Finite Group Databasebeta

← #28362179

Subgroups — #28362179

Order 13952.

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

normal subgroups only

This group has 218 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#20295741C211yesmaximal, characteristic
2#20295406C211yesmaximal, characteristic, complemented
3#20295317C211yesmaximal, characteristic, complemented
4#20295316C211yesmaximal, characteristic, complemented
5#20294774C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7D4⋊C8×C109C211yesmaximal, characteristic, complemented
8C2×Dic436—22no—
9#16812699C2211yescharacteristic
10#16812699C2211yescharacteristic
11#16812685—22no—
12#16812673—21no—
13#16812670—21no—
14C4×D436C2211yescharacteristic
15#16812658—21no—
16#16812657—21no—
17#16812631—21no—
18#16812630—21no—
19C4⋊#11724784C2211yescharacteristic
20#16812621—21no—
21#16812620—21no—
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218—21no—
26C2×Dic218D412yes—
27C2×D436D411yescharacteristic
28C2×C22⋊D109—22no—
29C2×C4×D109—21no—
30Dic436—44no—
31C2×#11724784—21no—
32C4⋊Dic109—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D411yescharacteristic
37C22⋊Dic109—22no—
38#13182006—22no—
39#13182006—21no—
40C4×Dic109—22no—
41C2×D4×C109D411yescharacteristic
42C22×C4×C109—21no—
43C2×C8×C109—21no—
44C2×C8×C109—21no—
45C4⋊C4×C109D411yescharacteristic
46C22⋊C4×C109—21no—
47C42×C109C2311yescharacteristic
48C23×C109—21no—
49C22×D109—21no—
50D4×C109—21no—
51D4×C109—21no—
52C2×C4×C109—21no—
53C2×C4×C109—41no—
54C2×C4×C109—41no—
55C2×C4×C109C2×D411yescharacteristic
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C22⋊D109—82no—
59C2×Dic109—21no—
60C2×Dic109—22no—
61C2×Dic109—41no—
62D436—21no—
63D436—21no—
64C4×D109—41no—
65C4×D109—41no—
66Dic218—42no—
67Dic218—42no—
68C8×C109—22no—
69C8×C109—41no—
70#11724784—41no—
71C22×C109—41no—
72C22×C109—41no—
73C22×C109—41no—
74C22×C109#12011yescharacteristic
75C2×D109—41no—
76C2×D109—41no—
77C2×D109—41no—
78C4×C109—21no—
79C4×C109—41no—
80C4×C109#13511yescharacteristic
81C4×C109#13511yescharacteristic
82C4×C109#13711yescharacteristic
83C4×C109#13711yescharacteristic
84Dic109—41no—
85Dic109—42no—
86Dic109—81no—
87C2×C109—81no—
88C2×C109#45211yescharacteristic
89C2×C109#45211yescharacteristic
90C2×C109#45311yescharacteristic
91D109—81no—
92#1634—1091nomaximal, Sylow
93C109#163411yescharacteristic, complemented, Sylow
94#555—1091no—
95#494—1091no—
96#476—1091no—
97#476—1091no—
98#333—1091no—
99D4⋊C8—1091no—
100D4⋊C8D10911yescharacteristic, complemented
101C2×Q16—2182no—
102C4⋊Q8—1091no—
103C4⋊Q8—1091no—
104#124—2182no—
105#121—2181no—
106#121—2181no—
107C4×D4—1091no—
108C4×D4C2×D10911yescharacteristic
109#117—2181no—
110#117—2181no—
111#106—2181no—
112#106—2181no—
113C4⋊C8—1091no—
114C4⋊C8C2×D10911yescharacteristic
115#102—2181no—
116#102—2181no—
117C4×C8C2×D10911yescharacteristic
118C2×Q8—1092no—
119C2×Q8—2181no—
120C2×D4—1091no—
121C2×D4—2182no—
122C2×D4D43611yescharacteristic
123C22×C4—21no—
124C22×C4—2181no—
125Q16—4364no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—2181no—
129C4⋊C4—1091no—
130C4⋊C4—2181no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4D43611yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2182no—
137C22⋊C4—2182no—
138C22⋊C4—2181no—
139C42—2182no—
140C42C22×D10911yescharacteristic
141C23—21no—
142C23—2181no—
143Q8—4362no—
144Q8—4362no—
145D4—21no—
146D4—21no—
147D4—8722no—
148D4—2181no—
149D4—2181no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—4361no—
154C2×C4—4361no—
155C2×C4—4361no—
156C2×C4—2181no—
157C2×C4—2182no—
158C2×C4D4×D10911yescharacteristic
159C2×C4D4×D10911yescharacteristic
160C2×C4C2×D43611yescharacteristic
161C8—22no—
162C8—41no—
163C8—4361no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—4361no—
168C22—4361no—
169C22—4361no—
170C22#1681266911yescharacteristic
171C4—21no—
172C4—41no—
173C4—8721no—
174C4—4361no—
175C4—4362no—
176C4#1681271811yescharacteristic
177C4#1681272111yescharacteristic
178C4#1681272811yescharacteristic
179C4#1681273211yescharacteristic
180C2—81no—
181C2—8721no—
182C2#2029518911yescharacteristic
183C2#2029519011yescharacteristic
184C2#2029519511yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
FittingD4⋊C8×C109C2
socleC22×C109#120
prime radical#20295741C2
hypercenterD4⋊C8D109
hypocenterC109#1634
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20295406C2semidirect
3. #20295317C2semidirect
4. #20295316C2semidirect
5. #20294774C2semidirect
6. #20294755C2semidirect
7. D4⋊C8×C109C2semidirect
93. C109#1634semidirect
100. D4⋊C8D109semidirect

Maximal subgroups

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

subgroupindex
#202957412
#202954062
#202953172
#202953162
#202947742
#202947552
D4⋊C8×C1092
#1634109