Finite Group Databasebeta

← #27170175

Subgroups — #27170175

Order 12928.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#20265806C211yesmaximal, characteristic
2#20265513C211yesmaximal, characteristic
3#20265510C211yesmaximal, characteristic
4#20265117C211yesmaximal, characteristic
5#20264913C211yesmaximal, characteristic
6#20264902C211yesmaximal, characteristic
7#328×C101C211yesmaximal, characteristic
8#15692254—21no—
9#15692253—21no—
10#15692245—21no—
11#15692245—21no—
12#15692234C2211yescharacteristic
13#15692232—21no—
14#15692211—21no—
15C2×C4⋊Dic101C2211yescharacteristic
16C2×#13108053C2211yescharacteristic
17#15692189—21no—
18#15692188—21no—
19#15692180—21no—
20#15692179—21no—
21C22⋊#11717579C2211yescharacteristic
22#15692162—21no—
23#15692162—21no—
24C22⋊Q8×C101C2211yescharacteristic
25C22⋊C8×C101C2211yescharacteristic
26#95×C101C2211yescharacteristic
27C2×Dic202—21no—
28C2×Dic202D411yescharacteristic
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32C2×#11717579—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101—21no—
35C4⋊Dic101—21no—
36C4⋊Dic101D411yescharacteristic
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—21no—
43#13108053—21no—
44C22⋊Dic101—21no—
45C4×Dic101—21no—
46C4×Dic101—21no—
47C2×Q8×C101D411yescharacteristic
48C22×C4×C101—21no—
49C22×C4×C101C2311yescharacteristic
50C2×C8×C101—21no—
51C4⋊C4×C101—21no—
52C4⋊C4×C101D411yescharacteristic
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×C101C2×D411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C2×Dic101—21no—
65C2×Dic101—21no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101—41no—
70C2×Dic101—42no—
71C2×Dic101—41no—
72C2×Dic101Q1612yes—
73Dic202—41no—
74Dic202—81no—
75C8×C101—41no—
76#11717579—41no—
77C22×C101—21no—
78C22×C101—21no—
79C22×C101#12011yescharacteristic
80C22×C101C2×Q1611yescharacteristic
81C22×C101#13711yescharacteristic
82C4×C101—21no—
83C4×C101—21no—
84C4×C101—41no—
85C4×C101—41no—
86C4×C101—81no—
87Dic101—22no—
88Dic101—41no—
89Dic101—41no—
90Dic101—41no—
91Dic101—81no—
92C2×C101—21no—
93C2×C101—21no—
94C2×C101#45111yescharacteristic
95C2×C101#45411yescharacteristic
96C2×C101#45811yescharacteristic
97#1617—1011nomaximal, Sylow
98C101#161711yescharacteristic, complemented, Sylow
99#544—1011no—
100#484—1011no—
101#484—1011no—
102#400—1011no—
103#328—1011no—
104#328D10111yescharacteristic
105#324—1011no—
106C4⋊Q8—2021no—
107C4⋊Q8—2021no—
108#125—2021no—
109#125—2021no—
110C22⋊Q8—1011no—
111C22⋊Q8—2021no—
112C22⋊Q8C2×D10111yescharacteristic
113#117—2021no—
114C2×C4⋊C4—1011no—
115C2×C4⋊C4—1011no—
116#107—2021no—
117#107—2021no—
118#103—2021no—
119#103—2021no—
120C22⋊C8—1011no—
121C22⋊C8C2×D10111yescharacteristic
122#95—2021no—
123#95—2021no—
124#95C2×D10111yescharacteristic
125C2×Q8—1011no—
126C2×Q8—2021no—
127C2×Q8D40411yescharacteristic
128C22×C4—21no—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4—2021no—
132C22×C4C22×D10111yescharacteristic
133C2×C8—21no—
134C2×C8—2021no—
135C4⋊C4—21no—
136C4⋊C4—1011no—
137C4⋊C4—2021no—
138C4⋊C4—2021no—
139C4⋊C4—2021no—
140C4⋊C4—2021no—
141C4⋊C4—2021no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4D40411yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2021no—
150C42—2021no—
151C42—2021no—
152C23D4×D10111yescharacteristic
153Q8—41no—
154Q8—8081no—
155Q8—4041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1012no—
163C2×C4—4042no—
164C2×C4—4041no—
165C2×C4—4041no—
166C2×C4—2021no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4—2021no—
170C2×C4—2021no—
171C2×C4D4×D10111yescharacteristic
172C2×C4C2×D40411yescharacteristic
173C8—41no—
174C8—4041no—
175C22—21no—
176C22—21no—
177C22#1569222511yescharacteristic
178C22Q16×D10111yescharacteristic
179C22#1569228411yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—8081no—
186C4—4041no—
187C4—4041no—
188C4—4041no—
189C4—2022no—
190C2—21no—
191C2—21no—
192C2#2026533411yescharacteristic
193C2#2026535111yescharacteristic
194C2#2026536811yescharacteristic
subgroupG/H
centerC22#15692225
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#328×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#328D101
hypocenterC101#1617
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
98. C101#1617semidirect

Maximal subgroups

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

subgroupindex
#202658062
#202655132
#202655102
#202651172
#202649132
#202649022
#328×C1012
#1617101