Finite Group Databasebeta

← #28378555

Subgroups — #28378555

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
2#20296044C211yesmaximal, characteristic, complemented
3#20295885C212yesmaximal, complemented
4#20295884C212yesmaximal, complemented
5#20295573C211yesmaximal, characteristic
6#16812766C2212yes—
7#16812766C2212yes—
8#16812756—21no—
9#16812756—21no—
10#16812754—21no—
11C4×#11724786—21no—
12C2×#13182029—21no—
13#16812698C2211yescharacteristic
14#16812695C2211yescharacteristic
15#16812685—21no—
16#16812674C411yescharacteristic
17#16812672—21no—
18#16812670C411yescharacteristic
19C4×D436C411yescharacteristic
20C4×C22⋊D109—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25#13182029—44no—
26C2×Dic218—21no—
27C2×D436—21no—
28C2×D436C2×C411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C2×C4×D109—21no—
33C2×C4×D109C2×C411yescharacteristic
34C2×C4×D109D411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C4⋊Dic109C2×C411yescharacteristic
37#13182008—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109C2311yescharacteristic
44C2×D4×C109C2×C411yescharacteristic
45C22×C4×C109—21no—
46C4⋊C4×C109C2×C411yescharacteristic
47C22⋊C4×C109—21no—
48C42×C109C2×C411yescharacteristic
49C23×C109—21no—
50C22×D109—21no—
51C22×D109C22⋊C411yescharacteristic
52D4×C109—41no—
53C2×C4×C109—21no—
54C2×C4×C109—42no—
55C2×C4×C109C22⋊C411yescharacteristic
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—42no—
59C22⋊D109—42no—
60C22⋊D109—42no—
61C2×Dic109—21no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C2×D411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65D436—41no—
66D436—42no—
67C4×D109—22no—
68C4×D109—22no—
69C4×D109—41no—
70C4×D109—42no—
71Dic218—42no—
72#11724786—42no—
73#11724786—42no—
74C22×C109—41no—
75C22×C109—41no—
76C22×C109—41no—
77C22×C109C2×C22⋊C411yescharacteristic
78C2×D109—21no—
79C2×D109—21no—
80C2×D109—21no—
81C2×D109—41no—
82C2×D109—41no—
83C2×D109—41no—
84C4×C109—21no—
85C4×C109—21no—
86C4×C109—21no—
87C4×C109—41no—
88Dic109—21no—
89Dic109—41no—
90Dic109#13512yes—
91Dic109AGL(1,ℤ/8)12yes—
92C2×C109—81no—
93C2×C109#41311yescharacteristic
94C2×C109#41611yescharacteristic
95C2×C109#41811yescharacteristic
96D109—41no—
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—1091no—
111#121—2181no—
112C4×D4—1091no—
113C4×D4—2181no—
114C4×D4#8913711yescharacteristic
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—1091no—
125C2×D4—2181no—
126C2×D4—2181no—
127C2×D4—2181no—
128C2×D4—2181no—
129C2×D4C2×#8913711yescharacteristic
130C22×C4—21no—
131C22×C4—1091no—
132C22×C4—1091no—
133C22×C4—1091no—
134C22×C4—2181no—
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—
147C42C2×#8913711yescharacteristic
148C23—21no—
149C23—1091no—
150C23—2181no—
151Q8—4362no—
152D4—41no—
153D4—4361no—
154D4—4362no—
155D4—4362no—
156D4—4362no—
157D4—4362no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—1091no—
161C2×C4—1091no—
162C2×C4—1091no—
163C2×C4—4362no—
164C2×C4—4361no—
165C2×C4—2182no—
166C2×C4—2182no—
167C2×C4—2181no—
168C2×C4C22⋊#8913711yescharacteristic
169C2×C4C22⋊#8913711yescharacteristic
170C2×C4C22×#8913711yescharacteristic
171C8—4362no—
172C8—4362no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—4361no—
177C22—4361no—
178C22—4361no—
179C22—2181no—
180C22—2181no—
181C22—2181no—
182C22C2×C22⋊#8913711yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—1092no—
188C4—1092no—
189C4—4361no—
190C4—2181no—
191C2—81no—
192C2—8721no—
193C2—4361no—
194C2#2029601211yescharacteristic
195C2#2029601611yescharacteristic
196C2#2029601811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295573C2
cosocleC4×Dic109C23
hypercenterC4×D4#89137
hypocenterC109#1553
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296049C2semidirect
2. #20296044C2semidirect
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
#202960492
#202960442
#202958852
#202958842
#202955732
#1553109