Finite Group Databasebeta

← #27172796

Subgroups — #27172796

Order 12928.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#20265726C211yesmaximal, characteristic
2#20265149C212yesmaximal, complemented
3#20264972C211yesmaximal, characteristic, complemented
4#20264969C212yesmaximal, complemented
5#354×C101C211yesmaximal, characteristic, complemented
6C2×#13108075C411yescharacteristic, complemented
7C2×#13108073C2211yescharacteristic
8#15692253C411yescharacteristic, complemented
9#15692251C2211yescharacteristic
10#15692243C411yescharacteristic, complemented
11#15692228—22no—
12#15692215—22no—
13#15692211—22no—
14C42×D101C411yescharacteristic, complemented
15#15692170C2212yes—
16#15692169—22no—
17#124×C101C2211yescharacteristic
18#99×C101C2212yes—
19#13108075—41no—
20#13108075—41no—
21#13108073—41no—
22#13108073—41no—
23C2×Dic202C2×C411yescharacteristic
24C2×D404—21no—
25C2×D404C2×C411yescharacteristic
26C2×C22⋊D101—22no—
27C2×C22⋊D101D412yes—
28C22×Dic101D412yes—
29C2×C4×D101—21no—
30C2×C4×D101—21no—
31C2×C4×D101C2×C411yescharacteristic
32#13108053—22no—
33#13108053—42no—
34C22⋊Dic101—22no—
35#13108051—22no—
36C4×Dic101—21no—
37C4×Dic101—42no—
38C4×Dic101C2×C411yescharacteristic
39C2×Q8×C101C2×C411yescharacteristic
40C2×D4×C101C2311yescharacteristic
41C22⋊C4×C101—22no—
42C22⋊C4×C101—22no—
43C42×C101C2×C411yescharacteristic
44C23×C101C2×D412yes—
45C22×D101—21no—
46C22×D101C22⋊C411yescharacteristic
47Q8×C101—41no—
48D4×C101—41no—
49C2×C4×C101—21no—
50C2×C4×C101—21no—
51C2×C4×C101—42no—
52C2×C4×C101C22×C411yescharacteristic
53C22⋊D101—42no—
54C22⋊D101—44no—
55C2×Dic101—21no—
56C2×Dic101—22no—
57C2×Dic101—22no—
58C2×Dic101—42no—
59C2×Dic101C22⋊C412yes—
60C2×Dic101C22⋊C411yescharacteristic
61D404—41no—
62D404—42no—
63C4×D101—21no—
64C4×D101—21no—
65C4×D101—42no—
66C4×D101—41no—
67C4×D101—41no—
68Dic202—41no—
69C22×C101—22no—
70C22×C101—42no—
71C22×C101C2×C22⋊C411yescharacteristic
72C2×D101—21no—
73C2×D101—41no—
74C2×D101—42no—
75C2×D101—41no—
76C4×C101—21no—
77C4×C101—41no—
78C4×C101—41no—
79C4×C101—82no—
80Dic101—22no—
81Dic101—22no—
82Dic101—82no—
83Dic101#9911yescharacteristic
84Dic101#9911yescharacteristic
85C2×C101—21no—
86C2×C101—42no—
87C2×C101C2×#9911yescharacteristic
88D101—41no—
89D101—81no—
90#2126—1011nomaximal, Sylow
91C101#212611yescharacteristic, complemented, Sylow
92#532—1011no—
93#410—1012no—
94#354—1011no—
95#354D10111yescharacteristic, complemented
96#353—1012no—
97C2×#41—1011no—
98C2×#41—1011no—
99C4⋊Q8—1011no—
100#127—1011no—
101#124—1011no—
102#124C2×D10111yescharacteristic
103#121—2022no—
104C4×D4—2022no—
105#117—2022no—
106C2×C42—1011no—
107#99—1012no—
108#99—2022no—
109#99C2×D10112yes—
110#41—4041no—
111#41—4041no—
112#41—4041no—
113#41—4041no—
114C2×Q8—1011no—
115C2×Q8C4×D10111yescharacteristic
116C2×D4—1012no—
117C2×D4—1011no—
118C2×D4—2021no—
119C2×D4—2022no—
120C2×D4C22×D10111yescharacteristic
121C22×C4—1012no—
122C22×C4—1011no—
123C22×C4—2021no—
124C22×C4—2021no—
125C4⋊C4—4042no—
126C4⋊C4—2022no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—2022no—
130C22⋊C4—2022no—
131C42—1011no—
132C42—4042no—
133C42—2021no—
134C42C4×D10111yescharacteristic
135C23—1011no—
136C23—2021no—
137C23D4×D10112yes—
138Q8—41no—
139Q8—4041no—
140D4—41no—
141D4—4041no—
142D4—4042no—
143D4—4042no—
144D4—4044no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—1011no—
149C2×C4—1012no—
150C2×C4—4041no—
151C2×C4—4041no—
152C2×C4—4042no—
153C2×C4—4042no—
154C2×C4—2021no—
155C2×C4—2021no—
156C2×C4—2022no—
157C2×C4—2022no—
158C2×C4—2021no—
159C2×C4C2×C4×D10111yescharacteristic
160C22—22no—
161C22—42no—
162C22—4042no—
163C22—4041no—
164C22—4041no—
165C22—2021no—
166C22C22⋊C4×D10111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—8082no—
172C4—1011no—
173C4—1011no—
174C4—2022no—
175C4—2022no—
176C2—21no—
177C2—42no—
178C2—8081no—
179C2—4041no—
180C2#99×D10111yescharacteristic
subgroupG/H
centerC2#99×D101
commutatorC2×C4×C101C22×C4
FrattiniC2×D4C22×D101
Fitting#354×C101C2
socleC2×C101C2×#99
prime radical#20265726C2
cosocleC2×D4×C101C23
hypercenter#354D101
hypocenterC101#2126
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #20265149C2semidirect
3. #20264972C2semidirect
4. #20264969C2semidirect
5. #354×C101C2semidirect
6. C2×#13108075C4semidirect
8. #15692253C4semidirect
10. #15692243C4semidirect
14. C42×D101C4semidirect
91. C101#2126semidirect
95. #354D101semidirect

Maximal subgroups

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

subgroupindex
#202657262
#202651492
#202649722
#202649692
#354×C1012
#2126101