Finite Group Databasebeta

← #16858318

Subgroups — #16858318

Order 3968.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#14521749C212yesmaximal, complemented
2#14521451C211yesmaximal, characteristic, complemented
3#14521371C212yesmaximal, complemented
4#14521361C212yesmaximal, complemented
5#14521349C212yesmaximal, complemented
6#14521299C212yesmaximal, complemented
7#14521128C211yesmaximal, characteristic, complemented
8#14521090C212yesmaximal, complemented
9C4×D8×C31C211yesmaximal, characteristic, complemented
10C2×D8×C31C2211yescharacteristic
11C4×D4×C31C2212yes—
12#11758515C2212yes—
13#11758515C2212yes—
14#11758506—22no—
15C4×C22⋊D31—22no—
16C2×#92469C2212yes—
17#11758469C2212yes—
18C4⋊C4×D31C2212yes—
19#11758461—22no—
20#11758456—22no—
21C4×D124C2211yescharacteristic
22#11758447C2212yes—
23C31×#107C2211yescharacteristic
24C31×#102C2212yes—
25C4×C8×C31C2211yescharacteristic
26#11758420C2212yes—
27#11758420C2212yes—
28(C2×D31)⋊C8C2212yes—
29#11758406C2211yescharacteristic
30#11758406C2211yescharacteristic
31#11758405C2212yes—
32#11758396C2212yes—
33#11758395C2212yes—
34C4⋊(C31⋊C8)C2211yescharacteristic
35C2×D4×C31C2312yes—
36C22×C4×C31—22no—
37C2×C22⋊D31—22no—
38C2×C22⋊D31—22no—
39C2×D124D411yescharacteristic
40C2×C4×D31—22no—
41C2×C4×D31C2312yes—
42D8×C31—22no—
43C2×C8×C31C2311yescharacteristic
44C2×C8×C31C2311yescharacteristic
45C4⋊C4×C31C2312yes—
46C22⋊C4×C31—22no—
47C42×C31C2311yescharacteristic
48C22⋊Dic31—22no—
49C22⋊Dic31—22no—
50(C2×D31)⋊C4—22no—
51(C2×D31)⋊C4D412yes—
52C4⋊Dic31D411yescharacteristic
53C4⋊Dic31C2312yes—
54C4⋊Dic31C2312yes—
55Dic31⋊C4—22no—
56Dic31⋊C4—22no—
57Dic31⋊C4—22no—
58C4×Dic31—22no—
59C2×C31⋊C8C2312yes—
60#92469—24no—
61C23×C31—22no—
62C22×D31C2×D412yes—
63D4×C31—22no—
64D4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—82no—
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2411yescharacteristic
70C22⋊D31—44no—
71C22⋊D31—82no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31C2×D412yes—
75D124—41no—
76C4×D31—22no—
77C4×D31—22no—
78C4×D31—82no—
79C8×C31—21no—
80C8×C31#4112yes—
81C31⋊C8—22no—
82#3355—311nomaximal, Sylow
83C22×C31—42no—
84C22×C31—42no—
85C22×C31—42no—
86C22×C31C22×D411yescharacteristic
87C2×D31—22no—
88C2×D31—22no—
89C2×D31—22no—
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—42no—
93C4×C31C2×#4111yescharacteristic
94C4×C312−1+411yescharacteristic
95Dic31—22no—
96Dic31—42no—
97Dic31—42no—
98#553—312no—
99#499—311no—
100#482—312no—
101#480—312no—
102#478—312no—
103#469—312no—
104C4×D8D3111yescharacteristic, complemented
105#436—311no—
106#428—312no—
107C2×C31—82no—
108C2×C31#54711yescharacteristic
109C2×C31#57511yescharacteristic
110C2×C31#57611yescharacteristic
111D31—42no—
112C2×D8C2×D3111yescharacteristic
113C2×M16—312no—
114#126—622no—
115#125—312no—
116#123—622no—
117#121—312no—
118#121—312no—
119#121—622no—
120C4×D4—311no—
121C4×D4—622no—
122C4×D4C2×D3112yes—
123#117—312no—
124C2×C4⋊C4—312no—
125#107—311no—
126#107—311no—
127#107—312no—
128#107C2×D3111yescharacteristic
129#106—312no—
130#106—312no—
131C4⋊C8—311no—
132#102—312no—
133#102—312no—
134#102C2×D3112yes—
135C22⋊C8—312no—
136C4×C8C2×D3111yescharacteristic
137C31#335511yescharacteristic, complemented, Sylow
138C2×D4—311no—
139C2×D4—622no—
140C2×D4—622no—
141C2×D4C22×D3112yes—
142C22×C4—22no—
143C22×C4—312no—
144C22×C4—622no—
145D8—22no—
146M16—624no—
147C2×C8—312no—
148C2×C8C22×D3111yescharacteristic
149C2×C8C22×D3111yescharacteristic
150C4⋊C4—311no—
151C4⋊C4—312no—
152C4⋊C4—312no—
153C4⋊C4—622no—
154C4⋊C4—622no—
155C4⋊C4—622no—
156C4⋊C4C22×D3112yes—
157C22⋊C4—22no—
158C22⋊C4—312no—
159C22⋊C4—622no—
160C22⋊C4—622no—
161C22⋊C4—622no—
162C42—622no—
163C42C22×D3111yescharacteristic
164C23—22no—
165C23—312no—
166D4—22no—
167D4—22no—
168D4—1241no—
169D4—1244no—
170D4—2482no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—312no—
174C2×C4—622no—
175C2×C4—622no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4—2482no—
179C2×C4D4×D3111yescharacteristic
180C2×C4D4×D3111yescharacteristic
181C2×C4C23×D3111yescharacteristic
182C8—21no—
183C8—622no—
184C8#9249512yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—622no—
189C22—622no—
190C22—622no—
191C22C2×D4×D3111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—622no—
196C4—1242no—
197C4—1242no—
198C4C2×#9249511yescharacteristic
199C4#1175856711yescharacteristic
200C2—82no—
201C2—1242no—
202C2#1452170411yescharacteristic
203C2#1452184611yescharacteristic
204C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
hypercenterC4×D8D31
hypocenterC31#3355
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14521749C2semidirect
2. #14521451C2semidirect
3. #14521371C2semidirect
4. #14521361C2semidirect
5. #14521349C2semidirect
6. #14521299C2semidirect
7. #14521128C2semidirect
8. #14521090C2semidirect
9. C4×D8×C31C2semidirect
104. C4×D8D31semidirect
137. C31#3355semidirect

Maximal subgroups

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

subgroupindex
#145217492
#145214512
#145213712
#145213612
#145213492
#145212992
#145211282
#145210902
C4×D8×C312
#335531