Finite Group Databasebeta

← #28379332

Subgroups — #28379332

Order 13952.

262 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 52 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#20296013C212yesmaximal, complemented
2#20295935C212yesmaximal, complemented
3#20295934C212yesmaximal, complemented
4#20295589C211yesmaximal, characteristic
5C2×#13182038—22no—
6#16812760C2214yescomplemented
7#16812759—22no—
8C2×#13182028C2211yescharacteristic
9C2×D4×D109C411yescharacteristic
10#16812695C411yescharacteristic
11#16812687C2211yescharacteristic
12#16812686C2211yescharacteristic
13#16812671—22no—
14#16812667—22no—
15#16812656C411yescharacteristic
16#127×C109C411yescharacteristic
17#13182038—24no—
18#13182038—42no—
19C2×#11724786—42no—
20C23×D109—21no—
21#13182028—42no—
22C2×Dic218C2311yescharacteristic
23C2×D436C2×C411yescharacteristic
24C2×C22⋊D109—22no—
25C2×C22⋊D109—21no—
26C2×C22⋊D109D412yes—
27D4×D109—42no—
28C22×Dic109D412yes—
29C2×C4×D109C2×C411yescharacteristic
30#13182008—21no—
31C22⋊Dic109—22no—
32#13182006—21no—
33#13182006—22no—
34C4×Dic109C2×C411yescharacteristic
35C2×D4×C109—22no—
36C2×D4×C109C2×C411yescharacteristic
37C2×D4×C109C2×C411yescharacteristic
38C42×C109C2×C411yescharacteristic
39C23×C109—21no—
40C23×C109C22⋊C412yes—
41C22×D109—21no—
42C22×D109—42no—
43C22×D109—82no—
44C22×D109C22⋊C411yescharacteristic
45D4×C109—41no—
46D4×C109—41no—
47D4×C109—82no—
48C2×C4×C109—21no—
49C2×C4×C109C22×C411yescharacteristic
50C22⋊D109—42no—
51C22⋊D109—42no—
52C22⋊D109—82no—
53C2×Dic109—22no—
54C2×Dic109—22no—
55C2×Dic109—21no—
56C2×Dic109C22⋊C411yescharacteristic
57C2×Dic109C2×D412yes—
58D436—41no—
59C4×D109—22no—
60Dic218—41no—
61#11724786—44no—
62C22×C109—22no—
63C22×C109—42no—
64C22×C109—42no—
65C22×C109—41no—
66C22×C109C2×C22⋊C411yescharacteristic
67C2×D109—21no—
68C2×D109—41no—
69C2×D109—42no—
70C2×D109—41no—
71C2×D109—84no—
72C4×C109—21no—
73C4×C109—41no—
74Dic109—22no—
75Dic109—41no—
76Dic109#9912yes—
77C2×C109—21no—
78C2×C109—42no—
79C2×C109—81no—
80C2×C109C2×#9911yescharacteristic
81D109—41no—
82D109—81no—
83#2134—1091nomaximal, Sylow
84C109#213411yescharacteristic, complemented, Sylow
85#535—1091no—
86#413—1092no—
87#355—1092no—
88#355—1092no—
89C2×#41—1091no—
90C22×D4—1091no—
91C2×M16—2182no—
92#127—1091no—
93#127#8913711yescharacteristic
94#124—1091no—
95#124—1091no—
96#121—2182no—
97#120—2182no—
98#117—1091no—
99#101—1094no—
100#100—2182no—
101C24—2181no—
102#41—4362no—
103C2×Q8—1091no—
104C2×D4—22no—
105C2×D4—1092no—
106C2×D4—1091no—
107C2×D4—4362no—
108C2×D4—2181no—
109C2×D4—2182no—
110C2×D4C2×#8913711yescharacteristic
111C2×D4C2×#8913711yescharacteristic
112C22×C4—1092no—
113C22×C4—1091no—
114M16—4362no—
115M16—2184no—
116C2×C8—4362no—
117C4⋊C4—2181no—
118C22⋊C4—2182no—
119C22⋊C4—2181no—
120C22⋊C4—2182no—
121C42—1091no—
122C42C2×#8913711yescharacteristic
123C23—21no—
124C23—8722no—
125C23—1091no—
126C23—4362no—
127C23—2181no—
128C23C22⋊#8913712yes—
129Q8—4361no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—8722no—
134D4—4361no—
135D4—4362no—
136D4—4362no—
137C2×C4—21no—
138C2×C4—1091no—
139C2×C4—1092no—
140C2×C4—2182no—
141C2×C4—2182no—
142C2×C4—2182no—
143C2×C4—2181no—
144C2×C4C22×#8913711yescharacteristic
145C8—4364no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—8724no—
151C22—4362no—
152C22—4361no—
153C22—4361no—
154C22—2181no—
155C22C2×C22⋊#8913711yescharacteristic
156C4—21no—
157C4—41no—
158C4—1092no—
159C4—4361no—
160C4—2182no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—8721no—
165C2—4361no—
166C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#127×C109C4
socleC2×C109C2×#99
prime radical#20295589C2
cosocleC2×Dic218C23
hypercenter#127#89137
hypocenterC109#2134
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20296013C2semidirect
2. #20295935C2semidirect
3. #20295934C2semidirect
6. #16812760C22semidirect
84. C109#2134semidirect

Maximal subgroups

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

subgroupindex
#202960132
#202959352
#202959342
#202955892
#2134109