Finite Group Databasebeta

← #27170094

Subgroups — #27170094

Order 12928.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#20265776C211yesmaximal, characteristic
2#20265316C211yesmaximal, characteristic
3#20265096C211yesmaximal, characteristic, complemented
4#20264914C211yesmaximal, characteristic, complemented
5#20264912C211yesmaximal, characteristic
6#20264902C211yesmaximal, characteristic, complemented
7#451×C101C211yesmaximal, characteristic, complemented
8C2×#13108061—21no—
9#15692250—21no—
10#15692246—21no—
11#15692240—21no—
12#15692239—21no—
13#15692231—21no—
14#15692229C2211yescharacteristic
15#15692215—21no—
16C2×#13108053—21no—
17C2×#13108053C2211yescharacteristic
18#15692179—21no—
19C22⋊#11717579C2211yescharacteristic
20#15692162—21no—
21#15692162C2211yescharacteristic
22C22×Q8×C101C2211yescharacteristic
23C2×Q16×C101—21no—
24C22⋊Q8×C101C2211yescharacteristic
25#103×C101—21no—
26C22⋊C8×C101C2211yescharacteristic
27C2×D404D411yescharacteristic
28C2×C22⋊D101—21no—
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32C2×C4×D101—21no—
33#13108061—42no—
34C2×#11717579—21no—
35C4⋊Dic101—21no—
36C4⋊Dic101—21no—
37C4⋊Dic101D411yescharacteristic
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—42no—
42#13108051—21no—
43#13108051—21no—
44#13108051—21no—
45#13108051—21no—
46C4×Dic101—21no—
47C2×Q8×C101—21no—
48C2×Q8×C101—21no—
49C2×Q8×C101—42no—
50C2×Q8×C101D411yescharacteristic
51C22×C4×C101—21no—
52C22×C4×C101C2311yescharacteristic
53Q16×C101—42no—
54C2×C8×C101—21no—
55C4⋊C4×C101—21no—
56C4⋊C4×C101D411yescharacteristic
57C22⋊C4×C101—21no—
58C23×C101C2×D411yescharacteristic
59C22×D101—21no—
60Q8×C101—22no—
61Q8×C101—22no—
62Q8×C101—41no—
63Q8×C101—41no—
64Q8×C101—41no—
65C2×C4×C101—22no—
66C2×C4×C101—21no—
67C2×C4×C101—21no—
68C2×C4×C101—41no—
69C2×C4×C101—41no—
70C2×C4×C101—41no—
71C2×C4×C101C2×D411yescharacteristic
72C2×C4×C101C2×D411yescharacteristic
73C22⋊D101—41no—
74C22⋊D101—41no—
75C2×Dic101—22no—
76C2×Dic101—21no—
77C2×Dic101—21no—
78C2×Dic101—21no—
79C2×Dic101—21no—
80C2×Dic101—21no—
81C2×Dic101—41no—
82C2×Dic101—41no—
83C2×Dic101—41no—
84D404—41no—
85C4×D101—81no—
86C8×C101—41no—
87#11717579—41no—
88C22×C101—21no—
89C22×C101—21no—
90C22×C101#12011yescharacteristic
91C22×C101#13511yescharacteristic
92C22×C101#13711yescharacteristic
93C2×D101—41no—
94C2×D101—41no—
95C2×D101—41no—
96C4×C101—21no—
97C4×C101—21no—
98C4×C101—41no—
99C4×C101—41no—
100C4×C101—42no—
101Dic101—42no—
102Dic101—41no—
103Dic101—41no—
104Dic101—41no—
105C2×C101—21no—
106C2×C101—21no—
107C2×C101#45211yescharacteristic
108C2×C101#45611yescharacteristic
109C2×C101B(4,𝔽2)11yescharacteristic
110D101—81no—
111#1603—1011nomaximal, Sylow
112C101#160311yescharacteristic, complemented, Sylow
113#539—1011no—
114#451D10111yescharacteristic, complemented
115#448—1011no—
116#395—1011no—
117#328—1011no—
118#327—1011no—
119#324—1011no—
120C22×Q8C2×D10111yescharacteristic
121C2×Q16—21no—
122C2×SD16—2021no—
123#126—2021no—
124#125—2021no—
125#123—2021no—
126#123—2021no—
127C22⋊Q8—2021no—
128C22⋊Q8C2×D10111yescharacteristic
129#121—1011no—
130C4×D4—2021no—
131C2×C4⋊C4—1011no—
132C2×C4⋊C4—2021no—
133#103—21no—
134#103—2021no—
135C22⋊C8—1011no—
136C22⋊C8C2×D10111yescharacteristic
137#95—1011no—
138#95—2021no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8C22⋊D10111yescharacteristic
143C2×D4—1011no—
144C2×D4—2021no—
145C22×C4—21no—
146C22×C4—1011no—
147C22×C4—1011no—
148C22×C4—2021no—
149C22×C4—2021no—
150C22×C4C22×D10111yescharacteristic
151Q16—42no—
152SD16—4042no—
153C2×C8—21no—
154C2×C8—2021no—
155C4⋊C4—21no—
156C4⋊C4—1011no—
157C4⋊C4—4042no—
158C4⋊C4—2021no—
159C4⋊C4—2021no—
160C4⋊C4—2021no—
161C4⋊C4—2021no—
162C4⋊C4—2021no—
163C4⋊C4C22⋊D10111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2021no—
166C22⋊C4—2021no—
167C22⋊C4—2021no—
168C22⋊C4—2021no—
169C42—2021no—
170C23—2021no—
171C23D4×D10111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—4041no—
178D4—4041no—
179D4—4041no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—8081no—
187C2×C4—4041no—
188C2×C4—4041no—
189C2×C4—4041no—
190C2×C4—2022no—
191C2×C4—2021no—
192C2×C4—2021no—
193C2×C4—2021no—
194C2×C4—2021no—
195C2×C4—2021no—
196C2×C4D4×D10111yescharacteristic
197C2×C4C2×C22⋊D10111yescharacteristic
198C8—41no—
199C8—4041no—
200C22—21no—
201C22—21no—
202C22—4041no—
203C22—4041no—
204C22—4041no—
205C22#1569222311yescharacteristic
206C22#1569227811yescharacteristic
207C22#1569228711yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—41no—
213C4—4042no—
214C4—4041no—
215C4—4041no—
216C4—4041no—
217C2—21no—
218C2—21no—
219C2—8081no—
220C2#2026533811yescharacteristic
221C2#2026535811yescharacteristic
222C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#451×C101C2
socleC22×C101#120
prime radical#15692229C22
hypercenter#451D101
hypocenterC101#1603
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20265096C2semidirect
4. #20264914C2semidirect
6. #20264902C2semidirect
7. #451×C101C2semidirect
112. C101#1603semidirect
114. #451D101semidirect

Maximal subgroups

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

subgroupindex
#202657762
#202653162
#202650962
#202649142
#202649122
#202649022
#451×C1012
#1603101