Finite Group Databasebeta

← #27171543

Subgroups — #27171543

Order 12928.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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×#15692236C211yesmaximal, characteristic
2#20265652C211yesmaximal, characteristic
3#20265038C212yesmaximal, complemented
4#20264943C212yesmaximal, complemented
5C2×#99×C101C211yesmaximal, characteristic
6C23×Dic101C2211yescharacteristic
7#15692236—22no—
8#15692236C414yescomplemented
9D4×Dic101—24no—
10#15692214—21no—
11C2×#13108053—21no—
12C2×C22⋊Dic101—21no—
13C2×C22⋊Dic101—21no—
14C2×C22⋊Dic101C2212yes—
15C2×C22⋊Dic101C2211yescharacteristic
16#15692162—24no—
17C22×D4×C101C2211yescharacteristic
18C2×C22⋊C4×C101C2212yes—
19#99×C101—22no—
20C22×Dic101—22no—
21C22×Dic101—21no—
22C22×Dic101—21no—
23C22×Dic101—21no—
24C22×Dic101—22no—
25C22×Dic101—22no—
26C22×Dic101C2×C412yescomplemented
27C22×Dic101D414yes—
28C4⋊Dic101—22no—
29#13108053—24no—
30C22⋊Dic101—22no—
31C22⋊Dic101—24no—
32C22⋊Dic101—22no—
33C22⋊Dic101—22no—
34C22⋊Dic101—21no—
35C22⋊Dic101C2×C412yescomplemented
36C4×Dic101—22no—
37C24×C101D411yescharacteristic
38C24×C101C2311yescharacteristic
39C2×D4×C101—22no—
40C2×D4×C101—22no—
41C2×D4×C101C2×C412yes—
42C2×D4×C101D412yes—
43C22×C4×C101—22no—
44C22×C4×C101D411yescharacteristic
45C22⋊C4×C101—22no—
46C22⋊C4×C101—22no—
47C23×C101—21no—
48C23×C101—21no—
49C23×C101—42no—
50C23×C101—42no—
51C23×C101C22⋊C412yes—
52C23×C101C22×C411yescharacteristic
53C23×C101C2×D412yes—
54C23×C101C2×D411yescharacteristic
55C23×C101C2×D411yescharacteristic
56C23×C101#4112yes—
57D4×C101—24no—
58D4×C101—24no—
59C2×C4×C101—21no—
60C2×C4×C101—21no—
61C2×C4×C101—44no—
62C2×C4×C101—42no—
63C2×C4×C101C22⋊C412yes—
64C2×Dic101—22no—
65C2×Dic101—22no—
66C2×Dic101—24no—
67C2×Dic101—24no—
68C2×Dic101—42no—
69C2×Dic101—41no—
70C2×Dic101—42no—
71C2×Dic101—41no—
72C2×Dic101—44no—
73C2×Dic101—82no—
74C22×C101—24no—
75C22×C101—22no—
76C22×C101—22no—
77C22×C101—41no—
78C22×C101—41no—
79C22×C101—42no—
80C22×C101—42no—
81C22×C101—42no—
82C22×C101—81no—
83C22×C101C2×C22⋊C411yescharacteristic
84C22×C101C4×D412yes—
85C22×C101#12011yescharacteristic
86C22×C101#12112yes—
87C22×C101#12311yescharacteristic
88C4×C101—22no—
89C4×C101—82no—
90Dic101—42no—
91Dic101—42no—
92Dic101—44no—
93C2×C101—21no—
94C2×C101—22no—
95C2×C101—21no—
96C2×C101—22no—
97C2×C101—42no—
98C2×C101#38611yescharacteristic
99C2×C101#45812yes—
100#1890—1011nomaximal, Sylow
101C101#189011yescharacteristic, complemented, Sylow
102C2×#123—1011no—
103#518—1011no—
104C2×#99D10111yescharacteristic
105#381—1012no—
106#342—1012no—
107C22×D4C2×D10111yescharacteristic
108C23×C4—1011no—
109#123—1014no—
110#123—2022no—
111C4×D4—2024no—
112#117—2021no—
113C2×C4⋊C4—2021no—
114C2×C22⋊C4—1011no—
115C2×C22⋊C4—1012no—
116C2×C22⋊C4—2021no—
117C2×C22⋊C4—2021no—
118C2×C22⋊C4C2×D10112yes—
119#99—22no—
120#95—2024no—
121C24D40411yescharacteristic
122C24C22×D10111yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D10112yes—
126C2×D4C22⋊D10112yes—
127C22×C4—22no—
128C22×C4—1014no—
129C22×C4—1012no—
130C22×C4—2022no—
131C22×C4—2022no—
132C22×C4—2021no—
133C22×C4—2021no—
134C22×C4—2021no—
135C22×C4—2022no—
136C22×C4D40411yescharacteristic
137C4⋊C4—2022no—
138C4⋊C4—2024no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—1012no—
142C22⋊C4—2022no—
143C22⋊C4—2024no—
144C22⋊C4—2022no—
145C22⋊C4—2021no—
146C22⋊C4—2022no—
147C42—2022no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23#1310805112yes—
153C23C2×C4×D10111yescharacteristic
154C23D4×D10112yes—
155C23C2×C22⋊D10111yescharacteristic
156C23C2×D40411yescharacteristic
157C23#1310807312yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4—8082no—
165C2×C4—4042no—
166C2×C4—4041no—
167C2×C4—4042no—
168C2×C4—4041no—
169C2×C4—4044no—
170C2×C4—2022no—
171C2×C4—2022no—
172C2×C4—2024no—
173C2×C4—2024no—
174C2×C4#1310805112yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×#1310805111yescharacteristic
185C22#1569221512yes—
186C22#1569222511yescharacteristic
187C22#1569222712yes—
188C22#1569223911yescharacteristic
189C4—22no—
190C4—82no—
191C4—4042no—
192C4—4042no—
193C4—4044no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#2026505411yescharacteristic
200C2#2026536812yes—
subgroupG/H
centerC22#15692225
commutatorC23×C101C22×C4
FrattiniC24C22×D101
FittingC2×#99×C101C2
socleC22×C101#120
prime radicalC22×D4×C101C22
cosocleC24×C101C23
hypercenterC2×#99D101
hypocenterC101#1890
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #20265038C2semidirect
4. #20264943C2semidirect
8. #15692236C4semidirect
26. C22×Dic101C2×C4semidirect
35. C22⋊Dic101C2×C4semidirect
101. C101#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#156922362
#202656522
#202650382
#202649432
C2×#99×C1012
#1890101