Finite Group Databasebeta

← #27186649

Subgroups — #27186649

Order 12928.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266182C211yesmaximal, characteristic
2D101⋊(C4⋊C8)C211yesmaximal, characteristic
3#20266037C212yesmaximal, complemented
4#20266036C212yesmaximal, complemented
5#20265731C211yesmaximal, characteristic
6C2×#13108084—21no—
7C2×D101⋊C8—21no—
8#15692322—21no—
9#15692322C2212yes—
10#15692322C2212yes—
11C4⋊#11717581—21no—
12#15692254C2211yescharacteristic
13#15692253C2211yescharacteristic
14#15692245—21no—
15#15692235C411yescharacteristic
16#15692233—21no—
17#15692231C411yescharacteristic
18C4×Dic202—21no—
19C4×Dic202C411yescharacteristic
20#15692212—21no—
21C42×D101C2211yescharacteristic
22C4×Q8×C101C411yescharacteristic
23#13108084—42no—
24D101⋊C8—42no—
25C2×#11717581—22no—
26C2×#11717581—22no—
27C2×Dic202—21no—
28C2×Dic202C2×C411yescharacteristic
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C4⋊Dic101—21no—
33C4⋊Dic101C2×C411yescharacteristic
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101—21no—
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C2×Q8×C101C2×C411yescharacteristic
46C4⋊C4×C101—21no—
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101—21no—
49C42×C101C2×C411yescharacteristic
50C22×D101C22⋊C411yescharacteristic
51Q8×C101—41no—
52C2×C4×C101—21no—
53C2×C4×C101—21no—
54C2×C4×C101C22⋊C411yescharacteristic
55C2×C4×C101C22⋊C411yescharacteristic
56C2×C4×C101C22×C411yescharacteristic
57C2×Dic101—21no—
58C2×Dic101—21no—
59C2×Dic101C22⋊C411yescharacteristic
60C2×Dic101C2×D411yescharacteristic
61C2×Dic101C2×D411yescharacteristic
62C4×D101—21no—
63C4×D101—21no—
64C4×D101—41no—
65C4×D101SD1612yes—
66C4×D101Q1612yes—
67Dic202—41no—
68Dic202—41no—
69Dic202—41no—
70#11717581—42no—
71#11717581—42no—
72C22×C101C2×C22⋊C411yescharacteristic
73C2×D101—21no—
74C2×D101—21no—
75C2×D101#10312yes—
76C4×C101—21no—
77C4×C101—21no—
78C4×C101—41no—
79C4×C101—41no—
80C4×C101#10312yes—
81Dic101—21no—
82Dic101—41no—
83Dic101—41no—
84Dic101C2×SD1611yescharacteristic
85Dic101C2×Q1611yescharacteristic
86Dic101AGL(1,ℤ/8)11yescharacteristic
87Dic101#13711yescharacteristic
88C2×C101#41311yescharacteristic
89C2×C101C2×#10311yescharacteristic
90C2×C101#41711yescharacteristic
91D101—22no—
92#1550—1011nomaximal, Sylow
93C101#155011yescharacteristic, complemented, Sylow
94#533—1011no—
95#423—1011no—
96C2×C4⋊C8—1011no—
97#333—1012no—
98#332—1012no—
99C2×M16—2021no—
100C22×C8—2021no—
101C4⋊Q8—1011no—
102C4⋊Q8—1011no—
103#125—2021no—
104C22⋊Q8—1011no—
105C22⋊Q8—1011no—
106C22⋊Q8—2021no—
107C4×Q8—1011no—
108C4×Q8—2021no—
109C4×Q8#8793811yescharacteristic
110#117—2021no—
111C2×C42—1011no—
112C4⋊C8—1012no—
113C4⋊C8—1012no—
114C4⋊C8—2021no—
115C4⋊C8—2021no—
116C2×Q8—1011no—
117C2×Q8—2021no—
118C2×Q8C2×#8793811yescharacteristic
119C22×C4—1011no—
120C22×C4—1011no—
121C22×C4—1011no—
122M16—4042no—
123C2×C8—4042no—
124C2×C8—2022no—
125C2×C8—2022no—
126C4⋊C4—21no—
127C4⋊C4—1011no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C4⋊C4—2021no—
133C4⋊C4—2021no—
134C4⋊C4C2×#8793811yescharacteristic
135C22⋊C4—2021no—
136C22⋊C4—2021no—
137C42—21no—
138C42—1011no—
139C42—1011no—
140C42—1011no—
141C42—2021no—
142C42C2×#8793811yescharacteristic
143C23—1011no—
144Q8—41no—
145Q8—4041no—
146Q8—4041no—
147Q8—4041no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—1012no—
153C2×C4—1012no—
154C2×C4—1011no—
155C2×C4—4041no—
156C2×C4—2021no—
157C2×C4—2021no—
158C2×C4—2021no—
159C2×C4—2021no—
160C2×C4C22⋊#8793811yescharacteristic
161C2×C4C22⋊#8793811yescharacteristic
162C2×C4C22×#8793811yescharacteristic
163C8—4042no—
164C8—4042no—
165C22—1012no—
166C22—2021no—
167C22—2021no—
168C22C2×C22⋊#8793811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1011no—
174C4—1011no—
175C4—1011no—
176C4—1011no—
177C4—4041no—
178C4—4041no—
179C4—2021no—
180C4#1569231812yes—
181C2—2022no—
182C2#2026616311yescharacteristic
183C2C2×#1569231811yescharacteristic
184C2#2026616811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC4×Dic101C23
hypercenterC4×Q8#87938
hypocenterC101#1550
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20266037C2semidirect
4. #20266036C2semidirect
93. C101#1550semidirect

Maximal subgroups

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

subgroupindex
#202661822
D101⋊(C4⋊C8)2
#202660372
#202660362
#202657312
#1550101