Finite Group Databasebeta

← #28364981

Subgroups — #28364981

Order 13952.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#20295823C211yesmaximal, characteristic
2#20295467C211yesmaximal, characteristic, complemented
3#20295281C211yesmaximal, characteristic, complemented
4#20294837C211yesmaximal, characteristic, complemented
5#20294836C211yesmaximal, characteristic, complemented
6#20294807C211yesmaximal, characteristic, complemented
7#510×C109C211yesmaximal, characteristic, complemented
8#41×D109—21no—
9#16812731—21no—
10#16812728—21no—
11#16812726—21no—
12#16812723—21no—
13#16812721C2211yescharacteristic
14#16812719—21no—
15C2×#13182012C2211yescharacteristic
16#16812675—21no—
17#16812645—21no—
18#16812642—21no—
19#16812639C2211yescharacteristic, complemented
20#16812631C2211yescharacteristic, complemented
21#16812623—21no—
22#135×C109C2211yescharacteristic
23C2×Q16×C109C2211yescharacteristic, complemented
24Q32×C109—21no—
25SD32×C109—21no—
26M32×C109C2211yescharacteristic, complemented
27#13182030—21no—
28#13182029—21no—
29#13182029—41no—
30#13182028—21no—
31#13182028—41no—
32Q8×D109—21no—
33D4×D109—21no—
34D4×D109—41no—
35C2×C4×D109—41no—
36C2×C4×D109D411yescharacteristic
37Dic436D411yescharacteristic
38#13182019—21no—
39#13182018—21no—
40#13182017—21no—
41#13182016—21no—
42D872D411yescharacteristic
43#13182014—21no—
44#13182012—21no—
45#13182012—21no—
46C2×#11724784D411yescharacteristic
47C4⋊Dic109—21no—
48#13182008—41no—
49#13182006—41no—
50#13182004—21no—
51#41×C109—21no—
52C2×Q8×C109—21no—
53Q16×C109—21no—
54Q16×C109—21no—
55Q16×C109D411yescharacteristic
56SD16×C109—21no—
57D8×C109D411yescharacteristic
58C2×C8×C109C2311yescharacteristic
59C16×C109—21no—
60C22×D109—41no—
61C22×D109D811yescharacteristic
62Q8×C109—21no—
63Q8×C109—41no—
64Q8×C109—41no—
65D4×C109—21no—
66D4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109—41no—
69C2×C4×C109C2×D411yescharacteristic
70C22⋊D109—41no—
71C22⋊D109—41no—
72C22⋊D109—41no—
73C2×Dic109—41no—
74C2×Dic109—41no—
75C2×Dic109D811yescharacteristic
76D436—21no—
77D436—41no—
78C4×D109—21no—
79C4×D109—21no—
80C4×D109—41no—
81C4×D109—41no—
82C4×D109—41no—
83Dic218—21no—
84Dic218—41no—
85C8×C109C2×D411yescharacteristic
86C8×C109C2×D411yescharacteristic
87#11724784—21no—
88C22×C109—41no—
89C22×C109C2×D811yescharacteristic
90C2×D109—21no—
91C2×D109—41no—
92C2×D109—41no—
93C2×D109—82no—
94C4×C109—41no—
95C4×C109—81no—
96C4×C109#12011yescharacteristic
97C4×C109AGL(1,ℤ/8)11yescharacteristic
98Dic109—21no—
99Dic109—41no—
100Dic109—81no—
101C2×C109—21no—
102C2×C109—81no—
103C2×C109#44711yescharacteristic
104D109—41no—
105D109—81no—
106#2191—1091nomaximal, Sylow
107C109#219111yescharacteristic, complemented, Sylow
108#575—1091no—
109#510—1091no—
110#510D10911yescharacteristic, complemented
111#470—1091no—
112#360—1091no—
113#360—1091no—
114#349—1091no—
115C2×#41—2181no—
116#137—2181no—
117#137—2181no—
118AGL(1,ℤ/8)—2181no—
119AGL(1,ℤ/8)—2181no—
120#135—1091no—
121#135—2181no—
122#135C2×D10911yescharacteristic
123C2×Q16C2×D10911yescharacteristic, complemented
124C2×M16—1091no—
125C22⋊Q8—2181no—
126Q32—21no—
127Q32—2181no—
128SD32—21no—
129SD32—2181no—
130M32—1091no—
131M32C2×D10911yescharacteristic, complemented
132#106—1091no—
133#103—2181no—
134#41—21no—
135#41—4361no—
136#41—4361no—
137#41—2181no—
138#41—2181no—
139#41—2181no—
140C2×Q8—21no—
141C2×Q8—2181no—
142C2×D4—4361no—
143C2×D4—2181no—
144C22×C4—1091no—
145C22×C4—4361no—
146Q16—21no—
147Q16—21no—
148Q16—1091no—
149Q16—2181no—
150Q16C22⋊D10911yescharacteristic
151SD16—21no—
152SD16—2181no—
153SD16—2181no—
154SD16—2181no—
155D8—1091no—
156D8—2181no—
157D8C22⋊D10911yescharacteristic
158M16—2181no—
159M16—2181no—
160C2×C8—1091no—
161C2×C8C22×D10911yescharacteristic
162C4⋊C4—4361no—
163C4⋊C4—2181no—
164C22⋊C4—4361no—
165C16—21no—
166C16—2181no—
167C23—1091no—
168C23—4361no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—4361no—
173Q8—2181no—
174D4—21no—
175D4—41no—
176D4—4361no—
177D4—4361no—
178D4—4361no—
179D4—4361no—
180D4—2181no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—1091no—
184C2×C4—4361no—
185C2×C4—4361no—
186C2×C4—4361no—
187C2×C4—4361no—
188C2×C4—4361no—
189C2×C4—2181no—
190C2×C4—2181no—
191C2×C4D4×D10911yescharacteristic
192C8—2181no—
193C8D4×D10911yescharacteristic
194C8C2×C22⋊D10911yescharacteristic
195C22—41no—
196C22—8722no—
197C22—4361no—
198C22—4361no—
199C22—2181no—
200C22D8×D10911yescharacteristic
201C4—41no—
202C4—81no—
203C4—8721no—
204C4—4361no—
205C4—2181no—
206C4#1681266711yescharacteristic
207C4#1681272311yescharacteristic
208C2—21no—
209C2—81no—
210C2—8721no—
211C2—4361no—
212C2#2029515811yescharacteristic
subgroupG/H
centerC2#20295158
commutator, cosocleC2×C8×C109C23
FrattiniC2×C8C22×D109
Fitting#510×C109C2
socleC2×C109#447
prime radical#20295823C2
hypercenter#510D109
hypocenterC109#2191
LCSG ▷ C2×C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #20295467C2semidirect
3. #20295281C2semidirect
4. #20294837C2semidirect
5. #20294836C2semidirect
6. #20294807C2semidirect
7. #510×C109C2semidirect
19. #16812639C22semidirect
20. #16812631C22semidirect
23. C2×Q16×C109C22semidirect
26. M32×C109C22semidirect
107. C109#2191semidirect
110. #510D109semidirect
123. C2×Q16C2×D109semidirect
131. M32C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202958232
#202954672
#202952812
#202948372
#202948362
#202948072
#510×C1092
#2191109