Finite Group Databasebeta

← #28361622

Subgroups — #28361622

Order 13952.

270 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 63 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#20295575C211yesmaximal, characteristic
2#20294978C212yesmaximal, complemented
3#20294766C211yesmaximal, characteristic, complemented
4#20294765C212yesmaximal, complemented
5#329×C109C211yesmaximal, characteristic, complemented
6C2×#13182030C411yescharacteristic
7C2×#13182028C411yescharacteristic
8C2×#13182012—22no—
9#16812697C411yescharacteristic
10#16812695C411yescharacteristic
11#16812687C2211yescharacteristic
12#16812672—22no—
13#16812659—22no—
14C42×D109C2211yescharacteristic
15#16812610C2212yes—
16C8×Dic109—22no—
17#124×C109C2211yescharacteristic
18#97×C109C2212yes—
19#13182030—42no—
20#13182028—42no—
21C2×Dic218C2×C411yescharacteristic
22C2×D436—21no—
23C2×D436C2×C411yescharacteristic
24C2×C22⋊D109—21no—
25C2×C22⋊D109—22no—
26C22×Dic109—21no—
27C2×C4×D109—21no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D412yes—
30#13182012—28no—
31C2×#11724784—22no—
32#13182008—22no—
33#13182006—22no—
34C4×Dic109C2×C411yescharacteristic
35C4×Dic109D412yes—
36C2×Q8×C109C2×C411yescharacteristic
37C2×D4×C109C2×C411yescharacteristic
38C2×C8×C109—22no—
39C22⋊C4×C109—22no—
40C42×C109C2311yescharacteristic
41C23×C109—21no—
42C22×D109—21no—
43C22×D109C22⋊C411yescharacteristic
44Q8×C109—41no—
45D4×C109—41no—
46C2×C4×C109—21no—
47C2×C4×C109C22×C411yescharacteristic
48C2×C4×C109C2×D412yes—
49C22⋊D109—42no—
50C22⋊D109—44no—
51C2×Dic109—21no—
52C2×Dic109—42no—
53C2×Dic109C22⋊C411yescharacteristic
54C2×Dic109C22⋊C412yes—
55D436—41no—
56D436—42no—
57C4×D109—22no—
58C4×D109—24no—
59C4×D109—42no—
60Dic218—41no—
61C8×C109—24no—
62#11724784—24no—
63C22×C109—41no—
64C22×C109—42no—
65C22×C109C2×C22⋊C411yescharacteristic
66C2×D109—21no—
67C2×D109—22no—
68C2×D109—41no—
69C2×D109—42no—
70C4×C109—21no—
71C4×C109—22no—
72C4×C109—41no—
73Dic109—41no—
74Dic109#10012yes—
75Dic109#10414yes—
76C2×C109—81no—
77C2×C109C2×#10011yescharacteristic
78C2×C109C2×#10412yes—
79D109—41no—
80D109—81no—
81#1525—1091nomaximal, Sylow
82C109#152511yescharacteristic, complemented, Sylow
83#532—1091no—
84C4×M16—1092no—
85#329—1091no—
86#329—1092no—
87#329D10911yescharacteristic, complemented
88C2×#41—1091no—
89C2×#41—1091no—
90C2×M16—2182no—
91C4⋊Q8—1091no—
92#127—1091no—
93#124—1091no—
94#124C2×D10911yescharacteristic
95#121—2182no—
96C4×D4—2182no—
97C2×C42—1091no—
98#97—1092no—
99#97C2×D10912yes—
100C4×C8—2182no—
101#41—4362no—
102#41—4362no—
103C2×Q8—1091no—
104C2×Q8C4×D10911yescharacteristic
105C2×D4—1091no—
106C2×D4—2181no—
107C2×D4—2182no—
108C2×D4—2181no—
109C2×D4C4×D10911yescharacteristic
110C22×C4—1091no—
111C22×C4—1092no—
112C22×C4—2181no—
113C22×C4—2181no—
114M16—2188no—
115C2×C8—22no—
116C2×C8—2182no—
117C4⋊C4—2182no—
118C22⋊C4—22no—
119C22⋊C4—2182no—
120C42—1091no—
121C42—1092no—
122C42C22×D10911yescharacteristic
123C23—21no—
124C23—1091no—
125C23—2181no—
126Q8—41no—
127Q8—4361no—
128D4—41no—
129D4—4361no—
130D4—4362no—
131D4—4364no—
132D4—4362no—
133C2×C4—21no—
134C2×C4—1092no—
135C2×C4—1091no—
136C2×C4—4362no—
137C2×C4—4362no—
138C2×C4—2184no—
139C2×C4—2182no—
140C2×C4—2181no—
141C2×C4C2×C4×D10911yescharacteristic
142C2×C4D4×D10912yes—
143C8—24no—
144C8—2184no—
145C22—41no—
146C22—42no—
147C22—4361no—
148C22—4362no—
149C22—2181no—
150C22—2182no—
151C22C22⋊C4×D10911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—1092no—
156C4—1094no—
157C4—4361no—
158C2—81no—
159C2—8721no—
160C2—4361no—
161C2#100×D10911yescharacteristic
162C2#104×D10912yes—
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC42C22×D109
Fitting#329×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295575C2
cosocleC42×C109C23
hypercenter#329D109
hypocenterC109#1525
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20294978C2semidirect
3. #20294766C2semidirect
4. #20294765C2semidirect
5. #329×C109C2semidirect
82. C109#1525semidirect
87. #329D109semidirect

Maximal subgroups

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

subgroupindex
#202955752
#202949782
#202947662
#202947652
#329×C1092
#1525109