Finite Group Databasebeta

← #27169694

Subgroups — #27169694

Order 12928.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#20265227C211yesmaximal, characteristic
3#20265041C211yesmaximal, 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×#13108053—21no—
18C2×C4×Dic101C2211yescharacteristic
19#15692184—21no—
20C22⋊#11717579C2211yescharacteristic
21C8×Dic101—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—
40#13108053—42no—
41C22⋊Dic101—21no—
42C4×Dic101—21no—
43C4×Dic101—21no—
44C4×Dic101C2×C411yescharacteristic
45C4×Dic101C2×C411yescharacteristic
46C4×Dic101D411yescharacteristic
47C4×Dic101D411yescharacteristic
48C2×Q8×C101C2×C411yescharacteristic
49C22×C4×C101—21no—
50C22×C4×C101C2311yescharacteristic
51C2×C8×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101C2×C411yescharacteristic
54C22⋊C4×C101—21no—
55C23×C101C2×D411yescharacteristic
56Q8×C101—41no—
57C2×C4×C101—21no—
58C2×C4×C101—21no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101—41no—
63C2×C4×C101C22×C411yescharacteristic
64C2×C4×C101C2×D411yescharacteristic
65C2×Dic101—21no—
66C2×Dic101—21no—
67C2×Dic101—41no—
68C2×Dic101—41no—
69C2×Dic101—41no—
70C2×Dic101—41no—
71C2×Dic101C22⋊C411yescharacteristic
72C2×Dic101C22⋊C411yescharacteristic
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75C2×Dic101SD1612yes—
76C2×Dic101Q1612yes—
77Dic202—42no—
78Dic202—41no—
79C8×C101—41no—
80#11717579—41no—
81C22×C101—21no—
82C22×C101—21no—
83C22×C101C2×C22⋊C411yescharacteristic
84C22×C101C2×SD1611yescharacteristic
85C22×C101C2×Q1611yescharacteristic
86C4×C101—21no—
87C4×C101—21no—
88C4×C101—41no—
89C4×C101—41no—
90C4×C101—81no—
91Dic101—21no—
92Dic101—21no—
93Dic101—41no—
94Dic101—41no—
95Dic101—81no—
96Dic101#10312yes—
97Dic101#10312yes—
98C2×C101—21no—
99C2×C101—21no—
100C2×C101#41011yescharacteristic
101C2×C101C2×#10311yescharacteristic
102C2×C101#42111yescharacteristic
103#1518—1011nomaximal, Sylow
104C101#151811yescharacteristic, complemented, Sylow
105#533—1011no—
106#431—1011no—
107#382—1011no—
108#328—1011no—
109#328—1011no—
110#328—1011no—
111#328D10111yescharacteristic
112C4⋊Q8—1011no—
113C4⋊Q8—1011no—
114#125—2021no—
115C22⋊Q8—1011no—
116C22⋊Q8—2021no—
117C22⋊Q8C2×D10111yescharacteristic
118C4×Q8—1011no—
119C4×Q8—1011no—
120C4×Q8—2021no—
121#117—2021no—
122C2×C4⋊C4—2021no—
123C2×C42—1011no—
124C4⋊C8—2021no—
125C22⋊C8—1011no—
126C22⋊C8C2×D10111yescharacteristic
127C4×C8—2021no—
128#95—1011no—
129#95—2021no—
130#95C2×D10111yescharacteristic
131C2×Q8—1011no—
132C2×Q8—2021no—
133C2×Q8C4×D10111yescharacteristic
134C22×C4—21no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—2021no—
138C22×C4C22×D10111yescharacteristic
139C2×C8—21no—
140C2×C8—2021no—
141C4⋊C4—21no—
142C4⋊C4—1011no—
143C4⋊C4—4042no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4—2021no—
150C4⋊C4C4×D10111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2021no—
153C42—1011no—
154C42—1011no—
155C42—1011no—
156C42—1011no—
157C42—2021no—
158C42—2021no—
159C23D4×D10111yescharacteristic
160Q8—41no—
161Q8—4041no—
162Q8—4042no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—1011no—
170C2×C4—1011no—
171C2×C4—1012no—
172C2×C4—1012no—
173C2×C4—1011no—
174C2×C4—1011no—
175C2×C4—4041no—
176C2×C4—4041no—
177C2×C4—4041no—
178C2×C4—4041no—
179C2×C4—2021no—
180C2×C4—2021no—
181C2×C4C2×C4×D10111yescharacteristic
182C2×C4D4×D10111yescharacteristic
183C8—41no—
184C8—4041no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D10111yescharacteristic
188C22SD16×D10111yescharacteristic
189C22Q16×D10111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—8081no—
196C4—1012no—
197C4—1012no—
198C4—4041no—
199C4—4041no—
200C4—2021no—
201C4—2021no—
202C2—21no—
203C2—21no—
204C2#2026514911yescharacteristic
205C2#103×D10111yescharacteristic
206C2#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#1518
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
104. C101#1518semidirect

Maximal subgroups

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

subgroupindex
#202657292
#202652272
#202650412
#202649152
#202649142
#202649132
#328×C1012
#1518101