Finite Group Databasebeta

← #28363580

Subgroups — #28363580

Order 13952.

340 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 93 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#20295793C211yesmaximal, characteristic, complemented
2#20295010C211yesmaximal, characteristic, complemented
3C2×#16812616C212yesmaximal, complemented
4#20294796C212yesmaximal, complemented
5#535×C109C211yesmaximal, characteristic
6#16812706—24no—
7C2×#13182013—22no—
8C2×#13182013C2212yes—
9C2×#13182013C2212yes—
10#16812618—21no—
11#16812616—24no—
12#16812616—21no—
13C2×#41×C109C2211yescharacteristic
14C22×D4×C109C2211yescharacteristic
15#127×C109—21no—
16#124×C109—21no—
17#121×C109—22no—
18#120×C109C414yes—
19#117×C109C2211yescharacteristic
20#13182013—24no—
21#13182013—22no—
22#13182013—22no—
23#13182013—22no—
24#13182013D414yescomplemented
25C2×#11724784—24no—
26C2×#11724784—22no—
27C2×#11724784—22no—
28C24×C109C2×C412yes—
29#41×C109—22no—
30#41×C109—22no—
31C2×Q8×C109D411yescharacteristic
32C2×D4×C109—24no—
33C2×D4×C109—21no—
34C2×D4×C109—21no—
35C2×D4×C109—22no—
36C2×D4×C109—22no—
37C2×D4×C109C2×C412yes—
38C2×D4×C109D411yescharacteristic
39C22×C4×C109D412yes—
40C22×C4×C109C2311yescharacteristic
41C4⋊C4×C109—21no—
42C22⋊C4×C109—24no—
43C22⋊C4×C109C2×C412yes—
44C42×C109—21no—
45C23×C109—22no—
46C23×C109—24no—
47C23×C109—82no—
48C23×C109C22⋊C412yes—
49C23×C109C22×C411yescharacteristic
50Q8×C109—22no—
51D4×C109—24no—
52D4×C109—22no—
53D4×C109—41no—
54D4×C109—42no—
55D4×C109—41no—
56D4×C109—84no—
57C2×C4×C109—22no—
58C2×C4×C109—22no—
59C2×C4×C109—22no—
60C2×C4×C109C22⋊C412yes—
61C2×C4×C109C2×D412yes—
62C2×C4×C109C2×D411yescharacteristic
63C2×C4×C109C2×D411yescharacteristic
64C2×C4×C109#4112yes—
65#11724784—24no—
66#11724784—42no—
67C22×C109—22no—
68C22×C109—41no—
69C22×C109—42no—
70C22×C109—44no—
71C22×C109—42no—
72C22×C109—84no—
73C22×C109C2×C22⋊C411yescharacteristic
74C22×C109C4×D412yes—
75C4×C109—22no—
76C4×C109—42no—
77C4×C109#12011yescharacteristic
78C4×C109#12112yes—
79C4×C109#12311yescharacteristic
80C2×C109—21no—
81C2×C109—22no—
82C2×C109—42no—
83C2×C109—82no—
84C2×C109#38611yescharacteristic
85#1914—1091nomaximal, Sylow
86C109#191411yescharacteristic, complemented, Sylow
87#568—1091no—
88#535D10911yescharacteristic
89#413—1091no—
90C2×#100—1092no—
91#344—1092no—
92C2×#41C2×D10911yescharacteristic
93C22×D4C2×D10911yescharacteristic
94#131—2184no—
95C2×M16—1092no—
96C2×M16—1092no—
97C2×M16—2182no—
98#127—21no—
99#124—21no—
100#121—22no—
101#120Dic10914yes—
102#117C2×D10911yescharacteristic
103#101—2181no—
104#100—2184no—
105#100—2181no—
106C24C2×Dic10912yes—
107#41—22no—
108#41—22no—
109C2×Q8C22⋊D10911yescharacteristic
110C2×D4—24no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4C2×Dic10912yes—
116C2×D4C22⋊D10911yescharacteristic
117C22×C4C22⋊D10912yes—
118C22×C4C22×D10911yescharacteristic
119M16—1094no—
120M16—2182no—
121M16—2182no—
122M16—2184no—
123M16—2182no—
124C2×C8—2182no—
125C2×C8—2184no—
126C2×C8—2182no—
127C4⋊C4—21no—
128C22⋊C4—24no—
129C22⋊C4C2×Dic10912yes—
130C42—21no—
131C23—22no—
132C23—24no—
133C23—82no—
134C23C22⋊Dic10912yes—
135C23C22×Dic10911yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—41no—
140D4—42no—
141D4—41no—
142D4—84no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4C22⋊Dic10912yes—
147C2×C4D4×D10912yes—
148C2×C4C2×C22⋊D10911yescharacteristic
149C2×C4C2×C22⋊D10911yescharacteristic
150C2×C4#1318202812yes—
151C8—4362no—
152C8—2184no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—44no—
157C22—42no—
158C22—84no—
159C22C2×C22⋊Dic10911yescharacteristic
160C22D4×Dic10912yes—
161C4—22no—
162C4—42no—
163C4#1681266711yescharacteristic
164C4#1681267112yes—
165C4#1681268011yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2029490611yescharacteristic
subgroupG/H
centerC2#20294906
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
Fitting, prime radical#535×C109C2
socleC2×C109#386
cosocleC22×C4×C109C23
hypercenter#535D109
hypocenterC109#1914
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20295793C2semidirect
2. #20295010C2semidirect
3. C2×#16812616C2semidirect
4. #20294796C2semidirect
24. #13182013D4semidirect
86. C109#1914semidirect

Maximal subgroups

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

subgroupindex
#202957932
#202950102
C2×#168126162
#202947962
#535×C1092
#1914109