Finite Group Databasebeta

← #27170104

Subgroups — #27170104

Order 12928.

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

normal subgroups only

This group has 238 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#20265333C211yesmaximal, characteristic
3#20265096C211yesmaximal, characteristic
4#20264915C211yesmaximal, characteristic
5#20264914C211yesmaximal, characteristic
6#20264902C211yesmaximal, characteristic
7#451×C101C211yesmaximal, characteristic
8C2×#13108064—21no—
9#15692254—21no—
10#15692253—21no—
11#15692245—21no—
12#15692245—21no—
13#15692234C2211yescharacteristic
14#15692232—21no—
15#15692211—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×Dic202—21no—
28C2×Dic202D411yescharacteristic
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32#13108064—42no—
33C2×#11717579—21no—
34C4⋊Dic101—21no—
35C4⋊Dic101D411yescharacteristic
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—21no—
43#13108053—42no—
44C22⋊Dic101—21no—
45C4×Dic101—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
59Q8×C101—22no—
60Q8×C101—22no—
61Q8×C101—41no—
62Q8×C101—41no—
63Q8×C101—41no—
64C2×C4×C101—22no—
65C2×C4×C101—21no—
66C2×C4×C101—21no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101—41no—
70C2×C4×C101C2×D411yescharacteristic
71C2×C4×C101C2×D411yescharacteristic
72C2×Dic101—21no—
73C2×Dic101—21no—
74C2×Dic101—22no—
75C2×Dic101—21no—
76C2×Dic101—21no—
77C2×Dic101—21no—
78C2×Dic101—41no—
79C2×Dic101—41no—
80C2×Dic101—41no—
81C2×Dic101Q1612yescomplemented
82Dic202—41no—
83Dic202—81no—
84C8×C101—41no—
85#11717579—41no—
86C22×C101—21no—
87C22×C101—21no—
88C22×C101#12011yescharacteristic
89C22×C101C2×Q1611yescharacteristic
90C22×C101#13711yescharacteristic
91C4×C101—21no—
92C4×C101—21no—
93C4×C101—41no—
94C4×C101—41no—
95C4×C101—42no—
96Dic101—22no—
97Dic101—42no—
98Dic101—41no—
99Dic101—41no—
100Dic101—41no—
101C2×C101—21no—
102C2×C101—21no—
103C2×C101#45111yescharacteristic
104C2×C101#45611yescharacteristic
105C2×C101B(4,𝔽2)11yescharacteristic
106#1605—1011nomaximal, Sylow
107C101#160511yescharacteristic, complemented, Sylow
108#544—1011no—
109#451—1011no—
110#451D10111yescharacteristic
111#395—1011no—
112#328—1011no—
113#328—1011no—
114#324—1011no—
115C22×Q8C2×D10111yescharacteristic
116C2×Q16—21no—
117C2×Q16—2021no—
118C4⋊Q8—2021no—
119C4⋊Q8—2021no—
120#125—2021no—
121#125—2021no—
122C22⋊Q8—1011no—
123C22⋊Q8—2021no—
124C22⋊Q8C2×D10111yescharacteristic
125#117—2021no—
126C2×C4⋊C4—1011no—
127C2×C4⋊C4—2021no—
128#103—21no—
129#103—2021no—
130C22⋊C8—1011no—
131C22⋊C8C2×D10111yescharacteristic
132#95—1011no—
133#95—2021no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—1011no—
138C2×Q8—2021no—
139C2×Q8C22⋊D10111yescharacteristic
140C22×C4—21no—
141C22×C4—1011no—
142C22×C4—1011no—
143C22×C4—2021no—
144C22×C4C22×D10111yescharacteristic
145Q16—42no—
146Q16—4042no—
147C2×C8—21no—
148C2×C8—2021no—
149C4⋊C4—21no—
150C4⋊C4—1011no—
151C4⋊C4—4042no—
152C4⋊C4—2021no—
153C4⋊C4—2021no—
154C4⋊C4—2021no—
155C4⋊C4—2021no—
156C4⋊C4—2021no—
157C4⋊C4—2021no—
158C4⋊C4—2021no—
159C4⋊C4—2021no—
160C4⋊C4C22⋊D10111yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2021no—
163C42—2021no—
164C42—2021no—
165C23D4×D10111yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—8081no—
172Q8—4041no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—1012no—
180C2×C4—4041no—
181C2×C4—4041no—
182C2×C4—4041no—
183C2×C4—2022no—
184C2×C4—2021no—
185C2×C4—2021no—
186C2×C4—2021no—
187C2×C4—2021no—
188C2×C4—2021no—
189C2×C4D4×D10111yescharacteristic
190C2×C4C2×C22⋊D10111yescharacteristic
191C8—41no—
192C8—4041no—
193C22—21no—
194C22—21no—
195C22#1569222311yescharacteristic
196C22Q16×D10111yescharacteristic
197C22#1569228711yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—4042no—
204C4—4041no—
205C4—4041no—
206C4—4041no—
207C4—2022no—
208C2—21no—
209C2—21no—
210C2#2026533111yescharacteristic
211C2#2026535811yescharacteristic
212C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#451×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#451D101
hypocenterC101#1605
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
81. C2×Dic101Q16semidirect
107. C101#1605semidirect

Maximal subgroups

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

subgroupindex
#202658062
#202653332
#202650962
#202649152
#202649142
#202649022
#451×C1012
#1605101