Finite Group Databasebeta

← #28362346

Subgroups — #28362346

Order 13952.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#20295770C211yesmaximal, characteristic
2#20295432C211yesmaximal, characteristic, complemented
3#20295388C211yesmaximal, characteristic, complemented
4#20294767C211yesmaximal, characteristic, complemented
5#20294766C211yesmaximal, characteristic, complemented
6#20294765C211yesmaximal, characteristic, complemented
7#497×C109C211yesmaximal, characteristic, complemented
8#16812691C2211yescharacteristic
9#16812687C2211yescharacteristic
10#16812683—21no—
11#16812681—21no—
12#16812676—21no—
13#16812675—21no—
14#16812672—21no—
15#16812671—21no—
16#16812632—21no—
17#16812630—21no—
18#16812622—21no—
19#16812619—21no—
20#16812610C2211yescharacteristic
21#16812610C2211yescharacteristic
22C2×Q16×C109—21no—
23C2×SD16×C109—21no—
24C4⋊Q8×C109C2211yescharacteristic
25#124×C109C2211yescharacteristic
26#97×C109C2211yescharacteristic
27C2×Dic218D411yescharacteristic
28C2×D436D411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C22×Dic109—21no—
32C2×C4×D109—21no—
33C2×#11724784—21no—
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D411yescharacteristic
37C4⋊Dic109D411yescharacteristic
38#13182008—21no—
39#13182008—21no—
40#13182008—21no—
41C22⋊Dic109—21no—
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45C2×Q8×C109—21no—
46C2×Q8×C109D411yescharacteristic
47C2×D4×C109D411yescharacteristic
48Q16×C109—42no—
49SD16×C109—42no—
50C2×C8×C109—21no—
51C4⋊C4×C109—21no—
52C4⋊C4×C109—21no—
53C22⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C42×C109C2311yescharacteristic
56C23×C109—21no—
57C22×D109—21no—
58Q8×C109—41no—
59Q8×C109—41no—
60Q8×C109—41no—
61D4×C109—41no—
62C2×C4×C109—21no—
63C2×C4×C109—41no—
64C2×C4×C109C2×D411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C22⋊D109—81no—
68C22⋊D109—81no—
69C2×Dic109—21no—
70C2×Dic109—21no—
71C2×Dic109—21no—
72C2×Dic109—81no—
73D436—41no—
74C4×D109—81no—
75Dic218—41no—
76C8×C109—22no—
77#11724784—22no—
78#11724784—41no—
79C22×C109—41no—
80C22×C109—41no—
81C22×C109—41no—
82C22×C109#12011yescharacteristic
83C2×D109—41no—
84C2×D109—41no—
85C2×D109—41no—
86C4×C109—21no—
87C4×C109—21no—
88C4×C109—21no—
89C4×C109—41no—
90C4×C109—81no—
91Dic109—41no—
92Dic109—41no—
93Dic109—41no—
94C2×C109—81no—
95C2×C109#45311yescharacteristic
96C2×C109#45511yescharacteristic
97C2×C109#45611yescharacteristic
98D109—81no—
99#1661—1091nomaximal, Sylow
100C109#166111yescharacteristic, complemented, Sylow
101#562—1091no—
102#501—1091no—
103#497D10911yescharacteristic, complemented
104#489—1091no—
105#330—1091no—
106#329—1091no—
107#329—1091no—
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D10911yescharacteristic
111#125—1091no—
112#124—1091no—
113#124C2×D10911yescharacteristic
114#123—2181no—
115#123—2181no—
116C22⋊Q8—2181no—
117C22⋊Q8—2181no—
118#121—2181no—
119#121—2181no—
120#107—2181no—
121#106—2181no—
122#103—2181no—
123#102—2181no—
124#97—1091no—
125#97—1091no—
126#97C2×D10911yescharacteristic
127C2×Q8—21no—
128C2×Q8—1091no—
129C2×Q8C22⋊D10911yescharacteristic
130C2×D4—1091no—
131C2×D4—2181no—
132C2×D4—2181no—
133C2×D4C22⋊D10911yescharacteristic
134C22×C4—2181no—
135C22×C4—2181no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—2181no—
140C2×C8—2181no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1091no—
144C4⋊C4—1091no—
145C4⋊C4—2181no—
146C4⋊C4—2181no—
147C4⋊C4—2181no—
148C4⋊C4—2181no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—2181no—
152C22⋊C4—2181no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C42C22×D10911yescharacteristic
156C23—21no—
157C23—2181no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—4361no—
162D4—41no—
163D4—8721no—
164D4—8721no—
165D4—4361no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—8721no—
169C2×C4—8721no—
170C2×C4—2181no—
171C2×C4—2181no—
172C2×C4—2181no—
173C2×C4D4×D10911yescharacteristic
174C2×C4D4×D10911yescharacteristic
175C2×C4C2×C22⋊D10911yescharacteristic
176C8—22no—
177C8—4361no—
178C8—2182no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—4361no—
183C22—4361no—
184C22—4361no—
185C22#1681266711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—4361no—
192C4—4361no—
193C4—4361no—
194C2—81no—
195C2—8721no—
196C2#2029519311yescharacteristic
197C2#2029520211yescharacteristic
198C2#2029520711yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#497×C109C2
socleC22×C109#120
prime radical#20295770C2
hypercenter#497D109
hypocenterC109#1661
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #20295432C2semidirect
3. #20295388C2semidirect
4. #20294767C2semidirect
5. #20294766C2semidirect
6. #20294765C2semidirect
7. #497×C109C2semidirect
100. C109#1661semidirect
103. #497D109semidirect

Maximal subgroups

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

subgroupindex
#202957702
#202954322
#202953882
#202947672
#202947662
#202947652
#497×C1092
#1661109