Finite Group Databasebeta

← #28361580

Subgroups — #28361580

Order 13952.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#20295576C211yesmaximal, characteristic
2#20294894C211yesmaximal, characteristic, complemented
3#20294761C214yesmaximal, complemented
4#432×C109C211yesmaximal, characteristic, complemented
5C2×#13182029—21no—
6#16812699C411yescharacteristic, complemented
7#16812696C411yescharacteristic, complemented
8#16812687—21no—
9#16812673—21no—
10#16812673C2212yes—
11C4×D436—21no—
12C4×D436C412yescomplemented
13#16812606—21no—
14#16812606—21no—
15#16812606C2212yes—
16C2×C42×C109C2211yescharacteristic
17C4⋊C8×C109—21no—
18C22⋊C8×C109C2212yes—
19#97×C109—21no—
20#13182029—44no—
21C2×Dic218—21no—
22C2×D436—21no—
23C2×D436—21no—
24C2×D436C2×C412yes—
25C2×C22⋊D109—22no—
26C22×Dic109—22no—
27C2×C4×D109—22no—
28C4⋊Dic109—21no—
29C4⋊Dic109C2×C412yes—
30#13182006—22no—
31#13182006—22no—
32C22×C4×C109D411yescharacteristic
33C22×C4×C109D411yescharacteristic
34C22×C4×C109C2311yescharacteristic
35C2×C8×C109—22no—
36C42×C109C2×C411yescharacteristic
37C42×C109C2×C411yescharacteristic
38C42×C109D411yescharacteristic
39C42×C109D411yescharacteristic
40C23×C109C2×D411yescharacteristic
41C22×D109—22no—
42C2×C4×C109—22no—
43C2×C4×C109—41no—
44C2×C4×C109—41no—
45C2×C4×C109C22⋊C411yescharacteristic
46C2×C4×C109C22⋊C411yescharacteristic
47C2×C4×C109C22⋊C411yescharacteristic
48C2×C4×C109C22⋊C411yescharacteristic
49C2×C4×C109C22×C411yescharacteristic
50C2×C4×C109C2×D411yescharacteristic
51C22⋊D109—44no—
52C2×Dic109—22no—
53C2×Dic109—42no—
54C2×Dic109—42no—
55C2×Dic109—42no—
56D436—42no—
57D436—42no—
58D436—42no—
59C4×D109—44no—
60Dic218—42no—
61C8×C109—42no—
62C22×C109—21no—
63C22×C109—21no—
64C22×C109C2×C22⋊C411yescharacteristic
65C22×C109AGL(1,ℤ/8)12yes—
66C2×D109—42no—
67C2×D109—42no—
68C2×D109—42no—
69C4×C109—21no—
70C4×C109—21no—
71C4×C109—21no—
72C4×C109—21no—
73C4×C109—21no—
74C4×C109—21no—
75Dic109—42no—
76Dic109—82no—
77C2×C109—22no—
78C2×C109#41011yescharacteristic
79C2×C109#41811yescharacteristic
80C2×C109#42111yescharacteristic
81D109—82no—
82#1514—1091nomaximal, Sylow
83C109#151411yescharacteristic, complemented, Sylow
84#532—1091no—
85#432D10911yescharacteristic, complemented
86#383—1091no—
87#327—1094no—
88C2×#41—2181no—
89C4⋊Q8—1091no—
90#127—1091no—
91#124—2181no—
92#121—1092no—
93#121—2181no—
94C4×D4—1092no—
95C4×D4—2181no—
96C2×C42C2×D10911yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D10912yes—
99#97—21no—
100#95—1092no—
101#95—2181no—
102#95—2181no—
103#41—4364no—
104C2×Q8—2181no—
105C2×D4—1092no—
106C2×D4—2182no—
107C2×D4—2181no—
108C2×D4—2181no—
109C22×C4—2182no—
110C22×C4—2182no—
111C22×C4D43611yescharacteristic
112C22×C4D43611yescharacteristic
113C22×C4C22×D10911yescharacteristic
114C2×C8—22no—
115C4⋊C4—1092no—
116C4⋊C4—2181no—
117C22⋊C4—2182no—
118C22⋊C4—2182no—
119C42C4×D10911yescharacteristic
120C42C4×D10911yescharacteristic
121C42C22⋊D10911yescharacteristic
122C42C22⋊D10911yescharacteristic
123C23—2182no—
124C23C2×D43611yescharacteristic
125Q8—4362no—
126D4—4362no—
127D4—4362no—
128D4—4362no—
129D4—4364no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—4364no—
134C2×C4—4362no—
135C2×C4—4362no—
136C2×C4—4362no—
137C2×C4—2182no—
138C2×C4#1318200611yescharacteristic
139C2×C4#1318200611yescharacteristic
140C2×C4#1318200611yescharacteristic
141C2×C4#1318200611yescharacteristic
142C2×C4C2×C4×D10911yescharacteristic
143C2×C4C2×C22⋊D10911yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—4362no—
148C22—4362no—
149C22—4362no—
150C22C2×#1318200611yescharacteristic
151C22#1681272712yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—8722no—
159C4—4362no—
160C2—22no—
161C2—8722no—
162C2#2029499911yescharacteristic
163C2#2029503211yescharacteristic
164C2#2029504211yescharacteristic
subgroupG/H
centerC22C2×#13182006
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#432×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295576C2
cosocleC22×C4×C109C23
hypercenter#432D109
hypocenterC109#1514
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20294894C2semidirect
3. #20294761C2semidirect
4. #432×C109C2semidirect
6. #16812699C4semidirect
7. #16812696C4semidirect
12. C4×D436C4semidirect
83. C109#1514semidirect
85. #432D109semidirect

Maximal subgroups

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

subgroupindex
#202955762
#202948942
#202947612
#432×C1092
#1514109