C2×C61#166511yescharacteristic
107C2×C61#220911yescharacteristic
108C2×C61#221211yescharacteristic
109C2×Q32—1221no—
110#500—611no—
111#498—1221no—
112#494—611no—
113#487—1221no—
114C8×Q8—1221no—
115C4×Q16—611no—
116#366—1221no—
117C4⋊C16C2×D6111yescharacteristic
118C4⋊C16C2×D6111yescharacteristic
119#358—1221no—
120#358—1221no—
121#335—611no—
122Q8⋊C8—1221no—
123C82C2×D6111yescharacteristic
124C61#1242111yescharacteristic, complemented, Sylow
125C2×Q16—611no—
126C2×Q16—1221no—
127C2×Q16—1221no—
128C4⋊Q8—1221no—
129C4⋊Q8—1221no—
130C4×Q8—1221no—
131Q32—2442no—
132C2×C16—21no—
133C2×C16—21no—
134#107—611no—
135#107—1221no—
136#107—1221no—
137#106—2441no—
138#106—2441no—
139C4⋊C8—1221no—
140C4⋊C8—2441no—
141#103—1221no—
142#103—2442no—
143C4×C8—2441no—
144C4×C8D24411yescharacteristic
145C4×C8D24411yescharacteristic
146C4×C8C22×D6111yescharacteristic
147C2×Q8—1221no—
148C2×Q8—2441no—
149C2×Q8—2441no—
150Q16—612no—
151Q16—1221no—
152Q16—4881no—
153Q16—2441no—
154Q16—2441no—
155C2×C8—21no—
156C2×C8—2441no—
157C2×C8D48811yescharacteristic
158C2×C8D48811yescharacteristic
159C2×C8D4×D6111yescharacteristic
160C2×C8#1175822611yescharacteristic
161C4⋊C4—1221no—
162C4⋊C4—2441no—
163C4⋊C4—2441no—
164C4⋊C4—2441no—
165C4⋊C4—2441no—
166C4⋊C4—2441no—
167C42—2441no—
168C42C2×D24411yescharacteristic
169C16—41no—
170C16—41no—
171Q8—1222no—
172Q8—4882no—
173Q8—4881no—
174Q8—4881no—
175Q8—2441no—
176C2×C4—4881no—
177C2×C4—4881no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4#1451975211yescharacteristic
181C2×C4C2×D48811yescharacteristic
182C2×C4#1451980511yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—4881no—
187C8Dic48812yescomplemented
188C8SD16×D6111yescharacteristic
189C8#1451979811yescharacteristic
190C22#1683995811yescharacteristic
191C4—21no—
192C4—9761no—
193C4—9761no—
194C4—4881no—
195C4—2442no—
196C4#1683999211yescharacteristic
197C4#1684002611yescharacteristic
198C4C2×Dic48811yescharacteristic
199C4#1684020511yescharacteristic
200C2#2144516111yescharacteristic
201C2#2144787011yescharacteristic
202C2#2144788911yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1367C2
socle, prime radicalC22×C61#459
hypercenter#1367D61
hypocenterC61#12421
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
84. C8×C61Q32semidirect
124. C61#12421semidirect
187. C8Dic488semidirect

Maximal subgroups

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

subgroupindex
#214479722
#214478702
#214454162
C8×Dic2442
#214438762
#214438692
C61×#13672
#1242161