Finite Group Databasebeta

← #28379324

Subgroups — #28379324

Order 13952.

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

normal subgroups only

This group has 250 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#20295937C212yesmaximal, complemented
3#20295934C212yesmaximal, complemented
4#20295574C211yesmaximal, characteristic
5C2×#13182038—22no—
6#16812760C2214yes—
7#16812759—22no—
8C2×#13182028C411yescharacteristic
9C2×#13182028C2211yescharacteristic
10#16812699C2211yescharacteristic
11#16812686C411yescharacteristic
12#16812686C2211yescharacteristic
13#16812670—22no—
14D4×Dic109—22no—
15C42×D109C411yescharacteristic
16#127×C109C411yescharacteristic
17#13182038—24no—
18#13182038—42no—
19C2×#11724786—42no—
20#13182028—41no—
21#13182028—41no—
22#13182028—41no—
23#13182028—41no—
24C2×Dic218C2×C411yescharacteristic
25C2×Dic218C2311yescharacteristic
26C2×C22⋊D109—21no—
27C2×C22⋊D109D412yes—
28C22×Dic109—21no—
29C22×Dic109D412yes—
30C2×C4×D109—21no—
31C2×C4×D109C2×C411yescharacteristic
32C4⋊Dic109—22no—
33C22⋊Dic109—22no—
34C22⋊Dic109—22no—
35C4×Dic109—21no—
36C4×Dic109C2×C411yescharacteristic
37C2×D4×C109—22no—
38C2×D4×C109C2×C411yescharacteristic
39C2×D4×C109C2×C411yescharacteristic
40C42×C109C2×C411yescharacteristic
41C23×C109—21no—
42C23×C109C22⋊C412yes—
43C22×D109C22⋊C411yescharacteristic
44D4×C109—41no—
45D4×C109—41no—
46D4×C109—44no—
47C2×C4×C109—21no—
48C2×C4×C109C22×C411yescharacteristic
49C22⋊D109—42no—
50C22⋊D109—42no—
51C2×Dic109—22no—
52C2×Dic109—22no—
53C2×Dic109—21no—
54C2×Dic109—21no—
55C2×Dic109—41no—
56C2×Dic109—41no—
57C2×Dic109C22⋊C411yescharacteristic
58C2×Dic109C2×D412yes—
59C4×D109—21no—
60C4×D109—21no—
61C4×D109—42no—
62Dic218—41no—
63Dic218—41no—
64#11724786—44no—
65C22×C109—22no—
66C22×C109—42no—
67C22×C109—42no—
68C22×C109—41no—
69C22×C109C2×C22⋊C411yescharacteristic
70C2×D109—21no—
71C2×D109—41no—
72C4×C109—22no—
73C4×C109—21no—
74Dic109—22no—
75Dic109—41no—
76Dic109—41no—
77Dic109#9911yescharacteristic
78Dic109#9911yescharacteristic
79C2×C109—21no—
80C2×C109—42no—
81C2×C109—81no—
82C2×C109C2×#9911yescharacteristic
83D109—41no—
84#2132—1091nomaximal, Sylow
85C109#213211yescharacteristic, complemented, Sylow
86#532—1091no—
87#413—1092no—
88#356—1092no—
89#355—1092no—
90C2×#41—1091no—
91C2×#41—1091no—
92C2×M16—2182no—
93C4⋊Q8—1091no—
94#127#8913711yescharacteristic
95#124—1091no—
96#124—1091no—
97#121—2182no—
98C4×D4—2182no—
99C2×C42—1091no—
100#101—1094no—
101#100—2182no—
102#41—4361no—
103#41—4361no—
104#41—4361no—
105#41—4361no—
106C2×Q8—1091no—
107C2×Q8—1091no—
108C2×D4—22no—
109C2×D4—1092no—
110C2×D4—2181no—
111C2×D4C2×#8913711yescharacteristic
112C2×D4C2×#8913711yescharacteristic
113C22×C4—1092no—
114C22×C4—1091no—
115C22×C4—2181no—
116C22×C4—2181no—
117M16—4362no—
118M16—2184no—
119C2×C8—4362no—
120C4⋊C4—2182no—
121C22⋊C4—2182no—
122C22⋊C4—2182no—
123C42—1091no—
124C42—2181no—
125C42C2×#8913711yescharacteristic
126C23—21no—
127C23—1091no—
128C23C22⋊#8913712yes—
129Q8—4361no—
130Q8—4361no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—4362no—
135D4—4362no—
136C2×C4—21no—
137C2×C4—1091no—
138C2×C4—1092no—
139C2×C4—4362no—
140C2×C4—4361no—
141C2×C4—4361no—
142C2×C4—2181no—
143C2×C4—2181no—
144C2×C4—2182no—
145C2×C4—2182no—
146C2×C4—2181no—
147C2×C4—2181no—
148C2×C4C22×#8913711yescharacteristic
149C8—4364no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—4361no—
155C22—2181no—
156C22C2×C22⋊#8913711yescharacteristic
157C4—22no—
158C4—21no—
159C4—1091no—
160C4—1091no—
161C4—4361no—
162C4—4361no—
163C4—2182no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—4361no—
168C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#127×C109C4
socleC2×C109C2×#99
prime radical#20295574C2
cosocleC2×Dic218C23
hypercenter#127#89137
hypocenterC109#2132
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. #20295937C2semidirect
3. #20295934C2semidirect
85. C109#2132semidirect

Maximal subgroups

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

subgroupindex
#202960132
#202959372
#202959342
#202955742
#2132109