Finite Group Databasebeta

← #28379336

Subgroups — #28379336

Order 13952.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#20296012C212yesmaximal
2#20295937C214yesmaximal, complemented
3#20295602C211yesmaximal, characteristic
4D109⋊M16—22no—
5#16812760C2214yes—
6#16812759—22no—
7C2×#13182029C2211yescharacteristic
8C22×Dic218C411yescharacteristic
9#16812699C2212yes—
10#16812687C412yes—
11#16812683—22no—
12#16812679—22no—
13#117×C109C411yescharacteristic
14#13182039—42no—
15#13182038—24no—
16D109⋊C8—42no—
17#13182029—42no—
18C2×Dic218—21no—
19C2×Dic218—42no—
20C2×Dic218C2×C412yes—
21C2×Dic218C2311yescharacteristic
22C2×D436C2×C411yescharacteristic
23C2×C22⋊D109D412yes—
24C22×Dic109—21no—
25C2×C4×D109D412yes—
26C4⋊Dic109—24no—
27#13182006—24no—
28C22×C4×C109C2×C411yescharacteristic
29C4⋊C4×C109—21no—
30C22⋊C4×C109—21no—
31C42×C109C2×C412yes—
32C23×C109C22⋊C411yescharacteristic
33C22×D109C22⋊C412yes—
34C2×C4×C109—22no—
35C2×C4×C109—22no—
36C2×C4×C109C22⋊C411yescharacteristic
37C2×C4×C109C22×C411yescharacteristic
38C22⋊D109—42no—
39C2×Dic109—22no—
40C2×Dic109—42no—
41C2×Dic109C2×D412yes—
42D436—41no—
43C4×D109—22no—
44C4×D109—22no—
45Dic218—41no—
46Dic218—42no—
47Dic218—42no—
48#11724786—44no—
49C22×C109—21no—
50C22×C109—41no—
51C22×C109C2×C22⋊C411yescharacteristic
52C2×D109—22no—
53C2×D109—42no—
54C4×C109—21no—
55C4×C109—42no—
56C4×C109#9912yes—
57Dic109—22no—
58Dic109—42no—
59C2×C109—21no—
60C2×C109—41no—
61C2×C109C2×#9911yescharacteristic
62D109—42no—
63#2135—1091nomaximal, Sylow
64C109#213511yescharacteristic, complemented, Sylow
65#536—1091no—
66#413—1092no—
67#356—1094no—
68C2×#41—1091no—
69C22×Q8—1091no—
70C2×M16—2182no—
71C4⋊Q8—1092no—
72#124—1092no—
73#123—2182no—
74C22⋊Q8—2182no—
75#117#8913711yescharacteristic
76#101—1094no—
77#100—2182no—
78#41—4362no—
79C2×Q8—1091no—
80C2×Q8—1092no—
81C2×Q8—4362no—
82C2×Q8—2181no—
83C2×D4—1092no—
84C2×D4—1091no—
85C22×C4—1092no—
86C22×C4—2181no—
87C22×C4C2×#8913711yescharacteristic
88M16—4362no—
89M16—2184no—
90C2×C8—4362no—
91C4⋊C4—21no—
92C4⋊C4—2184no—
93C22⋊C4—21no—
94C22⋊C4—2184no—
95C42C2×#8913712yes—
96C23—1092no—
97C23C22⋊#8913711yescharacteristic
98Q8—4362no—
99Q8—4361no—
100Q8—4362no—
101D4—4361no—
102D4—4362no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—1092no—
106C2×C4—4362no—
107C2×C4—2182no—
108C2×C4—2182no—
109C2×C4—2182no—
110C2×C4C22⋊#8913711yescharacteristic
111C2×C4C22×#8913711yescharacteristic
112C8—4364no—
113C22—21no—
114C22—41no—
115C22—4362no—
116C22—2182no—
117C22C2×C22⋊#8913711yescharacteristic
118C4—21no—
119C4—42no—
120C4—4362no—
121C4—2182no—
122C4#1681275812yes—
123C2—21no—
124C2—41no—
125C2—4362no—
126C2C2×#1681275811yescharacteristic
subgroupG/H
centerC2C2×#16812758
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#117×C109C4
socleC2×C109C2×#99
prime radicalC2×#13182029C22
cosocleC2×Dic218C23
hypercenter#117#89137
hypocenterC109#2135
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #20295937C2semidirect
64. C109#2135semidirect

Maximal subgroups

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

subgroupindex
#202960122
#202959372
#202956022
#2135109