Finite Group Databasebeta

← #28378446

Subgroups — #28378446

Order 13952.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#20296048C211yesmaximal, characteristic, complemented
2#20295970C211yesmaximal, characteristic, complemented
3#20295879C212yesmaximal, complemented
4#20295878C212yesmaximal
5#20295561C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C4⋊#11724786—21no—
8#16812756C2212yes—
9#16812754—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4C2212yes—
12#16812694—21no—
13#16812687C411yescharacteristic, complemented
14#16812684—21no—
15#16812679C2211yescharacteristic
16#16812674C2211yescharacteristic
17#16812664C411yescharacteristic, complemented
18#16812661—21no—
19#16812661C411yescharacteristic, complemented
20#16812657—21no—
21C42×D109C2211yescharacteristic
22#125×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C4⋊#89137—42no—
26C2×Dic218C2×C411yescharacteristic
27C2×D436—21no—
28C2×D436C2×C411yescharacteristic
29C2×C4×D109—21no—
30C2×C4×D109D411yescharacteristic
31C2×C4×D109D411yescharacteristic
32C2×C4×D109C2311yescharacteristic
33C4⋊Dic109—21no—
34#13182008—21no—
35#13182006—21no—
36#13182006—21no—
37#13182006—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4⋊C4×C109—21no—
45C4⋊C4×C109—21no—
46C4⋊C4×C109C2×C411yescharacteristic
47C4⋊C4×C109C2×C411yescharacteristic
48C42×C109C2×C411yescharacteristic
49C22×D109—21no—
50C22×D109C2×D411yescharacteristic
51C2×#89137—42no—
52C2×#89137—42no—
53C2×#89137—42no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63D436—41no—
64D436—41no—
65D436—41no—
66C4×D109—21no—
67C4×D109—21no—
68C4×D109—41no—
69C4×D109—41no—
70C4×D109—42no—
71Dic218—41no—
72#11724786—42no—
73C22×C109C2×C22⋊C411yescharacteristic
74C2×D109—21no—
75C2×D109—21no—
76C2×D109—41no—
77C2×D109—41no—
78C2×D109—41no—
79C2×D109AGL(1,ℤ/8)11yescharacteristic
80C2×D109#13711yescharacteristic
81#89137—82no—
82C4×C109—21no—
83C4×C109—21no—
84C4×C109—21no—
85C4×C109—41no—
86C4×C109—41no—
87Dic109—21no—
88Dic109—21no—
89Dic109—21no—
90Dic109—41no—
91C2×C109#41011yescharacteristic
92C2×C109#41711yescharacteristic
93C2×C109#42111yescharacteristic
94D109—21no—
95D109—21no—
96D109—81no—
97#1512—1091nomaximal, Sylow
98C109#151211yescharacteristic, complemented, Sylow
99#529—1091no—
100#432—1091no—
101#382—1091no—
102#328—1092no—
103#327—1092no—
104#126—2181no—
105#125#8913711yescharacteristic, complemented
106#124—1091no—
107#123—2181no—
108C22⋊Q8—1091no—
109#121—1091no—
110C4×Q8—1091no—
111C4×D4—1091no—
112C4×D4—2181no—
113#117—2181no—
114C2×C4⋊C4—2181no—
115C2×C42—1091no—
116C4⋊C8—2181no—
117C22⋊C8—1092no—
118#97—2181no—
119#95—1092no—
120#95—2181no—
121C2×Q8—1091no—
122C2×D4—1091no—
123C2×D4—2181no—
124C22×C4—1091no—
125C22×C4—1091no—
126C22×C4—1091no—
127C22×C4—2181no—
128C22×C4—2182no—
129C2×C8—2182no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—4362no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4C2×#8913711yescharacteristic
136C4⋊C4C2×#8913711yescharacteristic
137C22⋊C4—2181no—
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C22⋊C4—2181no—
141C22⋊C4—2181no—
142C42—1091no—
143C42—1091no—
144C42—1091no—
145C42—2181no—
146C42C2×#8913711yescharacteristic
147C23—1091no—
148C23—2181no—
149Q8—4361no—
150D4—4361no—
151D4—4361no—
152D4—4361no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—1091no—
156C2×C4—1091no—
157C2×C4—1091no—
158C2×C4—4361no—
159C2×C4—4361no—
160C2×C4—4362no—
161C2×C4—4362no—
162C2×C4—4362no—
163C2×C4—4362no—
164C2×C4—2181no—
165C2×C4—2181no—
166C2×C4—2181no—
167C2×C4C22⋊#8913711yescharacteristic
168C2×C4C22⋊#8913711yescharacteristic
169C2×C4C22×#8913711yescharacteristic
170C8—4362no—
171C22—1091no—
172C22—1091no—
173C22—4361no—
174C22—4361no—
175C22—4361no—
176C22—2181no—
177C22—2181no—
178C22C2×C22⋊#8913711yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—8722no—
185C4—4361no—
186C4—2181no—
187C4—2181no—
188C4—2181no—
189C2—8721no—
190C2—2181no—
191C2—2181no—
192C2#2029600711yescharacteristic
193C2#2029601711yescharacteristic
194C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#125×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812674C22
cosocleC2×C4×D109C23
hypercenter#125#89137
hypocenterC109#1512
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #20296048C2semidirect
2. #20295970C2semidirect
3. #20295879C2semidirect
13. #16812687C4semidirect
17. #16812664C4semidirect
19. #16812661C4semidirect
22. #125×C109C4semidirect
98. C109#1512semidirect
105. #125#89137semidirect

Maximal subgroups

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

subgroupindex
#202960482
#202959702
#202958792
#202958782
#202955612
#1512109