Finite Group Databasebeta

← #27172196

Subgroups — #27172196

Order 12928.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#20265684C212yesmaximal, complemented
2#20265194C212yesmaximal, complemented
3#20265140C211yesmaximal, characteristic, complemented
4#20264934C211yesmaximal, characteristic, complemented
5#575×C101C211yesmaximal, characteristic, complemented
6C22×C4×D101C2211yescharacteristic
7C2×#13108058C2211yescharacteristic
8#15692236—22no—
9#15692231—22no—
10#15692226—22no—
11#15692223—22no—
12C4×C22⋊D101—24no—
13#15692214C2212yes—
14#15692182—24no—
15#15692167—22no—
16C2×#41×C101C2212yes—
17#137×C101—22no—
18AGL(1,ℤ/8)×C101—22no—
19#135×C101—22no—
20C2×M16×C101C2211yescharacteristic
21C23×D101D411yescharacteristic
22C2×C22⋊D101—24no—
23C22×Dic101D411yescharacteristic
24C2×C4×D101—21no—
25C2×C4×D101—22no—
26C2×C4×D101—22no—
27C2×C4×D101—21no—
28#13108058—22no—
29C2×#11717579—21no—
30C4⋊Dic101—22no—
31#13108053—24no—
32C22⋊Dic101—24no—
33C22⋊Dic101—22no—
34#13108051—24no—
35C4×Dic101D414yescomplemented
36#41×C101—22no—
37#41×C101—22no—
38#41×C101—22no—
39#41×C101—22no—
40C2×Q8×C101D412yescomplemented
41C2×D4×C101—22no—
42C2×D4×C101D412yescomplemented
43C22×C4×C101—22no—
44C22×C4×C101C2311yescharacteristic
45Q16×C101—22no—
46SD16×C101—24no—
47D8×C101—22no—
48M16×C101—22no—
49C2×C8×C101D412yescomplemented
50C23×C101—22no—
51C23×C101C2×D411yescharacteristic
52C22×D101—22no—
53C22×D101—21no—
54C22×D101—42no—
55Q8×C101—22no—
56Q8×C101—22no—
57D4×C101—22no—
58D4×C101—22no—
59D4×C101—42no—
60D4×C101—42no—
61C2×C4×C101—22no—
62C2×C4×C101—42no—
63C2×C4×C101—42no—
64C2×C4×C101C2×D412yes—
65C2×C4×C101C2×D412yes—
66C2×C4×C101C2×D411yescharacteristic
67C2×C4×C101#4111yescharacteristic
68C22⋊D101—48no—
69C2×Dic101—24no—
70C2×Dic101—22no—
71C2×Dic101—21no—
72C4×D101—41no—
73C4×D101—42no—
74C4×D101—41no—
75C8×C101—22no—
76#11717579—41no—
77C22×C101—41no—
78C22×C101—44no—
79C22×C101—42no—
80C22×C101#12012yes—
81C22×C101#12111yescharacteristic
82C2×D101—24no—
83C2×D101—22no—
84C2×D101—42no—
85C2×D101—41no—
86C2×D101—41no—
87C4×C101—42no—
88C4×C101#12011yescharacteristic
89C4×C101#12112yes—
90C4×C101#12711yescharacteristic
91Dic101—44no—
92Dic101—41no—
93C2×C101—22no—
94C2×C101—21no—
95C2×C101—82no—
96C2×C101#39211yescharacteristic
97D101—42no—
98#2010—1011nomaximal, Sylow
99C101#201011yescharacteristic, complemented, Sylow
100#575D10111yescharacteristic, complemented
101#525—1012no—
102#421—1012no—
103#407—1011no—
104H(3,ℤ/4)—1011no—
105C2×#41C2×D10112yes—
106C23×C4—1011no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1011no—
111C2×M16C2×D10111yescharacteristic
112#123—2022no—
113C22⋊Q8—2022no—
114#121—2022no—
115#120—2022no—
116C4×D4—2024no—
117#117—1012no—
118#104—2024no—
119C22⋊C8—2022no—
120C24—1011no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D10112yescomplemented
126C2×D4—22no—
127C2×D4—2024no—
128C2×D4C22⋊D10112yescomplemented
129C22×C4—22no—
130C22×C4—1011no—
131C22×C4—2022no—
132C22×C4—2021no—
133C22×C4—2022no—
134C22×C4—2021no—
135C22×C4C22×D10111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—2022no—
141C2×C8—2021no—
142C2×C8C22⋊D10112yescomplemented
143C4⋊C4—2024no—
144C4⋊C4—2022no—
145C22⋊C4—2024no—
146C22⋊C4—2024no—
147C22⋊C4—2022no—
148C42—1014no—
149C23—22no—
150C23—4042no—
151C23—2022no—
152C23—2021no—
153C23D4×D10111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—4048no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—4041no—
165C2×C4—4042no—
166C2×C4—4041no—
167C2×C4—2024no—
168C2×C4—2022no—
169C2×C4—2021no—
170C2×C4D4×D10112yes—
171C2×C4C2×C22⋊D10112yes—
172C2×C4C2×C22⋊D10111yescharacteristic
173C2×C4#1310807311yescharacteristic
174C8—22no—
175C8—4041no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—4042no—
180C22—4041no—
181C22—4041no—
182C22—2024no—
183C22—2022no—
184C22#1569222312yes—
185C22#1569222611yescharacteristic
186C4—42no—
187C4—4044no—
188C4—4041no—
189C4#1569222411yescharacteristic
190C4#1569222712yes—
191C4#1569225111yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—4042no—
196C2#2026508511yescharacteristic
subgroupG/H
centerC4#15692251
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#575×C101C2
socleC2×C101#392
hypercenter#575D101
hypocenterC101#2010
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20265684C2semidirect
2. #20265194C2semidirect
3. #20265140C2semidirect
4. #20264934C2semidirect
5. #575×C101C2semidirect
35. C4×Dic101D4semidirect
40. C2×Q8×C101D4semidirect
42. C2×D4×C101D4semidirect
49. C2×C8×C101D4semidirect
99. C101#2010semidirect
100. #575D101semidirect
125. C2×Q8C22⋊D101semidirect
128. C2×D4C22⋊D101semidirect
142. C2×C8C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202656842
#202651942
#202651402
#202649342
#575×C1012
#2010101