Finite Group Databasebeta

← #27172199

Subgroups — #27172199

Order 12928.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#20265977C211yesmaximal, characteristic, complemented
2#20265688C212yesmaximal, complemented
3#20265193C212yesmaximal, complemented
4#20264934C211yesmaximal, characteristic, complemented
5#407×C101C211yesmaximal, characteristic, complemented
6C2×#13108074C2212yes—
7#15692288—22no—
8#15692283—22no—
9#15692277—22no—
10#15692238—22no—
11#15692234—22no—
12#15692229—22no—
13#15692224—22no—
14C4×C22⋊D101—24no—
15#15692214C2212yes—
16#15692181—24no—
17C23×C4×C101C2211yescharacteristic
18C2×M16×C101C2211yescharacteristic
19C2×M16×C101C2211yescharacteristic
20C22⋊C8×C101—22no—
21#13108074—22no—
22#13108074—22no—
23#13108074—22no—
24#13108074—22no—
25C2×Dic202D412yescomplemented
26C2×D404D412yescomplemented
27C2×C22⋊D101—24no—
28C2×C22⋊D101—22no—
29C2×C4×D101—22no—
30Dic404—22no—
31#13108063—24no—
32D808—22no—
33C4⋊Dic101—22no—
34#13108053—24no—
35C22⋊Dic101—24no—
36C22⋊Dic101—22no—
37#13108051—24no—
38C4×Dic101D414yescomplemented
39C24×C101D411yescharacteristic
40C22×C4×C101—21no—
41C22×C4×C101—22no—
42C22×C4×C101—22no—
43C22×C4×C101—21no—
44C22×C4×C101D411yescharacteristic
45C22×C4×C101C2311yescharacteristic
46M16×C101—22no—
47M16×C101—22no—
48C2×C8×C101—21no—
49C2×C8×C101D412yescomplemented
50C23×C101—22no—
51C23×C101—21no—
52C23×C101—42no—
53C23×C101C2×D411yescharacteristic
54C22×D101—22no—
55C2×C4×C101—22no—
56C2×C4×C101—21no—
57C2×C4×C101—41no—
58C2×C4×C101—42no—
59C2×C4×C101—41no—
60C2×C4×C101C2×D412yes—
61C2×C4×C101C2×D412yes—
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101#4111yescharacteristic
64C22⋊D101—48no—
65C22⋊D101—42no—
66C22⋊D101—42no—
67C2×Dic101—24no—
68C2×Dic101—22no—
69D404—22no—
70D404—22no—
71C4×D101—42no—
72C4×D101—42no—
73Dic202—22no—
74Dic202—22no—
75C8×C101—22no—
76C8×C101—41no—
77C22×C101—24no—
78C22×C101—22no—
79C22×C101—41no—
80C22×C101—42no—
81C22×C101—41no—
82C22×C101—41no—
83C22×C101#12012yes—
84C22×C101#12111yescharacteristic
85C2×D101—44no—
86C2×D101—42no—
87C4×C101—41no—
88C4×C101#12011yescharacteristic
89C4×C101#12112yes—
90C4×C101#12711yescharacteristic
91Dic101—44no—
92Dic101—42no—
93C2×C101—22no—
94C2×C101—21no—
95C2×C101—42no—
96C2×C101#39211yescharacteristic
97D101—82no—
98#2010—1011nomaximal, Sylow
99C101#201011yescharacteristic, complemented, Sylow
100#575—1011no—
101#525—1012no—
102#421—1012no—
103#407D10111yescharacteristic, complemented
104H(3,ℤ/4)—1011no—
105C2×#41—1012no—
106C23×C4C2×D10111yescharacteristic
107#137—2022no—
108AGL(1,ℤ/8)—2022no—
109#135—2022no—
110C2×M16C2×D10111yescharacteristic
111C2×M16C2×D10111yescharacteristic
112#123—2022no—
113C22⋊Q8—2022no—
114#121—2022no—
115#120—2022no—
116C4×D4—2024no—
117#117—1012no—
118#104—2024no—
119C22⋊C8—22no—
120C24D40411yescharacteristic
121#41—2022no—
122#41—2022no—
123#41—2022no—
124#41—2022no—
125C2×Q8—1012no—
126C2×D4—1012no—
127C2×D4—2024no—
128C2×D4—2022no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2022no—
134C22×C4D40411yescharacteristic
135C22×C4C22×D10111yescharacteristic
136Q16—2022no—
137SD16—2024no—
138D8—2022no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D10112yescomplemented
143C4⋊C4—2024no—
144C4⋊C4—2022no—
145C22⋊C4—2024no—
146C22⋊C4—2024no—
147C22⋊C4—2022no—
148C42—1014no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—2022no—
153C23C2×D40411yescharacteristic
154Q8—2022no—
155Q8—2022no—
156D4—4048no—
157D4—4042no—
158D4—4042no—
159D4—2022no—
160D4—2022no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—4042no—
167C2×C4—4042no—
168C2×C4—2024no—
169C2×C4—2022no—
170C2×C4D4×D10112yes—
171C2×C4D4×D10112yes—
172C2×C4C2×C22⋊D10111yescharacteristic
173C2×C4#1310807411yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—4044no—
183C22—4042no—
184C22#1569222512yes—
185C22#1569222911yescharacteristic
186C4—41no—
187C4—4044no—
188C4—4042no—
189C4#1569222311yescharacteristic
190C4#1569222812yes—
191C4#1569225111yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—8082no—
196C2#2026508611yescharacteristic
subgroupG/H
centerC4#15692251
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#407×C101C2
socleC2×C101#392
hypercenter#407D101
hypocenterC101#2010
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #20265977C2semidirect
2. #20265688C2semidirect
3. #20265193C2semidirect
4. #20264934C2semidirect
5. #407×C101C2semidirect
25. C2×Dic202D4semidirect
26. C2×D404D4semidirect
38. C4×Dic101D4semidirect
49. C2×C8×C101D4semidirect
99. C101#2010semidirect
103. #407D101semidirect
142. C2×C8C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202659772
#202656882
#202651932
#202649342
#407×C1012
#2010101