Finite Group Databasebeta

← #28363443

Subgroups — #28363443

Order 13952.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16812680C211yesmaximal, characteristic
2#20295501C211yesmaximal, characteristic
3#20294887C212yesmaximal, complemented
4#20294792C212yesmaximal, complemented
5C2×#99×C109C211yesmaximal, characteristic
6C23×Dic109C2211yescharacteristic
7#16812680—22no—
8#16812680C414yescomplemented
9D4×Dic109—24no—
10#16812658—21no—
11C2×#13182008—21no—
12C2×C22⋊Dic109—21no—
13C2×C22⋊Dic109—21no—
14C2×C22⋊Dic109C2212yes—
15C2×C22⋊Dic109C2211yescharacteristic
16#16812606—24no—
17C22×D4×C109C2211yescharacteristic
18C2×C22⋊C4×C109C2212yes—
19#99×C109—22no—
20C22×Dic109—22no—
21C22×Dic109—21no—
22C22×Dic109—21no—
23C22×Dic109—21no—
24C22×Dic109—22no—
25C22×Dic109—22no—
26C22×Dic109C2×C412yescomplemented
27C22×Dic109D414yes—
28C4⋊Dic109—22no—
29#13182008—24no—
30C22⋊Dic109—22no—
31C22⋊Dic109—24no—
32C22⋊Dic109—22no—
33C22⋊Dic109—22no—
34C22⋊Dic109—21no—
35C22⋊Dic109C2×C412yescomplemented
36C4×Dic109—22no—
37C24×C109D411yescharacteristic
38C24×C109C2311yescharacteristic
39C2×D4×C109—22no—
40C2×D4×C109—22no—
41C2×D4×C109C2×C412yes—
42C2×D4×C109D412yes—
43C22×C4×C109—22no—
44C22×C4×C109D411yescharacteristic
45C22⋊C4×C109—22no—
46C22⋊C4×C109—22no—
47C23×C109—21no—
48C23×C109—21no—
49C23×C109—42no—
50C23×C109—42no—
51C23×C109C22⋊C412yes—
52C23×C109C22×C411yescharacteristic
53C23×C109C2×D412yes—
54C23×C109C2×D411yescharacteristic
55C23×C109C2×D411yescharacteristic
56C23×C109#4112yes—
57D4×C109—24no—
58D4×C109—24no—
59C2×C4×C109—21no—
60C2×C4×C109—21no—
61C2×C4×C109—44no—
62C2×C4×C109—42no—
63C2×C4×C109C22⋊C412yes—
64C2×Dic109—22no—
65C2×Dic109—22no—
66C2×Dic109—24no—
67C2×Dic109—24no—
68C2×Dic109—42no—
69C2×Dic109—41no—
70C2×Dic109—42no—
71C2×Dic109—41no—
72C2×Dic109—44no—
73C2×Dic109—82no—
74C22×C109—24no—
75C22×C109—22no—
76C22×C109—22no—
77C22×C109—41no—
78C22×C109—41no—
79C22×C109—42no—
80C22×C109—42no—
81C22×C109—42no—
82C22×C109—81no—
83C22×C109C2×C22⋊C411yescharacteristic
84C22×C109C4×D412yes—
85C22×C109#12011yescharacteristic
86C22×C109#12112yes—
87C22×C109#12311yescharacteristic
88C4×C109—22no—
89C4×C109—82no—
90Dic109—42no—
91Dic109—42no—
92Dic109—44no—
93C2×C109—21no—
94C2×C109—22no—
95C2×C109—21no—
96C2×C109—22no—
97C2×C109—42no—
98C2×C109#38611yescharacteristic
99C2×C109#45812yes—
100#1890—1091nomaximal, Sylow
101C109#189011yescharacteristic, complemented, Sylow
102C2×#123—1091no—
103#518—1091no—
104C2×#99D10911yescharacteristic
105#381—1092no—
106#342—1092no—
107C22×D4C2×D10911yescharacteristic
108C23×C4—1091no—
109#123—1094no—
110#123—2182no—
111C4×D4—2184no—
112#117—2181no—
113C2×C4⋊C4—2181no—
114C2×C22⋊C4—1091no—
115C2×C22⋊C4—1092no—
116C2×C22⋊C4—2181no—
117C2×C22⋊C4—2181no—
118C2×C22⋊C4C2×D10912yes—
119#99—22no—
120#95—2184no—
121C24D43611yescharacteristic
122C24C22×D10911yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D10912yes—
126C2×D4C22⋊D10912yes—
127C22×C4—22no—
128C22×C4—1094no—
129C22×C4—1092no—
130C22×C4—2182no—
131C22×C4—2182no—
132C22×C4—2181no—
133C22×C4—2181no—
134C22×C4—2181no—
135C22×C4—2182no—
136C22×C4D43611yescharacteristic
137C4⋊C4—2182no—
138C4⋊C4—2184no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—1092no—
142C22⋊C4—2182no—
143C22⋊C4—2184no—
144C22⋊C4—2182no—
145C22⋊C4—2181no—
146C22⋊C4—2182no—
147C42—2182no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23#1318200612yes—
153C23C2×C4×D10911yescharacteristic
154C23D4×D10912yes—
155C23C2×C22⋊D10911yescharacteristic
156C23C2×D43611yescharacteristic
157C23#1318202812yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4—8722no—
165C2×C4—4362no—
166C2×C4—4361no—
167C2×C4—4362no—
168C2×C4—4361no—
169C2×C4—4364no—
170C2×C4—2182no—
171C2×C4—2182no—
172C2×C4—2184no—
173C2×C4—2184no—
174C2×C4#1318200612yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×#1318200611yescharacteristic
185C22#1681265912yes—
186C22#1681266911yescharacteristic
187C22#1681267112yes—
188C22#1681268311yescharacteristic
189C4—22no—
190C4—82no—
191C4—4362no—
192C4—4364no—
193C4—4362no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#2029490311yescharacteristic
200C2#2029521712yes—
subgroupG/H
centerC22#16812669
commutatorC23×C109C22×C4
FrattiniC24C22×D109
FittingC2×#99×C109C2
socleC22×C109#120
prime radicalC22×D4×C109C22
cosocleC24×C109C23
hypercenterC2×#99D109
hypocenterC109#1890
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #20294887C2semidirect
4. #20294792C2semidirect
8. #16812680C4semidirect
26. C22×Dic109C2×C4semidirect
35. C22⋊Dic109C2×C4semidirect
101. C109#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#168126802
#202955012
#202948872
#202947922
C2×#99×C1092
#1890109