Finite Group Databasebeta

← #28362206

Subgroups — #28362206

Order 13952.

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

normal subgroups only

This group has 194 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#20295746C211yesmaximal, characteristic
2#20295377C211yesmaximal, characteristic, complemented
3#20295322C211yesmaximal, characteristic, complemented
4#20295316C211yesmaximal, characteristic
5#20294771C211yesmaximal, characteristic, complemented
6#20294758C211yesmaximal, characteristic, complemented
7D4⋊C8×C109C211yesmaximal, characteristic
8#16812699C2211yescharacteristic
9#16812699C2211yescharacteristic
10#16812692—22no—
11#16812686—21no—
12#16812678—21no—
13C4×Dic218C2211yescharacteristic
14#16812664—21no—
15#16812658—21no—
16#16812633—21no—
17#16812630—21no—
18C4⋊#11724784C2211yescharacteristic
19#16812624—21no—
20#16812624—22no—
21#16812620—21no—
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218—21no—
26C2×Dic218—21no—
27C2×Dic218D411yescharacteristic
28C2×#11724784—21no—
29C4⋊Dic109—21no—
30C4⋊Dic109—21no—
31C4⋊Dic109—21no—
32C4⋊Dic109D412yes—
33C4⋊Dic109D411yescharacteristic
34#13182008—22no—
35#13182008—21no—
36C22⋊Dic109—22no—
37C22⋊Dic109—22no—
38C4×Dic109—22no—
39C4×Dic109—21no—
40C2×D4×C109D411yescharacteristic
41C22×C4×C109—21no—
42C2×C8×C109—21no—
43C2×C8×C109—21no—
44C4⋊C4×C109D411yescharacteristic
45C22⋊C4×C109—21no—
46C42×C109C2311yescharacteristic
47C23×C109—21no—
48D4×C109—21no—
49D4×C109—21no—
50C2×C4×C109—21no—
51C2×C4×C109—41no—
52C2×C4×C109—41no—
53C2×C4×C109C2×D411yescharacteristic
54C2×C4×C109C2×D411yescharacteristic
55C2×C4×C109C2×D411yescharacteristic
56C2×Dic109—21no—
57C2×Dic109—21no—
58C2×Dic109—22no—
59C2×Dic109—41no—
60Dic218—21no—
61Dic218—21no—
62Dic218—41no—
63Dic218—41no—
64Dic218—42no—
65C8×C109—41no—
66C8×C109—41no—
67#11724784—41no—
68C22×C109—41no—
69C22×C109—41no—
70C22×C109—41no—
71C22×C109#12011yescharacteristic
72C4×C109—21no—
73C4×C109—41no—
74C4×C109#13511yescharacteristic
75C4×C109#13511yescharacteristic
76C4×C109#13711yescharacteristic
77C4×C109#13711yescharacteristic
78Dic109—41no—
79Dic109—42no—
80Dic109—41no—
81Dic109—81no—
82C2×C109—81no—
83C2×C109#45211yescharacteristic
84C2×C109#45211yescharacteristic
85C2×C109#45411yescharacteristic
86#1638—1091nomaximal, Sylow
87C109#163811yescharacteristic, complemented, Sylow
88#556—1091no—
89#487—1091no—
90#477—1091no—
91#476—1091no—
92#332—1091no—
93Q8⋊C8—1091no—
94D4⋊C8D10911yescharacteristic
95C4⋊Q8—1091no—
96C4⋊Q8—1091no—
97#126—2182no—
98#124—2181no—
99C22⋊Q8—2181no—
100C4×Q8—1091no—
101C4×Q8—2181no—
102C4×D4C2×D10911yescharacteristic
103#117—2181no—
104#107—2181no—
105#106—2181no—
106C4⋊C8—1091no—
107C4⋊C8C2×D10911yescharacteristic
108#103—2182no—
109#103—2181no—
110#102—2181no—
111C4×C8C2×D10911yescharacteristic
112C2×Q8—1091no—
113C2×Q8—2181no—
114C2×Q8—2181no—
115C2×D4D43611yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2181no—
120C4⋊C4—1092no—
121C4⋊C4—1091no—
122C4⋊C4—2182no—
123C4⋊C4—2181no—
124C4⋊C4—2181no—
125C4⋊C4—2181no—
126C4⋊C4—2181no—
127C4⋊C4D43611yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2182no—
130C22⋊C4—2182no—
131C42—2182no—
132C42—2181no—
133C42C22×D10911yescharacteristic
134C23—21no—
135Q8—4362no—
136Q8—4361no—
137Q8—4361no—
138Q8—2181no—
139Q8—2181no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—4361no—
146C2×C4—2181no—
147C2×C4—2182no—
148C2×C4—2181no—
149C2×C4D4×D10911yescharacteristic
150C2×C4D4×D10911yescharacteristic
151C2×C4C2×D43611yescharacteristic
152C8—41no—
153C8—41no—
154C8—4361no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1681266911yescharacteristic
159C4—21no—
160C4—41no—
161C4—8721no—
162C4—4361no—
163C4—4362no—
164C4—4361no—
165C4#1681271811yescharacteristic
166C4#1681272111yescharacteristic
167C4#1681272811yescharacteristic
168C4#1681273211yescharacteristic
169C2—81no—
170C2#2029518911yescharacteristic
171C2#2029519011yescharacteristic
172C2#2029520011yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
FittingD4⋊C8×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenterD4⋊C8D109
hypocenterC109#1638
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. #20295377C2semidirect
3. #20295322C2semidirect
5. #20294771C2semidirect
6. #20294758C2semidirect
87. C109#1638semidirect

Maximal subgroups

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

subgroupindex
#202957462
#202953772
#202953222
#202953162
#202947712
#202947582
D4⋊C8×C1092
#1638109