Finite Group Databasebeta

← #28378557

Subgroups — #28378557

Order 13952.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#20296049C211yesmaximal, characteristic
2#20296044C211yesmaximal, characteristic
3#20295886C212yesmaximal, complemented
4#20295885C212yesmaximal, complemented
5#20295580C211yesmaximal, characteristic
6#16812766C2212yes—
7#16812766C2212yes—
8#16812756—21no—
9#16812756—21no—
10#16812754—21no—
11C4×#11724786—21no—
12#16812698C2211yescharacteristic
13#16812697C2211yescharacteristic
14#16812689—21no—
15#16812679C411yescharacteristic
16#16812677—21no—
17#16812675C411yescharacteristic
18C4×Dic218—21no—
19C4×Dic218C411yescharacteristic
20#16812656—21no—
21C42×D109C2211yescharacteristic
22C4×Q8×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25C2×Dic218—21no—
26C2×Dic218C2×C411yescharacteristic
27C2×C4×D109C2×C411yescharacteristic
28C2×C4×D109D411yescharacteristic
29C2×C4×D109D411yescharacteristic
30C4⋊Dic109—21no—
31C4⋊Dic109C2×C411yescharacteristic
32#13182008—21no—
33#13182008—21no—
34#13182008—21no—
35#13182008—21no—
36#13182008—21no—
37#13182006—21no—
38#13182006—21no—
39C4×Dic109—21no—
40C4×Dic109D411yescharacteristic
41C4×Dic109D411yescharacteristic
42C4×Dic109C2311yescharacteristic
43C2×Q8×C109C2×C411yescharacteristic
44C4⋊C4×C109—21no—
45C4⋊C4×C109C2×C411yescharacteristic
46C42×C109—21no—
47C42×C109C2×C411yescharacteristic
48C22×D109C22⋊C411yescharacteristic
49Q8×C109—41no—
50C2×C4×C109—21no—
51C2×C4×C109—21no—
52C2×C4×C109C22⋊C411yescharacteristic
53C2×C4×C109C22⋊C411yescharacteristic
54C2×C4×C109C22×C411yescharacteristic
55C2×Dic109—21no—
56C2×Dic109—21no—
57C2×Dic109C22⋊C411yescharacteristic
58C2×Dic109C2×D411yescharacteristic
59C2×Dic109C2×D411yescharacteristic
60C4×D109—22no—
61C4×D109—22no—
62C4×D109—41no—
63Dic218—42no—
64Dic218—41no—
65#11724786—42no—
66#11724786—42no—
67C22×C109C2×C22⋊C411yescharacteristic
68C2×D109—21no—
69C2×D109—21no—
70C2×D109—21no—
71C4×C109—21no—
72C4×C109—21no—
73C4×C109—21no—
74C4×C109—41no—
75C4×C109—41no—
76Dic109—21no—
77Dic109—41no—
78Dic109—41no—
79Dic109#13512yes—
80Dic109#13712yes—
81C2×C109#41311yescharacteristic
82C2×C109#41611yescharacteristic
83C2×C109#41911yescharacteristic
84D109—41no—
85#1554—1091nomaximal, Sylow
86C109#155411yescharacteristic, complemented, Sylow
87#533—1091no—
88#432—1091no—
89#431—1091no—
90#333—1092no—
91#332—1092no—
92C4⋊Q8—1091no—
93C4⋊Q8—1091no—
94#125—2181no—
95C22⋊Q8—1091no—
96C22⋊Q8—1091no—
97C22⋊Q8—2181no—
98C4×Q8—1091no—
99C4×Q8—2181no—
100C4×Q8#8913711yescharacteristic
101#117—2181no—
102C2×C42—1091no—
103C4⋊C8—1092no—
104C4⋊C8—1092no—
105C22⋊C8—2181no—
106C22⋊C8—2181no—
107#97—2181no—
108C4×C8—2181no—
109C2×Q8—1091no—
110C2×Q8—2181no—
111C2×Q8C2×#8913711yescharacteristic
112C22×C4—1091no—
113C22×C4—1091no—
114C22×C4—1091no—
115C2×C8—2182no—
116C2×C8—2182no—
117C4⋊C4—21no—
118C4⋊C4—1091no—
119C4⋊C4—2181no—
120C4⋊C4—2181no—
121C4⋊C4—2181no—
122C4⋊C4—2181no—
123C4⋊C4—2181no—
124C4⋊C4—2181no—
125C4⋊C4C2×#8913711yescharacteristic
126C22⋊C4—2181no—
127C22⋊C4—2181no—
128C42—21no—
129C42—1091no—
130C42—1091no—
131C42—1091no—
132C42—2181no—
133C42C2×#8913711yescharacteristic
134C23—1091no—
135Q8—41no—
136Q8—4361no—
137Q8—4362no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—1091no—
141C2×C4—1091no—
142C2×C4—1091no—
143C2×C4—4361no—
144C2×C4—2182no—
145C2×C4—2182no—
146C2×C4—2181no—
147C2×C4—2181no—
148C2×C4C22⋊#8913711yescharacteristic
149C2×C4C22⋊#8913711yescharacteristic
150C2×C4C22×#8913711yescharacteristic
151C8—4362no—
152C8—4362no—
153C22—2181no—
154C22—2181no—
155C22—2181no—
156C22C2×C22⋊#8913711yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—1092no—
163C4—1092no—
164C4—4361no—
165C4—4361no—
166C4—2181no—
167C2—4361no—
168C2#2029601211yescharacteristic
169C2#2029601611yescharacteristic
170C2#2029601911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C22⋊C4
cosocleC4×Dic109C23
hypercenterC4×Q8#89137
hypocenterC109#1554
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20295886C2semidirect
4. #20295885C2semidirect
86. C109#1554semidirect

Maximal subgroups

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

subgroupindex
#202960492
#202960442
#202958862
#202958852
#202955802
#1554109