Finite Group Databasebeta

← #28364161

Subgroups — #28364161

Order 13952.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16812680C212yesmaximal, complemented
2C2×#16812614C212yesmaximal, complemented
3#20294887C211yesmaximal, characteristic, complemented
4#20294793C211yesmaximal, characteristic, complemented
5#534×C109C211yesmaximal, characteristic
6C23×Dic109C2211yescharacteristic
7#16812680—24no—
8#16812680—24no—
9C2×#13182008—22no—
10C2×C22⋊Dic109—22no—
11C2×C22⋊Dic109C2211yescharacteristic
12C2×C22⋊Dic109C2212yes—
13#16812614—24no—
14#16812606—22no—
15C22×D4×C109C2212yes—
16#123×C109—22no—
17#121×C109—22no—
18#120×C109—22no—
19C2×C22⋊C4×C109C2211yescharacteristic
20C22×Dic109—21no—
21C22×Dic109—22no—
22C22×Dic109—22no—
23C22×Dic109—22no—
24C22×Dic109—21no—
25C22×Dic109—21no—
26C22×Dic109D412yescomplemented
27#13182008—28no—
28C22⋊Dic109—28no—
29C22⋊Dic109—22no—
30C22⋊Dic109—22no—
31C22⋊Dic109D414yescomplemented
32C24×C109D412yes—
33C24×C109C2311yescharacteristic
34C2×D4×C109—22no—
35C2×D4×C109—22no—
36C2×D4×C109—22no—
37C2×D4×C109—22no—
38C2×D4×C109—22no—
39C2×D4×C109—22no—
40C2×D4×C109—22no—
41C22×C4×C109D412yes—
42C22×C4×C109D412yes—
43C4⋊C4×C109—22no—
44C22⋊C4×C109—24no—
45C22⋊C4×C109—22no—
46C23×C109—22no—
47C23×C109—22no—
48C23×C109—22no—
49C23×C109—42no—
50C23×C109—44no—
51C23×C109C2×D411yescharacteristic
52C23×C109C2×D412yes—
53C23×C109C2×D412yes—
54C23×C109C2×D411yescharacteristic
55C23×C109#4111yescharacteristic
56D4×C109—42no—
57D4×C109—42no—
58D4×C109—42no—
59D4×C109—42no—
60D4×C109—82no—
61C2×C4×C109—22no—
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—42no—
66C2×Dic109—24no—
67C2×Dic109—24no—
68C2×Dic109—22no—
69C2×Dic109—44no—
70C2×Dic109—41no—
71C2×Dic109—42no—
72C2×Dic109—41no—
73C2×Dic109—42no—
74C2×Dic109—41no—
75C22×C109—22no—
76C22×C109—24no—
77C22×C109—41no—
78C22×C109—42no—
79C22×C109—41no—
80C22×C109—44no—
81C22×C109—42no—
82C22×C109—44no—
83C22×C109—82no—
84C22×C109#12012yes—
85C22×C109#12011yescharacteristic
86C22×C109#12111yescharacteristic
87C22×C109#12112yes—
88C22×C109#12711yescharacteristic
89C4×C109—42no—
90C4×C109—42no—
91Dic109—44no—
92Dic109—42no—
93Dic109—81no—
94C2×C109—22no—
95C2×C109—21no—
96C2×C109—22no—
97C2×C109—21no—
98C2×C109—82no—
99C2×C109#39211yescharacteristic
100C2×C109#45812yes—
101#2022—1091nomaximal, Sylow
102C109#202211yescharacteristic, complemented, Sylow
103#534D10911yescharacteristic
104C2×#123—1092no—
105C2×#99—1092no—
106#381—1091no—
107#342—1091no—
108C22×D4C2×D10912yes—
109C23×C4—1091no—
110#123—22no—
111#123—2184no—
112#123—2184no—
113#121—22no—
114#120—22no—
115C2×C4⋊C4—2182no—
116C2×C22⋊C4—1092no—
117C2×C22⋊C4—1091no—
118C2×C22⋊C4—2182no—
119C2×C22⋊C4C2×D10911yescharacteristic
120#99—2184no—
121#95—2182no—
122C24C22⋊D10912yes—
123C24C22×D10911yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C22×C4—1092no—
132C22×C4—2181no—
133C22×C4—2182no—
134C22×C4—2181no—
135C22×C4—2182no—
136C22×C4—2182no—
137C22×C4—2181no—
138C22×C4C22⋊D10912yes—
139C22×C4C22⋊D10912yes—
140C4⋊C4—22no—
141C4⋊C4—2188no—
142C22⋊C4—24no—
143C22⋊C4—22no—
144C22⋊C4—1094no—
145C22⋊C4—2182no—
146C22⋊C4—2188no—
147C22⋊C4—2182no—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—44no—
153C23D4×D10911yescharacteristic
154C23D4×D10912yes—
155C23C2×C22⋊D10912yes—
156C23C2×C22⋊D10911yescharacteristic
157C23#1318202811yescharacteristic
158D4—42no—
159D4—42no—
160D4—42no—
161D4—42no—
162D4—82no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—4362no—
169C2×C4—4361no—
170C2×C4—4364no—
171C2×C4—4361no—
172C2×C4—4362no—
173C2×C4—4361no—
174C2×C4—2184no—
175C2×C4—2184no—
176C2×C4—2182no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—44no—
183C22—42no—
184C22—44no—
185C22—82no—
186C22#1681266712yes—
187C22#1681266811yescharacteristic
188C22#1681267011yescharacteristic
189C22#1681267112yes—
190C22#1681269511yescharacteristic
191C4—42no—
192C4—42no—
193C4—8721no—
194C4—4364no—
195C4—4362no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—82no—
201C2#2029493411yescharacteristic
202C2#2029521612yes—
subgroupG/H
centerC22#16812668
commutator, cosocleC24×C109C23
FrattiniC24C22×D109
Fitting, prime radical#534×C109C2
socleC22×C109#120
hypercenter#534D109
hypocenterC109#2022
LCSG ▷ C24×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#16812680C2semidirect
2. C2×#16812614C2semidirect
3. #20294887C2semidirect
4. #20294793C2semidirect
26. C22×Dic109D4semidirect
31. C22⋊Dic109D4semidirect
102. C109#2022semidirect

Maximal subgroups

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

subgroupindex
C2×#168126802
C2×#168126142
#202948872
#202947932
#534×C1092
#2022109