Finite Group Databasebeta

← #27181418

Subgroups — #27181418

Order 12928.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#20265654C211yesmaximal, characteristic, complemented
2#20265498C212yesmaximal, complemented
3#20265481C212yesmaximal, complemented
4#20265374C212yesmaximal, complemented
5#20265315C212yesmaximal, complemented
6#20265277C212yesmaximal, complemented
7C4×#13108062C212yesmaximal, complemented
8#20265238C211yesmaximal, characteristic, complemented
9#540×C101C211yesmaximal, characteristic
10C22×Dic202C2211yescharacteristic
11C2×#13108062C2212yes—
12C2×#13108062C2212yes—
13C4×Dic202C2212yes—
14C4×Dic202C2212yes—
15#15692220—22no—
16#15692214C2211yescharacteristic
17#15692211—22no—
18#15692188C2212yes—
19#15692186C2212yes—
20C4⋊#11717579C2212yes—
21#15692178C2212yes—
22#15692178C2212yes—
23#15692176C2212yes—
24#15692176C2212yes—
25C22⋊#11717579C2212yes—
26#15692166C2211yescharacteristic
27C4×#11717579C2211yescharacteristic
28#127×C101C2211yescharacteristic
29#125×C101C2211yescharacteristic
30#123×C101—22no—
31#121×C101—22no—
32#121×C101C2212yes—
33C4×D4×C101C2212yes—
34#117×C101C2211yescharacteristic
35C2×Dic202—21no—
36C2×Dic202—24no—
37C2×Dic202C2312yes—
38C22×Dic101—21no—
39#13108062—24no—
40#13108062—24no—
41C2×#11717579C2312yes—
42C2×#11717579C2312yes—
43C4⋊Dic101C2312yes—
44#13108053—22no—
45#13108053—22no—
46C22⋊Dic101—21no—
47C4×Dic101—22no—
48C4×Dic101—22no—
49C4×Dic101—21no—
50C2×D4×C101—22no—
51C2×D4×C101—22no—
52C2×D4×C101C2312yes—
53C22×C4×C101—22no—
54C22×C4×C101C2311yescharacteristic
55C4⋊C4×C101—22no—
56C4⋊C4×C101D412yes—
57C4⋊C4×C101C2312yes—
58C22⋊C4×C101—22no—
59C22⋊C4×C101—22no—
60C22⋊C4×C101D412yes—
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101—22no—
64C23×C101C2×D411yescharacteristic
65D4×C101—22no—
66D4×C101—22no—
67D4×C101—82no—
68D4×C101—82no—
69C2×C4×C101—22no—
70C2×C4×C101—22no—
71C2×C4×C101—82no—
72C2×C4×C101C2×D412yes—
73C2×C4×C101C2×D412yes—
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2411yescharacteristic
76C2×Dic101—24no—
77C2×Dic101—22no—
78C2×Dic101—22no—
79Dic202—24no—
80Dic202—22no—
81Dic202#4114yes—
82#11717579—22no—
83#11717579—22no—
84C22×C101—21no—
85C22×C101—22no—
86C22×C101—42no—
87C22×C101—42no—
88C22×C101—42no—
89C22×C101C22×D411yescharacteristic
90C4×C101—21no—
91C4×C101—22no—
92C4×C101—22no—
93C4×C101—42no—
94C4×C101C2×#4112yes—
95Dic101—24no—
96Dic101—42no—
97C2×C101—41no—
98C2×C101—82no—
99C2×C101#52511yescharacteristic
100C2×C101#57712yes—
101#3126—1011nomaximal, Sylow
102C101#312611yescharacteristic, complemented, Sylow
103#540D10111yescharacteristic
104#519—1011no—
105#482—1012no—
106#479—1012no—
107#460—1012no—
108#448—1012no—
109#440—1012no—
110C4×SD16—1012no—
111#433—1011no—
112C22×Q8—1011no—
113C2×SD16—1012no—
114C2×SD16—1012no—
115#127C2×D10111yescharacteristic
116#125C2×D10111yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D10112yes—
120C4×Q8—1012no—
121C4×Q8—1012no—
122C4×Q8—2022no—
123C4×D4C2×D10112yes—
124#117—1011no—
125#117—2022no—
126#117C2×D10111yescharacteristic
127#107—1012no—
128#106—1012no—
129C4⋊C8—1012no—
130#103—1012no—
131#103—1012no—
132#102—1012no—
133#102—1012no—
134C22⋊C8—1012no—
135#97—1011no—
136C4×C8—1011no—
137C2×Q8—1012no—
138C2×Q8—2024no—
139C2×Q8—2021no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D10112yes—
143C22×C4—22no—
144C22×C4—2021no—
145C22×C4C22×D10111yescharacteristic
146SD16—2024no—
147SD16—2024no—
148C2×C8—1012no—
149C2×C8—1012no—
150C4⋊C4—22no—
151C4⋊C4—1012no—
152C4⋊C4—2022no—
153C4⋊C4—2022no—
154C4⋊C4C22⋊D10112yes—
155C4⋊C4C22×D10112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2021no—
159C22⋊C4C22⋊D10112yes—
160C42—2021no—
161C42—2022no—
162C42—2022no—
163C42C22×D10111yescharacteristic
164C42C22×D10111yescharacteristic
165C23—22no—
166C23C2×C22⋊D10111yescharacteristic
167Q8—1014no—
168Q8—2024no—
169Q8—2022no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—2022no—
178C2×C4—2024no—
179C2×C4—2022no—
180C2×C4C2×C22⋊D10112yes—
181C2×C4C2×C22⋊D10112yes—
182C2×C4C2×C22⋊D10111yescharacteristic
183C2×C4C23×D10111yescharacteristic
184C8—2022no—
185C8—2022no—
186C22—22no—
187C22—21no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D10111yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—42no—
196C4—4042no—
197C4—2024no—
198C4#41×D10112yes—
199C2—41no—
200C2—82no—
201C2#2026568411yescharacteristic
202C2#2026598812yes—
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#540×C101C2
socleC22×C101C22×D4
hypercenter#540D101
hypocenterC101#3126
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20265654C2semidirect
2. #20265498C2semidirect
3. #20265481C2semidirect
4. #20265374C2semidirect
5. #20265315C2semidirect
6. #20265277C2semidirect
7. C4×#13108062C2semidirect
8. #20265238C2semidirect
102. C101#3126semidirect

Maximal subgroups

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

subgroupindex
#202656542
#202654982
#202654812
#202653742
#202653152
#202652772
C4×#131080622
#202652382
#540×C1012
#3126101