Finite Group Databasebeta

← #28406004

Subgroups — #28406004

Order 14464.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#20299617C211yesmaximal, characteristic, complemented
2#20299542C211yesmaximal, characteristic, complemented
3#20299450C212yesmaximal, complemented
4#20299449C212yesmaximal, complemented
5#20299145C211yesmaximal, characteristic
6C2×C4⋊#90673—21no—
7C4⋊#11744753—21no—
8#16813679C2212yes—
9C4×#11744753—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12C2×#14268647—21no—
13#16813621C411yescharacteristic, complemented
14#16813618C411yescharacteristic, complemented
15#16813608—21no—
16#16813597C2211yescharacteristic
17#16813595—21no—
18#16813593C2211yescharacteristic
19C4×D452C411yescharacteristic, complemented
20C4×C22⋊D113—21no—
21C42×D113C2211yescharacteristic
22C4×D4×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C4⋊#90673—42no—
26#14268647—42no—
27#14268647—42no—
28C2×Dic226—21no—
29C2×D452—21no—
30C2×D452C2×C411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C4×D113—21no—
35C2×C4×D113D411yescharacteristic
36C2×C4×D113D411yescharacteristic
37C2×C4×D113C2311yescharacteristic
38C4⋊Dic113C2×C411yescharacteristic
39#14268626—21no—
40C22⋊Dic113—21no—
41#14268624—21no—
42#14268624—21no—
43C4×Dic113C2×C411yescharacteristic
44C4×Dic113D411yescharacteristic
45C4×Dic113D411yescharacteristic
46C2×D4×C113C2×C411yescharacteristic
47C22×C4×C113—21no—
48C4⋊C4×C113C2×C411yescharacteristic
49C22⋊C4×C113—21no—
50C42×C113C2×C411yescharacteristic
51C23×C113—21no—
52C22×D113—21no—
53C22×D113C2×D411yescharacteristic
54C2×#90673—42no—
55C2×#90673—42no—
56C2×#90673—42no—
57D4×C113—41no—
58C2×C4×C113—21no—
59C2×C4×C113—42no—
60C2×C4×C113C22⋊C411yescharacteristic
61C2×C4×C113C22⋊C411yescharacteristic
62C2×C4×C113C22×C411yescharacteristic
63C22⋊D113—42no—
64C22⋊D113—41no—
65C22⋊D113—41no—
66C22⋊D113—42no—
67C2×Dic113—21no—
68C2×Dic113C22⋊C411yescharacteristic
69C2×Dic113C22⋊C411yescharacteristic
70C2×Dic113C2×D411yescharacteristic
71D452—41no—
72D452—41no—
73D452—41no—
74C4×D113—41no—
75C4×D113—41no—
76C4×D113—42no—
77C4×D113D812yes—
78C4×D113SD1612yes—
79Dic226—42no—
80#11744753—42no—
81C22×C113—41no—
82C22×C113—41no—
83C22×C113—41no—
84C22×C113C2×C22⋊C411yescharacteristic
85C2×D113—21no—
86C2×D113—21no—
87C2×D113—41no—
88C2×D113—41no—
89C2×D113—41no—
90C2×D113C2×D811yescharacteristic
91C2×D113C2×SD1611yescharacteristic
92#90673—82no—
93C4×C113—21no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113#10212yes—
97Dic113—21no—
98Dic113—21no—
99Dic113—41no—
100Dic113#10212yes—
101C2×C113—81no—
102C2×C113#41011yescharacteristic
103C2×C113C2×#10211yescharacteristic
104C2×C113#42111yescharacteristic
105D113—21no—
106D113—21no—
107D113—81no—
108#1517—1131nomaximal, Sylow
109C113#151711yescharacteristic, complemented, Sylow
110#532—1131no—
111#431—1131no—
112#382—1131no—
113#327—1132no—
114#327—1132no—
115C2×#41—2261no—
116C4⋊Q8—1131no—
117#127—1131no—
118#124—2261no—
119#121—1131no—
120#121—1131no—
121#121—2261no—
122C4×D4—1131no—
123C4×D4—2261no—
124C4×D4#9067311yescharacteristic, complemented
125C2×C4⋊C4—2261no—
126C2×C42—1131no—
127C4⋊C8—2261no—
128C22⋊C8—1132no—
129C4×C8—2261no—
130#95—1132no—
131#95—2261no—
132#41—4522no—
133#41—4522no—
134C2×Q8—2261no—
135C2×D4—1131no—
136C2×D4—2261no—
137C2×D4—2261no—
138C2×D4—2261no—
139C2×D4—2261no—
140C2×D4C2×#9067311yescharacteristic
141C22×C4—21no—
142C22×C4—1131no—
143C22×C4—1131no—
144C22×C4—1131no—
145C22×C4—2262no—
146C22×C4—2261no—
147C2×C8—2262no—
148C4⋊C4—1131no—
149C4⋊C4—4522no—
150C4⋊C4—2261no—
151C4⋊C4C2×#9067311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C42—1131no—
157C42—1131no—
158C42—1131no—
159C42C2×#9067311yescharacteristic
160C23—21no—
161C23—1131no—
162C23—2261no—
163Q8—4522no—
164D4—41no—
165D4—4521no—
166D4—4521no—
167D4—4521no—
168D4—4522no—
169D4—4521no—
170D4—4521no—
171D4—4522no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—1131no—
175C2×C4—1132no—
176C2×C4—1132no—
177C2×C4—1131no—
178C2×C4—1131no—
179C2×C4—4521no—
180C2×C4—4521no—
181C2×C4—4522no—
182C2×C4—4522no—
183C2×C4—4522no—
184C2×C4—4522no—
185C2×C4—2261no—
186C2×C4C22⋊#9067311yescharacteristic
187C2×C4C22⋊#9067311yescharacteristic
188C2×C4C22×#9067311yescharacteristic
189C8—4522no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—1131no—
194C22—1131no—
195C22—4521no—
196C22—4521no—
197C22—4521no—
198C22—2261no—
199C22—2261no—
200C22C2×C22⋊#9067311yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—1132no—
205C4—9042no—
206C4—4521no—
207C4—2261no—
208C4—2261no—
209C4#1681368412yes—
210C2—81no—
211C2—9041no—
212C2—2261no—
213C2—2261no—
214C2#2029957711yescharacteristic
215C2C2×#1681368411yescharacteristic
216C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299145C2
cosocleC2×C4×D113C23
hypercenterC4×D4#90673
hypocenterC113#1517
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20299617C2semidirect
2. #20299542C2semidirect
3. #20299450C2semidirect
4. #20299449C2semidirect
13. #16813621C4semidirect
14. #16813618C4semidirect
19. C4×D452C4semidirect
22. C4×D4×C113C4semidirect
109. C113#1517semidirect
124. C4×D4#90673semidirect

Maximal subgroups

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

subgroupindex
#202996172
#202995422
#202994502
#202994492
#202991452
#1517113