Finite Group Databasebeta

← #28378433

Subgroups — #28378433

Order 13952.

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

normal subgroups only

This group has 242 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, complemented
2C4×C4⋊#89137C211yesmaximal, characteristic, complemented
3#20295880C212yesmaximal, complemented
4#20295877C212yesmaximal
5#20295555C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C2×C4×#89137—21no—
8#16812766—21no—
9#16812756C2212yes—
10#16812754—21no—
11(C2×#89137)⋊C4C2212yes—
12#16812692—21no—
13#16812691C411yescharacteristic, complemented
14#16812681—21no—
15#16812675C2211yescharacteristic
16#16812670C2211yescharacteristic
17Q8×Dic109C411yescharacteristic, complemented
18D4×Dic109C411yescharacteristic, complemented
19#16812659—21no—
20#16812655—21no—
21C42×D109C2211yescharacteristic
22#124×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C4⋊#89137—24no—
26C4×#89137—42no—
27C2×C22⋊D109—21no—
28C22×Dic109—21no—
29C2×C4×D109D411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C2×C4×D109C2311yescharacteristic
32C4⋊Dic109—21no—
33C4⋊Dic109C2×C411yescharacteristic
34C4⋊Dic109C2×C411yescharacteristic
35#13182008—21no—
36#13182008—21no—
37#13182008—21no—
38C22⋊Dic109—21no—
39C22⋊Dic109—21no—
40#13182006—21no—
41C4×Dic109—21no—
42C4×Dic109C2×C411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C2×D4×C109C2×C411yescharacteristic
47C22⋊C4×C109—21no—
48C22⋊C4×C109—21no—
49C42×C109C2×C411yescharacteristic
50C23×C109—21no—
51C22×D109C2×D411yescharacteristic
52C2×#89137—24no—
53C2×#89137—42no—
54C2×#89137—42no—
55Q8×C109—41no—
56D4×C109—41no—
57C2×C4×C109—21no—
58C2×C4×C109C22⋊C411yescharacteristic
59C2×C4×C109C22⋊C411yescharacteristic
60C2×C4×C109C22×C411yescharacteristic
61C22⋊D109—41no—
62C22⋊D109—41no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65C2×Dic109—42no—
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C22⋊C411yescharacteristic
68C2×Dic109C2×D411yescharacteristic
69C4×D109—21no—
70C4×D109—21no—
71C4×D109—22no—
72C4×D109—41no—
73#11724786—42no—
74C22×C109—41no—
75C22×C109—41no—
76C22×C109—41no—
77C22×C109C2×C22⋊C411yescharacteristic
78C2×D109—21no—
79C2×D109—21no—
80C2×D109AGL(1,ℤ/8)11yescharacteristic
81C2×D109#13711yescharacteristic
82#89137—44no—
83C4×C109—21no—
84C4×C109—21no—
85C4×C109—21no—
86C4×C109—41no—
87Dic109—21no—
88Dic109—21no—
89Dic109—41no—
90Dic109—41no—
91Dic109#10412yes—
92C2×C109—81no—
93C2×C109#41011yescharacteristic
94C2×C109#41711yescharacteristic
95C2×C109C2×#10411yescharacteristic
96D109—21no—
97D109—21no—
98#1509—1091nomaximal, Sylow
99C109#150911yescharacteristic, complemented, Sylow
100#529—1091no—
101#432—1091no—
102C4×C4⋊C4—1091no—
103#328—1092no—
104#327—1092no—
105#126—2181no—
106#125—1091no—
107#124#8913711yescharacteristic, complemented
108#123—2181no—
109C22⋊Q8—1091no—
110#121—1091no—
111C4×Q8—1091no—
112C4×D4—1091no—
113C4×D4—2181no—
114#117—2181no—
115C2×C4⋊C4—2181no—
116C2×C42—1091no—
117C2×C42—2181no—
118C4⋊C8—2181no—
119C22⋊C8—1092no—
120#97—2181no—
121#95—1092no—
122C2×Q8C2×#8913711yescharacteristic
123C2×D4—2181no—
124C2×D4C2×#8913711yescharacteristic
125C22×C4—1091no—
126C22×C4—1091no—
127C22×C4—1091no—
128C22×C4—2181no—
129C22×C4—2182no—
130C2×C8—2182no—
131C4⋊C4—1091no—
132C4⋊C4—1091no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4—2184no—
136C4⋊C4—2181no—
137C4⋊C4—2181no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—2181no—
141C22⋊C4—2181no—
142C22⋊C4—2181no—
143C42—1091no—
144C42—1091no—
145C42—1091no—
146C42—4362no—
147C42—2181no—
148C42C2×#8913711yescharacteristic
149C23—21no—
150C23—1091no—
151Q8—41no—
152D4—41no—
153D4—4361no—
154D4—4361no—
155C2×C4—21no—
156C2×C4—1091no—
157C2×C4—1091no—
158C2×C4—1091no—
159C2×C4—4361no—
160C2×C4—4362no—
161C2×C4—4362no—
162C2×C4—4362no—
163C2×C4—2182no—
164C2×C4—2181no—
165C2×C4—2181no—
166C2×C4—2184no—
167C2×C4—2181no—
168C2×C4—2181no—
169C2×C4C22⋊#8913711yescharacteristic
170C2×C4C22⋊#8913711yescharacteristic
171C2×C4C22×#8913711yescharacteristic
172C8—4362no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1091no—
177C22—1091no—
178C22—2181no—
179C22—2181no—
180C22C2×C22⋊#8913711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—1092no—
186C4—4364no—
187C4—4361no—
188C4—4361no—
189C4—2181no—
190C4—2181no—
191C2—81no—
192C2—2181no—
193C2—2181no—
194C2#2029600611yescharacteristic
195C2#2029601711yescharacteristic
196C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812670C22
cosocleC2×C4×D109C23
hypercenter#124#89137
hypocenterC109#1509
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296049C2semidirect
2. C4×C4⋊#89137C2semidirect
3. #20295880C2semidirect
13. #16812691C4semidirect
17. Q8×Dic109C4semidirect
18. D4×Dic109C4semidirect
22. #124×C109C4semidirect
99. C109#1509semidirect
107. #124#89137semidirect

Maximal subgroups

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

subgroupindex
#202960492
C4×C4⋊#891372
#202958802
#202958772
#202955552
#1509109