Finite Group Databasebeta

← #27186454

Subgroups — #27186454

Order 12928.

218 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 62 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#20266193C211yesmaximal, characteristic
2C4×#13108083C211yesmaximal, characteristic
3#20266027C212yesmaximal, complemented
4Q8⋊#11717581C212yesmaximal, complemented
5#20265729C211yesmaximal, characteristic
6C2×#13108083—21no—
7C4⋊#11717581C2212yes—
8C22⋊#11717581—21no—
9#15692310—21no—
10C4×#11717581—21no—
11C4×#11717581C2212yes—
12#15692254C411yescharacteristic
13#15692253C411yescharacteristic
14#15692245—21no—
15#15692234C411yescharacteristic
16#15692232—21no—
17Q8×Dic101C2211yescharacteristic
18#15692220—21no—
19#15692220C2211yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22C22⋊Q8×C101C411yescharacteristic
23#13108083—24no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×Dic202—21no—
27C2×Dic202C2×C411yescharacteristic
28C22×Dic101D411yescharacteristic
29C22×Dic101D411yescharacteristic
30C4⋊Dic101—21no—
31C4⋊Dic101C2×C411yescharacteristic
32#13108053—21no—
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37C22⋊Dic101—21no—
38C4×Dic101—21no—
39C4×Dic101—21no—
40C4×Dic101C2×C411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101C2311yescharacteristic
44C2×Q8×C101C2×C411yescharacteristic
45C22×C4×C101C2×C411yescharacteristic
46C4⋊C4×C101—21no—
47C4⋊C4×C101C2×C411yescharacteristic
48C22⋊C4×C101—21no—
49C23×C101C22⋊C411yescharacteristic
50Q8×C101—22no—
51C2×C4×C101—22no—
52C2×C4×C101—21no—
53C2×C4×C101—21no—
54C2×C4×C101C22⋊C411yescharacteristic
55C2×C4×C101C22×C411yescharacteristic
56C2×Dic101—22no—
57C2×Dic101—22no—
58C2×Dic101—21no—
59C2×Dic101—21no—
60C2×Dic101C22⋊C411yescharacteristic
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63C2×Dic101C2×D411yescharacteristic
64Dic202—22no—
65Dic202—42no—
66#11717581—24no—
67#11717581—42no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101—21no—
71C22×C101C2×C22⋊C411yescharacteristic
72C4×C101—21no—
73C4×C101—41no—
74C4×C101—41no—
75C4×C101#13112yes—
76Dic101—21no—
77Dic101—21no—
78Dic101—41no—
79Dic101—41no—
80Dic101#10412yes—
81Dic101#13712yes—
82C2×C101—41no—
83C2×C101#40811yescharacteristic
84C2×C101#41911yescharacteristic
85C2×C101C2×#10411yescharacteristic
86#1485—1011nomaximal, Sylow
87C101#148511yescharacteristic, complemented, Sylow
88#533—1011no—
89#431—1011no—
90C4×M16—1011no—
91Q8⋊C8—1012no—
92Q8⋊C8—1012no—
93C2×M16—2021no—
94C4⋊Q8—1011no—
95C4⋊Q8—1011no—
96#125—2021no—
97C22⋊Q8—1011no—
98C22⋊Q8—2021no—
99C22⋊Q8#8793811yescharacteristic
100C4×Q8—1011no—
101C4×Q8—1011no—
102C4×Q8—2021no—
103#117—2021no—
104C2×C42—1011no—
105C4⋊C8—1012no—
106C22⋊C8—2021no—
107#97—2021no—
108C4×C8—1012no—
109C4×C8—2021no—
110C2×Q8—1011no—
111C2×Q8—2021no—
112C2×Q8C2×#8793811yescharacteristic
113C22×C4—1011no—
114C22×C4—1011no—
115C22×C4C2×#8793811yescharacteristic
116M16—2024no—
117C2×C8—2022no—
118C2×C8—2022no—
119C4⋊C4—21no—
120C4⋊C4—1011no—
121C4⋊C4—2021no—
122C4⋊C4—2021no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4C2×#8793811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2021no—
130C42—1011no—
131C42—1011no—
132C42—1011no—
133C42—1011no—
134C42—2021no—
135C42—2021no—
136C23C22⋊#8793811yescharacteristic
137Q8—22no—
138Q8—4042no—
139Q8—2022no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—1011no—
144C2×C4—1011no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—2022no—
148C2×C4—2022no—
149C2×C4—2021no—
150C2×C4—2021no—
151C2×C4C22⋊#8793811yescharacteristic
152C2×C4C22×#8793811yescharacteristic
153C8—4042no—
154C8—2024no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22C2×C22⋊#8793811yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—1012no—
163C4—1012no—
164C4—4041no—
165C4—4041no—
166C4—2021no—
167C4—2021no—
168C4#1569234212yes—
169C2—41no—
170C2#2026615011yescharacteristic
171C2#2026617011yescharacteristic
172C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC22⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenterC22⋊Q8#87938
hypocenterC101#1485
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20266027C2semidirect
4. Q8⋊#11717581C2semidirect
87. C101#1485semidirect

Maximal subgroups

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

subgroupindex
#202661932
C4×#131080832
#202660272
Q8⋊#117175812
#202657292
#1485101