Finite Group Databasebeta

← #28378556

Subgroups — #28378556

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#20296046C211yesmaximal, characteristic, complemented
2#20296043C211yesmaximal, characteristic, complemented
3#20295885C212yesmaximal, complemented
4#20295884C212yesmaximal, complemented
5#20295571C211yesmaximal, characteristic
6#16812766C2212yes—
7#16812766C2212yes—
8C22⋊#11724786—21no—
9C22⋊#11724786—21no—
10#16812754—21no—
11C4×#11724786—21no—
12C2×#13182028—21no—
13#16812698C2211yescharacteristic
14#16812695C2211yescharacteristic
15#16812685—21no—
16#16812673C411yescharacteristic
17#16812671—21no—
18D4×Dic109C411yescharacteristic
19#16812661C411yescharacteristic
20#16812659—21no—
21C2×C4×Dic109C2211yescharacteristic
22#121×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25#13182028—44no—
26C2×Dic218—21no—
27C2×D436C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C22×Dic109—21no—
32C22×Dic109D411yescharacteristic
33C22×Dic109D411yescharacteristic
34C2×C4×D109—21no—
35C4⋊Dic109C2×C411yescharacteristic
36#13182008—21no—
37C22⋊Dic109—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109C2×C411yescharacteristic
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109C2311yescharacteristic
44C2×D4×C109—21no—
45C2×D4×C109C2×C411yescharacteristic
46C22×C4×C109C2×C411yescharacteristic
47C4⋊C4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C23×C109—21no—
50C23×C109C22⋊C411yescharacteristic
51C22×D109—21no—
52D4×C109—41no—
53D4×C109—42no—
54C2×C4×C109—21no—
55C2×C4×C109—41no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—42no—
59C22⋊D109—42no—
60C22⋊D109—42no—
61C2×Dic109—22no—
62C2×Dic109—22no—
63C2×Dic109—21no—
64C2×Dic109—42no—
65C2×Dic109C22⋊C411yescharacteristic
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C2×D411yescharacteristic
68C2×Dic109C2×D411yescharacteristic
69D436—41no—
70C4×D109—42no—
71Dic218—42no—
72#11724786—42no—
73#11724786—42no—
74C22×C109—21no—
75C22×C109—21no—
76C22×C109—21no—
77C22×C109—41no—
78C22×C109—41no—
79C22×C109—41no—
80C22×C109C2×C22⋊C411yescharacteristic
81C2×D109—41no—
82C2×D109—41no—
83C2×D109—41no—
84C4×C109—21no—
85C4×C109—21no—
86C4×C109—41no—
87Dic109—21no—
88Dic109—21no—
89Dic109—41no—
90Dic109#13512yes—
91Dic109AGL(1,ℤ/8)12yes—
92C2×C109—41no—
93C2×C109—81no—
94C2×C109#41311yescharacteristic
95C2×C109#41611yescharacteristic
96C2×C109#41811yescharacteristic
97D109—81no—
98#1553—1091nomaximal, Sylow
99C109#155311yescharacteristic, complemented, Sylow
100#532—1091no—
101#432—1091no—
102#431—1091no—
103#332—1092no—
104#331—1092no—
105C2×#41—2181no—
106C4⋊Q8—1091no—
107#127—1091no—
108#124—2181no—
109#121—1091no—
110#121—2181no—
111#121#8913711yescharacteristic
112C4×D4—1091no—
113C4×D4—1091no—
114C4×D4—2181no—
115C2×C42—1091no—
116C4⋊C8—1092no—
117C4⋊C8—1092no—
118C22⋊C8—2181no—
119C22⋊C8—2181no—
120#97—2181no—
121C4×C8—2181no—
122#41—4364no—
123C2×Q8—2181no—
124C2×D4—21no—
125C2×D4—1091no—
126C2×D4—2181no—
127C2×D4—2181no—
128C2×D4—2181no—
129C2×D4C2×#8913711yescharacteristic
130C22×C4—1091no—
131C22×C4—1091no—
132C22×C4—2181no—
133C22×C4—2181no—
134C22×C4C2×#8913711yescharacteristic
135C2×C8—2182no—
136C2×C8—2182no—
137C4⋊C4—1091no—
138C4⋊C4—2181no—
139C4⋊C4C2×#8913711yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—2181no—
142C22⋊C4—2181no—
143C22⋊C4—2181no—
144C42—1091no—
145C42—1091no—
146C42—1091no—
147C42—1091no—
148C23—21no—
149C23—2181no—
150C23C22⋊#8913711yescharacteristic
151Q8—4362no—
152D4—41no—
153D4—42no—
154D4—4361no—
155D4—4362no—
156D4—4362no—
157D4—4362no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—1091no—
161C2×C4—1091no—
162C2×C4—1091no—
163C2×C4—1091no—
164C2×C4—4362no—
165C2×C4—4362no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4—2181no—
169C2×C4C22⋊#8913711yescharacteristic
170C2×C4C22×#8913711yescharacteristic
171C8—4362no—
172C8—4362no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—4361no—
180C22—4361no—
181C22—4361no—
182C22C2×C22⋊#8913711yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—1092no—
187C4—1092no—
188C4—4361no—
189C4—2181no—
190C4—2181no—
191C2—41no—
192C2—81no—
193C2—8721no—
194C2#2029601311yescharacteristic
195C2#2029601611yescharacteristic
196C2#2029601811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#121×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295571C2
cosocleC4×Dic109C23
hypercenter#121#89137
hypocenterC109#1553
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20296046C2semidirect
2. #20296043C2semidirect
3. #20295885C2semidirect
4. #20295884C2semidirect
99. C109#1553semidirect

Maximal subgroups

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

subgroupindex
#202960462
#202960432
#202958852
#202958842
#202955712
#1553109