Finite Group Databasebeta

← #28379330

Subgroups — #28379330

Order 13952.

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

normal subgroups only

This group has 230 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
1D109⋊#101C212yesmaximal, complemented
2#20295936C212yesmaximal, complemented
3#20295935C212yesmaximal, complemented
4#20295601C211yesmaximal, characteristic
5D109⋊M16—22no—
6#16812760—22no—
7#16812760C2214yes—
8C2×#13182030C411yescharacteristic
9C2×Q8×D109C2211yescharacteristic
10#16812697C2211yescharacteristic
11#16812688C411yescharacteristic
12#16812687C2211yescharacteristic
13#16812684—22no—
14#16812677—22no—
15#16812656C411yescharacteristic
16C4⋊Q8×C109C411yescharacteristic
17#13182039—42no—
18#13182038—24no—
19D109⋊C8—42no—
20#13182030—42no—
21C2×Dic218D412yes—
22C2×Dic218C2311yescharacteristic
23Q8×D109—42no—
24C2×D436—21no—
25C2×D436C2×C411yescharacteristic
26C2×C4×D109—21no—
27C2×C4×D109C2×C411yescharacteristic
28C2×C4×D109D412yes—
29#13182008—21no—
30#13182008—22no—
31#13182006—21no—
32#13182006—22no—
33#13182006—22no—
34C4×Dic109C2×C411yescharacteristic
35C2×Q8×C109C2×C411yescharacteristic
36C2×Q8×C109C2×C411yescharacteristic
37C4⋊C4×C109—22no—
38C42×C109C2×C411yescharacteristic
39C22×D109—21no—
40C22×D109C22⋊C411yescharacteristic
41Q8×C109—41no—
42Q8×C109—41no—
43C2×C4×C109—21no—
44C2×C4×C109—21no—
45C2×C4×C109C22⋊C412yes—
46C2×C4×C109C22×C411yescharacteristic
47C2×Dic109—21no—
48C2×Dic109C22⋊C411yescharacteristic
49C2×Dic109C2×D412yes—
50D436—41no—
51D436—42no—
52C4×D109—22no—
53C4×D109—22no—
54C4×D109—22no—
55C4×D109—42no—
56Dic218—42no—
57Dic218—41no—
58#11724786—44no—
59C22×C109C2×C22⋊C411yescharacteristic
60C2×D109—41no—
61C2×D109—42no—
62C2×D109—41no—
63C2×D109#9912yes—
64C4×C109—21no—
65C4×C109—22no—
66C4×C109—41no—
67C4×C109—41no—
68Dic109—22no—
69Dic109—21no—
70Dic109—41no—
71C2×C109—21no—
72C2×C109C2×#9911yescharacteristic
73D109—22no—
74D109—81no—
75#2133—1091nomaximal, Sylow
76C109#213311yescharacteristic, complemented, Sylow
77#536—1091no—
78C2×#101—1092no—
79#356—1092no—
80#355—1092no—
81C2×#41—1091no—
82C22×Q8—1091no—
83C2×M16—2182no—
84C4⋊Q8—1091no—
85C4⋊Q8#8913711yescharacteristic
86#124—1091no—
87#124—1091no—
88#123—2182no—
89C22⋊Q8—2182no—
90#117—1091no—
91#101—1094no—
92#101—2182no—
93#41—4362no—
94C2×Q8—1092no—
95C2×Q8—1091no—
96C2×Q8—4362no—
97C2×Q8C2×#8913711yescharacteristic
98C2×Q8C2×#8913711yescharacteristic
99C2×D4—1091no—
100C2×D4—2181no—
101C22×C4—1092no—
102C22×C4—1091no—
103C22×C4—2181no—
104M16—4362no—
105M16—2184no—
106C2×C8—4362no—
107C4⋊C4—22no—
108C4⋊C4—2181no—
109C4⋊C4—2182no—
110C22⋊C4—2182no—
111C22⋊C4—2181no—
112C22⋊C4—2182no—
113C42—1091no—
114C42C2×#8913711yescharacteristic
115C23—1091no—
116C23—2181no—
117Q8—41no—
118Q8—41no—
119Q8—4362no—
120Q8—4361no—
121D4—4361no—
122D4—4362no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—1092no—
126C2×C4—1091no—
127C2×C4—4362no—
128C2×C4—2182no—
129C2×C4—2182no—
130C2×C4—2182no—
131C2×C4—2181no—
132C2×C4C22⋊#8913712yes—
133C2×C4C22×#8913711yescharacteristic
134C8—4364no—
135C22—1092no—
136C22—4362no—
137C22—4361no—
138C22—4361no—
139C22C2×C22⋊#8913711yescharacteristic
140C4—22no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—4361no—
145C4—2182no—
146C4—2181no—
147C2—21no—
148C2—8721no—
149C2—2182no—
150C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4⋊Q8×C109C4
socleC2×C109C2×#99
prime radicalC2×#13182030C4
cosocleC2×Dic218C23
hypercenterC4⋊Q8#89137
hypocenterC109#2133
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. D109⋊#101C2semidirect
2. #20295936C2semidirect
3. #20295935C2semidirect
76. C109#2133semidirect

Maximal subgroups

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

subgroupindex
D109⋊#1012
#202959362
#202959352
#202956012
#2133109