Finite Group Databasebeta

← #27169681

Subgroups — #27169681

Order 12928.

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

normal subgroups only

This group has 208 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#20265729C211yesmaximal, characteristic
2#20265231C211yesmaximal, characteristic
3#20265044C211yesmaximal, characteristic
4#20264915C211yesmaximal, characteristic
5#20264914C211yesmaximal, characteristic
6#20264913C211yesmaximal, characteristic
7#328×C101C211yesmaximal, characteristic
8#15692254C411yescharacteristic, complemented
9#15692253C411yescharacteristic, complemented
10#15692245—21no—
11#15692234C2211yescharacteristic
12#15692232—21no—
13Q8×Dic101C411yescharacteristic, complemented
14#15692220—21no—
15#15692220C411yescharacteristic, complemented
16#15692211—21no—
17C2×C4×Dic101C2211yescharacteristic
18#15692184—21no—
19C22⋊#11717579C2211yescharacteristic
20#15692165—21no—
21#15692162—21no—
22#15692162—21no—
23#15692162C2211yescharacteristic
24C22⋊Q8×C101C2211yescharacteristic
25C22⋊C8×C101C2211yescharacteristic
26#95×C101C2211yescharacteristic
27C2×Dic202—21no—
28C2×Dic202C2×C411yescharacteristic
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32C2×#11717579—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101C2×C411yescharacteristic
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40C22⋊Dic101—21no—
41C4×Dic101—21no—
42C4×Dic101—21no—
43C4×Dic101C2×C411yescharacteristic
44C4×Dic101C2×C411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101D411yescharacteristic
47C2×Q8×C101C2×C411yescharacteristic
48C22×C4×C101—21no—
49C22×C4×C101C2311yescharacteristic
50C2×C8×C101—21no—
51C4⋊C4×C101—21no—
52C4⋊C4×C101C2×C411yescharacteristic
53C22⋊C4×C101—21no—
54C23×C101C2×D411yescharacteristic
55Q8×C101—41no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—41no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101C22×C411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C2×Dic101—21no—
65C2×Dic101—21no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—41no—
69C2×Dic101—41no—
70C2×Dic101—41no—
71C2×Dic101—41no—
72C2×Dic101C22⋊C411yescharacteristic
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75C2×Dic101C22⋊C411yescharacteristic
76Dic202—42no—
77Dic202—41no—
78C8×C101—41no—
79#11717579—41no—
80C22×C101—21no—
81C22×C101—21no—
82C22×C101C2×C22⋊C411yescharacteristic
83C22×C101#13711yescharacteristic
84C22×C101#13711yescharacteristic
85C4×C101—21no—
86C4×C101—21no—
87C4×C101—41no—
88C4×C101—41no—
89C4×C101—81no—
90Dic101—21no—
91Dic101—21no—
92Dic101—21no—
93Dic101—21no—
94Dic101—41no—
95Dic101—41no—
96Dic101—81no—
97C2×C101—21no—
98C2×C101—21no—
99C2×C101#41011yescharacteristic
100C2×C101#41911yescharacteristic
101C2×C101#42111yescharacteristic
102#1515—1011nomaximal, Sylow
103C101#151511yescharacteristic, complemented, Sylow
104#533—1011no—
105#432—1011no—
106#383—1011no—
107#328—1011no—
108#328—1011no—
109#328—1011no—
110#328D10111yescharacteristic
111C4⋊Q8—1011no—
112C4⋊Q8—1011no—
113#125—2021no—
114C22⋊Q8—1011no—
115C22⋊Q8—2021no—
116C22⋊Q8C2×D10111yescharacteristic
117C4×Q8—1011no—
118C4×Q8—1011no—
119C4×Q8—2021no—
120#117—2021no—
121C2×C42—1011no—
122C4⋊C8—2021no—
123C22⋊C8—1011no—
124C22⋊C8C2×D10111yescharacteristic
125#97—2021no—
126#95—1011no—
127#95—2021no—
128#95—2021no—
129#95C2×D10111yescharacteristic
130C2×Q8—1011no—
131C2×Q8—2021no—
132C2×Q8C4×D10111yescharacteristic
133C22×C4—21no—
134C22×C4—1011no—
135C22×C4—1011no—
136C22×C4—2021no—
137C22×C4C22×D10111yescharacteristic
138C2×C8—21no—
139C2×C8—2021no—
140C4⋊C4—21no—
141C4⋊C4—1011no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4C4×D10111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—2021no—
151C42—1011no—
152C42—1011no—
153C42—1011no—
154C42—1011no—
155C42—2021no—
156C42—2021no—
157C23D4×D10111yescharacteristic
158Q8—41no—
159Q8—4041no—
160Q8—4042no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—1011no—
168C2×C4—1011no—
169C2×C4—1011no—
170C2×C4—1011no—
171C2×C4—4041no—
172C2×C4—4041no—
173C2×C4—4041no—
174C2×C4—4041no—
175C2×C4—2021no—
176C2×C4—2021no—
177C2×C4—2021no—
178C2×C4—2021no—
179C2×C4C2×C4×D10111yescharacteristic
180C2×C4D4×D10111yescharacteristic
181C8—41no—
182C8—4041no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D10111yescharacteristic
186C22#1569228411yescharacteristic
187C22#1569228711yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—8081no—
194C4—4041no—
195C4—4041no—
196C4—2021no—
197C4—2021no—
198C4—2021no—
199C4—2021no—
200C2—21no—
201C2—21no—
202C2#2026514911yescharacteristic
203C2#2026518411yescharacteristic
204C2#2026519211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#328×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C2×D4
cosocleC22×C4×C101C23
hypercenter#328D101
hypocenterC101#1515
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #15692254C4semidirect
9. #15692253C4semidirect
13. Q8×Dic101C4semidirect
15. #15692220C4semidirect
103. C101#1515semidirect

Maximal subgroups

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

subgroupindex
#202657292
#202652312
#202650442
#202649152
#202649142
#202649132
#328×C1012
#1515101