Finite Group Databasebeta

← #28373376

Subgroups — #28373376

Order 13952.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#20295582C211yesmaximal, characteristic, complemented
2#20295574C211yesmaximal, characteristic
3#20295396C211yesmaximal, characteristic, complemented
4#20295395C211yesmaximal, characteristic, complemented
5#20295390C211yesmaximal, characteristic, complemented
6#20295384C214yesmaximal, complemented
7#20295019C214yesmaximal, complemented
8#97×D109C211yesmaximal, characteristic, complemented
9#490×C109C211yesmaximal, characteristic, complemented
10C2×#13182028C2212yes—
11C2×C8×D109C2212yes—
12#16812699C2211yescharacteristic
13#16812698C2212yes—
14#16812691C2211yescharacteristic
15#16812686C2212yes—
16#16812677—22no—
17#16812670—22no—
18#16812664—22no—
19D4×Dic109—22no—
20#16812657C2212yes—
21C42×D109C2211yescharacteristic
22#16812624C2214yes—
23#16812622C2214yes—
24#16812620C2214yes—
25#16812610C2211yescharacteristic
26#16812609C2212yes—
27#127×C109C2211yescharacteristic
28#125×C109C2211yescharacteristic
29#102×C109C2214yes—
30#97×C109C2211yescharacteristic
31#13182028—28no—
32C2×Dic218—22no—
33C2×Dic218C2312yes—
34C2×C22⋊D109—22no—
35C22×Dic109—22no—
36C2×C4×D109D412yes—
37C2×C4×D109C2311yescharacteristic
38C2×#11724784C2312yes—
39C8×D109—24no—
40C4⋊Dic109—22no—
41C4⋊Dic109C2312yes—
42#13182008—22no—
43#13182008—22no—
44C22⋊Dic109—24no—
45#13182006—22no—
46C4×Dic109—22no—
47C4×Dic109D412yes—
48C4×Dic109C2311yescharacteristic
49C2×D4×C109—22no—
50C2×D4×C109C2312yes—
51C2×C8×C109C2312yes—
52C4⋊C4×C109—22no—
53C4⋊C4×C109C2312yes—
54C42×C109C2311yescharacteristic
55C23×C109—22no—
56C22×D109C2×D411yescharacteristic
57D4×C109—24no—
58D4×C109—44no—
59C2×C4×C109—22no—
60C2×C4×C109C2×D412yes—
61C2×C4×C109C2411yescharacteristic
62C22⋊D109—44no—
63C2×Dic109—22no—
64C2×Dic109—22no—
65C2×Dic109—44no—
66C2×Dic109C2×D412yes—
67C2×Dic109C2×D411yescharacteristic
68C4×D109—42no—
69C4×D109#4114yes—
70Dic218—24no—
71Dic218—44no—
72C8×C109—22no—
73#11724784—22no—
74C22×C109—42no—
75C22×C109—44no—
76C22×C109C22×D411yescharacteristic
77C2×D109—22no—
78C2×D109#12412yes—
79C4×C109—22no—
80C4×C109—42no—
81C4×C109C2×#4112yes—
82Dic109—22no—
83Dic109—42no—
84Dic109—42no—
85Dic109#12412yes—
86C2×C109—82no—
87C2×C109C2×#12411yescharacteristic
88C2×C109#57512yes—
89D109—22no—
90#3135—1091nomaximal, Sylow
91C109#313511yescharacteristic, complemented, Sylow
92#533—1091no—
93#532—1091no—
94#491—1091no—
95#491—1091no—
96#490—1091no—
97#490D10911yescharacteristic, complemented
98#489—1094no—
99#416—1094no—
100C2×#97—1091no—
101C2×#41—1092no—
102C22×C8—1092no—
103C4⋊Q8—1092no—
104C4⋊Q8—1091no—
105#127C2×D10911yescharacteristic
106#125—1091no—
107#125C2×D10911yescharacteristic
108#124—1092no—
109C22⋊Q8—2182no—
110#121—2182no—
111C4×Q8—2182no—
112C4×D4—2182no—
113#117—1092no—
114C2×C42—1091no—
115#103—1094no—
116#103—1094no—
117#102—1094no—
118#102C2×D10914yes—
119#97—1092no—
120#97—1091no—
121#97C2×D10911yescharacteristic
122#41—2188no—
123C2×Q8—1092no—
124C2×Q8—2182no—
125C2×D4—22no—
126C2×D4—2182no—
127C2×D4C22×D10912yes—
128C22×C4—1091no—
129C22×C4—1092no—
130C22×C4—2182no—
131C2×C8—1092no—
132C2×C8—2184no—
133C2×C8C22×D10912yes—
134C4⋊C4—22no—
135C4⋊C4—1092no—
136C4⋊C4—2182no—
137C4⋊C4—2182no—
138C4⋊C4—2182no—
139C4⋊C4C22×D10912yes—
140C22⋊C4—2182no—
141C22⋊C4—2184no—
142C42—1092no—
143C42—1091no—
144C42—2182no—
145C42C22×D10911yescharacteristic
146C23—22no—
147C23—1091no—
148Q8—4364no—
149Q8—2184no—
150D4—24no—
151D4—44no—
152D4—4364no—
153C2×C4—22no—
154C2×C4—1091no—
155C2×C4—1094no—
156C2×C4—1092no—
157C2×C4—4362no—
158C2×C4—4364no—
159C2×C4—2182no—
160C2×C4—2182no—
161C2×C4D4×D10912yes—
162C2×C4C23×D10911yescharacteristic
163C8—22no—
164C8—2182no—
165C22—42no—
166C22—44no—
167C22—1092no—
168C22—2182no—
169C22C2×D4×D10911yescharacteristic
170C4—22no—
171C4—42no—
172C4—1092no—
173C4—4362no—
174C4—4362no—
175C4—2182no—
176C4#41×D10912yes—
177C2—82no—
178C2—2182no—
179C2#124×D10911yescharacteristic
180C2#2029582212yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#490×C109C2
socleC22×C109C22×D4
prime radical#20295574C2
hypercenter#490D109
hypocenterC109#3135
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20295582C2semidirect
3. #20295396C2semidirect
4. #20295395C2semidirect
5. #20295390C2semidirect
6. #20295384C2semidirect
7. #20295019C2semidirect
8. #97×D109C2semidirect
9. #490×C109C2semidirect
91. C109#3135semidirect
97. #490D109semidirect

Maximal subgroups

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

subgroupindex
#202955822
#202955742
#202953962
#202953952
#202953902
#202953842
#202950192
#97×D1092
#490×C1092
#3135109