Finite Group Databasebeta

← #28362139

Subgroups — #28362139

Order 13952.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#20295750C211yesmaximal, characteristic, complemented
2#20295223C211yesmaximal, characteristic, complemented
3#20295218C211yesmaximal, characteristic
4#20294772C211yesmaximal, characteristic, complemented
5#20294758C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7#486×C109C211yesmaximal, characteristic, complemented
8C2×#13182017—21no—
9C2×#13182014—21no—
10#16812694—22no—
11#16812688—21no—
12#16812679—21no—
13Q8×Dic109—21no—
14C4×Dic218C2211yescharacteristic
15C4×D436C2211yescharacteristic
16#16812657—21no—
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812620—21no—
20#16812620—21no—
21C4⋊Q8×C109C2211yescharacteristic
22#127×C109C2211yescharacteristic
23#102×C109—22no—
24C4×C8×C109C2211yescharacteristic
25C2×Dic218D411yescharacteristic
26C2×D436D411yescharacteristic
27C2×C4×D109—21no—
28#13182017—42no—
29#13182014—42no—
30C2×#11724784—21no—
31C2×#11724784—21no—
32C4⋊Dic109—22no—
33C4⋊Dic109D411yescharacteristic
34C4⋊Dic109D411yescharacteristic
35#13182008—21no—
36#13182006—22no—
37#13182006—22no—
38#13182006—21no—
39C4×Dic109—22no—
40C4×Dic109—21no—
41C2×Q8×C109—21no—
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—21no—
45C2×C8×C109—21no—
46C4⋊C4×C109—21no—
47C4⋊C4×C109D412yes—
48C42×C109C2311yescharacteristic
49C23×C109—41no—
50C22×D109—21no—
51Q8×C109—41no—
52Q8×C109—41no—
53D4×C109—42no—
54D4×C109—41no—
55D4×C109—41no—
56D4×C109—41no—
57D4×C109—41no—
58C2×C4×C109—22no—
59C2×C4×C109C2×D411yescharacteristic
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109C2×D411yescharacteristic
62C2×Dic109—21no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65D436—21no—
66D436—21no—
67C4×D109—41no—
68C4×D109—41no—
69Dic218—21no—
70Dic218—21no—
71C8×C109—41no—
72#11724784—41no—
73#11724784—41no—
74C22×C109—81no—
75C22×C109—81no—
76C22×C109—81no—
77C22×C109#12011yescharacteristic
78C2×D109—41no—
79C2×D109—41no—
80C2×D109—41no—
81C4×C109—21no—
82C4×C109—42no—
83C4×C109#13511yescharacteristic
84C4×C109#13511yescharacteristic
85C4×C109AGL(1,ℤ/8)11yescharacteristic
86C4×C109AGL(1,ℤ/8)11yescharacteristic
87Dic109—41no—
88Dic109—41no—
89Dic109—41no—
90C2×C109—161no—
91C2×C109#44911yescharacteristic
92C2×C109#44911yescharacteristic
93C2×C109#45411yescharacteristic
94D109—81no—
95#1628—1091nomaximal, Sylow
96C109#162811yescharacteristic, complemented, Sylow
97#556—1091no—
98#486D10911yescharacteristic, complemented
99#460—1091no—
100#459—1091no—
101#332—1091no—
102Q8⋊C8—1091no—
103D4⋊C8—1091no—
104C2×SD16—2181no—
105C2×D8—2181no—
106C4⋊Q8C2×D10911yescharacteristic
107#127C2×D10911yescharacteristic
108#126—2182no—
109#124—2181no—
110C22⋊Q8—2181no—
111C4×Q8—1091no—
112C4×Q8—2181no—
113C4×D4—1091no—
114#117—2181no—
115C4⋊C8—1091no—
116C4⋊C8—1091no—
117#102—22no—
118#102—2181no—
119#102—2181no—
120C4×C8C2×D10911yescharacteristic
121C2×Q8—21no—
122C2×Q8—1091no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1091no—
127C22×C4—2181no—
128SD16—4362no—
129D8—4362no—
130C2×C8—21no—
131C2×C8—2181no—
132C2×C8—2181no—
133C4⋊C4—21no—
134C4⋊C4—1091no—
135C4⋊C4—1091no—
136C4⋊C4—2182no—
137C4⋊C4—2181no—
138C4⋊C4C22⋊D10912yes—
139C22⋊C4—2182no—
140C22⋊C4—2182no—
141C22⋊C4—2181no—
142C42—2182no—
143C42—2181no—
144C42C22×D10911yescharacteristic
145C23—41no—
146C23—2181no—
147Q8—41no—
148Q8—41no—
149Q8—2181no—
150Q8—2181no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2181no—
157D4—2181no—
158C2×C4—22no—
159C2×C4—4361no—
160C2×C4—4361no—
161C2×C4—2181no—
162C2×C4—2181no—
163C2×C4—2181no—
164C2×C4D4×D10911yescharacteristic
165C2×C4D4×D10911yescharacteristic
166C2×C4C2×C22⋊D10911yescharacteristic
167C8—41no—
168C8—4361no—
169C8—4361no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—4361no—
174C22—4361no—
175C22—4361no—
176C22#1681266711yescharacteristic
177C4—21no—
178C4—42no—
179C4—4361no—
180C4—4361no—
181C4—4361no—
182C4#1681271811yescharacteristic
183C4#1681272011yescharacteristic
184C4#1681272311yescharacteristic
185C4#1681272611yescharacteristic
186C2—161no—
187C2—8721no—
188C2#2029516811yescharacteristic
189C2#2029517011yescharacteristic
190C2#2029519811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#486×C109C2
socleC22×C109#120
prime radical#20295218C2
hypercenter#486D109
hypocenterC109#1628
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20295750C2semidirect
2. #20295223C2semidirect
4. #20294772C2semidirect
5. #20294758C2semidirect
6. #20294755C2semidirect
7. #486×C109C2semidirect
96. C109#1628semidirect
98. #486D109semidirect

Maximal subgroups

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

subgroupindex
#202957502
#202952232
#202952182
#202947722
#202947582
#202947552
#486×C1092
#1628109