Finite Group Databasebeta

← #27169762

Subgroups — #27169762

Order 12928.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#20265712C211yesmaximal, characteristic
2#20265232C211yesmaximal, characteristic, complemented
3#20265232C211yesmaximal, characteristic, complemented
4#20264919C211yesmaximal, characteristic, complemented
5#20264916C211yesmaximal, characteristic, complemented
6#20264916C211yesmaximal, characteristic, complemented
7#330×C101C211yesmaximal, characteristic, complemented
8#15692250—21no—
9#15692243C2211yescharacteristic
10#15692240—21no—
11#15692235C411yescharacteristic
12#15692230C411yescharacteristic
13#15692220C411yescharacteristic
14#15692217—21no—
15#15692217C411yescharacteristic
16#15692213—21no—
17C42×D101C2211yescharacteristic
18#15692184—21no—
19#15692184—21no—
20#15692167—21no—
21#15692167—21no—
22#15692166C2211yescharacteristic
23#15692166C2211yescharacteristic
24#125×C101C2211yescharacteristic
25#97×C101C2211yescharacteristic
26#97×C101C2211yescharacteristic
27C2×Dic202C2×C411yescharacteristic
28C2×D404—21no—
29C2×D404C2×C411yescharacteristic
30C2×C4×D101—21no—
31C2×C4×D101C2×C411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×#11717579—21no—
35C2×#11717579—21no—
36C4⋊Dic101—21no—
37#13108053—21no—
38#13108051—21no—
39#13108051—21no—
40#13108051—21no—
41#13108051—21no—
42#13108051—21no—
43C4×Dic101—21no—
44C4×Dic101C2×C411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101D411yescharacteristic
47C2×C8×C101—21no—
48C2×C8×C101—21no—
49C4⋊C4×C101—21no—
50C4⋊C4×C101—21no—
51C4⋊C4×C101C2×C411yescharacteristic
52C4⋊C4×C101C2×C411yescharacteristic
53C42×C101C2311yescharacteristic
54C22×D101—21no—
55C22×D101C22⋊C411yescharacteristic
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101C22×C411yescharacteristic
59C2×C4×C101C2×D411yescharacteristic
60C2×C4×C101C2×D411yescharacteristic
61C2×Dic101—21no—
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C22⋊C411yescharacteristic
65D404—41no—
66D404—42no—
67C4×D101—41no—
68C4×D101—41no—
69C4×D101—41no—
70C4×D101—42no—
71Dic202—41no—
72C8×C101—41no—
73C8×C101—41no—
74#11717579—41no—
75#11717579—41no—
76C22×C101C2×C22⋊C411yescharacteristic
77C2×D101—21no—
78C2×D101—21no—
79C2×D101—21no—
80C2×D101—41no—
81C2×D101—41no—
82C2×D101—41no—
83C4×C101—21no—
84C4×C101—21no—
85C4×C101—21no—
86C4×C101—41no—
87C4×C101—41no—
88Dic101—21no—
89Dic101—21no—
90Dic101—21no—
91Dic101—41no—
92C2×C101#41311yescharacteristic
93C2×C101#42111yescharacteristic
94C2×C101#42111yescharacteristic
95D101—41no—
96D101—81no—
97#1535—1011nomaximal, Sylow
98C101#153511yescharacteristic, complemented, Sylow
99#529—1011no—
100#432—1011no—
101#432—1011no—
102#330—1011no—
103#330D10111yescharacteristic, complemented
104#329—1011no—
105#329—1011no—
106#126—2021no—
107#125C2×D10111yescharacteristic
108#124—1011no—
109#123—2021no—
110C22⋊Q8—1011no—
111#121—1011no—
112C4×Q8—1011no—
113C4×D4—1011no—
114C4×D4—2021no—
115#117—2021no—
116C2×C42—1011no—
117C4⋊C8—2021no—
118C4⋊C8—2021no—
119C22⋊C8—2021no—
120C22⋊C8—2021no—
121#97—1011no—
122#97—1011no—
123#97C2×D10111yescharacteristic
124#97C2×D10111yescharacteristic
125C2×Q8—1011no—
126C2×D4—1011no—
127C2×D4—2021no—
128C22×C4—1011no—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4—2021no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—2021no—
135C2×C8—2021no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2021no—
139C4⋊C4—2021no—
140C4⋊C4C4×D10111yescharacteristic
141C4⋊C4C4×D10111yescharacteristic
142C22⋊C4—2021no—
143C22⋊C4—2021no—
144C22⋊C4—2021no—
145C22⋊C4—2021no—
146C22⋊C4—2021no—
147C42—1011no—
148C42—1011no—
149C42—1011no—
150C42—2021no—
151C42C22×D10111yescharacteristic
152C23—1011no—
153C23—2021no—
154Q8—4041no—
155D4—4041no—
156D4—4042no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1011no—
160C2×C4—1011no—
161C2×C4—1011no—
162C2×C4—4041no—
163C2×C4—4041no—
164C2×C4—4041no—
165C2×C4—4042no—
166C2×C4—2021no—
167C2×C4C2×C4×D10111yescharacteristic
168C2×C4D4×D10111yescharacteristic
169C2×C4D4×D10111yescharacteristic
170C8—41no—
171C8—41no—
172C8—4041no—
173C8—4041no—
174C22—4041no—
175C22—4041no—
176C22—4041no—
177C22—2021no—
178C22—2021no—
179C22—2021no—
180C22C22⋊C4×D10111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—4041no—
187C4—2021no—
188C4—2021no—
189C4—2021no—
190C2—8081no—
191C2—4041no—
192C2#2026516011yescharacteristic
193C2#2026519211yescharacteristic
194C2#2026519211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#330×C101C2
socleC22×C101C2×C22⋊C4
prime radical#15692230C4
cosocleC42×C101C23
hypercenter#330D101
hypocenterC101#1535
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20265232C2semidirect
3. #20265232C2semidirect
4. #20264919C2semidirect
5. #20264916C2semidirect
6. #20264916C2semidirect
7. #330×C101C2semidirect
98. C101#1535semidirect
103. #330D101semidirect

Maximal subgroups

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

subgroupindex
#202657122
#202652322
#202649192
#202649162
#330×C1012
#1535101