Finite Group Databasebeta

← #28362000

Subgroups — #28362000

Order 13952.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#20295607C211yesmaximal, characteristic
2#20295165C212yesmaximal, complemented
3#20294759C212yesmaximal, complemented
4#20294752C211yesmaximal, characteristic, complemented
5#395×C109C211yesmaximal, characteristic, complemented
6C2×#13182029—21no—
7C2×#13182016—22no—
8#16812679—22no—
9#16812674—22no—
10#16812673—21no—
11#16812673C2212yes—
12#16812623—22no—
13C22⋊#11724784C2212yes—
14C22×Q8×C109C2211yescharacteristic
15C2×C4⋊C4×C109—21no—
16C2×C4⋊C4×C109C2211yescharacteristic
17#95×C109—21no—
18#95×C109C2211yescharacteristic
19#13182029—42no—
20#13182029—42no—
21C2×Dic218—21no—
22C2×D436—21no—
23C2×D436—21no—
24C2×D436D412yes—
25C2×C22⋊D109—22no—
26C2×C4×D109—22no—
27#13182016—44no—
28C2×#11724784—22no—
29C4⋊Dic109—21no—
30C4⋊Dic109D412yes—
31#13182006—22no—
32#13182006—22no—
33C2×Q8×C109—22no—
34C2×Q8×C109—42no—
35C22×C4×C109—21no—
36C22×C4×C109—21no—
37C22×C4×C109D411yescharacteristic
38C22×C4×C109D411yescharacteristic
39C22×C4×C109C2311yescharacteristic
40C4⋊C4×C109—22no—
41C4⋊C4×C109—42no—
42C23×C109C2×D411yescharacteristic
43C22×D109—22no—
44Q8×C109—24no—
45Q8×C109—42no—
46C2×C4×C109—21no—
47C2×C4×C109—21no—
48C2×C4×C109—22no—
49C2×C4×C109—22no—
50C2×C4×C109—21no—
51C2×C4×C109—41no—
52C2×C4×C109—41no—
53C2×C4×C109—41no—
54C2×C4×C109—41no—
55C2×C4×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109SD1612yescomplemented
58C2×C4×C109C2×D412yes—
59C22⋊D109—42no—
60C22⋊D109—42no—
61C2×Dic109—22no—
62D436—42no—
63D436—42no—
64D436—81no—
65C4×D109—44no—
66Dic218—42no—
67#11724784—42no—
68C22×C109—21no—
69C22×C109—21no—
70C22×C109#12011yescharacteristic
71C22×C109C2×SD1611yescharacteristic
72C22×C109AGL(1,ℤ/8)11yescharacteristic
73C2×D109—42no—
74C2×D109—42no—
75C2×D109—42no—
76C4×C109—22no—
77C4×C109—22no—
78C4×C109—42no—
79C4×C109—41no—
80C4×C109—42no—
81Dic109—42no—
82C2×C109—21no—
83C2×C109—21no—
84C2×C109#45011yescharacteristic
85C2×C109#45611yescharacteristic
86C2×C109B(4,𝔽2)11yescharacteristic
87D109—82no—
88#1604—1091nomaximal, Sylow
89C109#160411yescharacteristic, complemented, Sylow
90#537—1091no—
91#448—1092no—
92#395D10911yescharacteristic, complemented
93#327—1092no—
94#324—1091no—
95C2×#41—2181no—
96C22×Q8C2×D10911yescharacteristic
97C2×SD16—2182no—
98C22⋊Q8—2182no—
99#121—1092no—
100#121—2182no—
101#121—2181no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D10911yescharacteristic
104#103—2182no—
105C22⋊C8—1092no—
106#95—21no—
107#95C2×D10911yescharacteristic
108#41—4362no—
109#41—4362no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—2181no—
113C2×D4—1092no—
114C2×D4—2181no—
115C2×D4—2181no—
116C2×D4—2182no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2182no—
120C22×C4C22⋊D10911yescharacteristic
121C22×C4C22⋊D10911yescharacteristic
122C22×C4C22×D10911yescharacteristic
123SD16—4364no—
124C2×C8—2182no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—1092no—
128C4⋊C4—2181no—
129C22⋊C4—2182no—
130C22⋊C4—2182no—
131C23—2182no—
132C23C2×C22⋊D10911yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—4362no—
136D4—8721no—
137D4—4362no—
138D4—4362no—
139D4—4362no—
140D4—4362no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—4364no—
153C2×C4—2182no—
154C2×C4#1318201612yescomplemented
155C2×C4D4×D10912yes—
156C8—4362no—
157C22—21no—
158C22—21no—
159C22—4362no—
160C22—4362no—
161C22—4362no—
162C22#1681266711yescharacteristic
163C22C2×#1318201611yescharacteristic
164C22#1681272411yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—4362no—
171C2—21no—
172C2—21no—
173C2—8722no—
174C2#2029517611yescharacteristic
175C2#2029520811yescharacteristic
176C2#2029521211yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#395×C109C2
socleC22×C109#120
prime radical#20295607C2
hypercenter#395D109
hypocenterC109#1604
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #20295165C2semidirect
3. #20294759C2semidirect
4. #20294752C2semidirect
5. #395×C109C2semidirect
57. C2×C4×C109SD16semidirect
89. C109#1604semidirect
92. #395D109semidirect
154. C2×C4#13182016semidirect

Maximal subgroups

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

subgroupindex
#202956072
#202951652
#202947592
#202947522
#395×C1092
#1604109