Finite Group Databasebeta

← #27171059

Subgroups — #27171059

Order 12928.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#13108075C211yesmaximal, characteristic
2C2×#15692174C211yesmaximal, characteristic, complemented
3C2×#15692171C212yesmaximal, complemented
4#20265140C212yesmaximal, complemented
5C2×#101×C101C211yesmaximal, characteristic, complemented
6C2×#13108075—24no—
7C2×#13108075—24no—
8C2×#13108075—22no—
9C2×#13108075—22no—
10C22×D404C412yes—
11C22×D404C2211yescharacteristic
12C22×C4×D101C412yes—
13C22×C4×D101C2211yescharacteristic
14C2×#13108058C2212yes—
15#15692174—22no—
16#15692171—24no—
17#15692167—24no—
18C22×Q8×C101C2211yescharacteristic
19C2×M16×C101C2212yes—
20#101×C101—22no—
21C23×D101C2×C412yes—
22C23×D101C2×C411yescharacteristic
23#13108075—216no—
24#13108075—216no—
25C2×D404—24no—
26C2×D404—24no—
27C2×D404—24no—
28C2×D404—22no—
29C2×D404—21no—
30C2×D404—21no—
31C2×D404D414yes—
32C22×Dic101C2×C411yescharacteristic
33C2×C4×D101—24no—
34C2×C4×D101—24no—
35C2×C4×D101—22no—
36C2×C4×D101—21no—
37C2×C4×D101—21no—
38C2×C4×D101—24no—
39C2×C4×D101D414yes—
40#13108058—22no—
41#13108058—22no—
42C2×#11717579—22no—
43C2×Q8×C101—22no—
44C2×Q8×C101—22no—
45C2×Q8×C101D412yes—
46C2×Q8×C101D412yes—
47C22×C4×C101C2×C412yes—
48C22×C4×C101C2311yescharacteristic
49M16×C101—22no—
50M16×C101—22no—
51C2×C8×C101—22no—
52C23×C101C22×C411yescharacteristic
53C22×D101—21no—
54C22×D101—22no—
55C22×D101—22no—
56C22×D101—21no—
57C22×D101—42no—
58C22×D101—44no—
59C22×D101C22⋊C412yes—
60C22×D101C22⋊C414yes—
61Q8×C101—24no—
62Q8×C101—24no—
63C2×C4×C101—22no—
64C2×C4×C101—22no—
65C2×C4×C101C22⋊C414yes—
66C2×C4×C101C2×D412yes—
67C2×C4×C101C2×D412yes—
68C2×C4×C101C2×D411yescharacteristic
69C2×C4×C101C2×D411yescharacteristic
70C2×Dic101—21no—
71C2×Dic101—21no—
72C2×Dic101C22⋊C412yes—
73D404—216no—
74D404—24no—
75D404—24no—
76C4×D101—216no—
77C4×D101—24no—
78C4×D101—24no—
79C8×C101—42no—
80#11717579—42no—
81C22×C101—22no—
82C22×C101C2×C22⋊C411yescharacteristic
83C22×C101C2×C22⋊C411yescharacteristic
84C22×C101C2×C22⋊C411yescharacteristic
85C2×D101—22no—
86C2×D101—24no—
87C2×D101—24no—
88C2×D101—42no—
89C2×D101—42no—
90C2×D101—44no—
91C2×D101—44no—
92C2×D101—44no—
93C4×C101—24no—
94C4×C101#12012yes—
95C4×C101#12012yes—
96Dic101—22no—
97C2×C101—21no—
98C2×C101—21no—
99C2×C101#37911yescharacteristic
100C2×C101#41312yes—
101D101—42no—
102D101—44no—
103#1785—1011nomaximal, Sylow
104C101#178511yescharacteristic, complemented, Sylow
105C22×#41—1011no—
106C2×#101—1011no—
107C2×#101D10111yescharacteristic, complemented
108C2×#100—1012no—
109#407—1012no—
110C2×#41—2024no—
111C2×#41—2024no—
112C2×#41—2022no—
113C2×#41—2022no—
114C22×Q8C2×D10111yescharacteristic
115C22×D4—1012no—
116C22×D4—1011no—
117C23×C4—1011no—
118C23×C4—1012no—
119C2×M16—1012no—
120C2×M16C2×D10112yes—
121#101—22no—
122#101—2022no—
123#100—2024no—
124C22⋊C8—2024no—
125C24—1012no—
126C24—1011no—
127#41—20216no—
128#41—20216no—
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8D40412yes—
132C2×Q8C22⋊D10112yes—
133C2×D4—1014no—
134C2×D4—2024no—
135C2×D4—2024no—
136C2×D4—2024no—
137C2×D4—2022no—
138C2×D4—2021no—
139C2×D4—2021no—
140C22×C4—1011no—
141C22×C4—1014no—
142C22×C4—2024no—
143C22×C4—2024no—
144C22×C4—2024no—
145C22×C4—2022no—
146C22×C4—2021no—
147C22×C4—2021no—
148C22×C4C4×D10112yes—
149C22×C4C22×D10111yescharacteristic
150M16—22no—
151M16—22no—
152M16—2022no—
153M16—2022no—
154C2×C8—22no—
155C2×C8—2022no—
156C23—1014no—
157C23—1012no—
158C23—4044no—
159C23—4042no—
160C23—2021no—
161C23—2022no—
162C23—2022no—
163C23—2021no—
164C23C2×C4×D10111yescharacteristic
165Q8—24no—
166Q8—24no—
167D4—20216no—
168D4—2024no—
169D4—2024no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—1012no—
173C2×C4—20216no—
174C2×C4—2021no—
175C2×C4—2021no—
176C2×C4—2024no—
177C2×C4—2024no—
178C2×C4#1310805114yes—
179C2×C4D4×D10112yes—
180C2×C4D4×D10112yes—
181C2×C4C2×C22⋊D10111yescharacteristic
182C2×C4C2×D40411yescharacteristic
183C8—42no—
184C8—4042no—
185C22—22no—
186C22—4044no—
187C22—4042no—
188C22—4044no—
189C22—4042no—
190C22—4044no—
191C22—2024no—
192C22—2022no—
193C22—2024no—
194C22C22⋊C4×D10111yescharacteristic
195C22C22⋊C4×D10111yescharacteristic
196C22C2×#1310805111yescharacteristic
197C4—24no—
198C4—2022no—
199C4#1569222312yes—
200C4#1569222512yes—
201C2—21no—
202C2—21no—
203C2—4044no—
204C2—4042no—
205C2#2026503211yescharacteristic
206C2#2026516012yes—
subgroupG/H
centerC22C22⋊C4×D101
commutatorC23×C101C22×C4
FrattiniC22×C4C22×D101
FittingC2×#101×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC22×#13108075C2
cosocleC22×C4×C101C23
hypercenterC2×#101D101
hypocenterC101#1785
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#15692174C2semidirect
3. C2×#15692171C2semidirect
4. #20265140C2semidirect
5. C2×#101×C101C2semidirect
104. C101#1785semidirect
107. C2×#101D101semidirect

Maximal subgroups

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

subgroupindex
C22×#131080752
C2×#156921742
C2×#156921712
#202651402
C2×#101×C1012
#1785101