Finite Group Databasebeta

← #27169834

Subgroups — #27169834

Order 12928.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#20265725C211yesmaximal, characteristic
2#20265233C211yesmaximal, characteristic, complemented
3#20265229C211yesmaximal, characteristic, complemented
4#20264924C211yesmaximal, characteristic, complemented
5#20264922C211yesmaximal, characteristic, complemented
6#20264921C211yesmaximal, characteristic, complemented
7#331×C101C211yesmaximal, characteristic, complemented
8C2×#13108073—21no—
9#15692255C2211yescharacteristic
10#15692242—21no—
11#15692226—21no—
12#15692226C412yes—
13D4×Dic101—21no—
14D4×Dic101C412yes—
15C42×D101C2211yescharacteristic
16C4⋊#11717579C2211yescharacteristic
17C4⋊#11717579C2211yescharacteristic
18#15692167—21no—
19#15692167—21no—
20#15692165—21no—
21C8×Dic101—21no—
22#127×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24C4⋊C8×C101C2211yescharacteristic
25#13108073—42no—
26#13108073—42no—
27C2×Dic202—21no—
28C2×C22⋊D101—22no—
29C22×Dic101—22no—
30C2×C4×D101C2×C411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×#11717579—21no—
34C2×#11717579—21no—
35C4⋊Dic101—21no—
36C4⋊Dic101C2×C412yes—
37C22⋊Dic101—22no—
38C22⋊Dic101—22no—
39C4×Dic101C2×C411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C2×D4×C101—21no—
43C2×D4×C101—21no—
44C2×D4×C101C2×C412yes—
45C2×C8×C101—21no—
46C2×C8×C101—21no—
47C42×C101C2311yescharacteristic
48C23×C101—22no—
49C22×D101C22⋊C411yescharacteristic
50D4×C101—42no—
51D4×C101—41no—
52D4×C101—41no—
53D4×C101—41no—
54D4×C101—41no—
55C2×C4×C101C22×C411yescharacteristic
56C2×C4×C101C2×D411yescharacteristic
57C2×C4×C101C2×D411yescharacteristic
58C22⋊D101—44no—
59C2×Dic101—22no—
60C2×Dic101—44no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C22⋊C411yescharacteristic
64C4×D101—21no—
65C4×D101—21no—
66C4×D101—21no—
67C4×D101—21no—
68C4×D101—41no—
69Dic202—41no—
70Dic202—41no—
71C8×C101—41no—
72C8×C101—41no—
73#11717579—41no—
74#11717579—41no—
75C22×C101—42no—
76C22×C101—42no—
77C22×C101—42no—
78C22×C101C2×C22⋊C411yescharacteristic
79C2×D101—21no—
80C2×D101—21no—
81C2×D101—21no—
82C4×C101—21no—
83C4×C101#13511yescharacteristic
84C4×C101#13511yescharacteristic
85C4×C101AGL(1,ℤ/8)11yescharacteristic
86C4×C101AGL(1,ℤ/8)11yescharacteristic
87Dic101—21no—
88Dic101—21no—
89Dic101—21no—
90Dic101—42no—
91C2×C101—82no—
92C2×C101#41311yescharacteristic
93C2×C101#41611yescharacteristic
94C2×C101#41811yescharacteristic
95D101—41no—
96#1553—1011nomaximal, Sylow
97C101#155311yescharacteristic, complemented, Sylow
98#532—1011no—
99#432—1011no—
100#431—1011no—
101#332—1011no—
102#332—1011no—
103#331—1011no—
104#331D10111yescharacteristic, complemented
105C2×#41—2021no—
106C4⋊Q8—1011no—
107#127C2×D10111yescharacteristic
108#124—2021no—
109#121—1012no—
110#121—2021no—
111C4×D4—1012no—
112C4×D4—2021no—
113C2×C42—1011no—
114C4⋊C8—1011no—
115C4⋊C8—1011no—
116C4⋊C8C2×D10111yescharacteristic
117C4⋊C8C2×D10111yescharacteristic
118C22⋊C8—2021no—
119C22⋊C8—2021no—
120#97—2021no—
121C4×C8—2021no—
122#41—4042no—
123#41—4042no—
124C2×Q8—2021no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2022no—
128C2×D4C4×D10112yes—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4—1011no—
132C22×C4—2022no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2021no—
136C2×C8—2021no—
137C4⋊C4—1012no—
138C4⋊C4—2021no—
139C22⋊C4—2022no—
140C22⋊C4—2022no—
141C42—1011no—
142C42—1011no—
143C42—1011no—
144C42C22×D10111yescharacteristic
145C23—22no—
146C23—1011no—
147Q8—4041no—
148Q8—4041no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—4044no—
155C2×C4—1011no—
156C2×C4—1011no—
157C2×C4—1011no—
158C2×C4—4041no—
159C2×C4—4044no—
160C2×C4—2022no—
161C2×C4—2021no—
162C2×C4—2021no—
163C2×C4—2021no—
164C2×C4—2021no—
165C2×C4C2×C4×D10111yescharacteristic
166C2×C4D4×D10111yescharacteristic
167C2×C4D4×D10111yescharacteristic
168C8—41no—
169C8—41no—
170C8—4041no—
171C8—4041no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—2021no—
176C22—2021no—
177C22—2021no—
178C22C22⋊C4×D10111yescharacteristic
179C4—21no—
180C4—4042no—
181C4—2021no—
182C4—2021no—
183C4—2021no—
184C4#1569227411yescharacteristic
185C4#1569227611yescharacteristic
186C4#1569227911yescharacteristic
187C4#1569228211yescharacteristic
188C2—82no—
189C2—4041no—
190C2#2026515811yescharacteristic
191C2#2026517011yescharacteristic
192C2#2026518011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#331×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265725C2
cosocleC42×C101C23
hypercenter#331D101
hypocenterC101#1553
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20265233C2semidirect
3. #20265229C2semidirect
4. #20264924C2semidirect
5. #20264922C2semidirect
6. #20264921C2semidirect
7. #331×C101C2semidirect
97. C101#1553semidirect
104. #331D101semidirect

Maximal subgroups

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

subgroupindex
#202657252
#202652332
#202652292
#202649242
#202649222
#202649212
#331×C1012
#1553101