Finite Group Databasebeta

← #28363422

Subgroups — #28363422

Order 13952.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#16812697C211yesmaximal, characteristic
2#20295503C211yesmaximal, characteristic
3#20295035C211yesmaximal, characteristic
4C2×#16812617C211yesmaximal, characteristic
5#20294787C211yesmaximal, characteristic
6#20294785C211yesmaximal, characteristic
7#419×C109C211yesmaximal, characteristic
8C22×Dic218C2211yescharacteristic
9C2×#13182013C2211yescharacteristic
10#16812697—22no—
11#16812697C414yescomplemented
12C4×Dic218—22no—
13#16812664—22no—
14#16812658C2211yescharacteristic
15#16812655—22no—
16C2×#13182008—22no—
17C2×C4×Dic109C2211yescharacteristic
18#16812623—22no—
19#16812617—22no—
20C22×Q8×C109C2211yescharacteristic
21C2×M16×C109C2211yescharacteristic
22#117×C109C2211yescharacteristic
23#103×C109—22no—
24C2×Dic218—21no—
25C2×Dic218—21no—
26C2×Dic218—21no—
27C2×Dic218—21no—
28C2×Dic218C2×C412yes—
29C2×Dic218D412yes—
30C22×Dic109—21no—
31C22×Dic109D412yes—
32#13182013—21no—
33#13182013—21no—
34C2×#11724784—21no—
35C4⋊Dic109D412yes—
36#13182008—24no—
37#13182008—28no—
38C22⋊Dic109—21no—
39C4×Dic109—24no—
40C4×Dic109—21no—
41C4×Dic109—21no—
42C4×Dic109C2×C412yes—
43C2×Q8×C109—21no—
44C2×Q8×C109—21no—
45C2×Q8×C109—21no—
46C2×Q8×C109—21no—
47C2×Q8×C109—21no—
48C2×Q8×C109C2×C412yes—
49C22×C4×C109—21no—
50C22×C4×C109C2311yescharacteristic
51M16×C109—21no—
52M16×C109—21no—
53C2×C8×C109—21no—
54C4⋊C4×C109D412yes—
55C22⋊C4×C109—21no—
56C42×C109—21no—
57C23×C109C2×D411yescharacteristic
58Q8×C109—22no—
59Q8×C109—22no—
60Q8×C109—41no—
61Q8×C109—41no—
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109—41no—
65C2×C4×C109—41no—
66C2×C4×C109C22×C411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109C2×D411yescharacteristic
70C2×C4×C109#4111yescharacteristic
71C2×C4×C109#4111yescharacteristic
72C2×Dic109—24no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—22no—
77C2×Dic109C22⋊C414yes—
78Dic218—22no—
79Dic218—22no—
80Dic218—22no—
81Dic218—22no—
82C8×C109—41no—
83#11724784—41no—
84C22×C109—22no—
85C22×C109C2×C22⋊C411yescharacteristic
86C22×C109#12011yescharacteristic
87C22×C109#12311yescharacteristic
88C4×C109—42no—
89C4×C109—42no—
90C4×C109C4×D411yescharacteristic
91C4×C109C4×D411yescharacteristic
92C4×C109#12111yescharacteristic
93C4×C109#12111yescharacteristic
94Dic109—24no—
95Dic109—24no—
96Dic109—42no—
97C2×C109—21no—
98C2×C109—21no—
99C2×C109#38611yescharacteristic
100C2×C109#45612yes—
101#1886—1091nomaximal, Sylow
102C109#188611yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—1091no—
104#519—1091no—
105#419—1091no—
106#419D10911yescharacteristic
107C2×#101—1091no—
108#339—1091no—
109#339—1091no—
110C22×Q8—1091no—
111C22×Q8C2×D10911yescharacteristic
112C2×M16—1091no—
113C2×M16C2×D10911yescharacteristic
114C4⋊Q8—1094no—
115C4⋊Q8—2182no—
116C4×Q8—2182no—
117C4×Q8—2182no—
118#117—1091no—
119#117—2182no—
120#117C2×D10911yescharacteristic
121C2×C4⋊C4—2182no—
122C2×C42—1091no—
123#103—22no—
124#103—2182no—
125#101—2182no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—1092no—
132C2×Q8—1092no—
133C2×Q8—2181no—
134C2×Q8—2181no—
135C2×Q8—2181no—
136C2×Q8—2181no—
137C2×Q8C4×D10912yes—
138C22×C4—21no—
139C22×C4—1092no—
140C22×C4—2181no—
141C22×C4C22×D10911yescharacteristic
142M16—21no—
143M16—21no—
144M16—2181no—
145M16—2181no—
146C2×C8—21no—
147C2×C8—2181no—
148C4⋊C4—1092no—
149C4⋊C4—2188no—
150C4⋊C4—2184no—
151C4⋊C4C22⋊D10912yes—
152C22⋊C4—21no—
153C22⋊C4—2181no—
154C42—21no—
155C42—1092no—
156C42—2184no—
157C42—2181no—
158C42—2181no—
159C23D4×D10911yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—2182no—
165Q8—2182no—
166Q8—2182no—
167Q8—2182no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—1094no—
173C2×C4—2182no—
174C2×C4—2184no—
175C2×C4—2182no—
176C2×C4—2182no—
177C2×C4—2182no—
178C2×C4C2×C4×D10911yescharacteristic
179C2×C4D4×D10911yescharacteristic
180C2×C4D4×D10911yescharacteristic
181C2×C4C2×C22⋊D10911yescharacteristic
182C2×C4#1318202811yescharacteristic
183C2×C4#1318202911yescharacteristic
184C8—41no—
185C8—4361no—
186C22—22no—
187C22C22⋊C4×D10911yescharacteristic
188C22#1681266711yescharacteristic
189C22#1681268111yescharacteristic
190C4—42no—
191C4—42no—
192C4—4362no—
193C4—2184no—
194C4—2184no—
195C4#1681265911yescharacteristic
196C4C4×C22⋊D10911yescharacteristic
197C4#1681267011yescharacteristic
198C4#1681267211yescharacteristic
199C2—21no—
200C2—21no—
201C2#2029490211yescharacteristic
202C2#2029520712yes—
subgroupG/H
centerC22#16812667
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#419×C109C2
socleC22×C109#120
prime radicalC23×C109C2×D4
cosocleC22×C4×C109C23
hypercenter#419D109
hypocenterC109#1886
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #16812697C4semidirect
102. C109#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#168126972
#202955032
#202950352
C2×#168126172
#202947872
#202947852
#419×C1092
#1886109