Finite Group Databasebeta

← #28400100

Subgroups — #28400100

Order 14464.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14268637C211yesmaximal, characteristic, complemented
3#20299075C211yesmaximal, characteristic, complemented
4#20298817C214yesmaximal, complemented
5#20298805C214yesmaximal, complemented
6#20298625C211yesmaximal, characteristic, complemented
7#20298607C211yesmaximal, characteristic, complemented
8#20298594C211yesmaximal, characteristic
9#536×C113C211yesmaximal, characteristic
10C22×Dic226C2211yescharacteristic
11#16813652—24no—
12C2×#14268637—24no—
13C2×#14268637C2212yes—
14C2×#14268637C2214yes—
15C2×#14268635C2212yes—
16C2×#14268631C2211yescharacteristic
17C22×#11744751C2211yescharacteristic
18C4×Dic226C2214yes—
19#16813587—22no—
20#16813581C2211yescharacteristic
21#16813578—22no—
22C4⋊#11744751C2214yes—
23#16813546C2212yes—
24#16813546C2214yes—
25#16813543C2212yes—
26C2×#41×C113C2211yescharacteristic
27C22×Q8×C113C2211yescharacteristic
28C4⋊Q8×C113C2212yes—
29#124×C113C2212yes—
30#123×C113—22no—
31C22⋊Q8×C113—22no—
32#117×C113C2211yescharacteristic
33C2×Dic226—21no—
34C2×Dic226—22no—
35C2×Dic226D414yes—
36C2×Dic226C2312yes—
37C22×Dic113—21no—
38#14268637—28no—
39#14268637—24no—
40#14268635—24no—
41#14268631—22no—
42C2×#11744751—22no—
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113C2312yes—
46#14268626—24no—
47C22⋊Dic113—21no—
48C4×Dic113—24no—
49C4×Dic113—21no—
50#41×C113—22no—
51#41×C113—22no—
52C2×Q8×C113—21no—
53C2×Q8×C113—22no—
54C2×Q8×C113—22no—
55C2×Q8×C113C2312yes—
56C2×Q8×C113C2311yescharacteristic
57C2×D4×C113—21no—
58C2×D4×C113C2311yescharacteristic
59C22×C4×C113—21no—
60C22×C4×C113—21no—
61C22×C4×C113C2311yescharacteristic
62C4⋊C4×C113—24no—
63C4⋊C4×C113D412yes—
64C22⋊C4×C113—24no—
65C22⋊C4×C113D412yes—
66C42×C113C2312yes—
67C23×C113—21no—
68C23×C113C2×D411yescharacteristic
69Q8×C113—22no—
70Q8×C113—21no—
71Q8×C113—22no—
72Q8×C113—21no—
73Q8×C113—42no—
74D4×C113—21no—
75D4×C113—21no—
76D4×C113—42no—
77C2×C4×C113—22no—
78C2×C4×C113—21no—
79C2×C4×C113—42no—
80C2×C4×C113—42no—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2×D414yes—
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113#4112yes—
85C2×C4×C113C2411yescharacteristic
86C2×Dic113—24no—
87C2×Dic113—22no—
88C2×Dic113—22no—
89Dic226—24no—
90Dic226—22no—
91Dic226C2×D414yes—
92#11744751—22no—
93#11744751—22no—
94C22×C113—22no—
95C22×C113—41no—
96C22×C113—42no—
97C22×C113#12112yes—
98C22×C113C22×D411yescharacteristic
99C4×C113—24no—
100C4×C113—41no—
101C4×C113—42no—
102C4×C113#12112yes—
103C4×C113C22×D411yescharacteristic
104C4×C113C2×#4111yescharacteristic
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#536D11311yescharacteristic
116#519—1131no—
117#464—1134no—
118#462—1134no—
119#424—1131no—
120#419—1131no—
121#416—1131no—
122C2×#41C2×D11311yescharacteristic
123C22×Q8—1131no—
124C22×Q8C2×D11311yescharacteristic
125#137—2264no—
126C2×Q16—1134no—
127C2×Q16—1132no—
128C2×Q16—2264no—
129C2×SD16—1132no—
130C2×M16—1131no—
131C22×C8—1131no—
132C4⋊Q8C2×D11312yes—
133#124C2×D11312yes—
134#123—22no—
135C22⋊Q8—22no—
136C4×Q8—1134no—
137C4×Q8—2262no—
138#117—1131no—
139#117—2262no—
140#117C2×D11311yescharacteristic
141C4⋊C8—1134no—
142#103—1132no—
143#103—1134no—
144#102—1132no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—1134no—
151C2×Q8—1132no—
152C2×Q8—2261no—
153C2×Q8—2262no—
154C2×Q8C22×D11312yes—
155C2×Q8C22×D11311yescharacteristic
156C2×D4—21no—
157C2×D4C22×D11311yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—2261no—
161C22×C4C22×D11311yescharacteristic
162Q16—2268no—
163Q16—2264no—
164SD16—2264no—
165M16—2262no—
166C2×C8—1132no—
167C2×C8—1132no—
168C2×C8—2262no—
169C4⋊C4—24no—
170C4⋊C4—1132no—
171C4⋊C4—2264no—
172C4⋊C4C22⋊D11312yes—
173C22⋊C4—24no—
174C22⋊C4—2261no—
175C22⋊C4C22⋊D11312yes—
176C42—2261no—
177C42—2264no—
178C42C22×D11312yes—
179C23—21no—
180C23C2×C22⋊D11311yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—1134no—
187Q8—2264no—
188Q8—2262no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—2262no—
197C2×C4—2264no—
198C2×C4—2262no—
199C2×C4D4×D11312yes—
200C2×C4C2×C22⋊D11314yes—
201C2×C4C2×C22⋊D11311yescharacteristic
202C2×C4#1426864612yes—
203C2×C4C23×D11311yescharacteristic
204C8—2262no—
205C8—2262no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1681359312yes—
210C22C22×C22⋊D11311yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—4522no—
215C4—2264no—
216C4#1681359312yes—
217C4C2×D4×D11311yescharacteristic
218C4C2×#1426864611yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1681359311yescharacteristic
222C2#2029941312yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#536×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#536D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#14268637C2semidirect
3. #20299075C2semidirect
4. #20298817C2semidirect
5. #20298805C2semidirect
6. #20298625C2semidirect
7. #20298607C2semidirect
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×#142686372
#202990752
#202988172
#202988052
#202986252
#202986072
#202985942
#536×C1132
#3044113