Finite Group Databasebeta

← #28362118

Subgroups — #28362118

Order 13952.

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

normal subgroups only

This group has 256 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, complemented
2#20295218C211yesmaximal, characteristic, complemented
3#20295218C211yesmaximal, characteristic, complemented
4#20294772C211yesmaximal, characteristic, complemented
5#20294755C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7#486×C109C211yesmaximal, characteristic, complemented
8C2×#13182030—21no—
9C2×#13182014—21no—
10C2×#13182014—21no—
11#16812684—22no—
12#16812675—21no—
13#16812674—21no—
14C4×D436C2211yescharacteristic
15C4×D436C2211yescharacteristic
16C4⋊C4×D109—21no—
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812620—21no—
20#16812620—21no—
21C4⋊Q8×C109C2211yescharacteristic
22#127×C109C2211yescharacteristic
23#102×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—
33#13182014—42no—
34#13182014—42no—
35C2×#11724784—21no—
36C2×#11724784—21no—
37C4⋊Dic109D411yescharacteristic
38C4⋊Dic109D411yescharacteristic
39#13182008—22no—
40#13182006—22no—
41#13182006—21no—
42#13182006—21no—
43C2×Q8×C109—21no—
44C2×D4×C109—21no—
45C2×D4×C109—21no—
46C2×D4×C109—21no—
47C2×C8×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109D412yes—
50C42×C109C2311yescharacteristic
51C23×C109—41no—
52C22×D109—21no—
53C22×D109—21no—
54Q8×C109—41no—
55Q8×C109—41no—
56D4×C109—42no—
57D4×C109—41no—
58D4×C109—41no—
59D4×C109—41no—
60D4×C109—41no—
61C2×C4×C109—22no—
62C2×C4×C109C2×D411yescharacteristic
63C2×C4×C109C2×D411yescharacteristic
64C2×C4×C109C2×D411yescharacteristic
65C2×Dic109—21no—
66C2×Dic109—21no—
67D436—21no—
68D436—21no—
69D436—21no—
70D436—44no—
71D436D812yescomplemented
72C4×D109—44no—
73C4×D109—41no—
74C4×D109—41no—
75C4×D109—41no—
76C4×D109—41no—
77C8×C109—41no—
78#11724784—41no—
79#11724784—41no—
80C22×C109—81no—
81C22×C109—81no—
82C22×C109—81no—
83C22×C109#12011yescharacteristic
84C2×D109—22no—
85C2×D109—41no—
86C2×D109—41no—
87C2×D109—41no—
88C2×D109—41no—
89C2×D109—41no—
90C4×C109—21no—
91C4×C109—42no—
92C4×C109C2×D811yescharacteristic
93C4×C109#13511yescharacteristic
94C4×C109AGL(1,ℤ/8)11yescharacteristic
95C4×C109AGL(1,ℤ/8)11yescharacteristic
96Dic109—41no—
97Dic109—41no—
98C2×C109—161no—
99C2×C109#44711yescharacteristic
100C2×C109#44911yescharacteristic
101C2×C109#45411yescharacteristic
102D109—42no—
103D109—81no—
104#1625—1091nomaximal, Sylow
105C109#162511yescharacteristic, complemented, Sylow
106#547—1091no—
107#486D10911yescharacteristic, complemented
108#459—1091no—
109#459—1091no—
110#332—1091no—
111D4⋊C8—1091no—
112D4⋊C8—1091no—
113C2×#41—2181no—
114C2×D8—2181no—
115C2×D8—2181no—
116C4⋊Q8C2×D10911yescharacteristic
117#127C2×D10911yescharacteristic
118#123—2182no—
119C22⋊Q8—2181no—
120#121—2181no—
121C4×D4—1091no—
122C4×D4—1091no—
123C2×C4⋊C4—2181no—
124C4⋊C8—1091no—
125C4⋊C8—1091no—
126#102—22no—
127#102—2181no—
128#102—2181no—
129C4×C8C2×D10911yescharacteristic
130#41—4362no—
131#41—4362no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—1091no—
137C2×D4—1091no—
138C2×D4—2182no—
139C22×C4—2182no—
140C22×C4—2181no—
141C22×C4—2181no—
142D8—4362no—
143D8—4362no—
144C2×C8—21no—
145C2×C8—2181no—
146C2×C8—2181no—
147C4⋊C4—21no—
148C4⋊C4—1091no—
149C4⋊C4—1091no—
150C4⋊C4—2182no—
151C4⋊C4C22⋊D10912yes—
152C22⋊C4—2182no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C42C22×D10911yescharacteristic
156C23—41no—
157C23—2181no—
158C23—2181no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—1092no—
167D4—4364no—
168D4—2181no—
169D4—2181no—
170D4—2181no—
171C2×C4—22no—
172C2×C4—4364no—
173C2×C4—4361no—
174C2×C4—4361no—
175C2×C4—4361no—
176C2×C4—4361no—
177C2×C4—2181no—
178C2×C4—2181no—
179C2×C4D4×D10911yescharacteristic
180C2×C4D4×D10911yescharacteristic
181C2×C4C2×C22⋊D10911yescharacteristic
182C8—41no—
183C8—4361no—
184C8—4361no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—4361no—
189C22—4361no—
190C22—4361no—
191C22—4361no—
192C22—4361no—
193C22—2182no—
194C22#1681266711yescharacteristic
195C4—21no—
196C4—42no—
197C4—4361no—
198C4—4361no—
199C4D8×D10911yescharacteristic
200C4#1681272011yescharacteristic
201C4#1681272311yescharacteristic
202C4#1681272611yescharacteristic
203C2—161no—
204C2—8721no—
205C2—4362no—
206C2#2029515811yescharacteristic
207C2#2029517011yescharacteristic
208C2#2029519811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#486×C109C2
socleC22×C109#120
hypercenter#486D109
hypocenterC109#1625
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. #20295679C2semidirect
2. #20295218C2semidirect
3. #20295218C2semidirect
4. #20294772C2semidirect
5. #20294755C2semidirect
6. #20294755C2semidirect
7. #486×C109C2semidirect
71. D436D8semidirect
105. C109#1625semidirect
107. #486D109semidirect

Maximal subgroups

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

subgroupindex
#202956792
#202952182
#202947722
#202947552
#486×C1092
#1625109