Finite Group Databasebeta

← #27179437

Subgroups — #27179437

Order 12928.

556 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 169 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×C42×D101C211yesmaximal, characteristic
2#20265073C212yesmaximal, complemented
3#20265058C214yesmaximal, complemented
4#20265048C214yesmaximal
5#20265043C211yesmaximal, characteristic, complemented
6#20265034C212yesmaximal
7C2×#125×C101C211yesmaximal, characteristic, complemented
8C22×C4×D101C2212yes—
9C22×C4×D101C2211yescharacteristic
10C2×C4⋊Dic101C2212yes—
11C2×#13108053C2214yes—
12C2×#13108051C2214yes—
13C2×C4×Dic101C2212yes—
14C2×C4×Dic101C2211yescharacteristic
15C42×D101—24no—
16#15692162C2214yes—
17#15692162C2214yes—
18#15692162C2214yes—
19#125×C101—24no—
20C2×C4⋊C4×C101C2212yes—
21C2×C4⋊C4×C101C2214yes—
22C2×C42×C101C2211yescharacteristic
23C23×D101C2311yescharacteristic
24C22×Dic101C2314yes—
25C22×Dic101C2311yescharacteristic
26C22×Dic101C2312yes—
27C2×C4×D101—24no—
28C2×C4×D101—24no—
29C2×C4×D101—22no—
30C2×C4×D101—22no—
31C2×C4×D101—24no—
32C2×C4×D101Q814yes—
33C4⋊Dic101—24no—
34#13108053—28no—
35#13108051—28no—
36C4×Dic101—24no—
37C4×Dic101—22no—
38C22×C4×C101C2314yes—
39C22×C4×C101C2312yes—
40C22×C4×C101C2311yescharacteristic
41C4⋊C4×C101—28no—
42C4⋊C4×C101—24no—
43C42×C101D414yes—
44C23×C101C2411yescharacteristic
45C22×D101—21no—
46C22×D101—22no—
47C22×D101—21no—
48C22×D101C2×Q812yes—
49C22×D101#4114yes—
50C2×C4×C101—22no—
51C2×C4×C101—22no—
52C2×C4×C101—24no—
53C2×C4×C101—24no—
54C2×C4×C101—24no—
55C2×C4×C101C2×D414yes—
56C2×C4×C101C2×D412yes—
57C2×C4×C101C2×Q812yes—
58C2×C4×C101#4112yes—
59C2×Dic101—21no—
60C2×Dic101—22no—
61C2×Dic101—22no—
62C2×Dic101—21no—
63C2×Dic101—24no—
64C2×Dic101—24no—
65C2×Dic101—24no—
66C2×Dic101C2×Q812yes—
67C2×Dic101#4114yes—
68C4×D101—216no—
69C4×D101—28no—
70C22×C101C22×D411yescharacteristic
71C22×C101C22×Q811yescharacteristic
72C22×C101C2×#4112yes—
73C22×C101C2×#4112yes—
74C22×C101C2×#4111yescharacteristic
75C2×D101—22no—
76C2×D101—24no—
77C2×D101—24no—
78C2×D101—22no—
79C2×D101#12514yescomplemented
80C4×C101—24no—
81C4×C101—44no—
82C4×C101C22⋊Q814yes—
83Dic101—22no—
84Dic101—24no—
85Dic101—44no—
86C2×C101C2×C22⋊Q811yescharacteristic
87C2×C101#52512yes—
88C2×C101C2×#12511yescharacteristic
89C2×C101#52912yes—
90C2×C101#53311yescharacteristic
91D101—24no—
92#2851—1011nomaximal, Sylow
93C101#285111yescharacteristic, complemented, Sylow
94C2×#125D10111yescharacteristic, complemented
95C22×C42—1011no—
96#389—1012no—
97#387—1014no—
98#385—1014no—
99#382—1011no—
100#380—1012no—
101C23×C4—1011no—
102C23×C4—1012no—
103#125—24no—
104C2×C4⋊C4—1012no—
105C2×C4⋊C4—1014no—
106C2×C4⋊C4C2×D10112yes—
107C2×C4⋊C4C2×D10114yes—
108C2×C22⋊C4—1014no—
109C2×C42—1012no—
110C2×C42—1011no—
111C2×C42—2024no—
112C2×C42C2×D10111yescharacteristic
113#95—1014no—
114#95—1014no—
115#95—1014no—
116C24—1011no—
117C22×C4—1011no—
118C22×C4—1012no—
119C22×C4—1014no—
120C22×C4—1014no—
121C22×C4—2024no—
122C22×C4—2024no—
123C22×C4—2024no—
124C22×C4—2022no—
125C22×C4—2022no—
126C22×C4C22×D10114yes—
127C22×C4C22×D10112yes—
128C22×C4C22×D10111yescharacteristic
129C4⋊C4—28no—
130C4⋊C4—24no—
131C4⋊C4—2028no—
132C4⋊C4—2024no—
133C22⋊C4—2028no—
134C42—2024no—
135C42—2022no—
136C42C22⋊D10114yes—
137C23—1012no—
138C23—1014no—
139C23—2021no—
140C23—2022no—
141C23—2021no—
142C23C23×D10111yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—24no—
147C2×C4—24no—
148C2×C4—1012no—
149C2×C4—1014no—
150C2×C4—20216no—
151C2×C4—2024no—
152C2×C4—2024no—
153C2×C4—2024no—
154C2×C4—2021no—
155C2×C4—2022no—
156C2×C4—2022no—
157C2×C4—2021no—
158C2×C4—2028no—
159C2×C4C2×C22⋊D10114yes—
160C2×C4C2×C22⋊D10112yes—
161C2×C4Q8×D10112yes—
162C2×C4#1310807512yes—
163C22—1014no—
164C22—2022no—
165C22—2022no—
166C22—2024no—
167C22—2024no—
168C22C22×C22⋊D10111yescharacteristic
169C22C2×Q8×D10111yescharacteristic
170C22#41×D10112yes—
171C22#41×D10112yes—
172C22C2×#1310807511yescharacteristic
173C4—24no—
174C4—44no—
175C4—4044no—
176C4—2022no—
177C4—2024no—
178C4#1569223114yes—
179C2—2024no—
180C2C2×#1569223111yescharacteristic
181C2#2026568412yes—
182C2#125×D10111yescharacteristic
183C2#2026571212yes—
184C2#2026573311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
FittingC2×#125×C101C2
prime radicalC23×D101C23
hypercenterC2×#125D101
hypocenterC101#2851
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #20265073C2semidirect
3. #20265058C2semidirect
5. #20265043C2semidirect
7. C2×#125×C101C2semidirect
79. C2×D101#125semidirect
93. C101#2851semidirect
94. C2×#125D101semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1012
#202650732
#202650582
#202650482
#202650432
#202650342
C2×#125×C1012
#2851101