Finite Group Databasebeta

← #27173081

Subgroups — #27173081

Order 12928.

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#20265974C211yesmaximal, characteristic
2#20265618C211yesmaximal, characteristic, complemented
3#20265432C211yesmaximal, characteristic, complemented
4#20264988C211yesmaximal, characteristic, complemented
5#20264987C211yesmaximal, characteristic, complemented
6#20264958C211yesmaximal, characteristic, complemented
7#510×C101C211yesmaximal, characteristic, complemented
8#41×D101—21no—
9#15692287—21no—
10#15692284—21no—
11#15692282—21no—
12#15692279—21no—
13#15692277C2211yescharacteristic
14#15692275—21no—
15C2×#13108057C2211yescharacteristic
16#15692231—21no—
17#15692201—21no—
18#15692198—21no—
19#15692195C2211yescharacteristic, complemented
20#15692187C2211yescharacteristic, complemented
21#15692179—21no—
22#135×C101C2211yescharacteristic
23C2×Q16×C101C2211yescharacteristic, complemented
24Q32×C101—21no—
25SD32×C101—21no—
26M32×C101C2211yescharacteristic, complemented
27#13108075—21no—
28#13108074—21no—
29#13108074—41no—
30#13108073—21no—
31#13108073—41no—
32Q8×D101—21no—
33D4×D101—21no—
34D4×D101—41no—
35C2×C4×D101—41no—
36C2×C4×D101D411yescharacteristic
37Dic404D411yescharacteristic
38#13108064—21no—
39#13108063—21no—
40#13108062—21no—
41#13108061—21no—
42D808D411yescharacteristic
43#13108059—21no—
44#13108057—21no—
45#13108057—21no—
46C2×#11717579D411yescharacteristic
47C4⋊Dic101—21no—
48#13108053—41no—
49#13108051—41no—
50#13108049—21no—
51#41×C101—21no—
52C2×Q8×C101—21no—
53Q16×C101—21no—
54Q16×C101—21no—
55Q16×C101D411yescharacteristic
56SD16×C101—21no—
57D8×C101D411yescharacteristic
58C2×C8×C101C2311yescharacteristic
59C16×C101—21no—
60C22×D101—41no—
61C22×D101D811yescharacteristic
62Q8×C101—21no—
63Q8×C101—41no—
64Q8×C101—41no—
65D4×C101—21no—
66D4×C101—41no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101C2×D411yescharacteristic
70C22⋊D101—41no—
71C22⋊D101—41no—
72C22⋊D101—41no—
73C2×Dic101—41no—
74C2×Dic101—41no—
75C2×Dic101D811yescharacteristic
76D404—21no—
77D404—41no—
78C4×D101—21no—
79C4×D101—21no—
80C4×D101—41no—
81C4×D101—41no—
82C4×D101—41no—
83Dic202—21no—
84Dic202—41no—
85C8×C101C2×D411yescharacteristic
86C8×C101C2×D411yescharacteristic
87#11717579—21no—
88C22×C101—41no—
89C22×C101C2×D811yescharacteristic
90C2×D101—21no—
91C2×D101—41no—
92C2×D101—41no—
93C2×D101—82no—
94C4×C101—41no—
95C4×C101—81no—
96C4×C101#12011yescharacteristic
97C4×C101AGL(1,ℤ/8)11yescharacteristic
98Dic101—21no—
99Dic101—41no—
100Dic101—81no—
101C2×C101—21no—
102C2×C101—81no—
103C2×C101#44711yescharacteristic
104D101—41no—
105D101—81no—
106#2191—1011nomaximal, Sylow
107C101#219111yescharacteristic, complemented, Sylow
108#575—1011no—
109#510—1011no—
110#510D10111yescharacteristic, complemented
111#470—1011no—
112#360—1011no—
113#360—1011no—
114#349—1011no—
115C2×#41—2021no—
116#137—2021no—
117#137—2021no—
118AGL(1,ℤ/8)—2021no—
119AGL(1,ℤ/8)—2021no—
120#135—1011no—
121#135—2021no—
122#135C2×D10111yescharacteristic
123C2×Q16C2×D10111yescharacteristic, complemented
124C2×M16—1011no—
125C22⋊Q8—2021no—
126Q32—21no—
127Q32—2021no—
128SD32—21no—
129SD32—2021no—
130M32—1011no—
131M32C2×D10111yescharacteristic, complemented
132#106—1011no—
133#103—2021no—
134#41—21no—
135#41—4041no—
136#41—4041no—
137#41—2021no—
138#41—2021no—
139#41—2021no—
140C2×Q8—21no—
141C2×Q8—2021no—
142C2×D4—4041no—
143C2×D4—2021no—
144C22×C4—1011no—
145C22×C4—4041no—
146Q16—21no—
147Q16—21no—
148Q16—1011no—
149Q16—2021no—
150Q16C22⋊D10111yescharacteristic
151SD16—21no—
152SD16—2021no—
153SD16—2021no—
154SD16—2021no—
155D8—1011no—
156D8—2021no—
157D8C22⋊D10111yescharacteristic
158M16—2021no—
159M16—2021no—
160C2×C8—1011no—
161C2×C8C22×D10111yescharacteristic
162C4⋊C4—4041no—
163C4⋊C4—2021no—
164C22⋊C4—4041no—
165C16—21no—
166C16—2021no—
167C23—1011no—
168C23—4041no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—4041no—
173Q8—2021no—
174D4—21no—
175D4—41no—
176D4—4041no—
177D4—4041no—
178D4—4041no—
179D4—4041no—
180D4—2021no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—1011no—
184C2×C4—4041no—
185C2×C4—4041no—
186C2×C4—4041no—
187C2×C4—4041no—
188C2×C4—4041no—
189C2×C4—2021no—
190C2×C4—2021no—
191C2×C4D4×D10111yescharacteristic
192C8—2021no—
193C8D4×D10111yescharacteristic
194C8C2×C22⋊D10111yescharacteristic
195C22—41no—
196C22—8082no—
197C22—4041no—
198C22—4041no—
199C22—2021no—
200C22D8×D10111yescharacteristic
201C4—41no—
202C4—81no—
203C4—8081no—
204C4—4041no—
205C4—2021no—
206C4#1569222311yescharacteristic
207C4#1569227911yescharacteristic
208C2—21no—
209C2—81no—
210C2—8081no—
211C2—4041no—
212C2#2026530911yescharacteristic
subgroupG/H
centerC2#20265309
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
Fitting#510×C101C2
socleC2×C101#447
prime radical#20265974C2
hypercenter#510D101
hypocenterC101#2191
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #20265618C2semidirect
3. #20265432C2semidirect
4. #20264988C2semidirect
5. #20264987C2semidirect
6. #20264958C2semidirect
7. #510×C101C2semidirect
19. #15692195C22semidirect
20. #15692187C22semidirect
23. C2×Q16×C101C22semidirect
26. M32×C101C22semidirect
107. C101#2191semidirect
110. #510D101semidirect
123. C2×Q16C2×D101semidirect
131. M32C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202659742
#202656182
#202654322
#202649882
#202649872
#202649582
#510×C1012
#2191101