Finite Group Databasebeta

← #27186668

Subgroups — #27186668

Order 12928.

202 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 58 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#20266197C211yesmaximal, characteristic
2#20266180C211yesmaximal, characteristic
3#20266037C212yesmaximal, complemented
4#20266036C212yesmaximal, complemented
5#20265729C211yesmaximal, characteristic
6C2×#13108083—21no—
7#15692322C2212yes—
8#15692322C2212yes—
9C4⋊#11717581—21no—
10C22⋊#11717581—21no—
11#15692310—21no—
12#15692254C2211yescharacteristic
13#15692253C2211yescharacteristic
14#15692245—21no—
15#15692234C411yescharacteristic
16#15692232—21no—
17Q8×Dic101C411yescharacteristic
18#15692220—21no—
19#15692220C411yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22C22⋊Q8×C101C411yescharacteristic
23#13108083—42no—
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—41no—
51C2×C4×C101—21no—
52C2×C4×C101—21no—
53C2×C4×C101—41no—
54C2×C4×C101C22⋊C411yescharacteristic
55C2×C4×C101C22×C411yescharacteristic
56C2×Dic101—21no—
57C2×Dic101—21no—
58C2×Dic101—22no—
59C2×Dic101—21no—
60C2×Dic101—21no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C2×D411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65Dic202—41no—
66Dic202—41no—
67Dic202—41no—
68#11717581—42no—
69#11717581—42no—
70C22×C101—21no—
71C22×C101—21no—
72C22×C101—21no—
73C22×C101C2×C22⋊C411yescharacteristic
74C4×C101—21no—
75C4×C101—21no—
76C4×C101—41no—
77C4×C101—41no—
78Dic101—21no—
79Dic101—21no—
80Dic101—41no—
81Dic101—41no—
82Dic101AGL(1,ℤ/8)11yescharacteristic
83Dic101#13711yescharacteristic
84Dic101#13712yes—
85C2×C101—41no—
86C2×C101#41311yescharacteristic
87C2×C101#41711yescharacteristic
88C2×C101#41911yescharacteristic
89#1559—1011nomaximal, Sylow
90C101#155911yescharacteristic, complemented, Sylow
91#533—1011no—
92#432—1011no—
93#423—1011no—
94#333—1012no—
95#332—1012no—
96C2×M16—2021no—
97C4⋊Q8—1011no—
98C4⋊Q8—1011no—
99#125—2021no—
100C22⋊Q8—1011no—
101C22⋊Q8—2021no—
102C22⋊Q8#8793811yescharacteristic
103C4×Q8—1011no—
104C4×Q8—1011no—
105C4×Q8—2021no—
106#117—2021no—
107C2×C42—1011no—
108C4⋊C8—1012no—
109C4⋊C8—1012no—
110C4⋊C8—2021no—
111C22⋊C8—2021no—
112#97—2021no—
113C2×Q8—1011no—
114C2×Q8—2021no—
115C2×Q8C2×#8793811yescharacteristic
116C22×C4—1011no—
117C22×C4—1011no—
118C22×C4C2×#8793811yescharacteristic
119M16—4042no—
120C2×C8—2022no—
121C2×C8—2022no—
122C4⋊C4—21no—
123C4⋊C4—1011no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4C2×#8793811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2021no—
133C42—1011no—
134C42—1011no—
135C42—1011no—
136C42—1011no—
137C42—2021no—
138C42—2021no—
139C23C22⋊#8793811yescharacteristic
140Q8—41no—
141Q8—4041no—
142Q8—4041no—
143Q8—4041no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—1011no—
148C2×C4—1011no—
149C2×C4—1011no—
150C2×C4—1011no—
151C2×C4—2021no—
152C2×C4—2021no—
153C2×C4—2022no—
154C2×C4—2021no—
155C2×C4—2021no—
156C2×C4C22⋊#8793811yescharacteristic
157C2×C4C22×#8793811yescharacteristic
158C8—4042no—
159C8—4042no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C2×C22⋊#8793811yescharacteristic
164C4—21no—
165C4—21no—
166C4—41no—
167C4—41no—
168C4—1011no—
169C4—1011no—
170C4—1012no—
171C4—4041no—
172C4—4041no—
173C4—2021no—
174C4—2021no—
175C2—41no—
176C2#2026616411yescharacteristic
177C2#2026616811yescharacteristic
178C2#2026617011yescharacteristic
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#1559
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20266037C2semidirect
4. #20266036C2semidirect
90. C101#1559semidirect

Maximal subgroups

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

subgroupindex
#202661972
#202661802
#202660372
#202660362
#202657292
#1559101