Finite Group Databasebeta

← #27169717

Subgroups — #27169717

Order 12928.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#20265706C211yesmaximal, characteristic
2#20265129C211yesmaximal, characteristic, complemented
3#97×D101C211yesmaximal, characteristic, complemented
4#20264918C211yesmaximal, characteristic, complemented
5#20264918C211yesmaximal, characteristic, complemented
6#20264917C211yesmaximal, characteristic, complemented
7#329×C101C211yesmaximal, characteristic, complemented
8C2×#13108057—21no—
9C2×C8×D101—21no—
10#15692248—21no—
11#15692247C2211yescharacteristic
12#15692237—21no—
13#15692231C411yescharacteristic
14#15692226C411yescharacteristic
15Q8×Dic101C411yescharacteristic
16D4×Dic101C411yescharacteristic
17#15692215—21no—
18#15692211—21no—
19C42×D101C2211yescharacteristic
20#15692166C2211yescharacteristic
21#15692166C2211yescharacteristic
22#15692165—21no—
23C8×Dic101—21no—
24#124×C101C2211yescharacteristic
25#97×C101C2211yescharacteristic
26#97×C101C2211yescharacteristic
27C2×C22⋊D101—21no—
28C22×Dic101—21no—
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32#13108057—24no—
33C2×#11717579—21no—
34C2×#11717579—21no—
35C8×D101—24no—
36C4⋊Dic101—21no—
37C4⋊Dic101C2×C411yescharacteristic
38C4⋊Dic101C2×C411yescharacteristic
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42C22⋊Dic101—21no—
43C22⋊Dic101—21no—
44#13108051—21no—
45C4×Dic101—21no—
46C4×Dic101C2×C411yescharacteristic
47C4×Dic101D411yescharacteristic
48C4×Dic101D411yescharacteristic
49C2×Q8×C101C2×C411yescharacteristic
50C2×D4×C101C2×C411yescharacteristic
51C2×C8×C101—21no—
52C2×C8×C101—21no—
53C22⋊C4×C101—21no—
54C22⋊C4×C101—21no—
55C42×C101C2311yescharacteristic
56C23×C101—21no—
57C22×D101C22⋊C411yescharacteristic
58Q8×C101—41no—
59D4×C101—41no—
60C2×C4×C101—21no—
61C2×C4×C101C22×C411yescharacteristic
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C22⋊D101—42no—
65C2×Dic101—21no—
66C2×Dic101—21no—
67C2×Dic101—42no—
68C2×Dic101C22⋊C411yescharacteristic
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C22⋊C411yescharacteristic
71C4×D101—22no—
72C4×D101—22no—
73C4×D101—41no—
74C8×C101—22no—
75C8×C101—22no—
76#11717579—22no—
77#11717579—22no—
78C22×C101—41no—
79C22×C101—41no—
80C22×C101—41no—
81C22×C101C2×C22⋊C411yescharacteristic
82C2×D101—21no—
83C2×D101—21no—
84C2×D101#10412yes—
85C4×C101—21no—
86C4×C101—21no—
87C4×C101—21no—
88C4×C101—41no—
89Dic101—21no—
90Dic101—21no—
91Dic101—41no—
92Dic101—41no—
93Dic101#10412yes—
94C2×C101—81no—
95C2×C101#41311yescharacteristic
96C2×C101C2×#10411yescharacteristic
97C2×C101C2×#10411yescharacteristic
98D101—22no—
99#1524—1011nomaximal, Sylow
100C101#152411yescharacteristic, complemented, Sylow
101#529—1011no—
102C4×M16—1011no—
103C2×#97—1011no—
104#330—1011no—
105#330—1011no—
106#329—1011no—
107#329D10111yescharacteristic, complemented
108C2×M16—2021no—
109C22×C8—2021no—
110#126—2021no—
111#125—1011no—
112#124C2×D10111yescharacteristic
113#123—2021no—
114C22⋊Q8—1011no—
115#121—1011no—
116C4×Q8—1011no—
117C4×D4—1011no—
118C4×D4—2021no—
119#117—2021no—
120C2×C42—1011no—
121#97—1011no—
122#97—1011no—
123#97—2021no—
124#97C2×D10111yescharacteristic
125#97C2×D10111yescharacteristic
126C4×C8—2021no—
127C2×Q8C4×D10111yescharacteristic
128C2×D4—2021no—
129C2×D4C4×D10111yescharacteristic
130C22×C4—1011no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—2021no—
134M16—2024no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—2024no—
138C2×C8—2021no—
139C2×C8—2021no—
140C4⋊C4—1011no—
141C4⋊C4—1011no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C22⋊C4—21no—
147C22⋊C4—21no—
148C22⋊C4—2021no—
149C22⋊C4—2021no—
150C22⋊C4—2021no—
151C42—1011no—
152C42—1011no—
153C42—1011no—
154C42—2021no—
155C42C22×D10111yescharacteristic
156C23—21no—
157C23—1011no—
158Q8—41no—
159D4—41no—
160D4—4042no—
161C2×C4—21no—
162C2×C4—1011no—
163C2×C4—1011no—
164C2×C4—1011no—
165C2×C4—4041no—
166C2×C4—4042no—
167C2×C4—2022no—
168C2×C4—2022no—
169C2×C4—2021no—
170C2×C4—2021no—
171C2×C4C2×C4×D10111yescharacteristic
172C2×C4D4×D10111yescharacteristic
173C2×C4D4×D10111yescharacteristic
174C8—22no—
175C8—22no—
176C8—2022no—
177C8—2022no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1012no—
182C22—2021no—
183C22—2021no—
184C22C22⋊C4×D10111yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—1012no—
190C4—4041no—
191C4—4041no—
192C4—2021no—
193C4—2021no—
194C2—81no—
195C2—2022no—
196C2#2026515811yescharacteristic
197C2#104×D10111yescharacteristic
198C2#104×D10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#329×C101C2
socleC22×C101C2×C22⋊C4
prime radical#15692226C4
cosocleC42×C101C23
hypercenter#329D101
hypocenterC101#1524
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20265129C2semidirect
3. #97×D101C2semidirect
4. #20264918C2semidirect
5. #20264918C2semidirect
6. #20264917C2semidirect
7. #329×C101C2semidirect
100. C101#1524semidirect
107. #329D101semidirect

Maximal subgroups

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

subgroupindex
#202657062
#202651292
#97×D1012
#202649182
#202649172
#329×C1012
#1524101