Finite Group Databasebeta

← #27169486

Subgroups — #27169486

Order 12928.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#15692245C211yesmaximal, characteristic
2#20265231C211yesmaximal, characteristic
3#20265227C211yesmaximal, characteristic
4#20264903C211yesmaximal, characteristic
5#20264902C211yesmaximal, characteristic
6#20264902C211yesmaximal, characteristic
7#324×C101C211yesmaximal, characteristic
8#15692245—21no—
9#15692245—21no—
10#15692245—21no—
11#15692245—21no—
12C2×C4⋊Dic101C411yescharacteristic
13C2×#13108053C411yescharacteristic
14C2×#13108053C411yescharacteristic
15C2×#13108053C411yescharacteristic
16C2×#13108053C2211yescharacteristic
17C2×C4×Dic101C2211yescharacteristic
18#15692184—21no—
19#15692184—21no—
20C22⋊#11717579C2211yescharacteristic
21C22⋊#11717579C2211yescharacteristic
22#15692165—21no—
23C8×Dic101—21no—
24C2×C4⋊C4×C101C2211yescharacteristic
25C22⋊C8×C101C2211yescharacteristic
26C22⋊C8×C101C2211yescharacteristic
27C22×Dic101C2×C411yescharacteristic
28C22×Dic101C2×C411yescharacteristic
29C22×Dic101C2×C411yescharacteristic
30C22×Dic101C2×C411yescharacteristic
31C2×#11717579—21no—
32C2×#11717579—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101—21no—
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—21no—
43C4×Dic101D411yescharacteristic
44C4×Dic101D411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101D411yescharacteristic
47C22×C4×C101C2×C411yescharacteristic
48C22×C4×C101C2×C411yescharacteristic
49C22×C4×C101C2311yescharacteristic
50C2×C8×C101—21no—
51C2×C8×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101—21no—
54C23×C101C22×C411yescharacteristic
55C2×C4×C101—21no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—21no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101C2×D411yescharacteristic
62C2×C4×C101C2×D411yescharacteristic
63C2×Dic101—21no—
64C2×Dic101—21no—
65C2×Dic101—22no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101—21no—
70C2×Dic101—41no—
71C2×Dic101C22⋊C411yescharacteristic
72C2×Dic101C22⋊C411yescharacteristic
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75C8×C101—41no—
76C8×C101—41no—
77#11717579—41no—
78#11717579—41no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101C2×C22⋊C411yescharacteristic
82C22×C101#13111yescharacteristic
83C22×C101#13111yescharacteristic
84C4×C101—21no—
85C4×C101—21no—
86C4×C101—41no—
87C4×C101—41no—
88Dic101—21no—
89Dic101—21no—
90Dic101—21no—
91Dic101—41no—
92Dic101—41no—
93Dic101#10112yes—
94C2×C101—21no—
95C2×C101—21no—
96C2×C101#40811yescharacteristic
97C2×C101#41011yescharacteristic
98C2×C101C2×#10111yescharacteristic
99#1470—1011nomaximal, Sylow
100C101#147011yescharacteristic, complemented, Sylow
101C2×#125—1011no—
102#432—1011no—
103#431—1011no—
104#324—1011no—
105#324—1011no—
106#324—1011no—
107#324D10111yescharacteristic
108#125—2021no—
109#125—2021no—
110#125—2021no—
111#125—2021no—
112C2×C4⋊C4—1011no—
113C2×C4⋊C4—1011no—
114C2×C4⋊C4—1011no—
115C2×C4⋊C4—1011no—
116C2×C4⋊C4—1011no—
117C2×C4⋊C4C2×D10111yescharacteristic
118C2×C42—1011no—
119C4⋊C8—2021no—
120C4⋊C8—2021no—
121C22⋊C8—1011no—
122C22⋊C8—1011no—
123C22⋊C8C2×D10111yescharacteristic
124C22⋊C8C2×D10111yescharacteristic
125#97—2021no—
126C4×C8—2021no—
127C22×C4—1011no—
128C22×C4—1011no—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4C4×D10111yescharacteristic
132C22×C4C4×D10111yescharacteristic
133C22×C4C22×D10111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—2021no—
137C2×C8—2021no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—2021no—
141C4⋊C4—2021no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4—2021no—
150C42—1011no—
151C42—1011no—
152C42—1011no—
153C42—1011no—
154C23C2×C4×D10111yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—1011no—
162C2×C4—1011no—
163C2×C4—1011no—
164C2×C4—1011no—
165C2×C4—4041no—
166C2×C4—2022no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4—2021no—
170C2×C4—2021no—
171C2×C4—2021no—
172C2×C4—2021no—
173C2×C4D4×D10111yescharacteristic
174C2×C4D4×D10111yescharacteristic
175C8—41no—
176C8—41no—
177C8—4041no—
178C8—4041no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D10111yescharacteristic
182C22#1569226111yescharacteristic
183C22#1569226311yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—1012no—
189C4—4041no—
190C4—4041no—
191C4—2021no—
192C4—2021no—
193C4—2021no—
194C2—21no—
195C2—21no—
196C2#2026514211yescharacteristic
197C2#2026514911yescharacteristic
198C2#101×D10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutator, prime radicalC23×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#324×C101C2
socleC22×C101C2×C22⋊C4
cosocleC22×C4×C101C23
hypercenter#324D101
hypocenterC101#1470
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
100. C101#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#156922452
#202652312
#202652272
#202649032
#202649022
#324×C1012
#1470101