Finite Group Databasebeta

← #28400104

Subgroups — #28400104

Order 14464.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813653C211yesmaximal, characteristic
2C22×#14268637C211yesmaximal, characteristic, complemented
3#20299174C211yesmaximal, characteristic
4#20298820C214yesmaximal, complemented
5#20298808C214yesmaximal, complemented
6#20298625C211yesmaximal, characteristic, complemented
7#20298606C211yesmaximal, characteristic, complemented
8#20298592C211yesmaximal, characteristic
9#519×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×Dic226C2211yescharacteristic
12#16813653—24no—
13C2×#14268637—24no—
14C2×#14268637C2212yes—
15C2×#14268637C2214yes—
16C2×#14268634C2212yes—
17C2×#14268631C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813622C2212yes—
20#16813610C2212yes—
21#16813606—22no—
22#16813602—22no—
23C4⋊#11744751C2214yes—
24#16813545C2212yes—
25#16813545C2214yes—
26#16813542C2212yes—
27C22×Q8×C113C2211yescharacteristic
28C4×Q8×C113—22no—
29C4×Q8×C113C2214yes—
30#117×C113—22no—
31#117×C113C2211yescharacteristic
32#117×C113C2211yescharacteristic
33#14268647—22no—
34#14268647—22no—
35C2×Dic226—22no—
36C2×Dic226—22no—
37C2×Dic226—21no—
38C2×Dic226C2312yes—
39C2×Dic226C2311yescharacteristic
40C2×D452C2311yescharacteristic
41C2×C22⋊D113—21no—
42C22×Dic113—21no—
43C2×C4×D113—21no—
44#14268637—28no—
45#14268637—24no—
46#14268634—24no—
47#14268631—22no—
48C2×#11744751—22no—
49C2×#11744751C2312yes—
50C2×#11744751C2312yes—
51C4⋊Dic113—24no—
52#14268624—24no—
53C2×Q8×C113—21no—
54C2×Q8×C113—22no—
55C2×Q8×C113D414yes—
56C2×Q8×C113C2312yes—
57C22×C4×C113—21no—
58C22×C4×C113C2311yescharacteristic
59C4⋊C4×C113—24no—
60C4⋊C4×C113D412yes—
61C4⋊C4×C113C2312yes—
62C22⋊C4×C113—21no—
63C22⋊C4×C113D412yes—
64C42×C113—24no—
65C42×C113—21no—
66C42×C113C2312yes—
67C23×C113C2×D411yescharacteristic
68C22×D113—21no—
69Q8×C113—24no—
70Q8×C113—22no—
71Q8×C113C2×D414yes—
72C2×C4×C113—24no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113C2×D414yes—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D412yes—
78C2×C4×C113#4112yes—
79C2×C4×C113C2411yescharacteristic
80C22⋊D113—42no—
81C2×Dic113—22no—
82C2×Dic113—21no—
83C2×Dic113—42no—
84D452—21no—
85D452—21no—
86C4×D113—42no—
87Dic226—22no—
88Dic226—21no—
89Dic226—22no—
90Dic226—21no—
91Dic226—42no—
92#11744751—22no—
93#11744751—22no—
94C22×C113—22no—
95C22×C113#12112yes—
96C22×C113C22×D411yescharacteristic
97C2×D113—41no—
98C2×D113—42no—
99C4×C113—24no—
100C4×C113—24no—
101C4×C113—42no—
102C4×C113#12112yes—
103C4×C113C22×D411yescharacteristic
104C4×C113C2×#4111yescharacteristic
105Dic113—42no—
106Dic113—41no—
107C2×C113—22no—
108C2×C113C2×#12111yescharacteristic
109C2×C113#57812yes—
110D113—81no—
111#3044—1131nomaximal, Sylow
112C113#304411yescharacteristic, complemented, Sylow
113C2×#137—1131no—
114C22×Q16—1131no—
115#536—1131no—
116#519D11311yescharacteristic, complemented
117#464—1134no—
118#462—1134no—
119#424—1131no—
120#419—1131no—
121#416—1131no—
122C2×#41—1131no—
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⋊Q8—1132no—
133#124—1132no—
134#123—2262no—
135C22⋊Q8—2262no—
136C4×Q8—22no—
137C4×Q8C2×D11314yes—
138#117—22no—
139#117C2×D11311yescharacteristic
140#117C2×D11311yescharacteristic
141C4⋊C8—1134no—
142#103—1132no—
143#103—1134no—
144#102—1132no—
145#41—2262no—
146#41—2262no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—1132no—
150C2×Q8—1131no—
151C2×Q8—2262no—
152C2×Q8—2262no—
153C2×Q8—2261no—
154C2×Q8D45214yes—
155C2×Q8C22×D11312yes—
156C2×D4—1131no—
157C2×D4—2261no—
158C22×C4—21no—
159C22×C4—2261no—
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—2264no—
171C4⋊C4C22⋊D11312yes—
172C4⋊C4C22×D11312yes—
173C22⋊C4—21no—
174C22⋊C4—2264no—
175C22⋊C4C22⋊D11312yes—
176C42—24no—
177C42—21no—
178C42C22×D11312yes—
179C23—2261no—
180C23C2×C22⋊D11311yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—4522no—
184Q8—2262no—
185Q8—2261no—
186Q8—2262no—
187Q8—2261no—
188Q8C2×D45214yes—
189D4—4522no—
190D4—2261no—
191D4—2261no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—4522no—
196C2×C4—4522no—
197C2×C4—2262no—
198C2×C4—2261no—
199C2×C4C2×C22⋊D11314yes—
200C2×C4C2×C22⋊D11311yescharacteristic
201C2×C4C2×D45212yes—
202C2×C4#1426864712yes—
203C2×C4C23×D11311yescharacteristic
204C8—2262no—
205C8—2262no—
206C22—22no—
207C22—4521no—
208C22—4522no—
209C22#1681359612yes—
210C22C22×C22⋊D11311yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—4521no—
215C4—4522no—
216C4#1681359612yes—
217C4C22×D45211yescharacteristic
218C4C2×#1426864711yescharacteristic
219C2—22no—
220C2—9041no—
221C2C2×#1681359611yescharacteristic
222C2#2029941312yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#519×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#519D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#14268637C2semidirect
4. #20298820C2semidirect
5. #20298808C2semidirect
6. #20298625C2semidirect
7. #20298606C2semidirect
9. #519×C113C2semidirect
112. C113#3044semidirect
116. #519D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C22×#142686372
#202991742
#202988202
#202988082
#202986252
#202986062
#202985922
#519×C1132
#3044113