Finite Group Databasebeta

← #27186583

Subgroups — #27186583

Order 12928.

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

normal subgroups only

This group has 234 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
1C4×#13108083C211yesmaximal, characteristic, complemented
2C2×#15692310C211yesmaximal, characteristic, complemented
3#20266034C212yesmaximal, complemented
4#20266032C212yesmaximal, complemented
5#20265708C211yesmaximal, characteristic
6C2×#13108083—21no—
7C22×#11717581—21no—
8#15692310—21no—
9#15692310C2212yes—
10#15692310C2212yes—
11C4×#11717581—21no—
12#15692248—21no—
13#15692246C2211yescharacteristic
14#15692242C2211yescharacteristic
15#15692236—21no—
16#15692234C411yescharacteristic
17#15692220C411yescharacteristic
18D4×Dic101—21no—
19D4×Dic101C411yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22#121×C101C411yescharacteristic
23#13108083—24no—
24C2×#11717581—24no—
25C2×#11717581—22no—
26C2×#11717581—22no—
27C2×Dic202C2×C411yescharacteristic
28C22×Dic101—21no—
29C22×Dic101D411yescharacteristic
30C22×Dic101D411yescharacteristic
31C4⋊Dic101—21no—
32C4⋊Dic101C2×C411yescharacteristic
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39C22⋊Dic101—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C2×D4×C101—21no—
46C2×D4×C101C2×C411yescharacteristic
47C22×C4×C101C2×C411yescharacteristic
48C4⋊C4×C101C2×C411yescharacteristic
49C22⋊C4×C101—21no—
50C23×C101—21no—
51C23×C101C22⋊C411yescharacteristic
52D4×C101—41no—
53D4×C101—42no—
54C2×C4×C101—21no—
55C2×C4×C101—41no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22×C411yescharacteristic
58C2×Dic101—22no—
59C2×Dic101—22no—
60C2×Dic101—21no—
61C2×Dic101—21no—
62C2×Dic101—42no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66C2×Dic101C2×D411yescharacteristic
67Dic202—41no—
68#11717581—24no—
69#11717581—24no—
70C22×C101—21no—
71C22×C101—21no—
72C22×C101—41no—
73C22×C101—41no—
74C22×C101—41no—
75C22×C101#10412yes—
76C22×C101C2×C22⋊C411yescharacteristic
77C4×C101—21no—
78C4×C101—21no—
79C4×C101—41no—
80Dic101—21no—
81Dic101—21no—
82Dic101—21no—
83Dic101—41no—
84Dic101—41no—
85Dic101#10412yes—
86C2×C101—22no—
87C2×C101—81no—
88C2×C101#41311yescharacteristic
89C2×C101C2×#10411yescharacteristic
90C2×C101C2×#10411yescharacteristic
91#1524—1011nomaximal, Sylow
92C101#152411yescharacteristic, complemented, Sylow
93#529—1011no—
94C4×M16—1011no—
95C2×#97—1011no—
96#330—1012no—
97#329—1012no—
98C2×M16—2021no—
99C22×C8—2021no—
100#126—2021no—
101#125—1011no—
102#124—1011no—
103#123—2021no—
104C22⋊Q8—1011no—
105#121#8793811yescharacteristic
106C4×Q8—1011no—
107C4×D4—1011no—
108C4×D4—2021no—
109#117—2021no—
110C2×C42—1011no—
111#97—1012no—
112#97—1012no—
113#97—2021no—
114C4×C8—2021no—
115C2×Q8—1011no—
116C2×D4—21no—
117C2×D4C2×#8793811yescharacteristic
118C22×C4—1011no—
119C22×C4—1011no—
120C22×C4—2021no—
121C22×C4C2×#8793811yescharacteristic
122M16—2024no—
123C2×C8—2022no—
124C2×C8—2022no—
125C2×C8—2024no—
126C4⋊C4—1011no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4C2×#8793811yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2021no—
134C22⋊C4—2021no—
135C22⋊C4—2021no—
136C22⋊C4—2021no—
137C42—1011no—
138C42—1011no—
139C42—1011no—
140C42—1011no—
141C42—2021no—
142C23—21no—
143C23C22⋊#8793811yescharacteristic
144Q8—4041no—
145D4—41no—
146D4—42no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—1011no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—1011no—
153C2×C4—4042no—
154C2×C4—2022no—
155C2×C4—2021no—
156C2×C4—2021no—
157C2×C4—2022no—
158C2×C4C22⋊#8793811yescharacteristic
159C2×C4C22×#8793811yescharacteristic
160C8—2024no—
161C8—2024no—
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22#1569231912yes—
168C22C2×C22⋊#8793811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—1012no—
173C4—4041no—
174C4—4041no—
175C4—2021no—
176C4—2021no—
177C4—2021no—
178C2—22no—
179C2—81no—
180C2#2026616411yescharacteristic
181C2C2×#1569231911yescharacteristic
182C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting, prime radical#121×C101C4
socleC22×C101C2×C22⋊C4
cosocleC4×Dic101C23
hypercenter#121#87938
hypocenterC101#1524
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C4×#13108083C2semidirect
2. C2×#15692310C2semidirect
3. #20266034C2semidirect
4. #20266032C2semidirect
92. C101#1524semidirect

Maximal subgroups

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

subgroupindex
C4×#131080832
C2×#156923102
#202660342
#202660322
#202657082
#1524101