Finite Group Databasebeta

← #27197112

Subgroups — #27197112

Order 13184.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#20268593C211yesmaximal, characteristic
2C2×#15692964C211yesmaximal, characteristic, complemented
3#20268063C211yesmaximal, characteristic, complemented
4#20267605C211yesmaximal, characteristic, complemented
5#20267598C211yesmaximal, characteristic, complemented
6#20267576C211yesmaximal, characteristic, complemented
7#510×C103C211yesmaximal, characteristic, complemented
8#15693067—21no—
9#15693052—21no—
10#15693048—22no—
11#15693046—21no—
12#15693044—21no—
13C2×D824C2211yescharacteristic
14D8×D103—21no—
15#15693027C2211yescharacteristic
16#15692964—22no—
17C2×C103⋊C16C2211yescharacteristic, complemented
18#15692957C2211yescharacteristic, complemented
19#15692940—21no—
20#135×C103C2211yescharacteristic
21C2×Q16×C103C2211yescharacteristic, complemented
22Q32×C103—21no—
23SD32×C103—21no—
24M32×C103C2211yescharacteristic, complemented
25#13110106—22no—
26#13110105—41no—
27#13110105D411yescharacteristic
28C2×D412—21no—
29C2×D412—41no—
30D4×D103—22no—
31D4×D103—42no—
32#13110095—41no—
33#13110092—22no—
34#13110092—41no—
35D824—21no—
36D824D412yes—
37#13110090—22no—
38#13110089—21no—
39#13110089D411yescharacteristic
40#13110088—21no—
41C8×D103—21no—
42C103⋊C16—21no—
43#41×C103—21no—
44C2×Q8×C103—21no—
45Q16×C103—21no—
46Q16×C103—21no—
47Q16×C103D411yescharacteristic
48SD16×C103—21no—
49D8×C103D411yescharacteristic
50C2×C8×C103C2311yescharacteristic
51C16×C103—21no—
52C22×D103—42no—
53C22×D103—41no—
54Q8×C103—21no—
55Q8×C103—41no—
56Q8×C103—41no—
57D4×C103—21no—
58D4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103—41no—
61C2×C4×C103C2×D411yescharacteristic
62C22⋊D103—21no—
63C22⋊D103—42no—
64D412—22no—
65D412—42no—
66D412—41no—
67D412D811yescharacteristic
68C4×D103—21no—
69C4×D103—42no—
70Dic206D811yescharacteristic
71C8×C103C2×D411yescharacteristic
72C8×C103C2×D411yescharacteristic
73C103⋊C8—21no—
74C103⋊C8—41no—
75C22×C103—41no—
76C22×C103AGL(1,ℤ/8)11yescharacteristic
77C2×D103—21no—
78C2×D103—42no—
79C2×D103—162no—
80C2×D103—161no—
81C4×C103—41no—
82C4×C103—81no—
83C4×C103#12011yescharacteristic
84C4×C103C2×D811yescharacteristic
85Dic103—21no—
86C2×C103—21no—
87C2×C103—81no—
88C2×C103#44711yescharacteristic
89D103—41no—
90D103—82no—
91#2194—1031nomaximal, Sylow
92C103#219411yescharacteristic, complemented, Sylow
93#576—1031no—
94#510D10311yescharacteristic, complemented
95C2×SD32—1031no—
96#473—1031no—
97#361—1031no—
98#359—1031no—
99#350—1031no—
100H(5,𝔽2)—2061no—
101#137—2061no—
102AGL(1,ℤ/8)—2061no—
103AGL(1,ℤ/8)—2062no—
104#135—2061no—
105#135C2×D10311yescharacteristic
106C2×Q16C2×D10311yescharacteristic, complemented
107C2×D8—1031no—
108C2×D8—2061no—
109#131—1031no—
110Q32—21no—
111SD32—21no—
112SD32—2062no—
113M32C2×D10311yescharacteristic, complemented
114C2×C16—1031no—
115#108—1031no—
116#101—2061no—
117#41—21no—
118#41—1031no—
119#41—4121no—
120#41—2062no—
121C2×Q8—21no—
122C2×D4—4121no—
123C2×D4—4122no—
124C2×D4—2062no—
125C2×D4—2061no—
126Q16—21no—
127Q16—21no—
128Q16—4121no—
129Q16C22⋊D10311yescharacteristic
130SD16—21no—
131SD16—4121no—
132SD16—2062no—
133D8—1032no—
134D8—2062no—
135D8—2061no—
136D8C22⋊D10311yescharacteristic
137M16—1031no—
138M16—2061no—
139M16—2061no—
140C2×C8—2061no—
141C2×C8C22×D10311yescharacteristic
142C16—21no—
143C16—2061no—
144C23—4122no—
145C23—4121no—
146Q8—21no—
147Q8—41no—
148Q8—41no—
149Q8—1031no—
150D4—21no—
151D4—41no—
152D4—1031no—
153D4—4122no—
154D4—4122no—
155D4—4121no—
156D4—2061no—
157D4—2062no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—4122no—
161C2×C4—2061no—
162C2×C4D4×D10311yescharacteristic
163C8—4121no—
164C8—2061no—
165C8D4×D10311yescharacteristic
166C8C2×C22⋊D10311yescharacteristic
167C22—41no—
168C22—16481no—
169C22—16482no—
170C22—4122no—
171C22—2061no—
172C22#1569304511yescharacteristic
173C4—41no—
174C4—81no—
175C4—2061no—
176C4#1569298911yescharacteristic
177C4D8×D10311yescharacteristic
178C2—21no—
179C2—81no—
180C2—8242no—
181C2—4121no—
182C2#2026792311yescharacteristic
subgroupG/H
centerC2#20267923
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#510×C103C2
socleC2×C103#447
prime radical#20268593C2
hypercenter#510D103
hypocenterC103#2194
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#15692964C2semidirect
3. #20268063C2semidirect
4. #20267605C2semidirect
5. #20267598C2semidirect
6. #20267576C2semidirect
7. #510×C103C2semidirect
17. C2×C103⋊C16C22semidirect
18. #15692957C22semidirect
21. C2×Q16×C103C22semidirect
24. M32×C103C22semidirect
92. C103#2194semidirect
94. #510D103semidirect
106. C2×Q16C2×D103semidirect
113. M32C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685932
C2×#156929642
#202680632
#202676052
#202675982
#202675762
#510×C1032
#2194103