Finite Group Databasebeta

← #28362180

Subgroups — #28362180

Order 13952.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295679C211yesmaximal, characteristic
2#20295313C211yesmaximal, characteristic, complemented
3#20295313C211yesmaximal, characteristic, complemented
4#20294772C211yesmaximal, characteristic, complemented
5#20294755C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7#487×C109C211yesmaximal, characteristic, complemented
8C2×#13182030—21no—
9#16812684—22no—
10#16812675—21no—
11#16812674—21no—
12C4×D436C2211yescharacteristic
13C4×D436C2211yescharacteristic
14C4⋊C4×D109—21no—
15#16812630—21no—
16#16812630—21no—
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812619—21no—
20#16812619—21no—
21C4⋊Q8×C109C2211yescharacteristic
22C4⋊Q8×C109C2211yescharacteristic
23#103×C109—22no—
24C4×C8×C109C2211yescharacteristic
25#13182030—42no—
26#13182030—42no—
27C2×D436—22no—
28C2×D436D411yescharacteristic
29C2×D436D411yescharacteristic
30C2×C4×D109—22no—
31C2×C4×D109—21no—
32C2×C4×D109—21no—
33C2×#11724784—21no—
34C2×#11724784—21no—
35C4⋊Dic109D411yescharacteristic
36C4⋊Dic109D411yescharacteristic
37#13182008—22no—
38#13182006—22no—
39#13182006—21no—
40#13182006—21no—
41C2×Q8×C109—21no—
42C2×Q8×C109—21no—
43C2×C8×C109—21no—
44C4⋊C4×C109—21no—
45C4⋊C4×C109—21no—
46C4⋊C4×C109—21no—
47C4⋊C4×C109D412yes—
48C42×C109C2311yescharacteristic
49C22×D109—21no—
50C22×D109—21no—
51Q8×C109—42no—
52Q8×C109—41no—
53Q8×C109—41no—
54C2×C4×C109—22no—
55C2×C4×C109—41no—
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109—21no—
61D436—21no—
62D436—21no—
63D436—21no—
64D436—44no—
65D436SD1612yes—
66C4×D109—44no—
67C4×D109—41no—
68C4×D109—41no—
69C4×D109—41no—
70C4×D109—41no—
71C8×C109—41no—
72#11724784—41no—
73#11724784—41no—
74C22×C109#12011yescharacteristic
75C2×D109—22no—
76C2×D109—41no—
77C2×D109—41no—
78C2×D109—41no—
79C2×D109—41no—
80C2×D109—41no—
81C4×C109—21no—
82C4×C109—42no—
83C4×C109—81no—
84C4×C109C2×SD1611yescharacteristic
85C4×C109#13511yescharacteristic
86C4×C109AGL(1,ℤ/8)11yescharacteristic
87C4×C109#13711yescharacteristic
88Dic109—41no—
89Dic109—41no—
90C2×C109#45011yescharacteristic
91C2×C109#45211yescharacteristic
92C2×C109#45411yescharacteristic
93D109—42no—
94D109—81no—
95#1635—1091nomaximal, Sylow
96C109#163511yescharacteristic, complemented, Sylow
97#547—1091no—
98#487D10911yescharacteristic, complemented
99#476—1091no—
100#476—1091no—
101#332—1091no—
102D4⋊C8—1091no—
103D4⋊C8—1091no—
104C2×#41—2181no—
105C4⋊Q8C2×D10911yescharacteristic
106C4⋊Q8C2×D10911yescharacteristic
107#123—2182no—
108C22⋊Q8—2181no—
109#121—2181no—
110C4×D4—1091no—
111C4×D4—1091no—
112C2×C4⋊C4—2181no—
113#106—2181no—
114#106—2181no—
115C4⋊C8—1091no—
116C4⋊C8—1091no—
117#103—22no—
118#102—2181no—
119#102—2181no—
120C4×C8C2×D10911yescharacteristic
121#41—4362no—
122#41—4362no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—1091no—
126C2×D4—1091no—
127C2×D4—2182no—
128C22×C4—2182no—
129C22×C4—2181no—
130C22×C4—2181no—
131C2×C8—21no—
132C2×C8—2181no—
133C2×C8—2181no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—1091no—
138C4⋊C4—1091no—
139C4⋊C4—2182no—
140C4⋊C4C22⋊D10912yes—
141C22⋊C4—2182no—
142C22⋊C4—2181no—
143C22⋊C4—2181no—
144C42C22×D10911yescharacteristic
145C23—2181no—
146C23—2181no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—1092no—
151D4—4364no—
152D4—2181no—
153D4—2181no—
154D4—2181no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—4364no—
158C2×C4—4361no—
159C2×C4—4361no—
160C2×C4—4361no—
161C2×C4—4361no—
162C2×C4—2181no—
163C2×C4—2181no—
164C2×C4D4×D10911yescharacteristic
165C2×C4D4×D10911yescharacteristic
166C2×C4C2×C22⋊D10911yescharacteristic
167C8—41no—
168C8—4361no—
169C8—4361no—
170C22—4361no—
171C22—4361no—
172C22—4361no—
173C22—4361no—
174C22—4361no—
175C22—2182no—
176C22#1681266711yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—4361no—
181C4—4361no—
182C4SD16×D10911yescharacteristic
183C4#1681272211yescharacteristic
184C4#1681272611yescharacteristic
185C4#1681273111yescharacteristic
186C2—8721no—
187C2—4362no—
188C2#2029517511yescharacteristic
189C2#2029518711yescharacteristic
190C2#2029519811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#487×C109C2
socleC22×C109#120
prime radical#20295679C2
hypercenter#487D109
hypocenterC109#1635
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20295313C2semidirect
3. #20295313C2semidirect
4. #20294772C2semidirect
5. #20294755C2semidirect
6. #20294755C2semidirect
7. #487×C109C2semidirect
96. C109#1635semidirect
98. #487D109semidirect

Maximal subgroups

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

subgroupindex
#202956792
#202953132
#202947722
#202947552
#487×C1092
#1635109