Finite Group Databasebeta

← #27181424

Subgroups — #27181424

Order 12928.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#20265782C211yesmaximal, characteristic
2#20265654C211yesmaximal, characteristic, complemented
3#20265502C212yesmaximal, complemented
4#20265485C212yesmaximal, complemented
5#20265378C212yesmaximal, complemented
6#20265318C212yesmaximal, complemented
7#20265279C212yesmaximal, complemented
8C4×#13108063C212yesmaximal, complemented
9#433×C101C211yesmaximal, characteristic, complemented
10C22×Dic202C2211yescharacteristic
11C2×#13108063C2212yes—
12C2×#13108063C2212yes—
13#15692252C2211yescharacteristic
14#15692247C2211yescharacteristic
15#15692240—22no—
16#15692229C2212yes—
17#15692228—22no—
18C4×Dic202C2212yes—
19C4×Dic202C2212yes—
20#15692220—22no—
21C4×D404C2212yes—
22#15692214C2211yescharacteristic
23#15692211—22no—
24#15692189C2212yes—
25#15692187C2212yes—
26#15692180C2212yes—
27#15692180C2212yes—
28#15692177C2212yes—
29#15692177C2212yes—
30#117×C101C2211yescharacteristic
31C4⋊C8×C101C2212yes—
32C22⋊C8×C101C2212yes—
33#97×C101C2211yescharacteristic
34C4×C8×C101C2211yescharacteristic
35C2×Dic202—21no—
36C2×Dic202—24no—
37C2×Dic202C2312yes—
38C2×D404—22no—
39C2×D404C2312yes—
40C2×C22⋊D101—22no—
41C22×Dic101—21no—
42C2×C4×D101—22no—
43#13108063—24no—
44#13108063—24no—
45C4⋊Dic101C2312yes—
46C4⋊Dic101C2312yes—
47#13108053—22no—
48#13108053—22no—
49#13108053—22no—
50C22⋊Dic101—21no—
51#13108051—22no—
52#13108051—22no—
53C4×Dic101—22no—
54C4×Dic101—22no—
55C4×Dic101—21no—
56C22×C4×C101C2311yescharacteristic
57C2×C8×C101C2312yes—
58C2×C8×C101C2312yes—
59C4⋊C4×C101D412yes—
60C22⋊C4×C101D412yes—
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101C2×D411yescharacteristic
64C22×D101—22no—
65C2×C4×C101—22no—
66C2×C4×C101C2×D412yes—
67C2×C4×C101C2×D412yes—
68C2×C4×C101C2×D411yescharacteristic
69C2×C4×C101C2411yescharacteristic
70C22⋊D101—82no—
71C2×Dic101—24no—
72C2×Dic101—22no—
73C2×Dic101—22no—
74C2×Dic101—22no—
75D404—22no—
76D404—22no—
77D404—82no—
78C4×D101—82no—
79Dic202—24no—
80Dic202—22no—
81Dic202#4114yes—
82C8×C101—22no—
83C8×C101—22no—
84C22×C101—21no—
85C22×C101—22no—
86C22×C101C22×D411yescharacteristic
87C2×D101—42no—
88C2×D101—42no—
89C2×D101—42no—
90C4×C101—21no—
91C4×C101—22no—
92C4×C101—22no—
93C4×C101C2×#4112yes—
94Dic101—24no—
95Dic101—42no—
96Dic101—42no—
97C2×C101—41no—
98C2×C101#52511yescharacteristic
99C2×C101#57712yes—
100D101—82no—
101#3126—1011nomaximal, Sylow
102C101#312611yescharacteristic, complemented, Sylow
103#540—1011no—
104#519—1011no—
105#482—1012no—
106#479—1012no—
107#460—1012no—
108#448—1012no—
109#440—1012no—
110C4×SD16—1012no—
111#433D10111yescharacteristic, complemented
112C22×Q8—1011no—
113C2×SD16—1012no—
114C2×SD16—1012no—
115#127—1011no—
116#125—1011no—
117#123—2022no—
118#121—1012no—
119#121—2022no—
120C4×Q8—1012no—
121C4×Q8—1012no—
122C4×Q8—2022no—
123C4×D4—1012no—
124#117—1011no—
125#117—2022no—
126#117C2×D10111yescharacteristic
127#107—1012no—
128#106—1012no—
129C4⋊C8C2×D10112yes—
130#103—1012no—
131#103—1012no—
132#102—1012no—
133#102—1012no—
134C22⋊C8C2×D10112yes—
135#97C2×D10111yescharacteristic
136C4×C8C2×D10111yescharacteristic
137C2×Q8—1012no—
138C2×Q8—2024no—
139C2×Q8—2021no—
140C2×D4—1012no—
141C2×D4—2022no—
142C2×D4—2022no—
143C22×C4—2022no—
144C22×C4—2021no—
145C22×C4C22×D10111yescharacteristic
146SD16—2024no—
147SD16—2024no—
148C2×C8C22×D10112yes—
149C2×C8C22×D10112yes—
150C4⋊C4—1012no—
151C4⋊C4—1012no—
152C4⋊C4—2022no—
153C4⋊C4—2022no—
154C4⋊C4—2022no—
155C4⋊C4D40412yes—
156C22⋊C4—2021no—
157C22⋊C4—2022no—
158C22⋊C4—2022no—
159C22⋊C4D40412yes—
160C42—2021no—
161C42—2022no—
162C42—2022no—
163C42C22×D10111yescharacteristic
164C42C22×D10111yescharacteristic
165C23—2022no—
166C23C2×D40411yescharacteristic
167Q8—1014no—
168Q8—2024no—
169Q8—2022no—
170D4—8082no—
171D4—8082no—
172D4—2022no—
173D4—2022no—
174C2×C4—22no—
175C2×C4—8082no—
176C2×C4—2022no—
177C2×C4—2022no—
178C2×C4—2024no—
179C2×C4—2022no—
180C2×C4C2×D40412yes—
181C2×C4C2×D40412yes—
182C2×C4C2×D40411yescharacteristic
183C2×C4C23×D10111yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—4042no—
189C22—4042no—
190C22—4042no—
191C22C22×D40411yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—4042no—
196C4—4042no—
197C4—2024no—
198C4#41×D10112yes—
199C2—41no—
200C2—8082no—
201C2#2026568911yescharacteristic
202C2#2026598912yes—
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#433×C101C2
socleC22×C101C22×D4
prime radical#20265782C2
hypercenter#433D101
hypocenterC101#3126
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20265654C2semidirect
3. #20265502C2semidirect
4. #20265485C2semidirect
5. #20265378C2semidirect
6. #20265318C2semidirect
7. #20265279C2semidirect
8. C4×#13108063C2semidirect
9. #433×C101C2semidirect
102. C101#3126semidirect
111. #433D101semidirect

Maximal subgroups

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

subgroupindex
#202657822
#202656542
#202655022
#202654852
#202653782
#202653182
#202652792
C4×#131080632
#433×C1012
#3126101