Finite Group Databasebeta

← #28364261

Subgroups — #28364261

Order 13952.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#20295607C211yesmaximal, characteristic
2C2×#16812627C212yesmaximal, complemented
3#20295025C212yesmaximal, complemented
4#20294795C211yesmaximal, characteristic, complemented
5#382×C109C211yesmaximal, characteristic, complemented
6C2×#13182029C2212yes—
7C2×#13182013C2212yes—
8#16812679—22no—
9#16812674—22no—
10#16812673—22no—
11#16812627—24no—
12#16812622—22no—
13#16812619—22no—
14C2×C4⋊C4×C109C2211yescharacteristic
15C2×C4⋊C4×C109C2211yescharacteristic
16C2×C42×C109C2211yescharacteristic
17#95×C109—22no—
18#13182029—22no—
19#13182029—22no—
20#13182029—22no—
21#13182029—22no—
22C2×Dic218D412yes—
23C2×D436—22no—
24C2×D436D412yes—
25C2×C22⋊D109—22no—
26C2×C4×D109—22no—
27#13182013—22no—
28#13182013—22no—
29C2×#11724784—22no—
30C4⋊Dic109—22no—
31#13182006—24no—
32C22×C4×C109—21no—
33C22×C4×C109—21no—
34C22×C4×C109D412yes—
35C22×C4×C109C2311yescharacteristic
36C4⋊C4×C109—22no—
37C4⋊C4×C109—22no—
38C42×C109—21no—
39C42×C109D412yescomplemented
40C23×C109C2×D411yescharacteristic
41C22×D109—22no—
42C2×C4×C109—22no—
43C2×C4×C109—22no—
44C2×C4×C109—41no—
45C2×C4×C109—41no—
46C2×C4×C109—42no—
47C2×C4×C109—42no—
48C2×C4×C109—41no—
49C2×C4×C109C2×D412yes—
50C2×C4×C109C2×D411yescharacteristic
51C2×C4×C109#4111yescharacteristic
52C2×C4×C109#4112yes—
53C22⋊D109—42no—
54C22⋊D109—42no—
55C2×Dic109—22no—
56D436—22no—
57D436—22no—
58D436—82no—
59C4×D109—42no—
60C4×D109—42no—
61Dic218—22no—
62Dic218—22no—
63#11724784—42no—
64C22×C109—21no—
65C22×C109—21no—
66C22×C109#12011yescharacteristic
67C22×C109#12111yescharacteristic
68C22×C109#12411yescharacteristic
69C2×D109—42no—
70C2×D109—42no—
71C2×D109—42no—
72C4×C109—42no—
73C4×C109—42no—
74C4×C109—81no—
75C4×C109#12112yes—
76C4×C109#12312yes—
77Dic109—42no—
78C2×C109—21no—
79C2×C109—21no—
80C2×C109#39411yescharacteristic
81C2×C109#45411yescharacteristic
82C2×C109#45511yescharacteristic
83D109—82no—
84#2040—1091nomaximal, Sylow
85C109#204011yescharacteristic, complemented, Sylow
86#537—1091no—
87C2×#104—1092no—
88#417—1092no—
89#382D10911yescharacteristic, complemented
90#343—1091no—
91C2×#41—1092no—
92C2×M16—1092no—
93C22⋊Q8—2182no—
94#121—2182no—
95#121—2182no—
96C2×C4⋊C4C2×D10911yescharacteristic
97C2×C4⋊C4C2×D10911yescharacteristic
98C2×C42C2×D10911yescharacteristic
99#104—2184no—
100#103—2182no—
101#102—2182no—
102#95—22no—
103#41—2182no—
104#41—2182no—
105#41—2182no—
106#41—2182no—
107C2×Q8—1092no—
108C2×D4—1092no—
109C2×D4—2182no—
110C2×D4—2182no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2182no—
114C22×C4C22⋊D10912yes—
115C22×C4C22×D10911yescharacteristic
116M16—2182no—
117M16—2182no—
118C2×C8—2182no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—2182no—
122C22⋊C4—2184no—
123C42—21no—
124C42D43612yescomplemented
125C23—2182no—
126C23C2×C22⋊D10911yescharacteristic
127Q8—2182no—
128Q8—2182no—
129D4—8722no—
130D4—4362no—
131D4—4362no—
132D4—2182no—
133D4—2182no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—4362no—
142C2×C4—4362no—
143C2×C4—2182no—
144C2×C4D4×D10912yes—
145C2×C4C2×D43611yescharacteristic
146C2×C4#1318202911yescharacteristic
147C2×C4#1318203012yes—
148C8—4362no—
149C22—21no—
150C22—21no—
151C22—4362no—
152C22—4362no—
153C22—4362no—
154C22#1681266711yescharacteristic
155C22#1681267311yescharacteristic
156C22#1681268811yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—4362no—
161C4#1681267412yes—
162C4#1681268412yes—
163C2—21no—
164C2—21no—
165C2—8722no—
166C2#2029494311yescharacteristic
167C2#2029519811yescharacteristic
168C2#2029520311yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#382×C109C2
socleC22×C109#120
prime radical#20295607C2
hypercenter#382D109
hypocenterC109#2040
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#16812627C2semidirect
3. #20295025C2semidirect
4. #20294795C2semidirect
5. #382×C109C2semidirect
39. C42×C109D4semidirect
85. C109#2040semidirect
89. #382D109semidirect
124. C42D436semidirect

Maximal subgroups

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

subgroupindex
#202956072
C2×#168126272
#202950252
#202947952
#382×C1092
#2040109