Finite Group Databasebeta

← #28362215

Subgroups — #28362215

Order 13952.

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

normal subgroups only

This group has 212 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#20295762C211yesmaximal, characteristic
2#20295308C211yesmaximal, characteristic, complemented
3#20295233C211yesmaximal, characteristic, complemented
4#20294770C211yesmaximal, characteristic
5#20294758C211yesmaximal, characteristic, complemented
6#20294758C211yesmaximal, characteristic, complemented
7#486×C109C211yesmaximal, characteristic
8C2×#13182019—21no—
9#16812686—21no—
10#16812686—21no—
11#16812680—22no—
12C4×Dic218C2211yescharacteristic
13C4×Dic218C2211yescharacteristic
14D4×Dic109—21no—
15D4×Dic109—21no—
16#16812630—21no—
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812623—21no—
20#16812622—21no—
21C4⋊Q8×C109C2211yescharacteristic
22#127×C109C2211yescharacteristic
23#102×C109—22no—
24C4×C8×C109C2211yescharacteristic
25C2×Dic218D411yescharacteristic
26C2×Dic218D411yescharacteristic
27C22×Dic109—22no—
28#13182019—42no—
29C2×#11724784—21no—
30C2×#11724784—21no—
31C4⋊Dic109D411yescharacteristic
32C4⋊Dic109D411yescharacteristic
33#13182008—21no—
34#13182008—21no—
35C22⋊Dic109—22no—
36C22⋊Dic109—22no—
37C22⋊Dic109—22no—
38C4×Dic109—21no—
39C4×Dic109—21no—
40C2×Q8×C109—21no—
41C2×D4×C109—21no—
42C2×D4×C109—21no—
43C2×D4×C109D412yes—
44C2×C8×C109—21no—
45C4⋊C4×C109—21no—
46C4⋊C4×C109—21no—
47C42×C109C2311yescharacteristic
48C23×C109—22no—
49Q8×C109—41no—
50Q8×C109—41no—
51D4×C109—42no—
52D4×C109—41no—
53D4×C109—41no—
54D4×C109—41no—
55D4×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×C4×C109C2×D411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109—21no—
62C2×Dic109—21no—
63C2×Dic109—21no—
64C2×Dic109—82no—
65Dic218—21no—
66Dic218—21no—
67Dic218—21no—
68Dic218—21no—
69C8×C109—41no—
70#11724784—41no—
71#11724784—41no—
72C22×C109—42no—
73C22×C109—42no—
74C22×C109—42no—
75C22×C109#12011yescharacteristic
76C4×C109—21no—
77C4×C109—81no—
78C4×C109#13511yescharacteristic
79C4×C109#13511yescharacteristic
80C4×C109AGL(1,ℤ/8)11yescharacteristic
81C4×C109#13711yescharacteristic
82Dic109—41no—
83Dic109—41no—
84Dic109—41no—
85Dic109—41no—
86C2×C109—82no—
87C2×C109#44911yescharacteristic
88C2×C109#45211yescharacteristic
89C2×C109#45511yescharacteristic
90#1640—1091nomaximal, Sylow
91C109#164011yescharacteristic, complemented, Sylow
92#559—1091no—
93#486D10911yescharacteristic
94#475—1091no—
95#462—1091no—
96#331—1091no—
97Q8⋊C8—1091no—
98Q8⋊C8—1091no—
99C2×Q16—2181no—
100C4⋊Q8C2×D10911yescharacteristic
101#127C2×D10911yescharacteristic
102#124—2181no—
103#124—2181no—
104#123—2182no—
105C4×Q8—1091no—
106C4×Q8—1091no—
107C4×D4—2181no—
108C4×D4—2181no—
109#106—2181no—
110C4⋊C8—1091no—
111C4⋊C8—1091no—
112#103—2181no—
113#103—2181no—
114#102—22no—
115C4×C8C2×D10911yescharacteristic
116C2×Q8—21no—
117C2×Q8—1091no—
118C2×Q8—1091no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D10912yes—
122C22×C4—2182no—
123Q16—4362no—
124C2×C8—21no—
125C2×C8—2181no—
126C2×C8—2181no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1091no—
130C4⋊C4—1091no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C22⋊C4—2182no—
134C22⋊C4—2182no—
135C22⋊C4—2182no—
136C42—2181no—
137C42—2181no—
138C42C22×D10911yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—2181no—
143Q8—2181no—
144Q8—2181no—
145Q8—2181no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—8722no—
153C2×C4—2181no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4—2181no—
157C2×C4D4×D10911yescharacteristic
158C2×C4D4×D10911yescharacteristic
159C2×C4C2×C22⋊D10911yescharacteristic
160C8—41no—
161C8—4361no—
162C8—4361no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1681266711yescharacteristic
167C4—21no—
168C4—81no—
169C4—4361no—
170C4—4361no—
171C4—4361no—
172C4—4361no—
173C4#1681271811yescharacteristic
174C4#1681272011yescharacteristic
175C4#1681272311yescharacteristic
176C4#1681272811yescharacteristic
177C2—82no—
178C2#2029516811yescharacteristic
179C2#2029518511yescharacteristic
180C2#2029520311yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#486×C109C2
socleC22×C109#120
prime radical#127×C109C22
hypercenter#486D109
hypocenterC109#1640
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #20295308C2semidirect
3. #20295233C2semidirect
5. #20294758C2semidirect
6. #20294758C2semidirect
91. C109#1640semidirect

Maximal subgroups

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

subgroupindex
#202957622
#202953082
#202952332
#202947702
#202947582
#486×C1092
#1640109