Finite Group Databasebeta

← #27169500

Subgroups — #27169500

Order 12928.

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

normal subgroups only

This group has 214 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
1C2×#15692250C211yesmaximal, characteristic
2#20265231C211yesmaximal, characteristic, complemented
3#20265227C211yesmaximal, characteristic, complemented
4#20264903C211yesmaximal, characteristic, complemented
5#20264900C211yesmaximal, characteristic
6#20264900C211yesmaximal, characteristic
7#324×C101C211yesmaximal, characteristic, complemented
8#15692250—21no—
9#15692250—21no—
10#15692250—21no—
11#15692250—21no—
12C2×C4⋊Dic101C411yescharacteristic
13C2×#13108053C411yescharacteristic
14C2×#13108051C411yescharacteristic
15C2×#13108051C411yescharacteristic
16C2×#13108051C2211yescharacteristic
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
27C23×D101C2×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#13108051—21no—
38#13108051—21no—
39#13108051—21no—
40#13108051—21no—
41#13108051—21no—
42#13108051—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
55C22×D101—21no—
56C22×D101—21no—
57C22×D101—21no—
58C22×D101—41no—
59C22×D101—41no—
60C2×C4×C101—21no—
61C2×C4×C101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—41no—
65C2×C4×C101—41no—
66C2×C4×C101C2×D411yescharacteristic
67C2×C4×C101C2×D411yescharacteristic
68C2×Dic101—21no—
69C2×Dic101—21no—
70C2×Dic101—21no—
71C2×Dic101—41no—
72C2×Dic101—41no—
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75C2×Dic101C22⋊C411yescharacteristic
76C2×Dic101C22⋊C411yescharacteristic
77C8×C101—41no—
78C8×C101—41no—
79#11717579—41no—
80#11717579—41no—
81C22×C101—21no—
82C22×C101—21no—
83C22×C101C2×C22⋊C411yescharacteristic
84C22×C101#13111yescharacteristic
85C22×C101#13111yescharacteristic
86C2×D101—41no—
87C2×D101—41no—
88C2×D101—41no—
89C2×D101—81no—
90C2×D101—81no—
91C4×C101—21no—
92C4×C101—21no—
93C4×C101—41no—
94C4×C101—41no—
95Dic101—21no—
96Dic101—21no—
97Dic101—21no—
98Dic101—21no—
99Dic101—41no—
100C2×C101—21no—
101C2×C101—21no—
102C2×C101#40811yescharacteristic
103C2×C101#41011yescharacteristic
104C2×C101#41311yescharacteristic
105D101—81no—
106#1473—1011nomaximal, Sylow
107C101#147311yescharacteristic, complemented, Sylow
108C2×#126—1011no—
109#432—1011no—
110#431—1011no—
111#324—1011no—
112#324D10111yescharacteristic, complemented
113#323—1011no—
114#323—1011no—
115#126—2021no—
116#126—2021no—
117#126—2021no—
118#126—2021no—
119C2×C4⋊C4—1011no—
120C2×C4⋊C4—1011no—
121C2×C4⋊C4C2×D10111yescharacteristic
122C2×C22⋊C4—1011no—
123C2×C22⋊C4—1011no—
124C2×C22⋊C4—1011no—
125C2×C42—1011no—
126C4⋊C8—2021no—
127C4⋊C8—2021no—
128C22⋊C8—1011no—
129C22⋊C8—1011no—
130C22⋊C8C2×D10111yescharacteristic
131C22⋊C8C2×D10111yescharacteristic
132#97—2021no—
133C4×C8—2021no—
134C24—1011no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—1011no—
138C22×C4C4×D10111yescharacteristic
139C22×C4C4×D10111yescharacteristic
140C22×C4C22×D10111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—2021no—
144C2×C8—2021no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4—2021no—
150C4⋊C4—2021no—
151C22⋊C4—2021no—
152C22⋊C4—2021no—
153C22⋊C4—2021no—
154C22⋊C4—2021no—
155C22⋊C4—2021no—
156C22⋊C4—2021no—
157C42—1011no—
158C42—1011no—
159C42—1011no—
160C42—1011no—
161C23—4041no—
162C23—4041no—
163C23—2021no—
164C23—2021no—
165C23—2021no—
166C23C2×C4×D10111yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1011no—
174C2×C4—1011no—
175C2×C4—1011no—
176C2×C4—1011no—
177C2×C4—4041no—
178C2×C4—4041no—
179C2×C4—2021no—
180C2×C4—2021no—
181C2×C4—2021no—
182C2×C4D4×D10111yescharacteristic
183C2×C4D4×D10111yescharacteristic
184C8—41no—
185C8—41no—
186C8—4041no—
187C8—4041no—
188C22—21no—
189C22—21no—
190C22—8081no—
191C22—8081no—
192C22—4041no—
193C22—4041no—
194C22—4041no—
195C22C22⋊C4×D10111yescharacteristic
196C22#1569226111yescharacteristic
197C22#1569226311yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—4041no—
203C4—2021no—
204C4—2021no—
205C4—2021no—
206C4—2021no—
207C2—21no—
208C2—21no—
209C2—8081no—
210C2#2026514211yescharacteristic
211C2#2026514911yescharacteristic
212C2#2026516011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC23×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#324×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC23×D101C2×C4
cosocleC22×C4×C101C23
hypercenter#324D101
hypocenterC101#1473
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
2. #20265231C2semidirect
3. #20265227C2semidirect
4. #20264903C2semidirect
7. #324×C101C2semidirect
107. C101#1473semidirect
112. #324D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922502
#202652312
#202652272
#202649032
#202649002
#324×C1012
#1473101