Finite Group Databasebeta

← #28389879

Subgroups — #28389879

Order 14464.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#20299340C211yesmaximal, characteristic
2#20298990C211yesmaximal, characteristic, complemented
3#20298960C211yesmaximal, characteristic, complemented
4#20298338C211yesmaximal, characteristic, complemented
5#20298337C211yesmaximal, characteristic, complemented
6#20298337C211yesmaximal, characteristic, complemented
7#489×C113C211yesmaximal, characteristic, complemented
8C2×#14268637—21no—
9C2×#14268634—21no—
10#16813611—21no—
11#16813610C2211yescharacteristic
12#16813610C2211yescharacteristic
13#16813608—21no—
14#16813608—21no—
15#16813592—21no—
16#16813592—21no—
17#16813590—21no—
18#16813545—21no—
19#16813542—21no—
20#16813533C2211yescharacteristic, complemented
21#16813533C2211yescharacteristic, complemented
22C4⋊Q8×C113C2211yescharacteristic, complemented
23#124×C113C2211yescharacteristic
24#103×C113—21no—
25#102×C113—21no—
26#97×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C2×Dic226D411yescharacteristic
29C2×Dic226D411yescharacteristic
30C2×D452—21no—
31C2×D452D411yescharacteristic
32C2×D452D411yescharacteristic
33C2×C22⋊D113—21no—
34C2×C22⋊D113—21no—
35#14268637—42no—
36#14268634—42no—
37C2×#11744751—21no—
38C2×#11744751—21no—
39C22⋊Dic113—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46C4×Dic113—21no—
47C2×Q8×C113—21no—
48C2×Q8×C113D411yescharacteristic
49C2×D4×C113D411yescharacteristic
50C2×C8×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113—21no—
53C22⋊C4×C113—21no—
54C22⋊C4×C113—21no—
55C42×C113C2311yescharacteristic
56C23×C113—21no—
57C22×D113—21no—
58C22×D113—21no—
59C22×D113—81no—
60C22×D113—81no—
61C22×D113—81no—
62Q8×C113—41no—
63Q8×C113—41no—
64Q8×C113—41no—
65D4×C113—41no—
66C2×C4×C113—21no—
67C2×C4×C113—41no—
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C22⋊D113—81no—
72C22⋊D113—81no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75D452—41no—
76D452—41no—
77D452—81no—
78Dic226—41no—
79Dic226—41no—
80C8×C113—41no—
81#11744751—22no—
82#11744751—41no—
83C22×C113—41no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113#12011yescharacteristic
87C2×D113—41no—
88C2×D113—41no—
89C2×D113—41no—
90C2×D113—41no—
91C2×D113—41no—
92C2×D113—41no—
93C2×D113—84no—
94C4×C113—21no—
95C4×C113—21no—
96C4×C113—21no—
97C4×C113—41no—
98C4×C113—81no—
99Dic113—41no—
100Dic113—41no—
101C2×C113—81no—
102C2×C113#45311yescharacteristic
103C2×C113#45511yescharacteristic
104C2×C113#45511yescharacteristic
105D113—81no—
106D113—81no—
107#1659—1131nomaximal, Sylow
108C113#165911yescharacteristic, complemented, Sylow
109H(3,𝔽4)—1131no—
110#497—1131no—
111#489—1131no—
112#489D11311yescharacteristic, complemented
113#329—1131no—
114#329—1131no—
115#329—1131no—
116C2×Q16—2261no—
117C2×SD16—2261no—
118C4⋊Q8C2×D11311yescharacteristic, complemented
119#124—1131no—
120#124—1131no—
121#124—2261no—
122#124—2261no—
123#124—2261no—
124#124C2×D11311yescharacteristic
125#120—2261no—
126#120—2261no—
127#120—2261no—
128#103—21no—
129#103—2261no—
130#102—21no—
131#102—2261no—
132#97—1131no—
133#97—1131no—
134#97C2×D11311yescharacteristic, complemented
135C24—2261no—
136C2×Q8—21no—
137C2×Q8—1131no—
138C2×Q8—1131no—
139C2×Q8C22⋊D11311yescharacteristic
140C2×D4—1131no—
141C2×D4—1131no—
142C2×D4—2261no—
143C2×D4—2261no—
144C2×D4—2261no—
145C2×D4C22⋊D11311yescharacteristic
146Q16—4522no—
147SD16—4522no—
148C2×C8—21no—
149C2×C8—2261no—
150C2×C8—2261no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—2261no—
156C22⋊C4—2261no—
157C22⋊C4—2261no—
158C22⋊C4—2261no—
159C22⋊C4—2261no—
160C22⋊C4—2261no—
161C22⋊C4—2261no—
162C42—2261no—
163C42C22×D11311yescharacteristic
164C23—21no—
165C23—9041no—
166C23—9041no—
167C23—9041no—
168C23—2261no—
169C23—2261no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—4521no—
174Q8—4521no—
175D4—41no—
176D4—9041no—
177D4—9041no—
178D4—9041no—
179D4—4521no—
180D4—4521no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—2261no—
184C2×C4—2261no—
185C2×C4D4×D11311yescharacteristic
186C2×C4D4×D11311yescharacteristic
187C2×C4C2×C22⋊D11311yescharacteristic
188C8—41no—
189C8—4521no—
190C8—2262no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—9044no—
195C22—4521no—
196C22—4521no—
197C22—4521no—
198C22—4521no—
199C22—4521no—
200C22—4521no—
201C22#1681359011yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—4521no—
208C4—4521no—
209C2—81no—
210C2—9041no—
211C2—9041no—
212C2#2029876411yescharacteristic
213C2#2029877411yescharacteristic
214C2#2029877511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#489×C113C2
socleC22×C113#120
prime radical#20299340C2
hypercenter#489D113
hypocenterC113#1659
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #20298990C2semidirect
3. #20298960C2semidirect
4. #20298338C2semidirect
5. #20298337C2semidirect
6. #20298337C2semidirect
7. #489×C113C2semidirect
20. #16813533C22semidirect
21. #16813533C22semidirect
22. C4⋊Q8×C113C22semidirect
26. #97×C113C22semidirect
108. C113#1659semidirect
112. #489D113semidirect
118. C4⋊Q8C2×D113semidirect
134. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993402
#202989902
#202989602
#202983382
#202983372
#489×C1132
#1659113