Finite Group Databasebeta

← #27186414

Subgroups — #27186414

Order 12928.

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

normal subgroups only

This group has 214 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, complemented
2#20266193C211yesmaximal, characteristic, complemented
3#20266023C212yesmaximal, complemented
4#20266020C212yesmaximal
5C2×#15692248C211yesmaximal, characteristic
6#15692322—21no—
7C4⋊#11717581—21no—
8C22⋊#11717581C2212yes—
9C22⋊#11717581C2212yes—
10#15692310—21no—
11C4×#11717581—21no—
12#15692248—21no—
13#15692248—21no—
14#15692248—21no—
15#15692248—21no—
16C2×C4⋊Dic101C411yescharacteristic
17C2×#13108053C411yescharacteristic
18C2×#13108053C2211yescharacteristic
19C2×C22⋊Dic101C411yescharacteristic
20C2×C22⋊Dic101C2211yescharacteristic
21C2×C4×Dic101C2211yescharacteristic
22C2×C22⋊C4×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C22×Dic101C2×C411yescharacteristic
26C22×Dic101C2×C411yescharacteristic
27C22×Dic101C2×C411yescharacteristic
28C22×Dic101C2311yescharacteristic
29C4⋊Dic101—21no—
30C4⋊Dic101—21no—
31#13108053—21no—
32#13108053—21no—
33#13108053—21no—
34#13108053—21no—
35C22⋊Dic101—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39C4×Dic101D411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C24×C101C2×C411yescharacteristic
44C22×C4×C101C2×C411yescharacteristic
45C22×C4×C101C2×C411yescharacteristic
46C22⋊C4×C101—21no—
47C22⋊C4×C101—21no—
48C23×C101—21no—
49C23×C101—22no—
50C23×C101—41no—
51C23×C101—41no—
52C23×C101C22×C411yescharacteristic
53C2×C4×C101—22no—
54C2×C4×C101—21no—
55C2×C4×C101—41no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×Dic101—21no—
59C2×Dic101—21no—
60C2×Dic101—22no—
61C2×Dic101—41no—
62C2×Dic101—41no—
63C2×Dic101—41no—
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C22⋊C411yescharacteristic
66C2×Dic101C2×D411yescharacteristic
67C2×Dic101C2×D411yescharacteristic
68#11717581—42no—
69#11717581—42no—
70C22×C101—21no—
71C22×C101—21no—
72C22×C101—41no—
73C22×C101—41no—
74C22×C101—41no—
75C22×C101—82no—
76C22×C101C2×C22⋊C411yescharacteristic
77C22×C101#13112yes—
78C4×C101—21no—
79C4×C101—21no—
80C4×C101—41no—
81Dic101—21no—
82Dic101—21no—
83Dic101—21no—
84Dic101—21no—
85Dic101—41no—
86Dic101—41no—
87C2×C101—22no—
88C2×C101—81no—
89C2×C101#40811yescharacteristic
90C2×C101#41011yescharacteristic
91C2×C101#41311yescharacteristic
92#1473—1011nomaximal, Sylow
93C101#147311yescharacteristic, complemented, Sylow
94C2×#126—1011no—
95#432—1011no—
96#431—1011no—
97#324—1012no—
98#323—1012no—
99#126—2021no—
100#126—2021no—
101#126—2021no—
102#126—2021no—
103C2×C4⋊C4—1011no—
104C2×C4⋊C4—1011no—
105C2×C4⋊C4—1011no—
106C2×C22⋊C4—1011no—
107C2×C22⋊C4—1011no—
108C2×C22⋊C4#8793811yescharacteristic
109C2×C42—1011no—
110C4⋊C8—2021no—
111C4⋊C8—2021no—
112C22⋊C8—1012no—
113C22⋊C8—1012no—
114#97—2021no—
115C4×C8—2021no—
116C24C2×#8793811yescharacteristic
117C22×C4—1011no—
118C22×C4—1011no—
119C22×C4—1011no—
120C22×C4—1011no—
121C22×C4C2×#8793811yescharacteristic
122C22×C4C2×#8793811yescharacteristic
123C2×C8—2022no—
124C2×C8—2022no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—2021no—
134C22⋊C4—2021no—
135C22⋊C4—2021no—
136C22⋊C4—2021no—
137C42—1011no—
138C42—1011no—
139C42—1011no—
140C42—1011no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#8793811yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—1011no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—1011no—
153C2×C4—4041no—
154C2×C4—4041no—
155C2×C4—4041no—
156C2×C4—2021no—
157C2×C4—2021no—
158C2×C4—2022no—
159C2×C4C22⋊#8793811yescharacteristic
160C2×C4C22⋊#8793811yescharacteristic
161C8—4042no—
162C8—4042no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊#8793811yescharacteristic
170C22#1569234212yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—4041no—
175C4—4041no—
176C4—2021no—
177C4—2021no—
178C4—2021no—
179C4—2021no—
180C2—22no—
181C2—81no—
182C2#2026615011yescharacteristic
183C2#2026615711yescharacteristic
184C2#2026616311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC24×C101C2×C4
cosocleC22×Dic101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101#1473
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266197C2semidirect
2. #20266193C2semidirect
3. #20266023C2semidirect
93. C101#1473semidirect

Maximal subgroups

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

subgroupindex
#202661972
#202661932
#202660232
#202660202
C2×#156922482
#1473101