Finite Group Databasebeta

← #27186654

Subgroups — #27186654

Order 12928.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266200C211yesmaximal, characteristic
2D101⋊(C4⋊C8)C211yesmaximal, characteristic
3#20266036C212yesmaximal, complemented
4#20266036C212yesmaximal, complemented
5#20265733C211yesmaximal, characteristic
6C2×D101⋊C8—21no—
7#15692322C2212yes—
8#15692322C2212yes—
9C4⋊#11717581—21no—
10#15692312—21no—
11#15692310—21no—
12#15692254C2211yescharacteristic
13#15692254C2211yescharacteristic
14#15692247C411yescharacteristic
15#15692233—21no—
16#15692233—21no—
17#15692220—21no—
18#15692220—21no—
19#15692213C411yescharacteristic
20#15692213C411yescharacteristic
21C42×D101C2211yescharacteristic
22#125×C101C411yescharacteristic
23D101⋊C8—42no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×Dic202—21no—
27C2×Dic202—21no—
28C2×C4×D101C2×C411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C4⋊Dic101C2×C411yescharacteristic
32C4⋊Dic101C2×C411yescharacteristic
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108051—21no—
38#13108051—21no—
39C4×Dic101—21no—
40C4×Dic101—21no—
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101C2311yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101C2×C411yescharacteristic
49C22×D101C22⋊C411yescharacteristic
50C2×C4×C101—21no—
51C2×C4×C101—21no—
52C2×C4×C101C22⋊C411yescharacteristic
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C2×Dic101—21no—
56C2×Dic101—21no—
57C2×Dic101C22⋊C411yescharacteristic
58C2×Dic101C2×D411yescharacteristic
59C2×Dic101C2×D411yescharacteristic
60C4×D101—22no—
61C4×D101—22no—
62C4×D101—21no—
63C4×D101—21no—
64Dic202—42no—
65Dic202—41no—
66Dic202—41no—
67#11717581—42no—
68#11717581—42no—
69C22×C101C2×C22⋊C411yescharacteristic
70C2×D101—21no—
71C2×D101—21no—
72C2×D101#10112yes—
73C4×C101—21no—
74C4×C101—21no—
75C4×C101—21no—
76C4×C101—41no—
77C4×C101—41no—
78Dic101—21no—
79Dic101—41no—
80Dic101—41no—
81Dic101#13512yes—
82Dic101AGL(1,ℤ/8)11yescharacteristic
83Dic101#13711yescharacteristic
84C2×C101C2×#10111yescharacteristic
85C2×C101#41611yescharacteristic
86C2×C101#41711yescharacteristic
87D101—22no—
88#1552—1011nomaximal, Sylow
89C101#155211yescharacteristic, complemented, Sylow
90#533—1011no—
91#432—1011no—
92C2×C4⋊C8—1011no—
93#332—1012no—
94#332—1012no—
95C22×C8—2021no—
96C4⋊Q8—1011no—
97C4⋊Q8—1011no—
98#125—1011no—
99#125#8793811yescharacteristic
100C22⋊Q8—2021no—
101C22⋊Q8—2021no—
102C4×Q8—2021no—
103C4×Q8—2021no—
104#117—1011no—
105#117—1011no—
106C2×C42—1011no—
107C4⋊C8—1012no—
108C4⋊C8—1012no—
109C4⋊C8—2021no—
110C22⋊C8—2021no—
111#97—2021no—
112C2×Q8—2021no—
113C2×Q8—2021no—
114C22×C4—1011no—
115C22×C4—1011no—
116C22×C4—1011no—
117C2×C8—4042no—
118C2×C8—2022no—
119C2×C8—2022no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—1011no—
123C4⋊C4—1011no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4C2×#8793811yescharacteristic
129C4⋊C4C2×#8793811yescharacteristic
130C22⋊C4—2021no—
131C22⋊C4—2021no—
132C42—1011no—
133C42—1011no—
134C42—1011no—
135C42—2021no—
136C42—2021no—
137C42C2×#8793811yescharacteristic
138C23—1011no—
139Q8—4042no—
140Q8—4041no—
141Q8—4041no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—1011no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—2021no—
148C2×C4—2022no—
149C2×C4—2021no—
150C2×C4—2022no—
151C2×C4—2021no—
152C2×C4—2021no—
153C2×C4C22⋊#8793811yescharacteristic
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22×#8793811yescharacteristic
156C8—4042no—
157C8—4042no—
158C22—1012no—
159C22—2021no—
160C22—2021no—
161C22C2×C22⋊#8793811yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—1012no—
168C4—1011no—
169C4—1011no—
170C4—4041no—
171C4—4041no—
172C4—2021no—
173C2—2022no—
174C2D101⋊#10111yescharacteristic
175C2#2026616711yescharacteristic
176C2#2026616811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#125×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC4×Dic101C23
hypercenter#125#87938
hypocenterC101#1552
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #20266036C2semidirect
4. #20266036C2semidirect
89. C101#1552semidirect

Maximal subgroups

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

subgroupindex
#202662002
D101⋊(C4⋊C8)2
#202660362
#202657332
#1552101