Finite Group Databasebeta

← #28400107

Subgroups — #28400107

Order 14464.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813652C211yesmaximal, characteristic
2C22×Dic452C211yesmaximal, characteristic, complemented
3#20299169C211yesmaximal, characteristic
4#20299075C211yesmaximal, characteristic, complemented
5#20298819C214yesmaximal, complemented
6#20298807C214yesmaximal, complemented
7#20298624C211yesmaximal, characteristic, complemented
8#20298606C211yesmaximal, characteristic, complemented
9#416×C113C211yesmaximal, characteristic
10C22×Dic226C2211yescharacteristic
11C22×Dic226C2211yescharacteristic
12#16813652—24no—
13C2×Dic452—24no—
14C2×Dic452C2214yes—
15C2×#14268637C2212yes—
16C2×#14268635C2212yes—
17C2×#14268631C2211yescharacteristic
18#16813620C2212yes—
19#16813609C2212yes—
20#16813603—22no—
21#16813601—22no—
22C4×Dic226—22no—
23#16813587C2214yes—
24#16813581C2211yescharacteristic
25#16813578—22no—
26#16813551C2214yes—
27#16813545C2214yes—
28C2×#41×C113C2211yescharacteristic
29C22×C8×C113C2211yescharacteristic
30#117×C113C2211yescharacteristic
31#103×C113C2212yes—
32#102×C113C2212yes—
33C2×Dic226—21no—
34C2×Dic226—22no—
35C2×Dic226—22no—
36C2×Dic226—22no—
37C2×Dic226—21no—
38C2×Dic226D414yes—
39C2×Dic226C2312yes—
40C2×Dic226C2312yes—
41C22×Dic113—21no—
42C22×Dic113—21no—
43Dic452—28no—
44#14268637—24no—
45#14268635—24no—
46#14268631—22no—
47C2×#11744751C2312yes—
48C4⋊Dic113D412yes—
49#14268626—24no—
50#14268626—24no—
51C22⋊Dic113—24no—
52C22⋊Dic113D412yes—
53C4×Dic113—24no—
54C4×Dic113C2312yes—
55#41×C113—22no—
56#41×C113—22no—
57C2×Q8×C113C2311yescharacteristic
58C2×D4×C113—21no—
59C2×D4×C113C2311yescharacteristic
60C22×C4×C113—21no—
61C22×C4×C113C2311yescharacteristic
62C2×C8×C113—22no—
63C2×C8×C113C2312yes—
64C4⋊C4×C113C2312yes—
65C22⋊C4×C113—21no—
66C42×C113—21no—
67C23×C113—21no—
68C23×C113C2×D411yescharacteristic
69Q8×C113—21no—
70Q8×C113—21no—
71D4×C113—21no—
72D4×C113—21no—
73D4×C113—42no—
74C2×C4×C113—22no—
75C2×C4×C113—21no—
76C2×C4×C113—42no—
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D412yes—
79C2×C4×C113#4112yes—
80C2×C4×C113C2411yescharacteristic
81C2×Dic113—24no—
82C2×Dic113—22no—
83C2×Dic113—22no—
84C2×Dic113—42no—
85C2×Dic113C2×D414yes—
86Dic226—24no—
87Dic226—22no—
88Dic226—22no—
89Dic226—22no—
90Dic226—42no—
91Dic226C2×D414yes—
92C8×C113—22no—
93#11744751—22no—
94C22×C113—22no—
95C22×C113—41no—
96C22×C113—42no—
97C22×C113#12112yes—
98C22×C113C22×D411yescharacteristic
99C4×C113—41no—
100C4×C113—42no—
101C4×C113#12112yes—
102C4×C113C22×D411yescharacteristic
103C4×C113C2×#4111yescharacteristic
104Dic113—24no—
105Dic113—24no—
106Dic113—42no—
107C2×C113—22no—
108C2×C113—81no—
109C2×C113C2×#12111yescharacteristic
110C2×C113#57812yes—
111#3044—1131nomaximal, Sylow
112C113#304411yescharacteristic, complemented, Sylow
113C2×#137—1131no—
114C22×Q16—1131no—
115#536—1131no—
116#519—1131no—
117#464—1134no—
118#462—1134no—
119#424—1131no—
120#419—1131no—
121#416D11311yescharacteristic
122C2×#41C2×D11311yescharacteristic
123C22×Q8—1131no—
124C22×Q8—1131no—
125#137—2264no—
126C2×Q16—1132no—
127C2×Q16—1134no—
128C2×Q16—2264no—
129C2×SD16—1132no—
130C2×M16—1131no—
131C22×C8C2×D11311yescharacteristic
132C4⋊Q8—1132no—
133#124—1132no—
134#123—2262no—
135C22⋊Q8—2262no—
136C4×Q8—1134no—
137C4×Q8—2262no—
138#117—1131no—
139#117—2262no—
140#117C2×D11311yescharacteristic
141C4⋊C8—1134no—
142#103—1134no—
143#103C2×D11312yes—
144#102C2×D11312yes—
145#41—22no—
146#41—22no—
147C2×Q8—1134no—
148C2×Q8—1132no—
149C2×Q8—1132no—
150C2×Q8—2262no—
151C2×Q8—2262no—
152C2×Q8—2261no—
153C2×Q8—2261no—
154C2×Q8—2262no—
155C2×Q8C22×D11311yescharacteristic
156C2×D4—21no—
157C2×D4C22×D11311yescharacteristic
158C22×C4—21no—
159C22×C4—2261no—
160C22×C4—2261no—
161C22×C4C22×D11311yescharacteristic
162Q16—2268no—
163Q16—2264no—
164SD16—2264no—
165M16—2262no—
166C2×C8—22no—
167C2×C8—1132no—
168C2×C8C22×D11312yes—
169C4⋊C4—1132no—
170C4⋊C4—2264no—
171C4⋊C4—2264no—
172C4⋊C4C22×D11312yes—
173C22⋊C4—21no—
174C22⋊C4—1132no—
175C22⋊C4—2264no—
176C42—21no—
177C42—1132no—
178C42—2264no—
179C23—21no—
180C23D4×D11311yescharacteristic
181Q8—21no—
182Q8—21no—
183Q8—1134no—
184Q8—4522no—
185Q8—2262no—
186Q8—2262no—
187Q8—2264no—
188Q8—2262no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—1134no—
196C2×C4—4522no—
197C2×C4—2262no—
198C2×C4—2264no—
199C2×C4—2262no—
200C2×C4D4×D11311yescharacteristic
201C2×C4D4×D11312yes—
202C2×C4#1426864712yes—
203C2×C4C23×D11311yescharacteristic
204C8—22no—
205C8—2262no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1681359512yes—
210C22C2×D4×D11311yescharacteristic
211C4—41no—
212C4—42no—
213C4—4522no—
214C4—2264no—
215C4—2264no—
216C4#1681359512yes—
217C4C2×D4×D11311yescharacteristic
218C4C2×#1426864711yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1681359511yescharacteristic
222C2#2029941212yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#416D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×Dic452C2semidirect
4. #20299075C2semidirect
5. #20298819C2semidirect
6. #20298807C2semidirect
7. #20298624C2semidirect
8. #20298606C2semidirect
112. C113#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C22×Dic4522
#202991692
#202990752
#202988192
#202988072
#202986242
#202986062
#416×C1132
#3044113